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I,
ANALYTICAL STRENGTH ASSESSMENT 5t h Edition
II I
VDMA Verlag
Forschungskuratorium Maschinenbau
I
FKM-Guideline
ANALYTICAL STRENGTH ASSESSMENT OF COMPONENTS IN MECHANICAL ENGINEERING 5 th , revised edition, 2003, English Version
Translation by E. Haibach
Title of the original German Version:
RECHNERISCHER FESTIGKEITSNACHWEIS FUR MASCHINENBAUTEILE 5., iiberarbeitete Ausgabe, 2003
Editor: Forschungskuratorium Maschinenbau (FKM) Postfach 71 0864, D - 60498 Frankfurt / Main Phone *49 - 69 - 6603 - 1345
(c) 2003 byVDMA Verlag GmbH Lyoner StraBe 18 60528 Frankfurt am Main www.vdma-verlag.de All rights reserved
AIle Rechte, insbesondere das Recht der Vervielfaltigung und Verbreitung sowie der Ubersetzung vorbehalten. Kein Teil des Werkes darfin irgendeiner Form (Druck, Fotokopie, Mikrofilm oder anderes Verfahren) ohne schriftliche Genehmigung des Verlages reproduziert oder unter Verwendung elektronischer Systeme gespeichert, verarbeitet, vervielfaltigt oder verbreitet werden.
ISBN 3-8163-0425-7
3
This FKM-Guideline was elaborated under contract between Forschungskuratorium Maschinenbau e. V. (FKM), Frankfurt / Main, and IMA Materialforschung und Anwendungstechnik Gmhfl, Dresden, as contractor in charge, by
Dr.-Ing. Bernd Hanel, IMA Materialforschung und Anwendungstechnik GmbH, Dresden,
Prof. Dr.-Ing. Erwin Haibach, Wiesbaden,
Prof. Dr.-Ing. TimID Seeger, Technische Hochschule Darmstadt, Fachgebiet Werkstoffmechanik,
Dipl.-Ing. Gert Wlrthgen, IMA Materialforschung und Anwendungstechnik GmbH, Dresden,
Prof. Dr.-Ing. Harald Zenner, Technische Universitat Clausthal, Institut fur Maschinelle Anlagentechnik und Betriebsfestigkeit,
and it was discussed among experts from industry and research institutes in the FKM expert group "Strength of components" .
Financial grants were obtained from the "Bundesministerium fUr Wirtschaft (BMWi, Bonn)" through the "Arbeitsgemeinschaft industrieller Forschungsvereinigungen 'Otto von Guericke ' e.V. (AiF, K6ln)" under contract AiF-No. D-156 and B-9434. The "Forschungskuratorium Maschinenbau e.V." gratefully acknowledges the financial support from BMWi and AiF and the contributions by the experts involved.
Terms of liability The FKM-Guideline is intended to conform with the state of the art. It has been prepared with the necessary care. The user is expected to decide, whether the guideline meets his particular requirements, and to observe appropriate care in its application. Neither the publisher nor the editor, the involved experts, or the translator shall be liable to the purchaser or any other person or entity with respect to any liability, loss, or damage caused or alleged to have been caused directly or indirectly by this guideline.
4
Preface to the English Version of the 5th Edition. For engineers concerned with construction and calculation in mechanical engineering or in related fields of industry the FKM-Guideline for analytical strength assessment is available since 1994. This guideline was elaborated by an expert group "Strength of components" of the "Forschungskuratorium Maschinenbau (FKM), Frankfurt/Main," with financial support by the Bundesministerium fur Wirtschaft (BMWi), by the "Arbeitsgemeinschaft industrieller Forschungsvereinigungen 'Otto von Guericke" and by the "Forschungskuratorium Maschinenbau. Based on former TGL standards and on the former guideline VDI 2226, and referring to more recent sources it was developed to the current state of knowledge. The FKM-Guideline - is applicable in mechanical engineering and in related fields of industry, - allows the analytical strength assessment for rodshaped (lD), for shell-shaped (2D) and for block-shaped (3D) components under consideration of all relevant influences, - describes the assessment of the static strength and of the fatigue strength, the latter according to an assessment of the fatigue limit, of the constant amplitude fatigue strength, or of the variable amplitude fatigue strength according to the service stress conditions, - is valid for components from steel, cast steel, or cast iron materials at temperatures from -40°C to 500 °C, as well as for components from aluminum alloys and cast aluminum alloys at temperatures from -40°C to 200 °C, - is applicable for components produced with or without machining, or by welding, - allows an assessment in considering nominal stresses as well as local elastic stresses derived from finite element or boundary element analyses, from theoretical mechanics solutions, or from measurements. A uniformly structured calculation procedure applies to all of these cases of application. The calculation procedure is almost completely predetermined. The user has to make some decisions only. The FKM-Guideline is a commented algorithm, consisting of statements, formulae, and tables. Most of the included figures have an explanatory function only.
Textual declarations are given where appropriate to ensure a reliable application. Its content complies with the state of knowledge to an extend that may be presented in a guideline and it enables quite comprehensive possibilities of calculation. The employed symbols are adapted to the extended requirements of notation. The presented calculation procedure is complemented by explanatory examples. Practically the described procedure of strength assessment should be realized by means of a suitable computer program. Presently available are the PC computer programs "RIFESTPLUS" (applicable for a calculation using elastically determined local stresses, in particular with shell-shaped (2D) or block-shaped (3D) components) and "WELLE" (applicable for a calculation using nominal stresses as it is appropriate in the frequently arising case of axles or shafts with gears etc). The preceding editions of the FKM-Guideline observed a remarkably great interest from which the need of an up to date guideline for analytical strength analyses becomes apparent. Moreover the interest of users was confirmed by the well attended VDI conferences on "Computational Strength Analysis of Metallic Components", that were organized for presentation of the FKM-Guideline at Fulda in 1995, 1998 and 2002. The contents-related changes introduced with the third edition from 1998 were mainly concerned with the consideration of stainless steel and of forging steel, with the technological size factor, with the section factor for assessing the static strength, with the fatigue limit of grey cast iron and of malleable cast iron, with additional fatigue classes of welded structural details and with the local stress analysis for welded components, with the specification of an estimated damage sum smaller than one for the assessment of the variable amplitude fatigue strength, with the assessment of multiaxial stresses, and with the experimental determination of component strength values. An essential formal change in the third edition was a new textual structure providing four main chapters, that describe the assessment of the static strength or of the fatigue strength with either nominal stresses or local stresses, respectively. For ease of application each of these chapters gives a complete description of the particular calculation procedure, although this results in repetitions of the same or almost the same parts of text in the corresponding sections.
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The major change in the forth edition from 2002 is the possibility of considering structural components made from aluminum alloys or cast aluminum alloys by applying the same calculation procedure that was developed for components from steel, cast steel and cast iron materials so far. The decisions necessary to include aluminum materials were derived from literature evaluations. It had to be recognized, however, that some of the relevant factors of influence were not yet examined with the desirable clearness or that available results could not be evaluated objectively due to large scatter. In these cases the decision was based on a careful consideration of substantial relations.
Concerning an analytical strength assessment of components from aluminum alloys or from cast aluminum alloys this guideline is delivered to the technical community by supposing that for the time being it will be applied with appropriate caution and with particular reference to existing experience so far. The involved research institutes and the "Forschungskuratorium Maschinenbau (FKM)" will appreciate any reports on practical experience as well as any proposals for improvement. Further improvements may also be expected from ongoing research projects concerning the procedure of static strength assessment using local elastic stresses, Chapter 3, and the fatigue assessment of extremely sharp notches. Last not least the fifth edition of the FKM-Guideline is a revision of the forth edition with several necessary, mainly formal amendments being introduced. It is presented in both a German version and an English version with the expectation that it might observe similar attention as the preceding editions on a broadened international basis of application.
Notes of the translator This English translation is intended to keep as close as possible to the original German version, but by using a common vocabulary and simple sentences. If the given translation is different from a literal one, the technical meaning of the sentence and/or of the paragraph is maintained, however. The translation observes an almost identical structure of the headlines, of the chapters, of the paragraphs and of the sentences, and even of the numbering of the pages. Also the tables and the figures as well as their numbering and headlines are adapted as they are, while only the verbal terms have been translated.
In particular the original German notation of the mathematical symbols, indices and formulas, as well as their numbering, has not been modified in order to insure identity with the German original in this respect. The applier of this guideline is kindly asked to accept the more or less unusual kind of notation which is due to the need of clearly distinguishing between a great number of variables. In particular the applier is pointed to the speciality, that a comma ( , ) is used with numerical values instead of a decimal point ( . ), hence 1,5 equals 1.5 . for example.
For updates and amendments see www.fkm-guideline.de
6
References /1/
TGL 19 340 (1983). Ermiidungsfestigkeit, Dauerfestigkeit der Maschinenbauteile.
/2/
TGL 19 341 (1988). Festigkeitsnachweis fiir Bauteile aus Eisengusswerkstoffen.
/3/
TGL 19 333 (1979). Schwingfestigkeit, Zeitfestigkeit von Achsen und Wellen.
/4/
TGL 19 350 (1986). Ermiidungsfestigkeit, Betriebsfestigkeit der Maschinenbauteile.
/5/
TGL 19 352 (Entwurf 1988). Aufstellung und Uberlagerung von Beanspruchungskollektiven.
/6/
Richtlinie VDI 2226 (1965). Empfehlung fiir die Festigkeitsberechnung metallischer Bauteile.
/7/
DIN 18 800 Teil 1 (1990). Stahlbauten, Bemessung und Konstruktion.
/8/
DIN ENV 1993 (1993). Bemessung und Konstruktion von Stahlbauten, Teil1-1: Allgemeine Bemessungsregeln, ... (Eurocode 3).
/9/
Hobbacher, A.: Fatigue design of welded joints and components. Recommendations of the Joint Working Group XIII-XV, XIII-1539-96 / XV-845-96. Abbington Publishing, Abbington Hall, Abbington, Cambridge CB1 6AH, England, 19996
/10/
Haibach, E.: Betriebsfestigkeits - Verfahren und Daten zur Bauteilberechnung, 2.Aufl. Berlin und Heidelberg, Springer-Verlag, 2002, ISBN 3-540-43142-X.
/11/
Radaj, D.: Ermiidungsfestigkeit. Grundlage fur Leichtbau, Maschinenbau und Stahlbau. Berlin und Heidelberg: Springer-Verlag, 2003, ISBN 3-540-44063-1.
/12/
FKM-Forschungsheft 241 (1999). Rechnerischer Festigkeitsnachweis fiir Bauteile aus Alumininiumwerkstoff.
/13/
FKM-Forschungsheft 230 (1998). Randschichthartung.
/14/
FKM-Forschungsheft 227 (1997). Lebensdauervorhersage II.
/15/
FKM-Forschungsheft 221-2 (1997). Mehrachsige und zusammengesetzte Beanspruchungen.
/16/
FKM-Forschungsheft 221 (1996). Wechselfestigkeit von Flachproben aus Grauguss.
/17/
FKM-Forschungsheft 183-2 (1994). Rechnerischer Festigkeitsnachweis fur Maschinenbauteile, Richtlinie. *1
/18/
FKM-Forschungsheft 183-1 (1994). Rechnerischer Festigkeitsnachweis fiir Maschinenbauteile, Kommentare.
/19/
FKM-Forschungsheft 180 (1994). Schweillverbindungen II.
/20/
FKM-Forschungsheft 143 (1989). Schweillverbindungen I.
/21/
FKM-Richtlinie Rechnerischer Festigkeitsnachweis fiir Maschinenbauteile, 3., vollstandig iiberarbeitete und erweiterte Ausgabe (1998).
/22/
FKM-Richtlinie Rechnerischer Festigkeitsnachweis fur Maschinenbauteile, 4., erweiterte Ausgabe (2002).
Related Conference Proceedings Festigkeitsberechnung metallischer Bauteile, Empfehlungen fur Konstrukteure und Entwicklungsingenieure. VDI Berichte 1227, Diisseldorf, VDI-Verlag, 1995. Festigkeitsberechnung metallischer Bauteile, Empfehlungen fur Entwicklungsingenieure und Konstrukteure. VDI Berichte 1442, Diisseldorf, VDI-Verlag, 1998. Festigkeitsberechnung metallischer Bauteile, Empfehlungen fur Entwicklungsingenieure und Konstrukteure. VDI Berichte 1698, Dusseldorf, VDI-Verlag, 2002. Bauteillebensdauer Nachweiskonzepte. DVM-Bericht 800, Deutscher Verband fur Materialsforschung und -prufung, Berlin 1997. Betriebsfestigkeit - Neue Entwicklungen bei der Lebensdauerberechnung von Bauteilen. DVM-Bericht 802, Deutscher Verband fur Materialsforschung und -prufung, Berlin 2003.
1
1'" and 2 nd Edition ofthe FKM-Guideline
7
Contents Page
0
General survey
0.1 0.2 0.3
Scope Technical background Structure and elements
1
Assessment of the static strength using nominal stresses
1.0 1.1 1.2
General Characteristic stress values Material properties Design parameters Component strength Safety factors Assessment
1.3
1.4 1.5
1.6
2
9
19 22 30 33 34 36
Assessment of the fatigue strength using nominal stresses
2.0 2.1 2.2 2.3 2.4 2.5 2.6
General Parameters of the stress spectrum Material properties Design Parameters Component strength Safety factors Assessment
3
Assessment of the static strength using local stresses
3.0 3.1 3.2 3.3 3.4 3.5 3.6
General Characteristic stress values Material properties Design parameters Component strength Safety factors Assessment
4
Assessment of the fatigue strength using local stresses
4.0 4.1 4.2 4.3 4.4 4.5 4.6
General Parameters of the stress spectrum Material properties Design parameters Component strength Safety factors Assessment
41 47 50 57 68 70
5
Appendices
Page
5.1 5.2 5.3 5.4
Material tables. Stress concentration factors Fatigue notch factors Fatigue classes (FAT) for welded components of structural steel and of aluminum alloys 5.5 Comments about the fatigue strength of welded components 5.6 Adjusting the stress ratio of a stress spectrum to agree with that of the S-N curve and deriving a stepped spectrum 5.7 Assessment using classes of utilization 5.8 Particular strength characteristics of surface hardened components 5.9 An improved method for computing the component fatigue limit in the case of synchronous multiaxial stresses 5.10 Approximate assessment of the fatigue strength in the case of non-proportional multiaxial stresses 5.11 Experimental determination of component strength values 5.12 Stress concentration factor for a substitute structure
6
Examples
73
6.1 6.2 6.3
76 85 89 90 93
6.4 6.5 6.6
Shaft with shoulder Shaft with V-belt drive Compressor flange made of grey cast iron Welded notched component Cantilever subject to two independent loads Component made of a wrought aluminum alloy
97 103 106 113 125 127
131 178 187
195 209
216 218 222
223
226 227 230
231 236 241 245 250 256
7
Symbols and basic formulas
7.1 7.2 7.3 7.4 7.5 7.6
Abbreviations Indices Lower case characters Upper case characters Greek alphabetic characters Basic formulas
260 261 262
8
Subject index
263
259
8
9
o General survey
lRo2 EN.dog
0.1 Scope This guideline is valid for components in mechanical engineering and in related fields of industry. Its application has to be agreed between the contracting parties. For components subjected to mechanical loadings it allows an analytical assessment of the static strength and of the fatigue strength, the latter as an assessment of the fatigue limit, of the constant amplitude fatigue strength or of the variable amplitude fatigue strength, according to the service stress conditions. Other analytical assessments, for example of safety against brittle fracture, of stability, or of deformation under load, as well as an experimental assessment of strength *1, are not subject of this guideline. It is presupposed, that the components are professionally produced with regard to construction, material and workmanship, and that they are faultless in a technical sense. The guideline is valid for components produced with or without machining or by welding of steel, of iron or of aluminum materials that are intended for use under normal or elevated temperature conditions, and in detail - for components with geometrical notches, for components with welded joints, for static loading, - for fatigue loading with more than about 104 constant or variable amplitude cycles, - for milled or forged steel, also stainless steel, cast iron materials as well as aluminum alloys or cast aluminum alloys, - for component temperatures from- 40°C to 500°C for steel, from- 25°C to 500°C for cast iron materials and from- 25°C to 200°C for aluminum materials, - for a non-corrosive environment. If an application of the guideline is intended outside the mentioned field of application additional specifications are to be agreed upon.
The guideline is not valid if an assessment of strength is required according to other standards, rules or guidelines, or if more specific design codes are applicable, as for example for bolted joints.
1 Subject of Chapter 5.11 "Experimental determination of component strength values" is not the realization of an experimental assessment of strength, but the question how specific and sufficiently reliable component strength values suitable for the general procedure of strength assessment may be derived experimentally. 2 In particular, what critical points of the considered cross-sections or component.
o General survey 0.2 Technical Background Basis of the guideline are the references listed on page 7, in particular the former TGL-Standards, the former Vlrl-Guideline 2226, as well as the- regulations of DIN 18 800, the IIW-Recommendations and Eurocode 3. Moreover the guideline was developed to the current state of knowledge by taking into account the results of more recent investigations.
0.3 Structure and elements Page
Contents 0.3.0
General
0.3.1
Procedure of calculation
0.3.2
Service stresses
0.3.3 0.3.3.0 0.3.3.1
Methods of strength assessment General Assessment of the static strength using nominal stresses, Chapter 1 Assessment of the fatigue strength using nominal stresses, Chapter 2 Assessment of the static strength using local stresses, Chapter 3 Assessment of the fatigue strength using local stresses, Chapter 4
0.3.3.2 0.3.3.3 0.3.3.4
9
10
11
12
13
0.3.4 0.3.4.0 0.3.4.1 0.3.4.2 0.3.4.3
Kinds of components General Rod-shaped (lD) components Shell-shaped (2D) components Block-shaped (3D) components
13
0.3.5
Uniaxial and multiaxial stresses
16
14 15
0.3.0 General An assessment of the static strength is required prior to an assessment of the fatigue strength. Before applying the guideline it has to be decided -
what cross-sections or structural detail of the 2 component shall be assessed * and what service loadings are to be considered.
The service loadings are to be determined on the safe side, that is, with a sufficient probability they should be higher than most of the normally occurring loadings *3. The strength values are supposed to correspond to an anticipated probability of 97,5 % (average probability of survival Po = 97,5 %).
3 Usually this probability can hardly be quantified, however.
10
0.3.1 Procedure of calculation The procedure of calculation for an assessment of the static strength is presented in Figure 0.0.1, the almost identical procedure for an assessment of the fatigue strength in Figure 0.0.2 *4. Sequential procedure of calculation
Safety factors
o General survey At the assessment stage (box at bottom of either Figure) the characteristic values of service stress occurring in the component (box at top on the left) and the component strength values derived from the mechanical material properties and the design parameters (middle column) are compared by including the required safety factors (box at bottom on the right). In specifying component fatigue strength values the mean stress and the variable amplitude effects are regarded as essential factors of influence. The assessment of strength is successful if the degree of utilization is less or equal 1,00, where the degree of utilization is defined by the ratio of the characteristic service stress to the component strength value that has been reduced by the safety factor, Chapter 1.6. In Figure 0.0.1 and Figure 0.0.2 the arrangements of the individual boxes from top to bottom illustrate the sequential procedure of calculation.
0.3.2 Service stresses Figure 0.0.1 Procedure of calculation for an assessment of the static strength.
--
Characteristic service S~resses
Sequential procedure of caJc.ulation
For an application of the guideline the stresses resulting from the service loadings have to be determined for the so-called reference point of the component, that is the potential point of fatigue crack initiation at the crosssection or at the component under consideration. In case of doubt several reference points are to be considered, for example in the case of welded joints the toe and the root of the weld. There is a need to distinguish the names and subscripts of the different components or types of stress, that may act in rod-shaped (lD), in shell-shaped (2D) or in block-shaped (3D) components, respectively, Chapter 0.3.4.
Component fati;~~l;it~~~~~~~l forzeromean stress
.,
:
Component fatigiielimlt for-the actualmean stress
Component fatigue strength i I
.~~--
JI Safety factors
Figure 0.0.2 Procedure of calculation for an assessment of the fatigue strength.
4 A survey on the analytical procedures of assessment based on the equations of the guideline may be found in Chapter 7.6. 5 Nominal stresses can be computed for a well defmed cross-section only.
The stresses are to be determined according to known principles and techniques: analytically according to elementary or advanced methods of theoretical mechanics, numerically after the finite element or the boundary element method, or experimentally by measurement. All stresses, except the stress amplitudes, are combined with a sign, in particular compressive stresses are negative. To perform an assessment it is necessary to decide about the kind of stress determination for the reference point considered: The stresses can be determined as nominal stresses *5 (notation S and T), as elastically determined local stresses, effective 6 notch stresses or structural (hot spot) stresses * (notation o and r).
6 The elastic stress at the root of a notch exceeds the nominal stress by a stress concentration factor. In the case of welded joints effective notch stresses are applied to the assessment of the fatigue strength only. Structural stresses, also termed geometrical or hot spot stresses, are normally in use with welded joints only. For further information see Chapter 5.5.
11
Correspondingly the component strength values are to be determined as nominal strength values or as local strength values of the elastic local stress, of the effective notch stress or of the structural stress. With the procedures of calculation structured uniformly for both types of stress determination it is intended that more or less identical results will be obtained from comparable strength assessments based on either nominal stresses or local stresses.
0.3.3 Methods of strength assessment 0.3.3.0 General In order to present the guideline clearly arranged and user-friendly, it is organized in four chapters, Figure 0.0.3: - Assessment of the static strength using nominal stresses, Chapter I, Assessment of the fatigue strength using nominal stresses, Chapter 2, Assessment of the static strength using local stresses, Chapter 3, Assessment of the fatigue strength using local stresses, Chapter 4.
.~. Static strength
LNoml?al
Nominalstresses ) ;/ Static
strength
aSseSSlllent
~~. .r" Chapter 3: "<.
stresses
Nominal stresses
I
Fatigue strength' assessment
~tb
0.3.3.1 Assessment of the static strength using nominal stresses, Chapter 1 Relevant nominal characteristic service stresses are the extreme maximum and extreme minimum values of the individual types of stress or stress components, e.g. nominal values of the axial (or tension-compression) stress, Szd, of the bending stress, Sb, and so forth *7 *8, Chapter 1.1. Relevant material properties are the tensile strength and the yield strength (yield stress or 0.2 proof stress) as well as the strength values for shear derived from these. A technological size effect is taken into account if appropriate. The influence of an elevated temperature on the material properties - strength at elevated temperature and creep strength, yield strength at elevated temperature and I% creep limit - is allowed for by means of temperature factors, Chapter 1.2. Design parameters are the section factors, by which an experienced partial plasticity of the component is allowed .according to yield strength, type of loading, shape of cross-section, and stress concentration factor. From the section factor and from further parameters an overall design factor is derived, Chapter 1.3. The nominal values of the static component strength are derived from the tensile strength, divided by the respective overall design factor, Chapter 1.4. As common in practice the safety factor against the tensile strength is 2,0. For materials with a yield strength less than 0,75 times the tensile strength the safety factor is 1,5 against the yield strength, however. Under favorable conditions these safety factors may be reduced, Chapter 1.5.
~ Fatii:ue strength
Chapter 4:
o General survey
-,
( Stade. strength ) - . LO.cal. -....ali.ou. estr.c.·.n.. \ ".. IAcalstrcsses/" Stresses \.Li .. .) .~ ~~
Figure 0.0.3 Organization of the guideline.
The assessment is carried out by proving that the degree of utilization is less or equal 1,00 . The degree of utilization for an individual stress component or type of stress is the ratio of its nominal characteristic service stress value, divided by the allowable nominal static component strength value, which follows from the nominal static component strength divided by the safety factor.
In particular the procedure of calculation is completely presented in everyone of the four chapters, even if this results in repetitions of the same or almost the same parts of text in Chapter I and Chapter 3 or in Chapter 2 and Chapter 4, respectively.
If there are several stress components or types of stress their individual degrees of utilization are combined to obtain an entire degree of utilization. The interaction formula to be applied to that combination allows for the ductility of the material in question, Chapter 1.6.
The procedure of calculation using nominal stresses is to be preferred for simple rod-shaped (lD) and for shellshaped (2D) components. The procedure of calculation using local stresses has to be applied to block-shaped (3D) components, and moreover in general, if the stresses are determined by a finite-element or a boundary-element calculation, if there are no welldefined cross-sections or no simple cross-section shapes, if stress concentration factors or fatigue notch factors are not known, or (concerning the assessment of the static strength) in the case ofbrittIe materials.
For welded components the assessment of the static strength has to be carried out for the toe section as for non-welded components, and for the throat section with
7 According to rod-, shell- or block-shaped components, Chapter 0.3.4. 8 The extreme maximum or minimum stresses for the assessment of the static strength may be different from the maximum and minimum stresses for the assessment of the fatigue strength, that are determined from the largest amplitude and the related mean value of a stress spectrum.
12
an equivalent nominal stress, that is computed from the components of nominal stress acting in the weld seam *9.
o General survey amplitude value follows from the nominal amplitude of the derived component fatigue strength divided by the safetyfactor. If there are several stress components or types of stress
0.3.3.2 Assessment of the fatigue strength using nominal stresses, Chapter 2 Relevant nominal characteristic service stresses are the largest stress amplitudes in connection with the respective stress spectra and the related mean stress values. They are determined for the individual stress components or types of stress, e.g. amplitudes and mean values of the nominal axial (tension-compression) 7 8 stresses, Sa,zd and Sm,zd, and so forth * *, Chapter 2.1. Relevant material properties are the fatigue limit for completely reversed axial stress and the fatigue limit for completely reversed shear stress of the material in question. A technological size effect is taken into account where appropriate. The influence of an elevated temperature is allowed for by means of temperature factors, Chapter 2.2. Design parameters to be considered in particular are the fatigue notch factors, allowing for the design of the component (shape, size and type of loading), as well as the roughness factor and the surface treatment factor, by which the respective surface properties are accounted for. By specific combination of all these factors a summary design factor is calculated, Chapter 2.3. The nominal values of the component fatigue limit for completely reversed stresses follow from the derived fatigue limit values of the material, divided by the respective design factors, Chapter 2.4.1. From these fatigue limit values the amplitudes of the component fatigue limit according to the mean stress values (or the stress ratios) are to be derived, Chapter 2.4.2. The amplitudes that specify the variable amplitude fatigue strength of the component are obtained from the fatigue limit values multiplied by a factor depending on the parameters of the stress spectrum (total number of cycles and amplitude frequency distribution), Chapter 2.4.3. The basic value of the safety factor is 1,5. Under favorable conditions this safety factor may be reduced, Chapter 2.5. The assessment is carried out by proving that the degree of utilization is less or equal 1,00 . The degree of utilization for an individual stress component or type of stress is the ratio of its nominal characteristic service stress amplitude, divided by the allowable amplitude of the component fatigue limit or of the component variable amplitude fatigue strength. The allowable
9 This assessment of the static strength for welded components is according to DIN 18 800 part 1. As far conditionally weldable steel, stainless steel, weldable cast iron materials or weldable aluminum alloys are concerned, the rules of DIN 18 800 are provisional and may be applied with caution only.
as
their individual degrees of utilization are combined to obtain the total degree of utilization. The interaction formula to be applied to that combination allows for the ductility of the material in question, that is in the same way as for the assessment of the static strength, Chapter 2.6. For the assessment of the fatigue strength of welded components using nominal stresses basic fatigue limit values for completely reversed stress are given. They are independent of the tensile strength of the base material (which is different to non-welded components). They are converted by design factors that follow from a classification scheme of structural weld details. The combined effect of mean stress and of residual stresses in welded components is considered by means of a mean stress factor together with a residual stress factor *10.
0.3.3.3 Assessment of the static strength using local stresses, Chapter 3 Relevant characteristic local service stresses are the extreme maximum and extreme minimum stresses of the individual types of stress or stress components, e.g. local values of the normal (axial and/or bending) stress, 7 o, and of the shear (shear and/or torsional) stress * *8, Chapter 3.1. Relevant material properties are to be determined as for nominal stresses, Chapter 3.2. Design parameters are the section factors, by which an experienced partial plasticity of the component is allowed according to yield strength, type of loading, and shape of the component. The section factors are calculated on the basis of Neuber's formula, but by observing individual upper bound values that follows from the plastic limit load (plastic notch factor). From the .section factors and from further parameters an overall design factor is derived, Chapter 3.3 *11. The local values of the static component strength are derived from the tensile strength, divided by the respectiveoverall design factor, Chapter 3.4. The safety factors are to be determined as for nominal stresses, Chapter 3.5.
10 The assessment of the fatigue strength for welded components makes reference to the llW-Recommendations and Eurocode 3. As far as conditionally weldable steel, stainless steel, weldable cast iron materials or weldable aluminum alloys are concerned this kind of calculation is provisional and may be applied with caution only. 11 The assessment ofthe static strength using local stresses on the basis of Neuber's formula and the plastic limit load is an approximation which has to be regarded as provisional and is to be applied with caution only.
13
o General survey
The assessment is carried out by means of the degree of utilization as for nominal stresses, but with the respective local values of the characteristic service stress and the local component strength values, Chapter 3.6.
nominal stresses by means of a mean stress factor together with a residual stress factor *10.
For welded components the assessment of the static strength using local stresses is carried out using structural stresses (not with notch root stresses), for the weld toe as for non-welded components, for the root of the weld using an equivalent structural stress, that is to be derived from the structural stress components acting in the weld seam *9.
0.3.4 Kinds of components
0.3.3.4 Assessment of the fatigue strength using local stresses, Chapter 4
Relevant local characteristic service stresses are the largest stress amplitudes in connection with the respective stress spectra and the related mean stress values. They are determined for the individual stress components or types of stress, e.g. amplitudes and mean values of the local normal (axial and/or bending) stress, 7 8 0"a and O"m , and so forth * * , Chapter 4.1.
0.3.4.0 General
Rod-shaped (10), shell-shaped (2D) and block-shaped (3D) components are to be distinguished, as in each case other stress components or types of stresses, identified by differing symbols and subscripts, are of concern. The distinction is only a formal one, however, and the procedure of calculation is the same in all cases. Specific particulars apply to welded components.
0.3.4.1 Rod-shaped (ID) components
For rod-shaped (10) components - rod, bar, shaft, or beam for example - the following system of co-ordinates is introduced: x-axis is the longitudinal center line of the component, y- and z-axes are the main axes of the cross-section that are to be specified so, that for the moments of inertia Iy~ Iz is valid, Figure 0.0.4.
The relevant material properties are determined as for nominal stresses, Chapter 4.2. Design parameters to be considered in particular are the Kt-Kf ratios, allowing for the design of the component (shape and size), as well as the roughness factor and the surface treatment factor, by which the respective surface properties are accounted for. By specific combination of all these factors a summary design factor is calculated, Chapter 4.3. "0.0...·
The local values of the component fatigue limit for completely reversed stresses follow from the derived fatigue limit values of the material, divided by the respective design factors, Chapter 4.4.1. The conversions to the amplitude of the component fatigue limit and to the amplitude of the component variable amplitude fatigue strength are as for nominal stresses, Chapter 4.4.2 to 4.4.3. The safety factors are to be determined as for nominal stresses, Chapter 4.5. The assessment by means of the degree of utilization is as for nominal stresses, but with the respective local values of the characteristic stress amplitude and the value of the component fatigue limit or of the component variable amplitude fatigue strength, Chapter 4.6. For the assessment of the fatigue strength of welded components using structural stresses or effective notch stresses the same basic fatigue limit values for completely reversed stresses apply as for nominal stresses. They hold for effective notch stresses without conversion, but for structural stresses they have to be converted by factors given for some typical weld details. The combined effect of mean stress and of residual stresses in welded components is to be considered as for
'z
Figure 0.0.4 Rod-shaped (ID) component (round specimen with groove) in bending. Nominal stress S, and maximum local stress O"m"" at the reference point W.
Calculation using nominal stresses If the assessment of rod-shaped (ID) components is carried out by using nominal stresses, Chapter I and 2, the nominal stresses to be computed at the reference point are Szd from an axial load, Sb from a bending moment, T, from a shear load, and/or Tt from a torsional moment acting at the respective section. For the equations given in Chapter 1 and 2 it is provided, that both the bending stress Sb and the shear stress T, act in the x-z-plane. Otherwise stress components Sb,y and Sb,z , Ts,y and Ts,z are to be considered *12.
12 The indices y and z describe the direction ofthe related vectors ofthe bending moments My, Mz and ofthe lateral loads Fy, Fz .
14
In case of rotationally symmetrical cross-sections with circumferential notches a resultant bending stress and a resultant shear stress can be calculated from these stress components,
s, =Jr-S-~,y-+-S-~,-z ' 2
(0.3.1)
2
Ts = Ts,y +TS,z The equations given in Chapter 1 and 2 may be applied to Sb and T;
o General survey 0.3.4.2 Shell-shaped (2D) components (ID) welded components
Rod-shaped
For shell-shaped (2D) components - disk, plate, or shell for example - the following system of coordinates is introduced: The x- and y-axis are placed in the surface at the reference point, the z-axis is normal to the surface in thickness direction. The normal stress and the shear stress in thickness direction are supposed to be negligible, Figure 0.0.5.
In the general case of not rotationally symmetrical cross-sections a calculation using local stresses is normally to be preferred. Additional stresses at notches (as for example the circumferential stress associated with an axial stress of a shaft with groove) may be included in the stress concentration factor, otherwise they will be neglected.
Calculation using local stresses If the calculation of rod-shaped (ID) components is carried out using local stresses *13, Chapter 3 and 4, the local normal stresses at the reference point from axial and from bending loading (in x-direction), azd = a as well as the local shear stresses "ts = "t from shear and from torsion (normal to the x-direction) are considered. If the local stresses are calculated from the nominal stresses by multiplication with the respective stress concentration factors, the equations given in Chapter 3 and 4 are applicable. However, if the calculation yields the complete local state of stress at the reference point (as for example a finite-element calculation does), the principle stresses 0"1, 0"2, 0"3 are computed *14 and treated as described for block-shaped (3D) components.
Rod-shaped (ID) welded components For rod-shaped (ID) welded components *15 the notations a and "t apply to structural stresses and the notation aK and "tK apply to effective notch stresses *16.
Figure O. O. 5 Shell-shaped (2D) component (shell with cutout detail). Local stresses aa,x at the reference point W (peak value) and aa,x,ru. at the neighbouring point B.
Calculation using nominal stresses If the assessment of shell-shaped (2D) components is
carried out using nominal stresses, Chapter 1 and 2, the nominal stresses at the reference point to be computed are the normal stresses Szdx = S, and Szdy = S, from loadings in the x- and y-directions and T, = T from a shear loading.
Calculation using local stresses If the assessment of shell-shaped (2D) components is
carried out using local stresses, Chapter 3 and 4, the local stresses at the reference point azdx = ax and azdy = a y in the x- and y-directions and the local shear stress r, = t are considered. If the local stresses are computed from the nominal
stresses by multiplication with the respective stress concentration factors, the equations given in Chapter 3 and 4 are applicable. However, if the calculation yields the complete local state of stress at the reference point (as for example a finite-element calculation does), the principle stresses 0"1,0"2,0"3 are computed *14 and treated as described for block-shaped (3D) components.
13 The assessment of rod-shaped (ID) components should preferably be carried out using nominal stresses whenever possible. 14 Principle stresses are independent of the chosen coordinate system. In the special case of a proportional loading the directions of the principle stresses remain fixed to the coordinates of the component. In the more general case of non-proportional loading the directions and the amounts of the three principle stresses will change with time, see Chapter 0.3.5.
15 Rod-shaped (ID) welded components are rolled sections with circular, tube, 1-, box or other cross-sections connected or joined with butt welds and/or fillet welds.
15
o General survey
Shell-shaped (2D) welded components
0.3.4.3 Block-shaped (3D) components
For shell-shaped (2D) welded components the notations o"x , O"y and 't apply to structural stresses and the notations O"Kx , O"Ky and 'tK apply to effective notch stresses *16 .
In the general case block-shaped (3D) components are to be calculated using local stresses, Chapter 3 and 4
_. -
..
.
.
; (
- . .,
0':«,x'1l!~. ¥
... J~.~
;70.
/-~
... '. . - S x /Io-{
(It'd
<;,fI"c-(
:....--+--~-"'i
nO)'jJIr'rtfl.{
*17
~~--'-"
For block-shaped (3D) components the coordinate system at the reference point may be of cartesian, cylindrical or spherical type. The calculation is supposed to yield the complete state the reference point (as for example a ,finite-element calculation does). From that the principle >tl~esses_~!.....~2-,.~~~.,are computed *14, and for these the , degrees of utilization are determined.
--of local stress at
If the reference point W is located at a free surface of a
block-shaped (3D) component, Figure 0.0.8, it is supposed that 0"1 and 0"2 are the principle stresses at the surface, while the principle stress 0"3 is supposed to point normally to the surface inwards the component. Figure 0.0.6 Shell-shaped (2D) welded component. Example: Strap with longitudinal stiffner. After Radaj /10/. Top: Joint, Centre: Stress distribution, Bottom: Profile. Relevant is the stress at the reference point W (at the toe line of the weld). Calculation using nominal stresses: Stress Sx . Calculation using structural stress: Maximum stress O"x,max obtained from extrapolating the stress distribution towards the weld toe. Calculation using effective notch stresses: Maximum stress occurring at the weld toe, see Figure 0.0.7 .
O"Kx,max
In general stress gradients exist for all three principle stresses, ·both normal to the surface and in either direction of the surface. However, only the stress gradients for 0" 1 and 0"2 normal to the surface can be considered in the procedure of calculation, while the stress gradients for 0"1 and 0"2 in any directions of the surface and the gradients of 0"3 can not. Block-shaped (3D) components can be calculated as shell-shaped (2D) components if the stresses O"x , O"y and 't at the load free surface are of concern only.
.......Radius r = 1 mm
/ F
I
\
\/
F
Figure 0.0.7 Shell-shaped (2D) welded component. Example: Cruciform joint and butt weld. After Radaj /l0/. Calculation using effective notch stresses: The maximum stress O"Kx,max occurring at the toe or at the root of the weld has to be computed by introducing a fictitious effective notch radius r = 1 rom, unless the real radius is r > 1 rom (the fictitious notch radius is intended for the assessment of the fatigue strength only). The fictitious notch radius r = 1 rom applies to welded joints from structural steel. It is supposed, however, that it is applicable for other kinds of material as well, although this has to be considered as a preliminary specification for welded aluminum materials so far.
16 Structural stresses can be applied to the assessment of the static strength and to the assessment of the fatigue strength. Effective notch stresses can be applied to the assessment of the fatigue strength, but not to the assessment of the static strength.
Figure 0.0.8 Block-shaped (3D) component (flange). Local longitudinal stress 0"1 and circumferential stress 0"2 at the reference point W (peak values), stresses O"u,s and 0"2,~s at neighboring point B.
17 For block-shaped components the determination of a nominal stress is not possible since there is no well defmed cross-section.
16
o General survey
Block-shaped (3D) welded components
Assessment of the static strength
Welds at a load-free surface of block-shaped (3D) components having no inner defects can be assessed as shell-shaped (2D) welded components. Then the notations G x , Gy and 't apply to structural stresses and the notations O"Kx , O"Ky and 'tK apply to the notch root stresses at the surface, Figure 0.0.6.
For the assessment of the static strength the most unfavorable case to be considered is that the extreme values of all maximum and minimum stresses occur simultaneously. Accordingly the entire degree of utilization has to be computed. However, stresses of different sign that will decrease the entire degree of utilization are to be included only if they definitely occur together with the remaining stresses, Chapter 1.6 or 3.6.
0.3.5 Uniaxial and multiaxial stresses The stresses occurring in the cross-section or at the reference point of a component may be caused by a single load or - by several loads acting simultaneously. In both cases an uniaxial stress or multiaxial stresses may result at the reference point. An uniaxial stress occurs under special circumstances only, as for example in a tension loaded prismatic bar, or at an unloaded edge of shell-shaped (2D) or blockshaped (3D) components, the latter even if several loads act on these components simultaneously, Figure 0.0.9. In addition an uniaxial stress may be assumed at the reference point if, by comparison, any further stresses are small.
In general components are subject to multiaxial stresses, however. Then two or three normal stresses, or normal stresses and shear stresses occur at the reference point.
s,"-,-+ t T f
-
+-~ +~at .. ~
t
Sy -"-+T x
t-':
~
-{Q:Jt..:' ~
Figure 0.0.9 Uniaxial and multiaxial stresses. Nominal stresses Sx- Sy and T. Left: multiaxial stresses in a sheet section, Right: uniaxial stress in a sheet section at the edge of a cutout.
In this guideline a basic principle is defined both for an assessment of the static strength and of the fatigue strength in case of multiaxial stresses: the individual degrees of utilization for everyone of the computed types of stress or stress components have to be determined and assessed separately in a first step, and thereafter these individual degrees of utilization will be combined by means of an appropriate interaction formula to obtain the entire degree of utilization for final assessment.
Assessment of the fatigue strength For the assessment of the fatigue strength *18 multiaxial stresses varying with time have to be distinguished as follows: proportional stresses, synchronous stresses, or non-proportional stresses.
Proportional stresses Normally proportional stresses result from a single loading acting on the component. Examples of proportional stresses are the circumferential and the longitudinal stresses of a cylindrical vessel loaded by internal pressure, or the bending and torsional stresses of a round cantilever loaded eccentrically by a single load. If this single acting loading is varying with time, all multiaxial stresses are varying proportionally to that loading and proportionally to each other, which also is true with regard to their amplitudes and their mean values. Further, as a consequence, the principle stresses observe non-changing directions relative to the component. The amounts of the stresses, also in the stress amplitude spectra, may be converted by constant factors. Hence all stress spectra are of similar shape, but may differ in intensity (amount of their characteristic maximum stress).
Proportional stresses my also result from several loadings that act on the component simultaneously and, for their part, change proportionally with time as well. Then several stresses of the same kind are to be overlaid additively. For proportional multiaxial stresses, the interaction formulas given in Chapter 2.6 and 4.6 are exactly valid in the sense of material mechanics, if the related rules of signs are observed.
18 Both for the assessment ofthe fatigue limit and for the assessment of the variable amplitude strength.
17
Synchronous stresses Synchronous stresses are a simple case of nonproportional stresses. They are proportional with regard to their amplitudes, however non-proportional with regard to their mean values. Normally synchronous stresses result from a combined action of a constant loading with a second, different kind of loading, that is varying with time. Examples are a shaft with a non-changing torsional loading and a rotating bending loading. Or a long, lying cylindrical vessel under pulsating internal pressure, where the longitudinal stress is non-proportional to the circumferential stress because of the bending stress from the dead weight is additively overlaid. For synchronous multiaxial stresses, the interaction formulae given in Chapter 2.6 and 4.6 - if observing the related rules of sign - are valid as a useful approximation, because they are applied to the stress amplitudes, which are proportional to each other, and because the fatigue strength is determined by the stress amplitudes in the first place. Additional rules for considering the mean stresses are required, however.
o General survey determined degrees of utilization for the individual loadings are then added linearly in order to estimate the entire degree of utilization. Compared to usual interaction formulas developed for proportional stresses the linear addition may be assumed to produce results on the safe side *19. A necessary reservation for applying this approximate way of calculation is, that a thorough stress analysis is performed in every case and that careful evaluation of the result is performed finally. In order to reach an optimum degree of utilization of the component fatigue strength in the case of nonproportional multiaxial stresses, an experimental assessment of the fatigue strength has to be recommended according to the contemporary state of the art.
An improved procedure for the assessment of the component fatigue limit in the case of synchronous multiaxial stresses is presented in Chapter 5.9.
Non-proportional stresses Non-proportional stresses result from the action of at least two loadings that vary non-proportionally with time in a different manner. In this most general case of non-proportional loading different spectra apply to the individual types of stress that result from the combined loadings. In particular the amounts and the directions of the principle stresses are variable with time. The case of variable directions of the principle stresses can not be considered with the interaction formulas given in Chapter 2.6 and 4.6. Appropriate methods of calculation proposed for the assessment of the fatigue strength in the case of nonproportional stresses, that have been developed from a material mechanics point of view, require much computing effort and are applicable with computer programs for short stress sequences only. Their plausibility is currently subject of investigations. Therefore only an approximate way of calculation for the assessment of the fatigue strength in the case of nonproportional multi-axial stresses can be given, Chapter 5.10: As proportional stresses result from each of the acting loadings the degrees of utilization of these individual loadings can be correctly computed and assessed as described in Chapter 2.6 and 4.6. The so
19 For non-proportional multiaxialloadings the reference point may be at different positions in the case ofthe combined loadings and in the case of each ofthe individual loadings, respectively. This is because the most damaging stresses from the combined loadings may occur at positions different from the positions ofthe maximum stresses from the individual loadings. By the above mentioned approximation, however, the full damaging effect of each loading may be assumed to be superimposed at the reference point in question.
18
o General survey
19
1.1 Characteristic stress values
1 Assessment of the static strength
using nominal stresses
1 Assessment of the static strength using nominal stresses IR>11
N.doq
1.0 General According to this chapter the assessment of the static strength using nominal stresses is to be carried out.
1.1 Characteristic stress values Contents 1.1.0
General
1.1.1 1.1.1.0 1.1.1.1 1.1.1.2
Characteristic stress values General Rod-shaped (ID) components Shell-shaped (2D) components
Page 19
20
It should be observed that not necessarily the component
static strength is determined by a failure occurring at a notched section. Likewise a global failure occurring at a different, unnotched or moderately notched section of the component may be determining, Figure 1.0.1. Kt,A
~
-__ c------.~--+._._.
F
~
_
-- -------'---- .-...-... F
Figure 1.0.1 Different sections for a static failure occurring as a local failure (A) or as a global failure (B).
1.1.0 General According to this chapter the characteristic service stress values are to be determined. Relevant are the extreme maximum and rmmmum stresses Smax,ex,zd and Smin,ex,zd, ... of the individual stress components expected for the most unfavorable operating conditions and for special loads according to specification or due to physical limits *3. Both the maximum and minimum stresses can be positive or negative. It is assumed, that all stresses reach their extreme values simultaneously. Elevated temperature
For GGG sorts and wrought aluminium alloys with low elongation, A < 12,5 % , for all sorts GT and GG as well as for cast aluminium alloys the assessment of the static strength is to be carried out by using local stresses according to Chapter 3 *1. In the case of very high stress concentration factors the assessment of the static strength is to be carried out by using local stresses according to Chapter 3 *2. For block-shaped (3D) components the assessment of the static strength is to be carried out by using local stresses according to Chapter 3. For all other kinds of material (GGG sorts and wrought aluminium alloys with high elongation, A'2 12,5 % , GS, milled steel and forging-steel) and for smaller stress concentration factors of rod-shaped (lD) and of shell-shaped (2D) components the assessment of the static strength using nominal stresses is applicable.
In case of elevated temperature the values Smax,ex,zd, ... and Smin,ex,zd,... are relevant for a short-term loading (related to the high temperature strength or high temperature yield strength). For a long-term·loading (related to the creep strength or 1% creep limit) correct results will only be obtained in case of a constant (static) tensile stress Smax,ex,zd equally distributed over the section of concern. In all other cases of constant or variable loading the assessment will be more or less on the safe side if the values Smax,ex,zd , ... and Smin,ex,zd, ... refer to a stress distribution with a stress gradient, and/or if they refer to the peak values of a variable stress history, which are of short duration only, while for the rest of time the stress is lower. If in those cases it becomes necessary to make best use
of the long-term load bearing capacity of the component
general the values Smax,ex,zd and Smin,ex,zd for the assessment of the static strength are the extreme values of a stress history. For the assessment ofthe fatigue strength a stress spectrum is tobe derived from that history consisting ofstress cycles ofthe amplitudes Sa,zd,i and the mean values Sm,zd,i , Chapter 2.1. The largest amplitude ofthis stress spectrum is Sa,zd, 1 , and the related mean value is Sm,zd,l . The related maximum and minimum values are Smax,zd,l = Sm,zd,l + Sa,zd,l and Smin,zd,l = Sm,zd,l - Sa,zd,l .The values Smax,ex,zd and Smin,ex,zd may be different from the values Smax,zd, 1 and Smin,zd, 1 . This is because extreme, very seldom occurring events are important only for the assessment of the static strength, but hardly for the assessment ofthe fatigue strength. In a stress spectrum which issupposed toapply tonormal service conditions they do not have tobe considered therefore.
3 In
1 Because these materials lack sufficient plasticity. 2 Because extremely high local strains are associated with a very high stress concentration factor. The stress concentration factor Kt = 3 ofaflat bar with a hole issuggested asa limit value.
20
1.1 Characteristic stress values
1 Assessment of the static strength using nominal stresses
(because otherwise the assessment cannot be achieved) an expert stress analysis is recommended to define the appropriate stress value to be used for the assessment. Such an analysis is beyond the scope of the present guideline, however.
Superposition
If several stress components act simultaneously at the reference point, they are to be overlaid. For the same type of stress (for example tension and tension Smax,ex,zd,l, Smax,ex,zd,2 , ... ) the superposition is to be carried out at this stage, so that in the following a single stress value (Smax,ex,zd, ...) exists for each type of stress *4. For different types of stress (for example bending and torsion, or tension in direction x and tension in direction y) the superposition is to be carried out at the assessment stage, Chapter 1.6. Stress components acting opposed to each other and which do not or can not occur simultaneously, are not to be overlaid however.
1.1.1 Characteristic stress values
Figure 1.1.1 Components of nominal stress SII' Til' SJ. and TJ. in welds. After DIN 18800, Part 1. Left: Butt
weld, Right: Fi)let weld; the nominal stress isto becomputed with the throat thickness a.
Rod-shaped (ID) welded components For rod-shaped (ID) welded components the nominal stresses are in general to be determined separately for the toe section and for the throat section *7. For the toe section the nominal stresses are to be computed as for non-welded components, Eq. (1.1.1) .For the throat section equivalent nominal stresses have to be computed from the nominal stresses resulting from the particular types of loading, Figure 1.1.1 *8.
1.1.1.0 General Rod-shaped (lD) and shell-shaped (2D), as well as nonwelded and welded components are to be distinguished.
11.1.1 Rod-shaped (ID) components
(1.1.2)
S..L,zd Axial stress normal to the weld seam T..L,zd Shear stress normal to the weld seam, TII,zd Shear stress parallel to the weld seam. Swv,b, T WV,s and T wv,t in analogy.
Rod-shaped (ID) non-welded components For rod-shaped (lD) non-welded components an axial stress Szd , a bending stress Sb, a shear stress T, *5 and/or a torsional stress T t are to be considered. The extreme maximum and minimum stresses are Smax,ex,zd, Smax,ex,b, Tmax.exs . Tmax,ex,t, Smin,ex,zd, Smin,ex,b, T min.ex,s, Tmin,ex,t .
2 2 2 Swv,zd = S..L,zd + T..L,zd + 1j1 ,zd '
(1.1.1)
Stresses of different sign (Smax,ex,zd positive, Smin,ex,zd negative for instance) are generally to be considered separately *6. For shear and for torsion the highest absolute value is relevant.
The extreme maximum and minimum values of the equivalent nominal stresses are Smax,ex,wv,zd and Smin,ex,wv,zd, ....
(1.1.3)
Stresses of different sign (Smax,ex,wv,zd posiuve, Smin,ex,wv,zd negative for instance) are generally to be considered separately. For shear and for torsion the highest absolute value is relevant.
For welded components ingeneral anassessment ofthe static strength isto be carried out for the toe section and for the throat section, because the cross-sectional areas may be different and because the strength behavior is evaluated in a different way. The assessment for the toe section istobecarried out asfor non-welded components. The assessment for the throat section is to be carried out with the equivalent nominal stress Swv.zd . ... 7
4 Stress components having different signs may cancel out each other in part orcompletely.
Bending and shear in two planes (components y and z) are to be considered if appropriate, see Chapter 0.3.4.1 .
5
6 Particularly inthe case ofcast iron materials with different tension and compression strength values aswell asinthe case ofunsymmetrical crosssections.
8 According to DIN 18 800 part 1, page 36. The nominal stress SII (normal stress parallel tothe orientation ofthe seam) istobeneglected.
Normally Swv,zd will result mainly from S..Lzd. Further types of loading analogous.
9
21
1.1 Characteristic stress values
1.1.1.2 Shell-shaped (2D) components
Shell-shaped (2D) non-welded components For shell-shaped (2D) non-welded components normal stresses in the x- and y-directions Szd,x = Sx and Szd,y = Sy as well as a shear stress Ts = T are to be considered. The extreme maximum and minimum stresses are Smax,ex,x , Smax,ex,y , Tmax,ex , Smin,ex,x , Smin,ex,y , Tmin,ex .
(1.1.4)
Tension stresses (positive) or compression stresses (negative) are generally to be considered separately *10. For shear the highest absolute value is relevant.
Shell-shaped (2D) welded components For shell-shaped (2D) welded components, Figure 0.0.6, the nominal stresses are in general to be determined separately for the toe section and for the throat section *7. For the toe section the nominal stresses are to be computed as for non-welded components, Eq. (1.1.4), For the throat section equivalent nominal stresses Swv,x, Swv,y and Twv have to be computed from the nominal stresses resulting from the particular types of loading, Figure 1.1.1, according to Eq (1.1.2). The extreme maximum and minimum values of the equivalent stresses are Smax,ex,wv,x and Smin,ex,wv,x , ....
(1.1.5)
In case of opposing effect Smax,ex,wv,x is to be regarded as positive and Smin,ex,wv,x as negative. Tension and compression are generally to be considered separately. For shear the highest absolute value is relevant.
10 See footnote *6. And moreover because the second normal stress Sy may reduce the degree ofutilization.
1 Assessment of the static strength using nominal stresses
22
1.2 Material properties
1.2 Material properties
11m
EN.dog
Contents 1.2.0
General
1.2.1 Component values according to standards 1.2.1.0 General 1.2.1.1 Component values according to standards of semi-finished products or test pieces 1.2.1.2 Component values according to the drawing 1.2.1.3 Special case of actual component values 1.2.2 1.2.2.0 1.2.2.1 1.2.2.2
Technological size factor General Dependence on the effective diameter Effective diameter
1.2.3
Anisotropy factor
Compression strength factor and shear strength factor 1.2.4.0 General 1.2.4.1 Compression strength factor 1.2.4.2 Shear strength factor
1 Assessment of the static strength using nominal stresses
Page 22 23.
24
26
values '.' liCCj)tding.
1.2.4
1.2.5 1.2.5.0 1.2.5.1 1.2.5.2 1.2.5.3
to s.tanqai"ds
Component
values -
fIg)
27
Temperature factors General Normal temperature Low temperature Elevated temperature
1.2.0 General According to this chapter the mechanical material properties like tensile strength R.n, yield strength R, and further characteristics for non-welded and welded components are to be determined *1. All mechanical material properties are those of the material test specimen. Values according to standards, component values and component values according to standards are to be distinguished, Figure 1.2.1.
Figure 1.2.1 Values according to standards and component values according to standards, Rm and Rp, or values specified by drawings, R.n.z and Rp,z . Top: All kinds of material except GG, Rm =:; Rm,N, Rp =:; Rp,N . Semi-logarithmic decrease of the mechanical material properties with the effectivediameter deft'. Bottom: GG, Rm =:; or
~
Rm,N . Double-logarithmic decrease of the
mechanicalmaterial propertieswith the effectivediameter deff. Specified values according to drawings Rm,z and Rp,z.
Values according to standards The values according to standards
Material test specimen In the context of this guideline the material test specimen is an unnotched polished round specimen of do = 7,5 mID diameter *2 ..
Component values The component values
1 If in this chapter values are given for GT, GG or cast aluminum alloys, they are needed for the assessment of the fatigue strength only, Chapter 2, but not for the assessment of the static strength, which is to be carried out using local stresses for these materials, Chapter 3.
If specific values for a component
2 This definition is the basis of the presented calculation, although specimens for tensile tests may usually have diameters different from
determined experimentally, they normally apply to a probability of survival Po = 50 % ,. and therefore they
7,5mm.
Special case of actual component values
23
1.2 Material properties
are valid only for the particular component, but not for the entirety of all those components. They may be used, for instance, fora subsequent assessment of the strength of the particular component in case of a service failure, if for that purpose all safety factors are set to 1,00 in addition.
Component values according to standards The component values according to standards
1.2.1 Component values according to standards 1.2.1.0
1 Assessment of the static strength using nominal stresses product *4 , in the case of cast iron or cast aluminum it is the value from the test piece defined by the material standard. The yield strength, Rp,N , is the guaranteed minimum value specified for the smallest size of the semi-finished product *4 or for the test piece defined by the material standard *5. Moreover there are to be considered: for compressive stresses the compression strength factor f, , Chapter 1.2.4, for shear stresses the shear strength factor :4 , Chapter 1.2.4, and for elevated temperature the temperature factors Kt,m, ..., Chapter 1.2.5.
1.2.1.2 Component values according to the drawing The component value of the tensile strength, RID, is
Rm = 0,94 . Rm,z .
(1.2.2)
The component value according to the drawing Rm,z is the tensile strength of the material specified on the drawing. As the value Rm,z is normally verified by random inspection of small samples only *6, it is assumed to have a probability of survival less than Pu = 97,5 % . Eq. (1.2.2) converts the value Rm,z to a component value R; that is expected to conform with the probability of survival of Pu = 97,5 %. The yield strength R, corresponding to the tensile strength Rm is *7 . Rp= Kd,p . Rp,N . Rm, Kd,m
(1.2.3)
Rm,N
technological size factors, Chapter 1.2.2, values of the semi-finished product or of a test piece defined by standards, Chapter 5.1 .
1.2.1.1 Component values according to standards of semi-finished products or of test pieces The component values according to standards of the tensile strength, Rm , and of the yield strength, Rp, are
Rm = KJ,m' K A' Rm,N, R, = KJ,p . K A' Rp,N, KJ,m, KJ,p KA Rm,N , Rp,N
(1.2.1)
technological size factors, Chapter 1.2.2, anisotropy factor, Chapter 1.2.3, values of the semi-finished product or of a test piece defined by standards, Chapter 5.1 .
In the case of steel or wrought aluminum alloys the tensile strength, Rm,N js the guaranteed minimum value specified for the smallest size of the semi-finished 3 The term yield strength is used as a generalized term for the yield stress (of milled or forged steel as well as cast steel) and for the 0.2 proof stress (of nodular cast iron or malleable cast iron as well as aluminum alloys).
4 If different dimensions of that semi-finished product are given by the standard. 5 A probability of survival Po = 97,5 % is assumed for the component according to standards Rm,N ' Rp,N . This probability of survival should also apply to the values Rm ' Rp calculated therefrom. prop~ies
6 The value Rm Z is checked by three hardness measurements (n=3) for exampl~, where every test has to reach or to exceed the required value. The probability of survival of the lowest ofn=3 tests may be estimated to 75 % (= 1 - 1/(n+l) = 1 - 11(3+1) = 0,75), and may be assigned to Rm,Z . With a likely coefficient of variation of 4% the conversion to Po = 97,5 % follows from Eq. (1.2.2). 7 A conversion proportional to Rp N I Rm N would not be correct since the technological size effect is more pronounced for the yield strength than for the tensile strength.
24
1.2 Material properties
1.2.1.3 Special case of actual component values If only an experimental value of the tensile strength Rm,r is known the value of the yield strength Rp,r may be computed from Eq. (1.2.3) with Rm = Rm,r.
1 Assessment of the static strength using nominal stresses For milled steel there is deff,max,m = deff,max,p = 250 mm. For all other kinds of material there are no upper limit values cleff,max,... , (1.2.11) unless otherwise specified in the material standards.
1.2.2 Technological size factor
Aluminum alloys
1.2.2.0
For cast aluminum alloys the technological size factors for the tensile strength and for the yield strength are as follows: For deff~ defl;N,m = defl;N,p = 12 mm
1.2.2.1 Dependence on the effective diameter Non-welded components
:KI,m = :KI,p = 1,
Steel and cast iron materials
(1.2.4)
for cleff > 7,5 mm *9 Kt,m = 1,207 . (cleff /7,5 mm) - 0,1922 .
(1.2.5)
For stainless steel within the dimensions given in material standards there is Kt,m = Kd,p = 1.
(1.2.7)
For all other kinds of steel and cast iron materials the technological size factor is: For cleff 5 cleff,N,m Kt,m = Kd,p =1, for cleff,N,m < cleff 5 cleff,max,m *10:
(1.2.12)
for 12 mm < deff < defl;max.m =
For GG the following technological size factor applies to the tensile strength: For cleff 5 7,5 mm Kt,m = 1,207,
For wrought aluminum alloys the component values of the tensile strength, Rm , and of the yield strength, Rp, are given in Chapter 5 according to the type of material and its condition, and depending on the thickness or diameter of the semi-finished product. To these values the technological size factors Kt,m = Kt,p = 1 apply.
(1.2.8) (1.2.9)
defl;max,p
= 150 mm
v. = v. = 1, 1 . (,I ..I.~m .I.~p Ueff / 7 , 5 mm) - 0,2 for deff~
defl;max,m
=
defl;max,p
,
(1.2.13)
= 150 mm
:KI,m = :KI,p = 0,6 .
(1.2.14)
Welded components *11 For all kinds of material the technological size factor for the toe section and for the throat section of welded components is *12 (1.2.15) For materials such as conditionally weldable steel, stainless steel or weldable cast iron the subsequent calculation is provisional and therefore it is to be applied with caution.
!Cd,
1-0, 7686·ad,m ·lg(deff /7,5mm) . m 1- 0, 7686· ad,m ·lg(deff,N,m /7,5mm) ,
for cleff ~ deff,max,m it is: Kt,m = Kt,m (cleff,max,m)· cleff cleff,N,m, ~m
(1.2.10)
effective diameter, Chapter 1.2.2.2 , constants, Table 1.2.1 and 1.2.2 .
Considering the yield strength the values Kt,m, cleff,N,m , and ~m have to be replaced by the values Kt,p , deff,N,p , and ~p (except for GG).· .
8 The influence factors according toChapter 1.2.3 (KA ), Chapter 1.2.4 (fer, f't) and Chapter 1.2.5 (KT m- ...) aresupposed tobe valid for both non-welded and welded compon~ts.
Footnote and Eq. (1.2.6) cancelled. 10 0,7686 = l/ig 20.
9
1.2.2.2 Effective diameter For components with a simple shape of the cross section the effective diameter is given according to the cross section in Table 1.2,3.
In general the upper limit of the effective diameter is specified in the material standards. For the determination of the effective diameter cleff two cases are to be distinguished as to the kind of material.
11 Valid for steel, cast iron material and aluminum alloys. 12 For structural steel and fine grain structural steel according to DIN 18800, part 1, page 40.
25
1.2 Material properties
1 Assessment of the static strength using nominal stresses
Table 1.2.1 Constants deff,N,m , ... , and adm, ... , for steel Values in the upper row referto thetensile strength R m , Values in the lower rowreferto the yield strength R p . Kinds of material ~ 1
Non-alloyed structural steel DIN-EN 10 025 Fine grain structural steel DIN 17102 Fine grain structural steel DIN EN 10 113 Heat treatable steel, q&t DIN EN 10 083-1 Heat treatable steel, n DIN EN 10083-1 Case hardening steel, bh DIN EN 10 083-1 Nitriding steel, q&t DIN EN 10 083-1 stainless steel DIN EN 10 088-2 ~4 Steel for big forgings, q&t SEW 550 ~5 Steel for big forgings, n SEW 550
deff,N,m cleff,N,p
ad,m ad,p
inmm
~2
40 40 70 40 100 30 16 ~3 16 16 16 16 16 40 40
-
-
250 250 250 250
0,2 0,25 0 0,15
1 Within the kinds of material there are thetypes of material.
~2 More precise values depending on the kind of material (except for non-alloyed structural steel) seeTable 5.1.2 to Table 5.1.7. ~2 For 30 CrNiMo 8 and 36 NiCrMo 16: deff N m = 40 mm, values ad,mand ad,p as given above. ' , ~4 No technological size effect within the dimensions mentioned in the material standards.
~5
For 28 NiCrMoV 8 5 or 33 NiCrMo 145: deff,N,m = deff,N,p = 500mm or 1000 ~ resp., values ad.mandad,p asgiven above.
Case 1 Components (also forgings) made of heat treatable steel, of case hardening steel, of nitriding steel, both nitrided or quenched and tempered, of heat treatable cast steel, of GGG, GT or GG. The effective diameter cleff from Table 1.2.3, Case 1, applies. In general it is: deff= 4 . V /0, V,O
(1.2.16)
Volume and surface of the section of the component considered.
amn, ..., for
cast
Values in theupper row referto thetensile strength Rm ' Values in the lower row refer to the yield strength R p . Kinds of material
cleff,N,m deff,N,p
3.d,m ad,p
inmm
0,15 0,3 0,2 0,3 0,25 0,3 0,3 0,4 0,1 0,2 0,5 0,5 0,25 0,30
q&t=quenched a. tempered, n=normalized, bh=blank hardened ~
Table 1.2.2 Constants deff,N,m, ... , and iron materials
Cast steel DIN 1681 Heat treatable steel casting, DIN 17 205 Heat treatable steel casting, q&t, DIN 17 205, types ~2 No.1, 3, 4 as above types ~3 No. 2 as above . types No.5, 6, 8 as above types No.7, 9 GGG DIN EN 1563 GT~4
DIN EN 1562
100 100 300 ~1 300
0,15 0,3 0,15 0,3
100 100 200 200 200 200 500 500 60 60 15 15
0,3 0,3 0,15 0,3 0,15 0,3 0,15 0,3 0,15 0,15 0,15 0,15
q&t= quenched and tempered ~ 1 For GS-30 Mn 5 or GS-25 CrMo 4 there is deff N m = 800 mm or 500mm respectively, values ad,mand ad,p as gi~ed above. ~2
Material types see Table 5.1.11.
Valid for strength level V I, for level V II deff,N,m = deff,N,p = 100 mm with values ad,mandad,p as above. ~4 The values for GT are needed for the assessment of the fatigue strength only. ~3
Case 2 Components (also forgings) made of non-alloyed structural steel, of fine grained structural steel, of normalized quenched and tempered steel, of cast steel, or of aluminum materials. The effective diameter d eff is equal to the diameter or wall thickness of the component, Table 1.2.3, Case 2. Rod-shaped (1D) components made of quenched and tempered steel The effective diameter is the diameter existing while the heat treatment is performed. In case of machining subsequent to the heat treatment the effective diameter cleff is the largest diameter of the rod. In case of machining prior to the heat treatment the effective diameter cleff is defined as the local diameter in question. The diameter cleff according to the first sequence of machining is an estimate on the safe side .
26
1.2 Material properties
Table 1.2.3 Effective diameter No.
Cross section
~
1
deff
1 Assessment of the static strength using nominal stresses
Aluminum alloys The anisotropy factor for cast aluminum alloys is
deff
deff
Case 1
Case 2
d
KA = 1.
(1.2.20)
For forgings ·13, for which material standards specify the strength values as depending on the testing direction, the anisotropy factor is not to be applied:
d
(1.2.21)
~
2s
3
~
2s
s
4
~
2b·s
s
2
r:£13
5
For aluminum alloys the anisotropy factor for the strength values in the main direction of processing is
s
(1.2.22)
--
For the strength values transverse to the main direction of processing the anisotropy factor from Tab. 1.2.4 is to be applied.
Table 1.2.4 Anisotropy factor K A
b+s
Steel:
Rm b
b
The anisotropy factor allows for the fact that the strength values of milled steel and forgings are lower transverse to the main direction of milling or forging than in the main direction of processing. It is to be supposed that the specified strength values are valid for the main direction of processing. . In case of multiaxial stresses, and also with shear stress,
the anisotropy factor is KA = 1.
(1.2.17)
Steel and cast iron material
1.
KA
0,90
0,86
o.ss
0,80
KA
1,00
0,95
0,90
1.2.4 Compression strength factor and shear strength factor 1.2.4.0 (;eneral The compression strength factor allows for the fact that in general the material strength is higher in compression than in tension.
(1.2.18)
For milled steel and forgings *13 the anisotropy factor in the main direction of processing is (1.2.19) For the strength values transverse to the main direction of processing the anisotropy factor from Table 1.2.4 is to be applied.
13 With material properties depending on the direction.
up to 600 from 600 from 900 above to 900 to 1200 1200
The shear strength factor allows for the fact that the material strength in shear is different from the tensile strength.
The anisotropy factor for cast iron material is =
in Mpa
Aluminum aIIovs: up to 200 from 200 from 400 Rm in Mpa to 400 to 600
1.2.3 Anisotropy factor
KA
•
1.2.4.1 Compression strength factor For tensile stresses (axial or bending) the compression strength factor is (1.2.23) For compression stresses (axial or bending) the tensile strength Rm and the yield strength Rp are to be replaced by the compression strength Rc,m and the yield strength in compression Rc,p:
27
1.2 Material properties
Rc,m = Rc,F =
f, . Rm , f, . Rp,
(1.2.24)
f" compression strength factor, Table 1.2.5, Rm , Rp tensile strength and yield strength, see Eq. (1.2.1) to (1.2.3). The values Rc,m and Rc,p are not explicitly neededfor an assessment of the static strength, as only the compression strength factor f, is needed *14.
1 Assessment of the static strength using nominal stresses 1.2.5.1 Normal temperature Normal temperatures are as follows: - for fine grain structural steel from -40°C to 60°C, for other kinds of steel from -40°C to + lOO°C, for cast iron materials from -25°C to + lOO°C, for age-hardening aluminum alloys from -25°C to 50°C, for non-age-hardening aluminum alloys from -25°C to lOO°C. For normal temperature the temperature factors are
Table 1.2.5 Compression strength factor f, and shear strength factor f,; Kinds of material
r,
Case harden'g steel Stainless steel Forging steel Other kinds of steel GS GGG Aluminum alloys
for tension 1 1 1 1 1 1 1
f, for compress. 1 1 1 1 1 1,3 1
f, ~1
0,577 0,577 0,577 0,577 0,577 0,65 0,577
KT,m = ... =
I.
(1.2.26)
1.2.5.2 Low temperature Temperatures below the values listed above are outside the field of application of this guideline.
1.2.5.3 Elevated temperature In the field of elevated temperatures - up to 500 °C for
1.2.4.2 Shear strength factor
steel and cast iron materials and up to 200°C for aluminum materials - the influence of the temperature on the mechanical properties is to be considered. In case of elevated temperature the tensile strength Rm is to be replaced by the high temperature strength Rrn, T or by the creep strength Rrn, Tt • The yield strength Rp is to be replaced by the high temperature yield strength Rp,T or by the 1 % creep limit Rp,Tt *15.
For shear stresses the tensile strength Rm and the yield strength Rp are to be replaced by the shear strength Rs,m and the yield strength in shear Rs,p:
For the short-term values Rm,T and Rp,T as well as for the long-term values Rm,Tt and Rp,Tt Eq. (1.2.27) to (1.2.35) apply.
~ 1 0,577 = 1 /.J3, according to v. Mises criterion, also valid for welded components.
Rs,m = f't . Rm,
(1.2.25)
Rs,p = f't . Rp ,
Short-term values
f't shear strength factor, Table 1.2.5 Rm , Rp tensile strength and yield strength, Eq. (1.2.1) to (1.2.3).
Short term values of the static strength are
The values Rs,m and Rs,p are not explicitly needed for an assessment of the strength, as only the shear strength factor f't is needed.
KT,m, Kt,p.
Rm,T = KT,m . R m, Rp,T = KT,p . R p ,
Rm, Rp
1.2.5 Temperature factors 1.2.5.0 General
(1.2.27)
temperature factors, Eq. (1.2.28) to (1.2.33), tensile strength and yield strength, Eq. (1.2.1) to (1.2.3).
The values Rm,T and Rp,T are not explicitly needed for an assessment of the static strength, as only the temperature factors KT,m and KT,p are needed.
The temperature factors allow for the fact that the material strength decreases with increasing temperature.
Steel and cast iron materials
Normal temperature, low temperature and higher temperature are to be distinguished.
KT,m and KT,p
14 Tensile strength and yield strength in compressionare supposedto be positive, Rc,rn, Rc,p > 0, therefore for compressionfcr > 1.
15 The relevant temperature factors will be applied in combination with the safety factors at the assessment stage.
According to the temperature T the temperature factors apply as follows:
28
1.2 Material properties
1 Assessment of the static strength
using nominal stresses for fme grain structural steel, T > 60°C = KT,p = 1 - 1,2 . 10 -3 • T / DC,
KT,m
(1.2.28)
for other kinds of steel *17, T > 100°C, Figure 1.2.2: (1.2.29) 3 KT,m = KT,p = 1-1,7' 10- • (T / °C-100), for GS, T> 100°C: 1 - 1,5 . 10 -3 . (T /
°c -
(1.2.30) 100),
T / "C) 2.
(1.2.31)
Kr,m = Kr,p =
-
for GGG, T > 100°C: 1 - 2,4 . (10
K r. m = Kr,p =
-3 .
Kr,m = 1 - 4,5 . 10 -3 . (T / °C - 50) ~ 0,1, - 4, 5 . 10 -3 . (T / °C - 50) > KT=,1p - 0"1
*16.
- for not age-hardening aluminum alloys: T> 100°C, Figure 1.2.3 (1.2.33) Kr,m = 1 - 4,5 . 10 -3 . (T / °C - 100) ~ 0,1, 3 Kr,p = 1- 4,5' 10- . (T / °C - 100) ~ 0,1, Eq. (1.2.32) and (1.2.33) are valid from the indicated temperature T up to 200°C, and in general only, if the relevant characteristic stress does not act on long terms.
o,s
High temperature Rm,T strength
Eq. (1.2.28) to (1.2.31) are valid from the indicated temperature T up to 500°C. For a temperature above 350°C they are valid only, if the relevant characteristic stress does not act on long terms.
Rm;T
1
R. 'jm. Cre.ep.Strength I~TI Rm.Tl.
.1
If,;"' i.I
I 0/0 creep Iimit' Rp."f'
0,3 t--e-~+--'----+-~*+~'-Th-iL.".j
Rp,TiR p
I
I
.High temperature
Rp'Rm'}pt
fatigueslrength
O,l
CreepStreiiglh RmiTt O,21----,--+---+-~-+.......,,..-.;.1~~
·c:sw,zdiT-,....,...+~-------i'\----f'\-,--....-+\~-1
Rm,TI. I ~'jml'
. I
Q
()
ISO
5&lliQ
20.0
o
o
100200
300 400 500 ~~ Tin'C Figure 1.2.2 Temperature dependent values of the static strength of non-alloyed structural steel plotted for comparison. Rp I Rm = Rei Rm = 0,65, Rm,T/Rm = KTm = Rp,T/R = KT,p, Rm,Tt/Rm=KTt,m = Rp,Tt Rp=KTt,p·
r
Rm,T, Rp,T as well as Rm,Tt- Rp,Tt for t = 10 5 h, Safety factors according to Chapter 1.5 and 2.5: jm = 2,0, jp = Jmt = 1,5, jpt = 1,0 .Jn = 1,5 .
Aluminum alloys
According to the temperature T the temperature factors KT,m and KT,p for aluminum alloys apply as follows: -
Static strength values: Rp,T/Rm= KT,m= KT,p/Rp= KT,p Rm,Tt/Rm=KTt,m= KTt,p/Rp= KTt,p 5 Rm, rr. Rp,Tt for 1= 10 h. Fatigue limit for completely reversed stress (N = 106 cycles): O'W,zd
I Rm = 0,30;
O'W,zd,T
I O'w,zd
= KT,D.
Safety factors according to Chapter 1.5 and 2.5: Jm = 2,0 , jp = Jmt = 1,5 , jpt = 1,0,
Jn = 1,5 .
Long-tenn values Long term values of the static strength are
R""Tt = ~,Tt
R""
R,
KTt,m •
R", ,
(1.2.34)
= KTt,p • R, ,
KTt,m, KTt,p
17 For stainless steel no values are known up to now.
300
Figure 1.2.3 Temperature dependent values of the static strength of aluminum alloys plotted for comparison.
for age-hardening aluminum alloys: T > 50°C, Figure 1.2.3 (1.2.32)
16 There is an insignificant discontinuity at T = 60°C.
2S0
TIT.
1.2.3
temperature factors, Figure 1.2.2 and 1.2.3, Eq. (1.2.35), tensile strength and yield strength, Eq. (1.2.1) to (1.2.3).
29
1.2 Material properties
The values ~Tl and ~,Tl are not explicitly needed for an assessment of the static strength, as only the temperature factors KTl,m and KTt,p are needed.
1 Assessment of the static strength using nominal stresses
Table 1.2.7 Constants aTt,m, ..., Steel
Nonalloyed structural steel
Fine grain structural steel
Heattreatablesteel
~2
~3
~4
~5
Steel and cast iron materials Depending on the temperature T and on the operation time t at that temperature the temperature factors Krt,m and KTt,p apply, Figure 1.2.2 *18 K Tt,m K np
=10(aTt,m+ bTt,m . Pm+ CTt,m . Pm 2 ) = lO(aTt,p+ bTt,p . Pp+ CTt,p . Pp2 )
Creep strength
, (1.2.35)
aTLm bTLm cTt.m
,
Pm = 10 -4. (T / C + 273)' (C m + 19(t/h)), Pp
Cp ~1
em
= 10 - 4. (T / C + 273) . (C m + 19(t/ h)),
- 0,994 2,485 - 1,260 20
-1,127 2,485 - 1,260 20
- 3,001 3,987 - 1,423 24,27
1 % Creep limit
aTt,m, ..., C p constants, Table 1.2.7, operation time in hours h atthe t temperature T.
Eq. (1.2.35) apply to temperatures from approximately 350°C up to 500°C, but only for stresses acting on long terms. In general they do not apply to temperatures below about 350°C *19.
aTt.n bTLn Cn n Cn
- 5,019 7,227 - 2,636 20
- 6,352 9,305 - 3,456 20
Cast iron materials
GS <¢>6
GGG<¢>7
- 3,252 5,942 - 2,728 17,71
Creep strength
Aluminum alloys
aTt.m bTLm CTtm
5
For aluminum alloys and t = 10 hours Krt,m is given by Figure 1.2.4 *20. 1,0 R""TI I R",
0,8
em
1\
\
0,6 0,4 0,2
o
2,50 - 1,83 0 20
1 % Creep limit aTtn bTt.D cTt.n
\
\ I RT
-7,524 9,894 -3,417 19,57
100
Co :
0,12 1,52 - 1,28 18
<¢>1 Approximate values, applicable from about 350°Cto 500°C.
\..t200
- 10,582 8,127 - 1,607 35,76
<¢>2 Not valid for stainless steel. 300 400 TrC
Figure 1.2.4 Temperature factor Krt,m ~ Rm,Tt I R.n for aluminum alloys and t = 105 hours. The given curve is the same as in Figure 1.2.3, except that the factor (1 /jm ) isdifferent.
<¢>3 Initially for St38,Rm = 360MPa, similar toSt37. <¢>4 Initially for H 52, Rm = 490 MPa, similar to StE 355; the absolute values Rill,Tt are thesame asfor St38. <¢>5 Initially for C 45 N (normalized) with Rm = 620 MPa. For C 35 N, with Rm = 550 MPa the constants -3,001 and -3,252areto bereplaced by -2,949 and -3,198. The absolute values Rill,Tt arethe same asfor C45N. <¢>6 Initially for GS-C 25 with Rm = 440 MPa. -c-7
18 Larsen-Miller-parameter P andLarsen-Miller-constant C. 19 Because the values would be unrealistic for temperatures T < 350°C, where the values KT,m and KT,p are relevant instead. 20 The temperature factor Kt,p is not defmed up to now. It may be assumed, however, as it is essential for the assessment of the static strength, thattheterm Rp,Tt / jpt is more or less equal to Rill,Tt/ Jmt , see Figure 1.2.2 (required safety factorsjpt = 1,0 andjmt = 1,5). ALarsen-Miller equation similar to Eq. (1.2.32) or(1.2.33) applicable to derive the values of KTt,m and KTt,p according to temperature T and operation time T has notbeen specified for aluminum alloys uptonow.
Initially for GGG-40 with Rm = 423 MPa.
30
1.3 Design parameters
1.3 Design parameters Contents
11m
EN.dog
Page
1.3.0
General
1.3.1 1.3.1.0 1.3.1.1 1.3.1.2
Design factors General Non-welded components Welded components
1.3.2 1.3.3
Section factors Weld factor a.w
30
1 Assessment of the static strength using nominal stresses 1.3.1.2 Welded components For welded components the design factors are generally to be determined separately for the toe section and for the throat section. For the toe section the calculation is to be carried out as for non-welded components. For the throat section of rod-shaped (lD) welded components the design factors for axial (tension or compression), for bending, for shear and for torsional stress are KSK,zd = 1/ a.w, . KSK,b = I / (npl,b . a.w ), KsK,s = 1/ a.w , KSK,t = I / (npl,t . a.w ).
31
1.3.0 General According to this chapter the design parameters are to be determined.
For the throat section of shell-shaped (2D) welded components the design factors for normal stresses in the directions x and y as well as for shear stress are KsK,x= 1/ a.w, KsK,y= 1/ a.w, KsK,s = I / a.w ,
1.3.1 Design factors 1.3.1.0 General Non-welded and welded components are to be distinguished. They can be both rod-shaped (lD) or shell-shaped (2D).
1.3.1.1 Non-welded components The design factors of rod-shaped (lD) non-welded components for axial (tension or compression), for bending, for shear, and for torsional stress are KSK,zd=l, KSK,b = I / npl,b , KSK,s = I, KSK,t = I / npl,t , npl,b ...
npl,b ...
a.w
(1.3.5)
section factor, Chapter 1.3.2, weld factor, Chapter 1.3.3.
Weld factors a.w are given for tension, for compression and for shear stress. For tension and tension in bending a.w for tension is to be applied. For compression and compression in bending a.w for compression is to be applied. For shear and for torsion a w for shear is to be applied.
(1.3.1)
1.3.2 Section factors
section factor *1, Chapter 1.3.2.
The design factors of shell-shaped (2D) non-welded components for normal stresses in the directions x and y as well as for shear stress are KSK,x= I, KsK,y = I, KsK,s = 1.
(1.3.4)
(1.3.2)
The section factors npl,b and npl,t allow for the influence of the stress gradient in bending and/or torsion in connection with the shape of the cross section on the static strength of components, Figure 1.3.1. They serve to make best use of the load carrying capacity of a component by accepting some yielding as the outside fiber stress exceeds the yield strength. An essential condition is the existence of a stress gradient normal to the surface of the component, Figure 1.3.1.
It has to be observed, however, that the derived section factors only apply to the notched section considered and not to the component as a whole. Therefore other sections may have to be considered in addition, see Chapter 1.0 and Figure 1.0.1.
1 KsK,zd = is npl,zd =
= 1 means, that the value ofthe related section factor = 1.
31
1.3 Design parameters
1 Assessment of the static strength using nominal stresses For other types of steel, GS and GGG *4 the section factors for tension or compression, for bending, for
1- SSK,b (npl,b) 1-- R p ~I-----+-""'::
shear, and for torsion are *5 *6
(1.3.9)
npl,zd = 1, npl,b = MIN (JRp,max / R p ; Kp,b ),
1, npl,t = MIN (JRp,max / R p ; Kp,t),
npl,s =
Rp,max
n,
Kp,b,Kp,t
t
constant, Table 1.3.1, yield strength, Chapter 1.2, plastic notch factors, Table 1.3.2.
Figure 1.3.1 Definition of the section factor npl,b for bending of a notched bar, for instance. Bending moment Mb, yield strength R p , static component strength for bending SSK,b , section factor npl,b = SSK,b I Rp .
Table
1.3.1 Constant Rp,max ~ 1.
Kind of material
Steel, GS
GGG
Rp,max'/ MFa
1050
320
Aluminum alloys.
Light straight line: fictitious distribution of the stress calculated elastically. Solid angular line: real stress distribution when providing elastic ideal-plastic material behavior.
250
-c- 1 Constant defining an upper bound value of the sectionfactor dependingon the kind of material.
Surface hardened Components The section factors are not applicable if the component has been surface or case hardened, see Table npl,b, ... =
I
2.3.5 *2 (1.3.6)
Table
Bending
Torsion
Kp,b
Kp,t
circular ring
1,5 1,70 ~2 1,27 ~4
1,33 ~3 1 ~5
I-section or box
~6
Cross-section
Steel and cast iron material
rectangle ~ 1 circle
For austenitic steel in the solution annealed condition *3 the section factors for tension or compression, for bending, for shear, and for torsion are npl,zd = I,
1.3.2 Plastic notch factors Kp,b and Kp,t .
(1.3.8)
npl,b = Kp,b , npl,s = 1, n p1,t = Kp,t .
or plate, ~2 1,70 = 16/ (3 . It), thin-walled, 1,27 = 4 / It. ~ 5 thin-walled, otherwisethere is 3 K p t = 1,33' 1- (dID) , , 1-(dID)4
~1
d
-
1,33 = 4/3.
~4
(1.3.14)
d, D inner and outer diameters. ~6
1- (b I B) . (h I H)2 Kp b = 1,5· --'-----'---'---'-:, 1- (b I B)· (h I H)3
(1.3.15)
b, B inner and outer width, h, H inner and outer hight.
2 Because the plasticity of a hard surface layer - for example as a result of case hardening - is limited, it may observe cracks when yielding occurs, particularly at notches where the calculation of nominal stress neglects the stress and strain concentration. Possibly this rule is too far on the safe side, as npl = 1,1 is allowedfor case hardenedshafts accordingto the recent DIN 743 (launchedin 2000). 3 Because of the high ductility of austenitic steel in the solution annealed conditionthe plastic notch factors Kp,b and Kp,t are relevant and not the givenmaterial dependentsectionfactors.
4 GT and GO are not consideredhere becausethe assessmentof the static strengthhas to be carried out using local stressesfor these materials. 5 MIN means that the smaller value from the right side of the equation is valid. 6 Upper and lower bound values of the section factors are the plastic notch factor and 1,00
32
1.3 Design parameters
Aluminum alloys For ductile wrought aluminum alloys (A 2 12,5 %) the section factors are to be determined from Eq (1.3.9) *7.
1.3.3 Weld factor
Uw
The weld factor Ci.w accounts for the effect of a weld. It applies to the throat section of welded components only, Tab. 1.3.3 *8.
Table 1.3.3 Weld factor Ci.w ~1 Joint
Weld quality
full penetration
all
weld or with
verified
back weld
.
Type of
RmS
stress
360 MPa
Rm
>
360Mua
Compression ~2
1,0 Tension
1,0
10
not verified
partial
all
Compression
0,95
penetration
or
0,80
or fillet
Tension
0,80
weld all welds butt weld ~3
all
Shear Tension
0,55
-
055
~1
According to DIN 18 800 part 1, Table 21 and Eq. (75).
~2
For aluminum alloys (independent of Rm ) the values typed in in boldface should be applied for the time being.
~3
Butt welds of sectional steel from St 37-2 or USt 37-2 with a product thickness t> 16 mm.
7 Less ductile aluminum alloys (A < 12,5 %) and cast aluminum alloys are not considered here because the assessmentof the static strength has to be carried out using local stressesfor these materials. 8 For the toe section the calculation is to be carried out as for nonwelded components.
1 Assessment of the static strength using nominal stresses
33
1.4 Component strength
1.4 Component strength Contents
1R14 EN.do~
Page
1.4.0 General 1.4.1 Non-welded components 1.4.2 Welded components
33
1 Assessment of the static strength using nominal stresses
1.4.2 Welded components For welded components the strength values are generally to be determined separately for the toe section and for the throat section. For the toe section the calculation is to be carried out as for non-welded components.
1.4.0 General According to this chapter the nominal values of the component static strength are to be determined.
For the throat section of rod-shaped (lD) welded components the nominal values of the component static strength for axial (tension or compression), for bending, for shear, and for torsional stress are SSK,zd = fa' Rut/ KSK,zd, SSK,b = fa . Rut/ KSK,b , TSK,s = f't' Rut/KSK,s, TSK,t = f't . Rut/ KSK,t .
Non-welded and welded components are to be distinguished. They can be both rod-shaped (10) or shell-shaped (2D).
1.4.1 Non-welded components The nominal values of the component static strength of rod-shaped (lD) components for axial (tension or compression), for bending, for shear, and for torsional stress are * 1 *2 *3 SSK,zd = fa' Rut/ KSK,zd, SSK,b = fa . Rut/ KSK,b , TSK,s = f't . Rut/ KSK,s, TSK,t = f't' Rut/ KSK,t.
SSK,x = fa . Rut/ KsK,x , SSK,y = fa . Rut/ KsK,y , TSK = f't' Rut/ KsK,s, fa Rut SSK,zd ... f't
For the throat section of shell-shaped (2D) welded components the nominal values of the component static strength for axial (tension or compression) stresses in the directions x and y as well as for shear stress are SSK,x = fa . Rut/ KsK,x , SSK,y = fa . Rut/ KsK,y , TSK = f't' Rut/ KsK,s,
(1.4.1)
(1.4.2)
compression strength factor, Chapter 1.2.4, tensile strength, Chapter 1.2.1, design factor, Chapter 1.3.1, shear strength factor, Chapter 1.2.4.
1 The component static strength values are different for normal stress and for shear stress, and moreover they are different due todifferent section factors according tothe type ofstress.
Basically the tensile strength Rm is the reference value of static strength, even if inthe case ofa low Rp / Rm ratio the yield strength should to be used for the assessment ofthe static strength, a fact that is accounted for in Chapter 1.5.5, however. 2
3 The tensile static strength isthe reference value for the bending static strength, too. The difference instatic strength inbending compared tothe static strength intension orcompression is accounted for by the design factor. Torsional static strength inanalogy.
(1.4.5)
compression strength factor, Chapter 1.2.4, tensile strength, Chapter 1.2.1, Rut KsK,zd, ... design factor, Chapter 1.3.1. shear strength factor, Chapter 1.2.4. f't
fa
The nominal values of the component static strength of shell-shaped (2D) components for normal stresses (tension or compression) in the directions x and y as well as for shear stress are
(1.4.4)
34
1.5 Safety factors
1.5 Safety factors Contents
1.5.0 1.5.1 1.5.2 1.5.3 1.5.4 1.5.5
IR015
EN.dog
Page General Steel Cast iron materials Wrought aluminum alloys Cast aluminum alloys Total safety factor
34
Table 1.5.1 Safety factors jm and jp for steel (not for GS) and for ductile wrought aluminum alloys A5 ~ 12,5 %). -¢-1 Consequences offailure jm -¢-2 severe moderate jp -¢-3 jmt -¢-5 . -¢-4 Jpt
high
35
1.5.0 General According to this chapter the safety factors are to be determined. The safety factors are valid under the condition that the design loads are reliably determined on the safe side and that the material properties correspond to an average probability of survival of Po = 97,5 % *1 . The safety factors may be reduced under favorable conditions, that is depending on the probability of occurrence of the characteristic stress values in question and depending on the consequences of failure. The safety factors are valid for both non-welded and welded components. The safety factors given in the following are valid for ductile materials. In this respect any types of steel are ductile materials, as well as cast iron materials and wrought aluminum alloys with an elongation A5 ~ 12,5 %. *2.
1.5.1 Steel Safety factors that generally apply to the tensile strength and to the yield strength, to the creep strength and to the creep limit are given in Table 1.5.1.
1.5.2 Cast iron materials Cast iron materials with an elongation As ~ 12,5 % are considered as ductile, in particular all types of GS and some types of GGG, see Table 5.1.12. Safety factors for ductile cast iron materials are given in Table 1.5.2. Compared to Table 1.5.1 they are higher because of an additional partial safety factor jp that accounts for inevitable but allowable defects in castings. The factor is different for castings that have been subject to non-destructive testing or have not *3 .
1Statistical confidence S = 50 %.
1 Assessment of the static strength using nominal stresses
Probability of occurrence of the characteristic. service stress values
low -¢-6
2,0 1,5 1,5
1,75 1,3 1,3
1,0
1,0
1,8 1,35 1,35
1,6 1,2 1,2
1,0
1,0
-¢-1 referring tothe tensile strength Rm ortothe strength at elevated temperature RmT , -¢-2 referring tothe yield strength Rp ortothe hot yield strength Rp,T , -¢-3 referring tothe creep strength Rm, Tt , -¢-4 referring tothe creep limit Rp,Tt . -¢-5 moderate consequences offailure of a less important component in the sense of"no catastrophic effects" being associated with a failure; for example because of a load redistribution towards other members of a statically undeterminate system. Reduction by approximately 15 %. -¢-6 or only infrequent occurrences of the characteristic service stress values, for example stresses due toanapplication ofproof loads ordue to loads during anassembling operation. Reduction by approximately 10 %.
1.5.3 Wrought aluminum alloys Safety factors for ductile wrought aluminum alloys are the same as given for steel in Table 1.5.1, in particular all types of wrought aluminum alloys with an elongation A5 ~ 12,5 %, see Table 5.1.22 to 5.1.30 ·2.
1.5.4 Cast aluminum alloys Cast aluminum alloys are non-ductile materials for which there is no need of giving safety factors here ·2.
2 All types of GT, GG and cast aluminum alloys have elongations As < 12,5 % and are considered as non-ductile materials. Wrought aluminum alloys with elongations As < 12,5 % are considered asnonductile materials, too. Fornon-ductile materials the assessment of the static strength is to be carried out with local stresses according to Chapter 3. 3 In mechanical engineering cast components are of standard quality for which a further reduction of the partial safety factor to jF = 1,0 does not seem possible up to now. A safety factor jF = 1,0 may be applied to high quality cast components in the aircraft industry however. Those high quality cast components have to meet special demands and checks on qualification of the production process, as well as on the quality and extent of product testing in order to guarantee little scatter of their mechanical properties.
35
1.5 Safety factors
Table 1.5.2 Safety factors jm and jp for ductile cast iron materials (GS; GGG with A 5 ~ 12,5 %) ~1 jm jp jmt
Consequences offailure severe moderate
1 Assessment of the static strength using nominal stresses
1.5.5 Total safety factor From the individual safety factors the total safety factor jgesis to be derived *4:
Jpt
castings not subject to non-destructive testing ~2 high 2,8 2,45 2,1 1,8 2,1 Probability of 1,8 occurrence 1,4 1,4 low of the characteristic 2,55 2,2 stress 1,9 1,65 1,9 1,65 1,4 1,4 castings subject to non-destructive testing high 2,5 1,9 1,9 Probability of occurrence 1,25 of the characteristic low 2,25 stress 1,7 1,7 1,25 ~1
jm ... Kt,m···
Simplifications The following simplifications apply to Eq. (1.5.4) : In the case of normal temperature the third and fourth term have no relevance *6, and moreover there is KT,m = KT,p = 1,
~3
2,2 1,65 1,65 1,25 2,0 1,5 1,5 1,25
safety factors, Table 1.5.1 and 1.5.2, temperature factors, Chapter 1.2.5 *5.
-
j
for Rp / Rm~ 0,75 the first term has no relevance, for Rp / Rm > 0,75 the second term has no relevance *7.
Explanatory notes for the safety factors see Table 1.5.1.
~2 Compared to Table 1.5.1 anadditional partial safety factor iF = 1,4 isintroduced toaccount for inevitable but allowable defects incastings. ~3 Compared toTable 1.5.1 anadditional partial safety factor iF = 1,25 is introduced, for which it isassumed that a higher quality ofthe castings isobviously guaranteed when testing.
4 MAX means that the maximum value of the four terms in the parenthetical expression isvalid. 5 Applicable to the tensile strength Rm orthe yield strength Rp toallow for the tensile strength at elevated temperature ~ T ' the creep strength Rm,Tt , the hot yield strength ~,T' or the creep limit Rp,Tt , respectively.
6 The terms containing the factors KTt,m and KTt,f must not beapplied in the case of normal temperature, as they wil produce misleading results. 7 If there is a ratio ofthesafety factors ip lim = 0,75.
36
1 Assessment of the static strength using nominal stresses
1.6 Assessment
1.6 Assessment Contents
1*16 EN. dog
Page
1.6.0
General
1.6.1 1.6.1.1 1.6.1.2
Rod-shaped (ID) components Individual types of stress Combined types of stress
1.6.2 1.6.2.1 1.6.2.2
Shell-shaped (2D) components Individual types of stress Combined types of stress
36
Superposition For stress components of the same type of stress the superposition is to be carried out according to Chapter 1.1. If different types of stress like axial stress, bending stress ... *5 are to be considered and if the resulting
37 38 39
state of stress is multiaxial, see Figure 0.0.9 *6, the particular extreme maximum stresses and the extreme minimum stresses are to be overlaid as indicated in the following.
1.6.0 General
Kinds of component
According to this chapter the assessment of the static strength using nominal stresses is to be carried out.
Rod-shaped (lD) and shell-shaped (2D) components are to be distinguished. They can be both non-welded or welded
In general the assessments for the individual types of stress and for the combined types of stress are to be carried out separately *1 *2. In general the assessments for the extreme maximum and the extreme minimum stresses (axial stresses in tension or compression and/or bending stresses in tension or compression) are to be carried out separately. For steel or wrought aluminum alloys and a symmetrical cross-section the highest absolute value is relevant *3. The calculation applies to both non-welded and welded components. For welded components assessments are generally to be carried out separately for the toe section and for the throat section as indicated in the following.
1.6.1 Rod-shaped (ID) components 1.6.1.1 Individual types of stress
Rod-shaped (ID) non-welded components The degrees of utilization of rod-shaped non-welded components for the different types of stress like axial, bending, shear or torsional stress are aSK,zd -
aSK,b =
S max,ex,zd
< 1 . -, SSK,zd / Jges
(1.6.1)
Smax,ex,b
.:s:; 1,
SSK,b / Jges Degree of utilization The assessments are to be carried out by determining the degrees of utilization of the component static strength. In the context of the present Chapter the degree of utilization is the quotient of characteristic service stress (extreme stress Smax,ex,zd, ...) divided by the allowable static stress at the reference point *4. The allowable static stress is the quotient of the nominal component static strength, SSK,zd, ... , divided by the total safety factor jges . The degree of utilization is always a positive value.
a
- Tmax,ex,s :s:; 1, sK,s - T. / . SK,s Jges
_ Tmax,ex,t aSK,t .:s:; 1, TSK,t / Jges Smax,ex,zd ... extreme maximum stresses according to type of stress; the extreme minimum stresses, Smin,ex,zd ... , are to be considered in the same way as the maximum stresses, Chapter 1.1.1.1, SSKzd ...
1 It is a general principle for an assessment of the static strength to suppose that all types of stress observe their maximum (or minimum) values atthe same time.
This is in order to examine the degrees ofutilization ofthe individual types ofstress ingeneral, and inparticular ifthey may occur separately. 2
Not so for cast iron materials orcast aluminium alloys with different static tension and compression strength values orfor an unsymmetrical cross-section. 3
4 The reference point is the critical point ofthe cross section that observes the highest degree ofutilization.
related component static strength, Chapter 1.4.1, total safety factor, Chapter 1.5.5.
5 Bending stresses in two planes,' Sb,z and Sb,y, are different types of stress, also shear stresses intwo planes, Ts,z and Ts,y . 6 Only inthe case ofstresses acting simultaneously the character of Eq. (1.6.4) and (1.6.12) is that ofa strength hypothesis. If Eq. (1.6.4) and (1.6.12) are applied inother cases, they have the character ofan empirical
interaction formula only. For example the extreme stresses from bending and shear will - as a rule - occur atdifferent points ofthe cross-section, so that different reference points W are to be considered. As.a rule bending will be more important. Moreover see Footnote 1.
37
1.6 Assessment
1 Assessment of the static strength using nominal stresses
All extreme stresses are positive or negative (or zero). In general axial stresses (tension and compression) and bending stresses (tension and compression) are to be considered separately. For shear and torsion the highest absolute value of shear stress is relevant.
where *8
aNH=~{lsl+~s2 +4.t 2), aoH
Rod-shaped (ID) welded components S
For the toe section of rod-shaped (lD) welded components the calculation is to be carried out as for rod-shaped (lD) non-welded components. For the throat section of rod-shaped (lD) welded components the degrees of utilization for an axial, bending, shear and/or torsional type of loading follow from the equivalent nominal stresses, Chapter 1.1.1.1: a
a
SK,wv,zd
= S max,ex,wv,zd < 1 S /. -, SK,zd Jges
(1.6.2)
- Smax,ex,wv,b :::; 1 SK,wv,b - S / . , SK,b Jges
asK,wv,s =
Tmax,ex,wv,s .:::; 1, TSK,s / Jges T
aSK,wvt= max,ex,wv,t :::; 1, , T /. SK,t Jges Smax,ex,wv,zd, ... extreme maximum stresses (equivalent nominal stresses); the extreme minimum stresses, Smin,ex,wv,zd ... , are to be considered in the same way as the maximum stresses, Chapter 1.1.1.1, SSK,zd ...
related component static strength, values, Chapter 1.4.2, total safety factor, Chapter 1.5.5.
All extreme stresses are positive or negative (or zero). In general axial stresses (tension and compression) and bending stresses (tension and compression) are to be considered separately. For shear and torsion the highest absolute value of shear stress is relevant.
=Js
2
2 +t , (1.6.6)
t = aSK,s + aSK,t , aSK,zd, ... degree of utilization, Eq. (1.6.1). and (1.6.7) f,
shear strength factor, Table 1.2.5.
Rules of sign: If the individual types of stress (axial and bending, or shear and torsion, respectively) always act unidirectionally at the reference point *10, the degrees of utilization aSK,zd and aSK,b and/or asK,s and asK,t are to be inserted into Eq. (1.6.6) with equal (positive) signs (summation); then the result will be on the safe side. If they act always opposingly, however, *ll, they are to be inserted into Eq. (1.6.6) with different signs (subtraction) *12.
8 Inthe the case ofassessing the static strength the degrees ofutilization aSK,zd and aSK,b are defined by the static component strength values SSK,zd and SSK,b . Contained inthese are the section factors for tension or compression, npl,zd , and for bending, npl,b . aSK,zd and aSK,b are overlaid linearly when computing the value s. For shear and torsion in analogy. Compared to a more precise solution this procedure is on the safe side. . 9 Table 1.6.1 Constant q(f,).
Steel, Wrought
GOG
For rod-shaped (lD) non-welded components the degree of utilization for combined types of stresses is *7
q
0,577 0,00
GT, Cast
GG
Al-allovs
Al-allovs
Rod-shaped (ID) non-welded components
(1.6.5)
= aSK,zd + aSK,b ,
f',
1.6.1.2 Combined types of stress
(1.6.4)
aSK,Sv = q . aNH+ (l - q)' aoH:::; 1,
0,65 0,264
Caution: Here only ductile wrought aluminium alloys are considered (elongation A > 12,5 %). For non-ductile wrought aluminium alloys (as well asfor cast aluminium alloys, and for GT or GG) the assessment of the static strength istobe carried out according toChapter 3.
10 For example a tension stress from axial loading and a tension stress from bending acting at the reference point, where both result from the same single extemalload affecting the component 7 The applied strength hypothesis for combined types of stress is a combination ofthe normal stress criterion (NH) and the v. Mises criterion (GH). Depending on the ductility of the material the combination is controlled by a parameter q as a function off, according to Eq. (1.6.7) and Table 1.6.1. For steel is q = 0 so that only the v. Mises criterion isof effect. For GOG is q = 0,264 so that both the normal stress criterion and the v. Mises criterion are of partial influence.
11 For example a tension stress from axial loading and a compression stress from bending acting atthe reference point, where both result from the same single external load affecting the component. 12 Stress components acting opposingly may cancel each other inpart or completely.
38 1 Assessment of the static strength using nominal stresses
1.6 Assessment
In the general case - without knowing whether the stresses act unidirectionally or opposingly *13 - the degrees of utilization are to be inserted into Eq. (1.6.6) both with equal or with different signs; then the least favorable case is relevant. Moreover the degrees of utilization calculated with Smin,ex,zd , Smin,ex,b , T min.ex,s and T min.ex.t are to be included in this comparative evaluation.
1.6,2 Shell-shaped (2D) components 1.6.2.1 Individual types of stress Shell-shaped (2D) non-welded components The degrees of utilization of shell-shaped (2D) nonwelded components for the types of stress like normal stress in the directions x and y as well as shear stress are Smax,ex,x
aSK,x = Rod-shaped (1D) welded components For the toe section of rod-shaped (10) welded components the calculation is to be carried out as for rod-shaped (lD) non-welded components. For the throat section of rod-shaped (10) welded components the degree of utilization for combined types of stresses (or loadings) is *14
Smax,ex,y
aSK,y =
1,
(1.6.9)
aSK,s = Tmax,ex TSK / jges
Rules of sign: If the individual types of stress (tension or compression and bending, or shear and torsion, respectively) always act unidirectionally at the reference point *10, the degrees of utilization aSK,wv,zd and aSK,wv,b and/or aSK,wv,s and aSK,wv,t are to be inserted into Eq. (1.6.8) with equal (positive) signs (summation); then the result will be on the safe side. If they act always opposingly, however, *11, they are to be inserted into Eq. (1.6.8) with different signs (subtraction) *12. In the general case - without knowing whether the stresses act unidirectionally or opposingly '13 - the degrees of utilization are to be inserted into Eq. (1.6.8) both with equal or with different signs; then the least favorable case is relevant. Moreover the degrees of utilization calculated with Smin,ex,wv,zd , Smin,ex,wv,b , Tmin,ex,wv,s and Tmin,ex,wv,t are to be included in this comparative evaluation.
s
1·,
Smax,ex,x ...
extreme maximum stresses according to type of stress; the extreme minimum stresses, Smin,ex,x ... , are to be considered in the same way as the extreme maximum stresses, Chapter 1.1.1.2,
SSK,x ...
related component static strength, Chapter 1.4.1,
Jges
total safety factor, Chapter 1.5.5.
J(aSK,WV,Zd +aSK,wv,b)2 +(aSK,wv,s +aSK, wv.t )2 , aSK,wv,zd, ... degree of utilization, Eq. (1.6.2).
1,
::;;
SSK,y / jges
(1.6.8)
aSK,Swv =
s
SSK,x / jges
All extreme stresses may be positive or negative (or zero). In general tension and compression stresses are to be considered separately. For shear stress the highest absolute value is relevant.
Shell-shaped (2D) welded components For the toe section of shell-shaped (2D) welded components the calculation is to be carried out as for shell-shaped (2D) non-welded components. For the throat section of shell-shaped (2D) welded components the degrees of utilization for normal stresses in the directions x and y as well as for shear stress follow from the equivalent nominal stresses, Chapter 1.1.1.2: a
- Smax,ex,wv,x < 1 SK,wv,x - S / . -, SK,x Jges
(1.6.10)
I
aSK,wv,y =ISmax, ex,wv,y < , 1 . SSK,y / Jges a
13 For example,
iftwo loadings vary with time in a different manner.
14 Eq. (1.6.8) does not agree with the structure ofEq. (1.1.2) onpage 20 in all respects. It is an approximation which has to be regarded as provisional and therefore it istobeapplied with caution.
SK,wv,s
=
T.max,ex,wv < 1 T. / . -, SK,s Jges
Smax,ex,wv,x ... extreme maximum stresses (equivalent nominal stresses); the extreme minimum stresses, Smin,ex,wv,x ... , are to be considered in the same way as the . maximum stresses, Chapter 1.1.1.1,
39
1.6 Assessment
1 Assessment of the static strength using nominal stresses
related component static strength, Chapter 1.4.2,
SSK,x'"
Shell-shaped (2D)"welded components
total safety factor, Chapter 1.5.5. All extreme stresses may be positive or negative (or zero). In general tension and compression stresses are to be considered separately. For shear stress the highest absolute value is relevant.
For the toe section of shell-shaped (2D) welded components the calculation is to be carried out as for shell-shaped (2D) non-welded components. For the throat section of shell-shaped (2D) welded components the degree of utilization for combined types of stress (or loadings) is *14 222 asK,Swv = aSK,wv,x +aSK,wv,y +aSK,wv,s' (1.6.16)
1.6.2.2 Combined types of stress aSK,wv,x, ... degree of utilization, Eq. (1.6.10).
Shell-shaped (2D) non-welded components The degree of utilization of shell-shaped (2D) nonwelded components for combined stresses is *7 aSK,Sv = q . aNH + (1 - q) . aGH:::; 1,
(1.6.12)
where aNH=1{lsx
+syl+~(Sx _Sy)2 +4.t 2)'
(1.6.13)
2 2 2 aaH= Sx +Sy -sx 'Sy +t ,
J
sx= aSK,x,
(1.6.14)
Sy= asK,y, t = aSK,s, aSK,x, ... degree of utilization, Eq. (1.6.9), and (1.6.15) f't shear strength factor, Table 1.2.5. Rules of sign: If the individual types of stress always act unidirectionally at the reference point *15, the degrees of utilization aSK,x and aSK,y are to be inserted into Eq. (1.6.14) with equal (positive) signs (summation). If they always act opposingly, however *16, the degrees of utilization aSK,x and asK,y are to be inserted into Eq. (1.6.14) with different signs. In the general case - without knowing whether the stresses act unidirectionally or opposingly *13 - the degrees of utilization are to be inserted into Eq. (1.6.14) both with equal or with different signs; then the least favorable case is relevant. Moreover the degrees of utilization calculated with Smin,ex,x , Smin,ex,y and Tmin.ex,s are to be included in this "comparative evaluation.
15 For example tension in direction x and tension in direction y from a single loading affecting the component.
16 For example tension in direction x and compression in direction y from a single loading affecting the component.
40 1.6 Assessment
1 Assessment of the static strength using nominal stresses
41
2.1 Characteristic service stresses
2 Assessment of the fatigue strength using nominal stresses A special case is the constant amplitude spectrum, consisting of one step i = j = 1 only. For axial stress there is Sa,zd = Sa,zd,i = Sa,zd,1, Sm,zd = Sm,zd,i = Sm,zd,1 .
2 Assessment of the fatigue strength using nominal stresses 1R21 EN.do~
2.0 General
Superposition
According to this chapter the assessment of the fatigue strength using nominal stresses is to be carried out.
Proportional or synchronous stresses
2.1 Parameters of the stress spectrum Contents 2.1.0
Page
General
41
2.1.1
Characteristic service stresses according to the kind of component 2.1.1.0 General 2.1.1.1 Rod-shaped (lD) components 2.1.1.2 Shell-shaped (2D) components
42
2.1.2 2.1.2.0 2.1.2.1 2.1.2.2
Parameters of the service stress spectrum General Mean stress spectrum Stress ratio spectrum
2.1.3
Adjusting a stress spectrum to match the component constant amplitude S-N curve
2.1.4
Determination of the parameters of a service stress spectrum General Standard stress spectrum Class of utilization Damage-equivalent stress amplitude
2.1.4.0 2.1.4.1 2.1.4.2 2.1.4.3
several proportional or synchronous stress components act simultaneously at the reference point, Chapter 0.3.5, they are to be overlaid. For the same type of stress (for example unidirectional axial stresses Sa,zd,l. Sm,zd,1 and Sa,zd,2, Sm,zd,2 , ...) the superposition is to be carried out at this stage, so that in the following a single stress component (Sa,zd, Sm,zd, ...) exists for each type of stress *2. For different types of stress (for example bending and torsional stress or axial stresses in x- and y-direction) the superposition is to be carried out at the assessment stage, Chapter 2.6.
If
Non-proportional stresses 43
If several non-proportional stress components act
simultaneously at the reference point, Chapter 0.3.5, they are to be overlaid according to Chapter 5.10.
2.1.1 Characteristic service stresses according to the kind of component 44 45
2.1.1.0 General Rod-shaped (10) and shell-shaped (2D) components are to be distinguished. They may be both non-welded or welded.
2.1.0 General According to this chapter the parameters of the service stress spectra are to be determined. Spectra are applicable for N > 104 cycles approximately. Relevant are the stress spectra of the individual stress components. They are specified by a number of steps, i = 1 to j , giving the amplitudes Sa,zd,i. ... and the related mean values Sm,zd,i , ... of stress cycles, Figure 2.1.1, as well as the related numbers of cycles n, according to the required fatigue life *1.
2.1.1.1 Rod-shaped (ID) components Rod-shaped (ID) non-welded components For rod-shaped (lD) non-welded components an axial stress Szd , a bending stress Sb , a shear stress T s- and a torsional stress Tt are to be considered *3 . The respective amplitudes and mean values are Sa,zd,i , Sa,b,i , Ta,s,i , Ta,t,i , Sm,zd,i, Sm,b,i, Tm.s.i s Tm,t,i .
(2.1.1)
S.,zd,i
Figure 2.1.1 Sm,zd,f - -- -
Stress cycle Example: stress cycle (axial stress), stress ratio: . = Sm,zd,i -Sa,zd,i Zd,1 Sm,Z,1 d . + Sa,Z,1 d··
S.,zd,1
R
t
1 As a rule a stress spectrum is to be determined for normal service conditions, see footnote 3 on page 19. The largest amplitude Sa zd 1 ofa service stress spectrum with its related mean stress value Sm,zd,1' defme the step i = 1 and serve as the characteristic stress values. 2 Stress components acting opposingly can cancel each other inpart or completely.
42
2 Assessment of the fatigue strength using nominal stresses
2.1 Characteristic service stresses
(2.1.9)
Rod-shaped (ID) welded components
Parameters of the stress spectrum are:
For rod-shaped (lD) welded components the (nominal) stress values are in general to be determined separately for the toe section and for the throat section *4. Respective amplitudes and mean values see Eq. (2.1.1).
Sa,zd 1 characteristic (largest) stress amplitude of the , stress spectrum, equal to the amplitude in step 1 Sa,zd,i amplitude in step i, Sa,zd,i > 0, Sa,zd,i+ 1 / Sa,zd,i :s: 1, Sm,zd,i mean value in step i, N total number of cycles corresponding to the required fatigue life (required total number of cycles), N = Lni (summed up for 1 to j), n.1 related number of cycles in step i, N, = Lni (summed up for 1 to i), H total number of cycles of a given spectrum, 8 H = Hj = Lhi (summed up for 1 to j) * , h·1 related number of cycles in step i, Hi = Lhi (summed up for 1 to i), step, i = 1 to j, total number of steps, step for the smallest j amplitudes damage potential. Yzd
2.1.1.2 Shell-shaped (2D) components Shell-shaped (2D) non-welded components For shell-shaped (2D) non-welded components the (nominal) axial stresses in x- and y-direction, Szdx = Sx and Szdy = Sy, as well as a shear stress T, = T are to be considered. The respective amplitudes and related mean values are Sa,x,i, , Sa,y,i , Ta,i , Sm,x,i, , Sm,y,i, Tm,i .
(2.1.4)
Shell-shaped (2D) welded components For shell-shaped (2D) welded components, Figure 0.0.6, stress values are in general to be determined separately for the toe section and for the throat section *4. Respective amplitudes and mean values see Eq. (2.1.4).
2.1.2 Parameters of the stress spectrum 2.1.2.0 General A stress spectrum describes the stress cycles contained in the stress history of concern *5 • If the stress cycles show variable amplitudes a stress
spectrum is to be determined for every stress component *6. The constant amplitude stress spectrum may be regarded in the following as a special case '7 , for which i = I and Sa,zd = Sa,zd,i
=
Sa,zd,l ,
Yzd =
ke
j hi
Sa zd,i
kO"
L-=""' --'-
i=l H [ Sa,zd,l )
(2.1.10)
where 1<" is the exponent of the component S-N curve. Sa,zd,i / Sa,zd,l and hi /H describe the shape of the stress spectrum. The amplitudes Sa,zd,i are always positive, the mean values Sm,zd.i may be positive, negative, or zero. As a rule a restriction to the following kinds of stress spectra is possible: Mean stress spectra and stress ratio spectra (with the fluctuating stress spectra as a special case), Figure 2.1.2 *10.
(2.1.8)
N= N = ni = n1
Where appropriate bending and shear stresses in two planes are to be considered (components yand z), see Chapter 0.3.4.1 . 3
For welded components separate assessments ofthe fatigue strength for both the toe section and the throat section ofthe weld are to be carried out. Both assessments are ofthe same kind, but ingeneral the respective stresses and fatigue classes FAT are different. 4
5 In the following all variables and equations are presented for the axial stress component Szd only, but written with the appropriate indices they are valid for all other types ofstress aswell.. 6 In this
The damage potential is defined by *5 *9,
case an assessment ofthe variable amplitude fatigue strength isto be carried out.
7 In this case an assessment ofthe fatigue limit is to be carried out for type I S-N curves if N = N ~ ND 0" oranassessment ofthe endurance limit for type 11 S-N curves if N:" N ~ ND,O", 11 , respectively, oran assessment for fmite life based on the constant amplitude S-N curve (formally similar to an assessment of the variable amplitude fatigue strength) if N = N < ND,O" or N = N ~ ND,O", II for Typ I orTyp 11 S-N curves, respectively. ND,O" or ND,O", 11 isthe number ofcycles at the fatigue limit ofthe component constant amplitude S-N curve, Chapter
2.4.3.2.
The valuesN - total number ofcycles required - and if - total num~ ofcycle!!j!fa given spectrum - are different ingeneral. The terms niIN and hi I H are equivalent. 8
9 The damage potential is a value characterising the shape of a stress spectrum. The values ka = 5for normal stress and Ie,; = 8 for shear stress are valid for non-welded components. The values ka = 3 and k't = 8 are valid for welded components.
The term hi I H may be replaced by ni IN. lOA mean stress spectrum, for example, results from a static load with dynamic loads superimposed, a fluctuating stress spectrum, for example, results for a crane hook when lifting variable loads.
43 2.1 Characteristic service stresses
2 Assessment of the fatigue strength using nominal stresses
or Sm,zd,i / Sa,zd,i = (1 + ~d) / (l - ~d)'
(2.1.14)
Special case: Fluctuating stress spectrum A constant stress ratio of zero applies to all steps of a fluctuating stress spectrum:
(2.1.15) or Sm,zd,i / Sa,zd,i = 1.
(2.1.16)
2.1.3 Adjusting a stress spectrum to match the component constant amplitude S-Ncurve This chapter mainly applies to stress spectra, the steps of which do not have the same stress ratio *11. A mean stress spectrum, for example, has different amplitudes Sa,zd,i ' and constant mean stress values Sm,zd,i = Sm,zd ' and consequently the individual steps have different stress ratios Rzd,i . On the other hand the component constant amplitude S-N curve, Chapter 4.4.3.2, is derived for a constant stress ratio Rzd . To allow the proper application of Miner's rule, Chapter 4.4.3.1, all steps of a spectrum, however, must have or must be converted to that stress ratio RZd,i = Rzd , Chapter 5.6.1.
"1"
Smin,zd=O
Figure 2.1.2 Stress spectra Top: Mean stress spectrum. Midle: Stress ratio spectrum. Bottom: Fluctuating stress spectrum. Example: The presented stress spectra are standard type stress spectra, basicaUy defined by a binomial frequency distribution, a coefficient p = 1/3 , a total number of cyclesH = 106 , and extrapolated to the required total number of cyclesN.
2.1.2.1 Mean stress spectrum
A constant mean stress applies to all steps of a mean stress spectrum: Sm,zd,i = Sm,zd.
(2.1.11)
A constant stress ratio applies to all steps of a stress ratio spectrum: (2.1.12)
where ~d =
(Sm,zd,i - Sa,zd,i) / (Sm,zd,i -+ Sa,zd,i)
2.1.4.0 General If the
stress spectrum of a component under consideration is not known, or in case of high demands on its accuracy, the parameters of the stress spectrum are to be determined by calculation, by simulation, or by measurement. The determination of the stress spectrum from a stress history has to be realized according to the rainflow cycle counting procedure or in the sense of this procedure. From a measured and graphically presented continuous stress spectrum a stepped stress spectrum may be obtained according to Chapter 5.6.2.
2.1.2.2 Stress ratio spectrum
RZd,i = Rzd,
2.1.4 Determination of the parameters of a stress spectrum
In case of existing experiences - depending on the component and its application - the determination of the parameters of a stress spectrum may be simplified by applying a standard stress spectrum, a class of utilization, or a damage-equivalent stress amplitude.
(2.1.13) 11 Applies to a mean stress spectrum, for instance, but not for a stress ratio spectrum or a fluctuating stress spectrum.
44
2 Assessment of the fatigue strength using nominal stresses
2.1 Characteristic service stresses
2.1.4.1 Standard stress spectrum
1
Standard stress spectra are used to describe the shape of typical stress spectra. Standard stress spectra having a binomial or an exponential frequency distribution that may be modified by the spectrum parameter p , are presented in Figure 2.1.3. In addition, damage potentials Vzd according to Eq. (2.1.10) and Figure 2.1.1 are given in the graphical presentations. (These apply to an exponent of the component constant amplitude S-N curve 1<:" = 5 and a total number of cycles H = 106 ).
2 P 2/3
vzd = 1
0,5
a
0,739 0,499 0,326
1/3
.j........--,---,--~--.---,-----lO
106
Parameters of a so derived stress spectrum Step i
Sa,zd,l characteristic (largest) stress amplitude ofthe stress spectrum, equal to the amplitude in step 1 N Yzd
P
1 2 3 4 5 6 7 8
required total number of cycles, or Sa,zd,i / Sa,zd,l and hi, i = 1 to j, according to the shape of the standard stress spectrum
Sm,zd,i mean values, i = 1 to j.
Table 2.1.1 Damage potentials Vzd and v, for standard stress spectra having a binomial or exponential frequency distribution, modified by the spectrum parameter p, a total number of cycles H = 106 , for nonwelded and welded components, for normal stress and shear stress (exponents of the constant amplitude S-N curve 1<:" and k, ).
p Vzd
0 1/6 1/3 1/2 2/3 5/6 1 v, 0 1/6 1/3 1/2 2/3 5/6 1
non-welded welded binom. I expon. binom. expon. normal stress k, = 5 1<:" = 3 0,326 0,196 0,267 0,155 0,400 0,297 0,366 0,286 0,499 0,430 0,483 0,426 0,615 0,570 0,608 0,569 0,739 0,713 0,737 0,712 0,868 0,856 0,868 0,856 1 1 1 1 shear stress k, = 8 k, = 5 0,399 0,275 0,326 0,196 0,452 0,330 0,400 0,297 0,527 0,438 0,499 0,430 0,627 0,573 0,615 0,570 0,743 0,713 0,739 0,713 0,869 0,856 0,868 0,856 1 1 1 1
Sa' / Sal 1/3 1 0,967 0,900 0,817 0,717 0,617 0,517 0,417
0 1 0,950 0,850 0,725 0,575 0,425 0,275 0,125
1,0
1
I"""~-'
hi
H-I
2/3 1 0,983 0,950 0,908 0,858 0,808 0,758 0,708
2 2 18 16 280 298 2720 3018 20000 23000 92000 115000 280000 395000 604982 1000000
--.---.....,.---~·1
Sa,zd,1
Sa,zd,l 0,5
......--""'1/3
Step i P
1 2 3 4 5 6 7 8
0 1 0,875 0,750 0,625 0,500 0,375 0,250 0,125
Sa' / Sa 1/3 1 0,917 0,833 0,750 0,667 0,583 0,500 0,417
hi
H-I
2/3 1 0,958 0,917 0,875 0,833 0,792 0,750 0,708
2 2 10 12 64 76 340 416 2000 2400 13400 11000 61600 75000 924984 1000000
Figure 2.1.3 Standard stress spectra. Top: Binomial distribution. Bottom: Exponential distribution (Straight line distribution). Spectrum parameter p, total number of cyclesII = Hj E hi = 106, number of steps j = 8 , damage potential Yzd for an
=
exponent ko = 5 of the component constant amplitude SoN curve.
45
2.1 Characteristic service stresses
2 Assessment of the fatigue strength using nominal stresses
Analytical relationship:For standard stress spectra with spectrum parameters p > 0 (p = 1/6, 1/3, 1/2, 2/3, 5/6) there is
J
J .
Sa,zd,i = p + (l - p) .[Sa,zd,i [ Sa,zd,1 p Sa,zd,1 p=o
(2.1.17)
Application: In case of existing experiences about the shape of the stress spectrum a suitable standard stress spectrum may be applied to assess the variable amplitude fatigue strength in two ways:
Parameters of a so derived stress spectrum characteristic (largest) stress amplitude of the stress spectrum, equal to the amplitude in step 1 class of utilization (a combination of the shape of B the stress spectrum and of the required total number of cycles), Sm,zd mean stress *13.
Analytical relationship: See Chapter 5.7.
Application of the damage potential Vzd. Eq. (2.1.10) for an assessment of the variable amplitude fatigue strength according to the elementary version of Miner's rule, Chapter 2.4.3.1.
Application: In case of existing experiences about the shape of stress spectrum and the required total number of cycles a class of utilization may be applied to assess the variable amplitude fatigue strength, Chapter 2.4.3.1.
Application of the data on Sa,zd,i / Sa,zd,1 and hi of the steps i = I to j from Figure 2.1.3 for an assessment of the variable amplitude fatigue strength according to the consistent version of Miner's rule, Chapter
The class of utilization has to be specified separate from this guideline.
2.4.3.1.
2.1.4.3 Damage-equivalent stress amplitude
The appropriate standard stress spectrum has to be specified separate from this guideline.
2.1.4.2 Class of utilization *12
A class of utilization is an approximately damageequivalent combination of different shapes of stress spectra and of specific figures of the required total numbers of cycles, Figure 2.1.4, see also Chapter 5.7.
The damage-equivalent stress amplitude is a constant stress amplitude with an assigned number of cycles equal to the number of cycles at the knee point of the component constant amplitude S-N curve, ND,cr . It is damage-equivalent to the stress spectrum in question, In particular it is defined by the shape of stress spectrum, the required total number of cycles, N, and the largest stress amplitude Sa,zd,b Figure 2.1.5. S,;z!il
WL
Sa,zd,i
Sa,zd,1
S.,UI'l S.,zd:;~tr~~""""",----
-.....-.t-..:-
2;1.5'
N
Figure 2.1.4 Spectra corresponding to the same class of utilization. Example: Welded component, stress spectra with binomial distribution, axial stress. All three stress spectra are approximately damage-equivalent and correspond tothe same class ofutilization B5, Table 5.7.4.
Figure 2.1.5 Damage-equivalent stress amplitude. Component constant amplitude S-N curve, WL, number ofcycles atthe knee point ND,C" ' component variable amplitude fatigue life curve, ~. characteristic stress amplitude Sa,zd,l, required total number ofcycles N. Shown is the situation when full use is made of the fatigue strength capacity of the component (degree of utilization aBl(,zd = 100 %, Eq.2.6.3). As the damage-equivalent stress amplitude Sa,zd,eff isassigned toND,C" it allows an assessment ofthe variable amplitude fatigue strength to be performed as an assessment ofthe fatigue limit.
12
According toDIN 15018.
46
2.1 Characteristic service stresses
2 Assessment of the fatigue strength using nominal stresses
Parameters of the so derived stress spectrum Sa,zd,eff
Damage-equivalent stress amplitude (damage-equivalent to a combination of the shape of the stress spectrum, the required total number of cycles and of the largest amplitude in the stress spectrum).
Sm,zd
Related mean value.
Analytical relationship: Based on the elementary version of Miner's rule the damage-equivalent stress amplitude is obtained as *14 Sa,zd,eff
1 =
k
j
_ . '" N .L . Il:1 ·ska a,zd,i D,« 1=1
= (N / NO,a )
(2.1.18)
111m. Vzd . Sa,zd,1 ,
exponent of the component constant amplitude S-N curve No,a number of cycles at the knee point of the component constant amplitude S-N curve j, i, ni, ... seeEq. (2.1.9), Yzd damage potential, Eq. (2.1.10). ka
Application: In case of existing experiences about the damaging effect of the stress spectrum a damageequivalent stress amplitude Sa,zd,eff may be applied. It allows an assessment of the variable amplitude fatigue strength to be performed as an assessment of the fatigue limit, Chapter 2.6. The damage-equivalent stress amplitude has to be specified separate from this guideline.
14 Eq. (2.1.18) is valid for a damage sum OM = 1 , see Chapter 2.4.3.1.
47
2.2 Material properties
2.2 Material properties
*1
11m
EN.do~
Contents
Page
47
2.2.0
General
2.2.1 2.2.1.0 2.2.1.1 2.2.1.2
Component values according to standards General Non-welded components Welded components
2.2.2
Fatigue strength factors for normal stress and for shear stress
2.2.3 2.2.3.0 2.2.3.1 2.2.3.2 2.2.3.3
Temperature factor General Normal temperature Low temperature Elevated temperature
48
2.2.1.2 Welded components For the base material of welded components the material fatigue strength values for completely reversed stress are the same as for non-welded components. Steel and cast iron materials
According to this chapter the material fatigue strength values (component values according to standards) are to be determined. These are the material fatigue limit for completely reversed normal stress, crW,zd , and shear stress, 'tW,s, as well as further characteristics *2.
2.2.1 Component values according to standards
For the toe section and for the throat section of professionally welded components from weldable structural steel *5 specific values of the fatigue strength apply independent of the kind of material. These are for completely reversed normal stress at N ~ No,cr = 5' 106 cycles and for completely reversed shear stress at N ~ No,'t = 1 . 108 cycles *6, Chapter 5.5, crW,zd = crw,w = 92 MPa, 'tw,s = 'tw,w = 37 MPa.
(2.2.3)
Caution: For other kinds of material (stainless steel conditionally weldable steel, weldable cast iron material) these values are to be considered as provisional and are to be applied with caution.
2.2.1.0 General The determination of the material fatigue strength is different for non-welded and for welded components. 2.2.1.1 Non-welded components
For non-welded components the values according to standards of the material fatigue strength for completely reversed normal stress and shear stress *3 and for a number of cycles N ~ No,cr = No,'t = 106 are *4
I
fw,cr fatigue strength factor for completely reversed normal stress, Chapter 2.2.2, fw,'t fatigue strength factor for completely reversed shear stress, Chapter 2.2.2, Rm tensile strength, Chapter 1.2.1.1. Caution: For non-welded wrought and cast aluminum alloys the fatigue limit is different from the endurance limit associated with N ~ NO,cr,II =NO,'t,ll= 108 cycles.
2.2.0 General
crW,zd = fw,cr· Rm, 'tw,s = fw,'t' crW,zd,
2 Assessment of the fatigue strength using nominal stresses
Aluminum alloys For the toe section and for the throat section of professionally welded components from aluminum alloys *5 specific values of the fatigue strength apply in analogy to steel independent of the kind of material. These are for completely reversed normal stress at N ~ NO,cr = 5 . 106 cycles and for completely reversed shear stress at N ~ No,'t = 1 . 108 cycles *6, Chapter 5.5,
(2.2.1)
Chapters 2.2 and 4.2 are identical.
2 An influence offrequency on the material fatigue strength values isnot considered up to now although itmight be ofimportance for aluminum alloys. 3 For the tensile strength according to standards, Rm , a probability of survival Po = 97,5 % ispresumed. That probability should also apply to the values crW,zd and 'tW,s computed from Rm . Moreover Eq. (1.2.1) applies here too: crW,zd = I
crW,zd = crw,w = 33 MPa, 'tw,s = 'tw,w = 13 MPa.
(2.2.4)
Caution: These values are provisional and are to be applied with caution *7
4 The values crW,zd and 'tw., correspond tothe fatigue limit which is equal to the endurance limit of steel and cast iron material, but not of aluminum alloys, however, Figure 2.4.5 and Chapter 5.1.0. 5 Weld imperfections occurring with normal production standards are allowable. 6 The values crw,w and 'tw.w correspond tothe fatigue limit which is equal tothe endurance limit ofwelded steel and cast iron material aswell as of welded aluminum alloys, Figure 2.4.6 and Chapter 5.1.0.
Values derived from an average relation of0,36 ofthe FAT classes for aluminum alloys and for structural steel, Chapter 5.4.
7
48
2.2 Material properties
2.2.2 Fatigue strength factors for normal stress and for shear stress The fatigue strength factor for completely reversed normal stress, fw,O" , is the quotient of the axial fatigue strength value for completely reversed stress divided by the tensile strength, Table 2.2.1. The fatigue strength factor for shear stress, fw,~ , considers that the material fatigue strength is lower for shear stress than for normal stress, Table 2.2.1. Table 2.2.1 Fatigue strength factors for completely reversed normal stress, fw,O" , and shear stress, fw,~ -c- 1. Kind of material
fw,O"
fw,~
Case hardening steel Stainless steel Forging steel Steel other than these GS GGG GT GG Wrought aluminum alloys Cast aluminum alloys
0,40 ~2 0,40 ~4 0,40 ~4 0,45 0,34 0,34 0,30 0,30 0,30 ~5 0,30 ~5
0,577 ~2 ~3 0,577 0,577 0,577 0,577 0,65 0,75 0,85 0,577 0,75
fw,O" and fw, ~ arevalid for a number of cycles N = 106 • fw ~ equal to f~ , Table 1.2.5. ~2 Bl~-hardened. The influence of the carburization on the component fatigue strength is to by considered by the surface treatment factor, Ko, Chapter 2.3.4. ~3 0,577 = 1 / J3, according tothe v. Mises criterion. Also valid for welded components. ~4 Preliminary values.
2 Assessment of the fatigue strength using nominal stresses For normal temperature the temperature factor is KT,D = 1.
(2.2.5)
2.2.3.2 Low temperature Temperatures below the values listed above are outside the field of application of this guideline.
2.2.3.3 Elevated temperature In the field of elevated temperatures - up to 500°C for steel and cast iron materials and up to 200°C for aluminum materials - the influence of the temperature on the fatigue strength is to be considered. For elevated temperature the fatigue strength values for completely reversed normal stress and shear stress are
crW,zd,T = KT,D . crW,zd, 'tW,s,T = KT,D . 'tw,s ,
(2.2.6)
KT,D temperature factor, Eq. (2.2.7) to (2.2.11), crW,zd, ... material fatigue strength value for completely reversed normal stress, Chapter 2.2.1.1 and 2.2.1.2. 'tw,s, ... material fatigue strength value for completely reversed shear stress, Chapter 2. 2. 1. 1 and 2.2.1.2.
-c- 1
~5
fW,O" does not correspond tothe endurance limit for N =
<:i)
According to the temperature T the temperature factor KT,D is for fine grain structural steel, T KT,D = 1-10- 3 . T / DC,
> 60°C: (2.2.7)
for other kinds of steel *7, T> 100°C, Figure 2.2.1: KT,D = 1-1,4' 10- 3 . (T / °C-IOO), (2.2.8)
here!
for GS, T > 100°C: KT,D = 1- 1,2 . 10 -3. (T / °C_ 100),
2.2.3 Temperature factor 2.2.3.0 General
for GGG, GT and GG, T > 100°C, Figure 2.2.1: KT,D = 1- aT,D . (10 - 3 . T / oC)2, (2.2.10)
The temperature factors considers that the material fatigue strength for completely reversed stress decreases with increasing temperature.
for aluminum alloys, T > 50°C: KT,D = 1-1,2' 10 -3. (T / °C - 50)2, Figure 1.2.3 in the Chapter 1.2,
Normal temperature, low temperature and elevated temperature are to be distinguished.
-
(2.2.9)
aT,D Constant, Table 2.2.2.
2.2.3.1 Normal temperature Normal temperatures are as follows: for fine grain structural steel from -40°C to 60°C, for other kinds of steel from -40°C to + 100°C, for cast iron materials from-25°C to + 100°C, - for age-hardening aluminum alloys from -25°C to 50°C, - for non-age-hardening aluminum alloys from - -25°C to 100°C.
Table 2.2.2 Constant aT,D *8. Kind of material aT,D
8
GGG 1,6
GT 1,3
GG 1,0
Forstainless steel values aT.D arenot known up to now.
(2.2.11)
49
2.2 Material properties
Higb 'temperature strength Rm,T 1i1ghtemperature yieidStl'ellgthRp,t
2 Assessment of the fatigue strength using nominal stresses Eq. (2.2.7) to (2,1.10) apply to steel and cast iron materials from the indicated temperature T up to 500 o e. Eq. (2.2.11) applies to aluminum alloys up to 200 o e. The values crW,zd,T and "CW,s,T are not explicitly needed for an assessment of the fatigue strength, as only the temperature factor KT,D is used. For elevated temperature, and in particular when the mean stress Sill, i- 0 , the fatigue strength in terms of the maximum stress may be higher than the static strength so that the assessment is governed by the static strength.
Ojlf-~=
o
o
lOO
200
300
400
500
Tin·C
nt.
Rrn;T .~ R ln . 1m Crecp.Stn~ngth
It,,.,TI
Rrn;Tt J ~:m'jlJ1t
0,1 F:=:q:~::J=--.L--d-~~ oW~Z(n
aW,m
o
o
100
2;2,lb
200
300 400 Tin·C
500
Figure 2.2.1 Temperature dependent values of the static strength and of the fatigue strength, plotted for comparison. Safety factors j according to Chapter 1.5 or 2.5, respectively. Rm,T/Rm = KT,m, Rm,Tt/Rm = KTt,m,
Rp,T / Rp = KT,p, Rp,Tt / Rp = KTt,p .
Rm,T, Rp,T as well as Rill,Tt, Rp,Tt for t =
io' h.
Fatigue strength value at elevated temperature: crW,zd,T / crW,zd = KT,O· Top: Non-alloyed structural steel, as in Figure 1.2.2, Rp / Rm = n, / Rm = 0,65, crW,zd/ Rm = 0,45, Jm = 2,0, jp = Jmt = 1,5, Jpt = 1,0, In = 1,5 . Bottom: GG, as in Figure 3.2.2, crW,zd/ Rm = 0,30, jm = 3,0, Jmt = in = 2,4.
50
2.3 Design parameters
2.3 Design parameters
1R23
EN. dog
Contents 2.3.0 General 2.3.1 2.3.1.0 2.3.1.1 2.3.1.2
The design factors of shell-shaped (2D) non-welded components for normal stresses in the directions x and y as well as for shear stress are (2.3.2)
Page 50
KwK, =[K x
Design factors General Non-welded components Welded components
f
,x
+_1_ _ 1) . 1 _ KR,cr K y ·K s .KNL,E
KWK,y=[K f y +_1_ _ 1) . 1 KR,cr K y .K s .KNL,E ,
2.3.2 Fatigue notch factors 2.3.2.0 General 2.3.2.1 Fatigue notch factors computed from stress concentration factors 2.3.2.2 Fatigue notch factors computed from experimental values 2.3.2.3 Fatigue notch factors for superimposed notches 2.3.3 2.3.4 2.3.5 2.3.6 2.3.7
2 Assessment of the fatigue strength using nominal stresses
1 KwK,s = [Kf,S +_1__ 1)' KR,'t Ky.K s
51
52 54
Roughness factor Surface treatment and coating factors Constant KNL,E Fatigue classes (FAT) Thickness factor
55 56
Kf,zd ... fatigue notch factors, Chapter 2.3.2, roughness factor, Chapter 2.3.3, surface treatment factor, Chapter 2.3.4, coating factor, Chapter 2.3.4, constant for GG, Chapter 2.3.5.
2.3.1.2 Welded components For the base material of welded components the design factors are to be computed as for non-welded components.
2.3.0 General According to this chapter the design parameters are to be computed in terms of design factors.
For the toe section and for the throat section of welded components the design factors are in general to be determined separately, since the cross-section values, the nominal stresses and the fatigue classes FAT may be different. Rod-shaped (10) and shell-shaped components are to be distinguished.
2.3.1 Design factors
(2D) .welded
2.3.1.0 General Non-welded and distinguished.
welded
components
are
to
be
Steel and cast iron material The design factors of welded rod-shaped (lD) components made of steel or of cast iron materials *2 for axial, for bending, for shear and for torsional stress are,
2.3.1.1 Non-welded components
KWK,zd = 225 / (FAT' ft' Kv KNL,E), KWK,b = KWK,zd , KwK,s = 145/ (FAT' it· Ko ), KWK,t = KwK,s .
Rod-shaped (10) and shell-shaped (2D) non-welded components are to be distinguished. The design factors of rod-shaped (ID) non-welded components for axial, for bending, for shear and for torsional stresses are *1, (2.3.1) 1 KWK,Zd=[K f Zd +_1__ 1)' , KR,cr K y ·K s .KNL,E KWKb=[K fb +_1__ 1) . 1 , , KR,cr K y ·K s .KNL,E 1 KwK,s = [Kf,S +_1__ 1) . KR,'t Ky.K s
The design factors of shell-shaped (2D) welded components made of steel or of cast iron materials for normal stresses in the directions x and y as well as for shear stress are
1 The additive combination of the fatigue strength notch factor Kfzd ... with the reciprocal roughness factor Kk,c, ... reduces the effect 'of roughness for components with sharp notched (Kj is large) incomparison tocomponents with mild ornonotches (Kf '" 1).
To a major part the FAT values where derived with reference to the nw recommendations and Eurocode 3 (Ref 191, 18/). The design factors are supposed, however, to be valid notonly for weldable structural steel but also for other kinds of iron based materials (conditionally weldable steel, stainless steel, weldable cast iron materials). 2
1 . KWK,t =[K f t +_1__ 1) , , KR,'t Ky.K s
(2.3.4)
51
2.3 Design parameters
KwK,x = 225 / (FAT' ft' Kv KNL,E), KwK,y = 225 / (FAT' ft' Ko KNL,E), KwK,s = 145/ (FAT' it· Ky).
(2.3.5)
2 Assessment of the fatigue strength using nominal stresses concentration factors, K, , and from the Kj-K, ratios, l1o(r) , Ilo(d) , nt(r) , n'[(d) , *5. (2.3.10)
Aluminum alloys The design factors of rod-shaped (lD) welded components made of aluminum alloys *3 for axial, for bending, for shear and for torsional stress are KWK,zd = 81 / (FAT·:tt· Ky' K s), KWK,b = KWK,zd , KwK,s = 52 / (FAT' ft' Kv Ks), KWK,t = KwK,s .
(2.3.6)
The design factors of shell-shaped (2D) welded components made of aluminum alloys for normal stresses in the directions x and y as well as for shear stress are KwK,x = 81 / (FAT' ft' Ke : Ks), KwK,y = 81 / (FAT' ft' Kv Ks), KWK,s = 52 / (FAT' ft), FAT ft Kv Ks KNL,E
(2.3.7)
fatigue class, Chapter 2.3.6, thickness factor, Chapter 2.3.7, surface treatment factor, Chapter 2.3.4 *4, coating factor, Chapter 2.3.4, constant for GG, Chapter 2.3.5.
The fatigue classes FAT are in general different for normal stress in the direction x and in the direction y, as well as for shear stress.
2.3.2 Fatigue notch factors 2.3.2.0 General
The fatigue notch factors, Kf,x ,... , for normal stress in the directions x and y as well as for shear stress of shellshaped (2D) components are Ktx Kf,x =--'(-) , n crx r _ Kt,y Kf,y- Day (r) ,
K
(2.3.11)
- Kt,s f,s - n't (r) ,
Kt,zd ...
stress concentration factor according to type of stress, Chapter 5.2, ncr (r) ... Kt-Kf ratio of the component for normal stress or for shear stress as a function of r, ncr (d), .. Kj-K, ratio of the component for normal stress or for shear stress as a function of d, r notch radius at the reference point, d diameter or width of the net notch section.
Caution: IfEq. (2.3.10) or (2.3.11) yield a fatigue notch factors Kfzd, '" < 1 the realistic value to be applied is *7,
The fatigue notch factors, Kf,zd , ... , allow for the influence on the fatigue strength resulting from the design (contour and size) of a non-welded component. They are to be computed from stress concentration factors or, if these are not applicable or not known, from experimental values.
Kt-Kr ratios for normal stress
2.3.2.1 Fatigue notch factors computed from stress concentration factors
ForG cr ;; 0,1 mrrr ! there is
Rod-shaped (lD) and shell-shaped (2D) components are to be distinguished. The fatigue notch factors , Kf,zd , ... , for axial, for bending, for shear and for torsional stress of the rodshaped (lD) non-welded structural details presented in Chapter 5.2 are to be computed from the stress
Kf,zd = ...
recommendations. Moreover the design factors are supposed tobevalid, however, for all weldable aluminum alloys, except for the aluminum alloys 5000, 6000 and 7000. Numerical values see Footnote 6 onpage 47. 4 As
(2.3.12)
The Kt-Kf ratios for normal stress, ncr (r) and ncr (d), Figure 2.3.1, are to be computed from the related stress gradients Gcr(r) and Gcr(d), Eq. (2.3.13) to (2.3.15).
Ocr = 1 +G cr . mmTO
-(a G - 0,5 + R m )
bG·MPa ,
Ocr = 1 +~Gcr'rom ·10
vo =
!
-(aG + R m )
bG' MPa,
(2.3.14)
< Gcr;; 100 mnr ! there is
1 +~Gcr -rnm '10
-(aG + R m )
a G, bo constants, Table 2.3.2. a rule Ky isnot relevant for welded components, that isKy = 1.
(2.3.13)
for 0,1 mrrr !
for 1 mrrr 3 Tosome part the FAT values where derived with reference tothe IIW
= 1.
bG.MPa,
(2.3.15)
52
2.3 Design parameters
2 Assessment of the fatigue strength using nominal stresses For surface hardened components *8 (components with thermal or with chemo-thermal surface treatment) the K,-K r ratios are lower than for non surface hardened components *9 * 10.
Kt-Kr ratios for shear stress
r /VV . V:/VlI 1/. / /1 . IJ
1/
0,80
1,2
V.
V
800
.SteeV 1200
~~V~~{t~V
1,1
The Ki-K, ratios for shear stress, n, (r) und n, (d), are to be computed from the related stress gradients G,(r) and G,(d) according to Eq. (2.3.13) to (2.3.15), after having replaced cr by 't and the tensile strength Rm by fw" . Rm, where fw" is the fatigue strength factor for shear stress, Table 2.2.1.
·/l/Pl/ f/ l/
Related stress gradients
1,02
The related stress gradients as a function of the notch radius r at the reference point, G cr (r) andG,(r), are to be determined from Table 2.3.3. The related stress gradients from bending and torsion as a function of the diameter or width d at the notch net section are
V/tVI
Z I do=
'1111
I
0;267'
G cr (d) =G,(d) = 2/ d.
I
1 I I 101 . "", .. 0;01 0,020,050;1 0,2 0,5
5
2
1
to 2.3.2.2 Fatigue notch factors computed from experimental values
G(Jinmm~l
Figure 2.3.1 Kj-K; ratios ncr for normal stress. The diagram may be extended up to G cr = 100 mm
r
(2.3.17)
Rod-shaped (lD) and shell-shaped (2D) components are to be distinguished.
l
Indicated numerical values 1/0,65 to 1/0,95: Difference of the fatigue limit for completely reversed stress in tension-compression and in bending, valid for the material test specimen ofthe diameter do = 7,5 mm. Not included in the figure 2.3.1: Stainless steel. Threshold values forGcr = I mm -1 : largest value: ncr = 1,27 for Rm = 400 MPa and smallest value: ncr = 1,14 for Rm = 1070 MPa.
5 The fatigue notch factor depends on the notch root radius r and moreover in the case of bending or torsion on the diameter or width d at the notch net section.
Wrought aluminum alloys: Threshold values forGcr = 1 mm -1 : largest value: ncr = 1,69 for Rm = 95 MPa and smallest value: ncr = 1,18 for R m = 590 MPa.
6 See footnote 12.
Cast aluminum alloys: Threshold values for: G cr = 1 mm -1 : largest value: ncr = 2,02 for Rm = 130 MPa and smallest value: ncr = 1,88 for Rm = 330 MPa.
7 Exception in case of bending: IfKt,b / Ilo (r) < 1 then Kt,b / Ilo (r) = 1 is to be applied (without considering Ilo(d) ). Accordingly in case oftorsion. 8 Does not apply to cold rolled or shot peened surfaces. See the summary of special features ofthe fatigue strength of surface hardened components, Chapter 5.8.
Table 2.3.2 Constants l1G and bG . Kind of material
Stainless steel
l1G bG
0,40 2400
Kind of material l1G bG
Other GS kinds of steel 0,50 0,25 2700 2000 Wrought Al-alloys 0,05· 850
GGG
0,05 3200
GT
GG
-0,05 -0,05 3200 3200
Cast Al-alloys -0,05 3200
9 The Kt - Kf ratio for a crack originating in the hardened surface layer is lower because the tensile strength R m of the hard surface layer is higher than the tensile strength Rm of the core material according to the material standard. The Kt - Kf ratio for a crack origgiating ~the core material is lower because the related stress gradientGcr (or G, ) in the core material has decreased from its maximum value at the surface. 10 The tensile strength of the surface layer may be estimated approximately as Rm = (3,3 . HV) MPa , where HV is the Vickers hardness number. As this equation, however, was not specifically established for hardened surface layers, it is to be applied with caution. In particular the fatigue strength value crW,zd of the hardened surface layer must not be derived from that estimate of the tensile strength (crW,zd
* fW,cr' Rm)·
53
2.3 Design parameters
2 Assessment of the fatigue strength using nominal stresses
Table 2.2.3 Related stress gradients G c (r) andG't (r) for simple structural details ~ 1. G
Structural detail
.
(r) ~2~3
G~(r) ~4
-1
2 -·(I+
Mb~r ~(iD . d' ~--
Fzd
cr
The fatigue notch factors for shell-shaped (2D) non-
r
r
welded components applying to normal stresses in the
FZd
I
directions
x and y
as well as shear stress are:
t
MbBtfb
_( D
·-d'
FZd
x., I
K
2,3 -'(l+
Fzd
1,15
- K (d) n crx (rp ) f,x-f,xP' ()'
(2.3.19)
n crx r
r
t
Mb~rb )-
r
- ( B--b Fzd
-
2 -. (1+
Fzd
~5
Kf,zd (dp), .. fatigue notch factor of the test
t
Mb~b B - -- b ) -(-t
Fzd
'
2,3. (l +
-
specimen according to type of stress, Chapter
r
FZd
~5
t Mb
-
2,3 r
Mb
_(.~-Efr -\--~, I Fzd
Fzd '- "0
Round specimen or flat
5.3 *13,
ncr (rp)...
Kt-Kf ratio of the test specimen for normal
ncr (r) ...
stress or for shear stress according to r p *14, Kt-Kf ratio of the component for normal
ncr (d)...
Kt-Kf ratio of the component for normal
stress or for shear stress according to r *14, stress or for shear stress according to d,
~5
member ~ 1 r > O. The equations are valid for round members, approximately they apply to round members with a central borehole too. ~2
q>=
rp = 0 for t! d > 0,25 ort! b > 0,25,
1I(4.M +2)
for
t!d~ 0,25
or
11 In this case the fatigue notch factor depends on the notch radii r and rp and for bending and torsion on the diameter or width d at the notch net section. 12 The basic definition of the fatigue notch factor Kf,b for bending is:
t!b~ 0,25.
(2.3.20)
Kf,b = crW,zd/ SWK,b ' ~3
The related stress gradient Gcr(r) applies to axial stress and to bending stress; nevertheless there is a difference for bending because of the Kt-KfTatio ncr(d) additionally contained in Eq. (2.3.10) and (2.3.18).
~4 The related stress gradient G~(r) applies to shear stress and to torsion stress; nevertheless there is a difference for torsion because of the Kt-KfTatio n~(d) additionally contained in Eq. (2.3.10) and (2.3.18). ~5
flat member of thickness s.
SWK,b
fatigue strength value for completely reversed axial stress of the unnotched test specimen of the diameter do , fatigue strength value for completely reversed bending stress of the notched component of the diameter or width d.
Kfb in bending is dependent on the notch radius r and on the diameter or width d of the notch net section. Kf,t for torsion in analogy. The .defmition of the fatigue notch factor for bending derived from experimental data - under the provision that the unnotched and the notched specimen have the same diameter dp - is:
The fatigue notch factors, Kf,zd , ... , for axial, for bending, for shear and for torsional stress of the rodshaped (lD) non-welded structural details presented in Chapter
crW,zd
5.3 are to be computed from the experimentally
Kf,b (d p) = SW,b,P / SWK,b,P,
(2.3.21)
SW,b,P
fatigue limit for completely reversed bending stress of the unnotched test specimen of diameter dp, SWK,b,P Fatigue limit for completely reversed bending stress of the notched test specimen of diameter dp.
derived fatigue notch factors of test specimens given there,
and from the respective Kf
particular K
*II
- K (d) ncr (rp ) f,zd f,zd p ' --(-)- , ncr r
-K,
ratios.
In
(2.3.18)
Kf,b is dependent on the notch radius rp and on the diameter or width of the notch net section d. Kf,t for torsion in analogy. 13 The fatigue notch factors given in Chapter 5.3 are applicable to components from steel without surface treatment. Additionally, however, a procedure for components being surface hardened and for components made of cast iron materials and aluminum alloys is described there. 14 For computing Kt-Kf ratios the notch radii, r or rp , are required. Particularly for cases that may produce some doubt the radii are specified in Chapter 5.3. A possible incorrectness that may occur will be reduced by the division of ncr(rp ) / ncr(r).
54
2.3 Design parameters
r d rp dp
notch radius of the component, diameter or width of the component, notch radius of the test specimen, diameter or width of the test specimen.
2 Assessment of the fatigue strength using nominal stresses
1,0
1.1>
•r:::.::- '--": i"'.,1:'.: ~ :-:::: r--.. r--... O~9
KR,ta
~ ~ i'..
The Kt-Kf ratios Ila (rp), .., are to be computed according to the related stress gradient Gcr(rp ) with reference to Chapter 2.3.2.1 .... Because of similarity of the component it is
..
32 .zz:
<,
63
'\( ~. <,",
--.!...
12
...: ::\\.. <,
test specimen and
.
0,1
Q~ ~~~'\
~
"
~"":,\,,
25
~~ '\ r'.
$
i'
rid = rpl dp.
(2.3.22)
0,6
J-.00
Caution: If a fatigue notch factors Kf,zd , ... < 1 is obtained from Eq. (2.3.18) or (2.3.19) the realistic value to be applied is *15 Kf,zd = ... = 1.
2bo
(2.3.12)
0,4 300500 700. 1000 2000 2,Uil Rlil in MPil
2.3.2.3 Fatigue notch factors for superimposed notches For superimposed notches (for example a fillet and a borehole), the partial fatigue notch factors of which are Kf,1 and Kf,2 , the resulting fatigue notch factor in the most unfavorable case is Kf= 1 + (Kf,l- 1) + (Kf,2- 1).
KR;l!
0;9 '!o...~~-,-,,+-~+--"""'t-;;;;:
(2.3.24)
If the distance of notches is 2 r or above (where r is the larger one of both notch radii) *16 a superposition does not need to be considered.
40n
2.3.3 Roughness factor
600800 lOtIO
Rm hll\-IPafiir as, Cfu'G; GT "r ....
The roughness factor KR,cr or KR;t accounts for the influence of the surface roughness on the fatigue strength of the component.
100
OJ.
,
J
200 30ll 400 R m in MPa fUr G~
The roughness factor valid for a polished surface is KR,cr = KR,'t = 1.
(2.3.25)
For a rolling skin, a forging skin or the skin of castings an average roughness value R, = 200 11m applies.
Figure 2.3.3 Roughness factor KR,cr . Top, Steel. Bottom: Cast iron materials with skin, steel with rolling skin for comparison
The roughness factors for normal stress, Figure 2.3.3, and for shear stress are *17 KKR,cr (2.3.26) = 1 - aR,cr . 19 (Rz 111m ) . 19(2Rm I Rm,N,min ), KKR,'t= = 1 - fw,'t . aR,cr -lg (Rz /um) -lg (2Rm!Rm, N, min), aR,cr Rz
constant, Table 2.3.4, average roughness value of the surface in 11m , according to DIN 4768, tensile strength, Chapter 1.2.1.1, Rm Rm,N,min minimum tensile strength, Table 2.3.4, fatigue strength factor for shear stress, fw,'t Table 2.2.1.
15 Exception in case of bending: If Kr.b(lip ) . Ilo(rp ) / Ilo(r) < 1 then Kf,b(lip) . Ilo(rp) / Ilo(r) = 1 is to be applied (without considering Ilo(d) ). Accordingly in case of torsion. 16 The distance of 2 r is likely to be on the safe side. 17 In particular residual stresses as a result of manufacturing and of a surface treatment are determining the influence of the surface on the component fatigue limit, rather than the surface roughness. According to the current state of knowledge, however, improved regulations to allow for the surface effect are not yet developed, so that the traditional equations based on a roughness value have to be accepted for the time being.
55
2.3 Design parameters
Table 2.3.4 Constant aR,cr and nummum tensile strength. ~l1,N,min , for the kind of material considered. Kind of material
Steel
GS
GGG
GT
GG
aR,cr
0,22
0,20
0,16
0,12
0,06
Rm,N,min
400
400
400
350
100
2 Assessment of the fatigue strength using nominal stresses
Table 2.3.5 Upper and lower limits of the surface treatment factor for steel and cast iron materials ~H·2. Surface treatment
aR,cr ~,N,min
Wrought aluminum alloys 0,22 133
notched components
~3
Steel Chemo-thermal treatments 1,30 - 2,00 Nitriding 1,10 - 1,15 Depth of case 0,1...0,4 mm (1,15 - 1,25) (1,90 - 3,00)
inMPa Kind of material
unnotched components
Cast aluminum alloys 0,20
Surface hardness 700 to 1000 HV 10
Case hardening Depth of case 0,2 ... 0,8 mm Surface hardness 670 to 750 HV 10
133
inMPa
1,10 - 1,50 (1,20 - 2,00)
1,20 - 2,00 (1,50 - 2,50)
Carbo-nitriding Depth of case 0,2 ... 0,8 mm Surface hardness 670 to 750 HV 10
For surface hardened components *8 and an expected crack origine at the surface the roughness factor is less favorable (smaller) than for components not surface hardened, because of the higher tensile strength ~ of the hardened surface layer *10.
Mechanical treatment 1,10 - 1,25 Cold rolling (1,20 - 1,40) Shot peening 1,10 - 1,20 (1,10 - 1,30) Thermal treatment 1,20 - 1,50 Inductive hardening (1,30 - 1,60) Flame-hardening
Normally, in the case of experimentally determined fatigue notch factors the roughness factor does not need to be considered (KR,cr = KR,'t = 1). Otherwise, in the case of fatigue notch factors that are experimentally determined for specimens with a different surface roughness, KR,cr and KR,'t are to be replaced by K R,o
=
KR,cr (Rz ) / KR,cr (Rz,p ),
KR,'t
=
KR,'t (Rz) / KR,'t (Rz,p),
Cast iron materials 1,10 (1,15 ) Nitriding 1,1 (1,2) Case hardening 1,1 (1,2) Cold rolling 1,1 (1,1) Shot peening 1,2 (1,3) Inductive hardening, Flame-hardening
Rz average surface roughness of the component in urn, Rz,p average surface roughness of the specimen in urn,
The surface treatment factor, Kv , allows for the influence of a treated surface layer on the fatigue strength of the component. Without a surface treatment there is Kv= 1.
(2.3.28)
1,30 - 1,80 (1,50 - 2,20) 1,10 - 1,50 (1,40 - 2,50) 1,50 - 2,50 (1,60 - 2,80)
Depth of case 0,9 ... 1,5 mm Surface hardness 51 to 64 HRC
(2.3.27)
2.3.4 Surface treatment and coating factors
(1,80)
1,3 (1,9) 1,2 (1,5) 1,3 (1,5) 1,1 (1,4) 1,5 (1,6)
~ 1 Concerning typical component values and further kinds of treatments, see also FVA-worksheet "Schwingfestigkeitssteigerung (increasing the fatigue strength)".
~ 2 The given values typically apply to the component fatigue limit. Values applying to the variable amplitude fatigue strength are in general somewhat lower.
The values are valid for specimens of 30 to 40 mm diameter; values in parenthesis for specimens of 8 to 15 mm diameter. ~
3 For unnotched or slightly notched components.
For components with surface treatment *8 the surface treatment factor depends on whether a crack origin is to be expected at the surface or in the core. Essential factors of influence are the ratio of the fatigue limits of the surface layer and of the core material, as well as the ratio of the local stress values on the surface and in the core just below the surface layer. Upper and lower limits of the surface treatment factors for steel and cast iron materials are given in Table 2.3.5. A definite value is to be determined by the user *18.
18 Provided that the procedures of surface treatment can be applied to components of aluminum alloys, the Ko-values for cast iron material may approximately be taken into account.
56
2.3 Design parameters
The coating factor K s allows for the influence of a surface coating on the fatigue strength of a component made of an aluminum alloy. For steel and cast iron material there is Ks = 1.
(2.3.29)
For aluminum alloy without coating there is Ks = 1.
(2.3.30)
2 Assessment of the fatigue strength using nominal stresses
2.3.6 Fatigue class (FAT) The fatigue classes (FAT) for nominal stresses allow for the influences of both the form of welded components, of the shape of the weld seam and of the weld seam itself on the fatigue strength of the toe section or of the throat section) *19. A complete catalogue of fatigue classes with reference to the IIW Recommendations is given in Chapter 5.4.1 *20
For aluminum alloy with coating there is
K s < 1.
(2.3.31)
Ks for example after Figure 2.3.4 (provisional values).
'Ks
--..,J
0.9 0,1 ,
"'"
'"""
.I
0.7 ~
o..s
1-'111T1n --- 'ffi'!r ~:. d-H~~JJ. ••I• "f
I
r.
, I
I.
o,a
.r...........
.
.ld··· r-irti. 1--1-'rn.-rr I
I
1
I
T--T~i
l:\!.
.•:
. iiTi'Y
'_--H-'-'l~,"L.
l _
"j
j-
:!:J'iJ
! f4+!- r' I ! !',•.1i :1
_
r
..iH+i-H
0;1
o
,.
I ;; !;-1!
_...LL.1.J
!
Q~
Ii
o
.I
'B.~
I!' .;- !
10
1
100
Thickness ·.of layerinp.ID
Figure 2.3.4 Influence of anodic coating on the fatigue limit (at 106 cycles) of a component from aluminum alloy as a function of the layer thickness (after Wilson). Provisional values.
2.3.7 Thickness factor When using nominal stresses for the calculation of transversely loaded welds the thickness factor ft accounts for the influence of the sheet metal thickness on the fatigue strength *21 .. The thickness factor ft is of no effect, however, - if there is no weld, - if there is no transversely loaded weld, or - if the sheet metal thickness is t :::: 25 mm. In these cases the thickness factor is ft
= 1.
(2.3.33)
For a transversely loaded weld and a sheet metal thickness t > 25 min the thickness factor is a function of the sheet metal thickness t (in mm):
:tt =
(25 mm / t)
n,
(2.3.34)
n after Table 2.3.7.
Table 2.3.7 Exponent n for the thickness factor.
2.3.5 Constant KNL,E The constant KNL,E accounts for the non-linear elastic stress strain behavior of GG when loaded in tensioncompression or bending. For all kinds of material except for GG there is KNL,E = 1.
(2.3.32)
KNL,E for GG after Table 2.3.6.
Type of the welded joint cruciform joints, transverse T-joints, plates with transverse attachments - as welded - toe ground transverse butt welds, - as welded butt welds ground flush, base material, longitudinal welds or attachments, - as welded or ground
n
0,3 0,2 0,2 0,1
Table 2.3.6 Constant KNL,E ~ I. Kind of material KNL,E
GG -10
I
GG -15
1,075
I
GG GG -20 -25 1,05
GG -30
I
GG -35
1,025
-e- 1 For unnotched or slightly notched components in tension-compression KNL.E =
1.
19 Different from an assessment with structural stresses or with effective notch stresses, see Chapter 4.3 and Chapter 5.5.
20 All fatigue classes, except those for the base material, are considered here: for steel FAT::;; 140 for nomial stress and FAT::;; 100 for shear stress, for aluminum alloys FATS; 50 for normal stress and FAT::;; 36 for shear stress. The assessment ofthe base material ofwelded components is to be carried out as for non-welded components.
21 The thickness factor is supposed to be valid for steel, but also for aluminum alloys.
57 2.4 Component strength 2.4.1 Component fatigue limit for completely reversed stress
2.4 Component strength
\R24 EN.dog
Content
Page
2.4.0
General
2.4.1
Component fatigue limit for completely reversed stress
2.4.2
Component fatigue limit according to mean stress 2.4.2.0 General 2.4.2.1 Mean stress factor Calculation for type of overloading F2 Calculation for type of overloading Fl Calculation for type of overloading F3 Calculation for type of overloading F4 2.4.2.2 Individual or equivalent mean stress 2.4.2.3 Residual stress factor 2.4.2.4 Mean stress sensitivity
Caution: See the comment in the second paragraph of Chapter 4.4.2.
57
Rod-shaped (lD) and shell-shaped (2D) components are to be distinguished.
58
The component fatigue limits of rod-shaped (lD) components for completely reversed axial, bending, shear and torsional stress are *1
59 60
SWK,zd = crW,zd I KWK,zd , SWK,b = crW,zd I KWK,b *2 , TwK,s = 'tw,sl KwK,s, TWK,t = 'tw,sl KWK,t, crW,zd, 'tW,s
61 62
2.4.3
Component variable amplitude fatigue strength 2A.3.G General 2.4.3.1 Variable amplitude fatigue strength factor Calculation for a constant amplitude spectrum Calculation for a variable amplitude spectrum Elementary version of Miner's rule based on the damage potential Calculation according to the consistent version of Miner's rule Calculation using a class of utilization Calculation using a damage-equivalent stress amplitude 2.4.3.2 Component constant amplitude S-N curve
2 Assessment of the fatigue strength with nominal stresses
63
KWK,zd...
(2.4.1)
material or weld specific fatigue limit for completely reversed stress, Chapter 2.2.1, design factor, Chapter 2.3.1.
Eq. (2.4.1) is based on thefatigue limit for completely reversed stress, Eq. (2.2.1) or (2.2.3) and (2.2.4), and on the design factor, Eq. (2.3.1) or (2.3.4) and (2.3.6). It applies to non-welded and to welded components.
64 The component fatigue limits of shell-shaped (2D) components for completely reversed normal stresses in the directions x and y as well as for shear stress are SWK,x = crW,zd l KwK,x , SWK,y = crW,zd I KwK,y , TWK = 'tw,s I KwK,s ,
65 66
2.4.0 General
crW,zd, 'tw,s KWK,x, ...
(2.4.2)
material or weld specific fatigue limit for completely reversed stress, Chapter 2.2.1, design factor, Chapter 2.3.1.
Eq. (2.4.2) is based on the fatigue limit for completely reversed stress, Eq. (2.2.1) or (2.2.3) and (2.2.4), and on the design factor, Eq. (2.3.2) or (2.3.5) and (2.3.7). It applies to non-welded and to welded components.
According to this chapter the component fatigue strength is to be calculated as follows: Step 1: component fatigue limit for completely reversed stress in considering the design factor, Chapter 2.4.1, Step 2: component fatigue limit in considering the mean stress factor, Chapter 2.4.2, Step 3: component variable amplitude fatigue strength in considering the variable amplitude fatigue strength factor, Chapter 2.4.3.
2.4.1 Component fatigue limit for completely reversed stress According to this chapter the component fatigue limit for completely reversed stress is to be calculated in considering the design factor.
1 The component fatigue limits for completely reversed stress are different for normal stress and for shear stress, and moreover because of different stress gradients ordifferent weld characteristics depending onthe type ofstress.
2 The material fatigue limit forcompletely reversed stress isthebasis for both axial and bending stress. The difference is allowed for bythe design factor. Forshear and torsion inanalogy.
58
2 Assessment of the fatigue strength using nominal stresses
2.4 Component strength 2.4.2 Component fatigue limit according to mean stress
2.4.2 Component fatigue limit according to mean stress 1R242 EN.dog 2.4.2.0 General According to this chapter the amplitude of the component fatigue limit is to be determined according to a given mean stress, and where appropriate, in considering a multi axial state of stress. Comment: For non-welded components of austenitic steel, or of wrought or cast aluminum alloys the component fatigue limit is different from the component endurance limit for N = 00 , Chapter 2.4.3.2. Observing the specific input values the calculation applies to non-welded and to welded components.
An improved procedure for non-welded components of steel to compute the component fatigue limit in the case of synchronous multiaxial stresses is given in Chapter 5.9. In combination with a stress spectrum the indicated stress ratio Rzd, ... commonly refers to step I of the stress spectrum (maximum amplitude), R zd,l, .,. *1 *2. The mean stress factor, Figure 2.4.1, allows for the influence of the mean stress on the fatigue strength. Without mean stress the mean stress factor is KAK,zd = ... = I.
(2.4.4)
The residual stress factor accounts for the influence of the residual stress on the fatigue strength. For nonwelded components the residual stress factor for normal stress and for shear stress is (2.4.5) Rod-shaped (ID) and shell-shaped (2D) components are to be distinguished. Rod-shaped (ID) components The mean stress dependent amplitudes of the component fatigue limit of rod-shaped (lD) components for axial, for bending, for shear and for torsional stress are SAK,zd = KAK,zd . KE,cr . SWK,zd, SAK,b = KAK,b . KE,cr' SWK,b, TAK,s = KAK,s . KE;t . TWK,s , TAK,t = KAK,t . KE,'t . TWK,t ,
(2.4.6)
KAK,zd .., mean stress factor, Chapter 2.4.2.1, residual stress factor, Chapter 2.4.2.3, KE,cr ... SWK,zd ... component fatigue limit for completely reversed stress, Chapter 2.4.1. Eq. (2.4.6) applies to non-welded and to welded components. Shell-shaped (2D) components The mean stress dependent amplitudes of the component fatigue limit of shell-shaped (2D) components for normal stresses in the directions x and y as well as for shear stress are SAK,x = KAK,x . KE,cr' SWK,x, SAK,y = KAK,y . KE,cr . SWK,y, TAJ( = KAK,s' KE,'t' TWK, KAK,x... KE,cr... SWK,x ...
(2.4.7)
mean stress factor, Chapter 2.4.2.1, residual stress factor, Chapter 2.4.2.3, component fatigue limit for completely reversed stress, Chapter 2.4.1.
Eq. (2.4.7) applies to non-welded arid to welded components. Type of overloading The mean stress factor KAK,zd, ... is dependent on the type of overloading, FI to F4. It distinguishes the way how the stress may increase in the case of a possible overload in service (not by crash). Therefore it is to be determined in the sense of "safety of operation in service", that is for normal stress as follows: - Type FI: the mean stress Sm,zd remains the same, - TypeF2: the stress ratio Rzd remains the same, - Type F3: the minimum stress Smin,zd remains the same, - TypeF4: the maximum stress Smax,zd remains the same. For bending, shear or torsion Sm,zd, Rzd, .., are to be replaced by Sm,b, ~, ..., T rn.s- Rg, ... or T m.t- Rt . Intermediate types of overloading are possible. Dependent on the type of overloading the amplitude of the component fatigue limit is different, Figure 2.4.1.
Fields of mean stress In determining the mean stress factor KAK,zd, ... four fields of mean stress are to be distinguished. These are dependent on the stress ratio Rzd, ..., or on the mean stress Sm,zd, ... , respectively, see Chapter 2.4.2.2. 1 This definition is necessary only for mean stress spectra, not for stress ratio spectra or for fluctuating stress spectra, for which the stress ratios of allsteps are identical.
2 For more details see Chapter 5.6.
2.4 Component strength 2.4.2 Component fatigue limit according to mean stress
Figure 2.4.1 Amplitude of the component fatigue strength as a function of mean stress or stress ratio (Haigh diagram), described in four fields of mean stress
59
2 Assessment of the fatigue strength using nominal stresses
Rad=-=
®
Rzd =-1 (M~=M.)
Example: Nonnal stress, types of overloading F1 and F2. Given:
S
.
WK.zd
Component fatigue strength for completelyreversed
SAK,zd,Fl
stress SWK,zd , service stress amplitude Sa,zd , stress ratio Rzd , Derived:
Amplitudes of the componentfatigue limit SAK,zd
(M~=M
(M~=O)
®
b2U
for the types of overloading F1 and F2.
Normal stress:
Calculation for the type of overloading F2 * 4
Field I: Rzd > 1, field of fluctuating compression stress, where Rzd = + or - ex) is the zero compression stress. Field II: - ex) ~ Rzd~ 0, where Rzd < -1 is the field of alternating compression stress, Rzd = -1 is the completely reversed stress, Rzd > -1 is the field of alternating tension stress.
In case of a possible overload in service the stress ratio Rzd remains the same. Normal stress:
Field I:
KAK,zd =
Field III: 0 < Rzd < 0,5, field of fluctuating tension stress, where Rzd = 0 is the zero tension stress. Field IV: stress.
Rzd ~
Rzd
> 1: 1/ ( 1-
Ma) ,
0,5, field of high fluctuating tension KAK,zd-
For bending b the index zd is to be replaced by the index b, "tension stress" by "tension bending stress", and "compression stress" by "compression bending stress".
KAK,zd =
(not existing), (lower boundary changed), (unchanged), (unchanged).
(2.4.10)
1+ _cr_ . m,zd
'
(2.4.12)
Sa,zd
Field IV, Rzd~ 0,5:
AK,zd-
For torsion the index s is to be replaced by the index 1.
The mean stress factor KAK,zd ... is dependent on the mean stress and on the mean stress sensitivity.
, / Sa,zd
1+ M cr /3 I+M cr M S 3
K
2.4.2.1 Mean stress factor
1
1+M cr . Sm,zd
Field III, 0< Rzd < 0,5:
Shear stress: *3:
Field I: Field II: - 1 ~ Rs~ 0 Field III: 0 < n, < 0,5 Field IV: Rs~ 0,5
(2.4.9)
Rzd
Ma Sm,zd Sa,zd
3+M cr 3.(I+M ) 2 cr
'
(2.4.13)
stress ratio *6, Chapter 2.4.2.2, mean stress sensitivity, Chapter 2.4.2.4, mean stress *6, Chapter 2.4.2.2, stress amplitude.
For bending the index zd is to be replaced by b.
3 The fatigue limit diagram (Haigh diagram) for normal stress shows . increasing amplitudes for Rzd < -1 (negative mean stress). For negative mean stress the fatigue limit diagram (Haigh diagram) for shear stress is the same as for positive mean stress and symmetrical to Tm,s = O. Practically it is restricted to the fields of positive mean stress or a stress ratio Rs ~ -1 , as the mean stress in shear is always regarded to be positive, Tm,s ~ O.
Using the term Sm zd I Sa zd instead of (1 + Rzd ) I (1 - Rzd ) avoids numerical probl~, when the stress ratio becomes Rzd =- 00.
4 The type of overloading F2 is described first because it is of primary practical importance .
6 Or equivalent mean stress, equivalent minimum stress, equivalent maximum stress, Chapter 2.4.2.2.
5 Sm,zd / Sa,zd=(l+Rzd)/(l-Rzd)'
(2.4.11)
2.4 Component strength 2.4.2 Component fatigue limit according to mean stress Shear stress:
60
2 Assessment of the fatigue strength using nominal stresses For positive mean stresses, tm,s ~ 0, the same equations are valid if Sm,zd is replaced by tm,s and M, is replaced by M,
For KAK,s Field I is not existing and Field II is restricted to positive mean stresses R, ~ -1 . For positive mean stress, or R, ~ -1 , the same equations are valid if M cr is replaced by M.
For torsion the index s is to be replaced by t.
For torsion the index s is to be replaced by t.
Calculation for the type of overloading F3 In case of a possible overload in service the minimum stress Smin,zd remains the same.
Calculation for the type of overloading Fl In case of a possible overload in service the mean stress Sm,zd remains the same.
Normal stress:
Normal stress:
Smin,zd
For Smin,zd =
<
KE,cr ,SWK,zd -1
Smzd
For Sm,zd =
< - - - there is
'
KE,oo ,SWK,zd
I-M cr
KAK,zd = 1 1 (1 -
*7
KAK,zd = 11 (1 - M cr),
Ma) s
KAK,zd = 1 -
*7
I-Moo
Ma ),
(2.4.18)
Smin,zd
~
0 there is
1-M cr .Smin,zd I+M oo
(2.4.19)
(2.4.15)
Field III
(2.4.16)
2. 3+M oo for 0 < Smin,zd < there is 3 (1 + M cr )2 1+M cr 13 M cr 1+ M - -3-' Smin,zd KAK, d - _ _----"'cr _ z I+Moo 13
Field III
1 3 +M cr for - - < Sm,zd < ( )2 I+M oo I+M cr
Ma)~
for - 2 1(1 -
Sm,zd s 1 1 (1 + Ma) there is
Ma . Sm,zd,
there is
Field II (2.4.14)
Field II for -1 1 (1 -
-2
there is
(2.4.20)
Field IV Field IV for Smin,zd;?:
_2 . 3 + Moo 3
K
AK,zd -
(2.4.17) Sm,zd KE,cr SWK,zd
M,
mean stress *6, Chapter 2.4.2.2, residual stress factor, Chapter 2.4.2.3, component fatigue limit for completely reversed stress, Chapter 2.4.1, mean stress sensitivity, Chapter 2.4.2.4.
For bending the index zd is to be replaced by b.
M,
(I+M oo
Y
there is
3+Moo ( )2' 3· I+M oo
(2.4.21)
minimum stress *6, Chapter 2.4.2.2, residual stress factor, Chapter 2.4.2.3, component fatigue limit for completely reversed stress, Chapter 2.4.1, mean stress sensitivity, Chapter 2.4.2.4.
For bending the index zd is to be replaced by b.
Shear stress: Shear stress: For KAK,s Field I is not existing and Field II is restricted to positive mean stresses tm,s ~ 0 or o ~tm,s = Tm,s I(KE,< ' TWK,s) ~ 1/(1 + M"t).
7 The abbreviation Srn,zd = Sm,zd / (KE,cr' SWK,zd) applies inthe following to Smin,zd, Smax,zd , tm,s , ..., accordingly.
For KAK,s Field I is not existing and Field II is restricted to positive mean stresses Tm,s ~ 0 or - 1 s tmin,s = Tmin,s 1 (KE,< . TWK,s) s 0 . For positive mean stresses, tm,s ~ 0 , the same equations are valid if Smin,zd is replaced by tmin,s and M, is replaced by M r . For torsion the index s is to be replaced by t.
2.4 Component strength 2.4.2 Component fatigue limit according to mean stress
61
2 Assessment of the fatigue strength using nominal stresses
Calculation for the type of overloading F4
Individual mean stress
In case of a possible overload in service the maximum stress Smax,zd remains the same.
As a rule the individual mean stress Sm,zd is used to determine Smin,zd , Smax,zd and Rzd . For normal stress the respective equations are Smin,zd = Sm,zd - Sa,zd , (2.4.26) Smax,zd = Sm,zd + Sa,zd , Rzd= Smin,zd 1 Smax,zd ,
Normal stress:
Smax,zd
For Smax,zd =
KE,cr ,SWK,zd
KAK,zd = 1 1 (l -
< 0 there is
*7
110- ),
(2.4.22)
KAK,zd
s
2 1 (l + 110-) there is
I-M cr 'smax I-M cr
(2.4.23)
Field III 2 4 . 3 +M cr there is for - - - < Smax,zd
1+ M cr 13 M - - -cr . smax,zd 1+ M cr 3 KAK,zd = - - - - - - " - - - - - - I-M cr /3
(2.4.24)
~ .
3
3+M cr ( )2 1+ M cr
there is
(2.4.25) Smax,zd K E•cr SWK,zd
Equivalent mean stress In the case "bending and torsion", which is typical for numerous applications in machine design, and in similar cases, where normal stresses are combined with shear stresses, the variables Smin,zd,v , Smax,zd,v and Rzd,v are to be used. They are derived from an equivalent mean stress Sm,v , to be computed as a function of the respective individual mean stress values, Eq. (2.4.28). For normal stress there is Smin,zd,v = Sm,v - Sa,zd , Smax,zd,v = Sill,v + Sa,zd , Rzd,v = Smin,zd,v l Smax,zd,v,
Field IV for Smax,zd->
stress amplitude, minimum stress, maximum stress, stress ratio.
For bending, shear and torsion the appropriate variables are Smin,b, ..., ~, Tmin,s , ..., R, or Tmin,t , ..., Rt·
Field II for O:s; Smax,zd
Sa,zd Smin,zd Smax,zd Rzd
maximum stress *6, Chapter 2.4.2.2, residual stress factor, Chapter 2.4.2.3, component fatigue limit for completely reversed stress, Chapter 2.4.1, mean stress sensitivity, Chapter 2.4.2.4.
For bending the index zd is to be replaced by b.
Sa,zd Rzd,v Smin,zd,v Smax,zd,v
(2.4.27)
individual stress amplitude, equivalent stress ratio, equivalent minimum stress, equivalent maximum stress.
For bending, shear and torsion the appropriate variables are Smin,b,v, ..., ~,v, Tmin,s,v , ..., Rs,v or Tmin,t,v
Rt,v The equivalent mean stress, Eq. (2.4.27), for normal stress is Sm,v = q . Sm,v,NH + (l - q) . Sm,v,GH,
(2.4.28)
Shear stress: For shear stress the type of overloading F4 (Tmax,s remaining constant) can practically not being realized.
where q=
2.4.2.2 Individual or equivalent mean stress In each case Rzd , ..., Smin,zd, ... and Smax,zd , ... are . determined by mean stress and stress amplitude. The mean stress may be taken either as the individual mean stress according to type of stress or as an equivalent mean stress from the individual mean stresses of all types of stress.
13 -(l/f-c)
13-1 Sm,v,NH -~ (ISml+~S~ +4.T~ )
Sm,vGH ,
=~S2m +3.Tm2
.
(2.4.29)
2.4 Component strength 2.4.2 Component fatigue limit according to mean stress material dependent parameter after Table 2.6.1. Sm , Tm individual mean stress, Eq. (2.4.31) and (2.4.32),
Moderate residual stresses are to be assumed in case of welding with residual stress reducing precautions, for example by observing a suitable weld sequence.
For shear stress there is
fw"
2 Assessment of the fatigue strength using nominal stresses High residual stresses are to be assumed in case of welding without residual stress reducing precautions.
q
(2.4.30)
Tm,v=fw,, ' Sm,v,
62
shear strength factor, Table 2.2.1.
Low residual stresses are to be assumed in case of welding with subsequent stress-relief heat treatment, or if residual stress may evidentially be excluded.
Rod-shaped (ID) components
2.4.2.4 Mean stress sensitivity
For rod-shaped (lD) components the equivalent mean stress after Eq. (2.4.28) is to be computed only if Sm,zd + Sm,b ~ O. It is
The mean stress sensitivity M, or M, , in connection with the mean stress factor, describes to what extent the mean stress affects the amplitude of the component fatigue strength, Figure 2.4.1.
Sm = Sm,zd + Sm,b, Tm = Tm,s + Tm,t,
(2.4.31)
Sm,zd, ... individual mean stresses, Chapter 2.1.1.1.
For non-welded components the mean stress sensitivity for normal stress and for shear stress, applicable in case of normal or elevated temperature, is
Sm,zd , Sm,b , Tm,s and Tm,t are to be inserted into Eq. (2.4.31) with proper sign to be added or subtracted.
M, = aM' 10 -3. Rm/ MPa + bl\.:f, M't = fw" . Mq,
aM, bM constants, Table 2.4.2, fw " shear fatigue strength factor, Table 2.2.1.
Shell-shaped (2D) components For shell-shaped (2D) components the equivalent mean stress afterEq. (2.4.28) is to be computed only if Sm,y = 0 and Sm,x ~ 0 (or in reverse). It is
(2.4.32)
Sm = Sm,x (or Sm = Sm,y), T m = Tm,s, Sm,x, ... individual mean stress, Chapter 2.1.1.2.
2.4.2.3 Residual stress factor The residual stress factor for non-welded components is KE,cr = KE;t = 1.
(2.4.33)
For components that have been surface hardened *8 the mean stress sensitivity is greater because of the tensile strength R.n of the hardened surface being higher than that of components not surface hardened. For welded components the mean stress sensitivity for normal stress and for shear stress, applicable in case of normal or elevated temperature, is dependent on the intensity of the residual stress, but independent of the tensile strength R.n of the base material. Values are given in Table 2.4.1, see also Chapter 5.5. Table 2.4.2 Constants aM and bM .
For welded components of structural steel and of aluminum alloys the residual stress factor is different for high, moderate or low residual stresses. It is given for normal stress and for shear stress in Table 2.4.1, see also Chapter 5.5.
Kind of material aM bM
Table 2.4.1 Residual stress factor KE,cr , KE;t and mean stress sensitivity Mcr, M, for welded components. Residual stress high moderate low
KE,cr
Mcr
KE,'t
M't ~1
1,00 1,26 1,54
0 0,15 0,30
1,00 1,15 1,30
0 0,09 0,17
~ 1 For Shear Stress there is M't = fw r ' Mcr Table 2.2.1. "
(2.4.34)
Steel
~1
0,35 - 0,1
GS
GGG
GT
GG
0,35 0,05
0,35 0,08
0,35 0,13
0 0,5
Kind of material
Wrought aluminum alloys
aM bM
1,0 - 0,04
Cast aluminum alloys 1,0 0,2
~
1 also stainless steel.
8
Not applicable to components being cold rolled or shot-peened.
fw,'t = 0,577 ,
2.4 Component fatigue strength 2.4.3 Component variable amplitude fatigue strength
2.4.3 Component variable amplitude fatigue strength \R243 EN.dog 2.4.3.0 General
63
2 Assessment of the fatigue strength using nominal stresses
Rp
yield strength, Chapter 1.2.1.1, Kp,b, Kp,t plastic notch factors, Table 1.3.2, ~ shear strength factor, Table 1.2.5. 4
According to this chapter the amplitude of the component variable amplitude fatigue strength is to be derived from the stress spectrum and the component constant amplitude S-N curve, Chapter 2.4.3.2.
N; N* Componentfatigue lifecurve N
ComponentScbrcurve
The variable amplitude fatigue strength factor KBK,zd , . ... , to be calculated depends on the stress spectrum, that is on the required total number of cycles '1 and on the shape of the stress spectrum, as well as on the component constant amplitude S-N curve, and in addition it depends on the type of stress (normal stress or shear stress). It has to be distinguished, whether in case of a constant
amplitude spectrum an assessment of the fatigue limit (or endurance limit) or an assessment of the fatigue strength for finite life is intended, or whether in case of a variable amplitude spectrum an assessment of the variable amplitude fatigue strength is intended *2. The calculation for a constant amplitude stress spectrum is a special case of the more general case of calculation for a variable amplitude stress spectrum. In each case the way of calculation is the same, but the variable amplitude fatigue strength factors are different. Observing the specific input values the calculation applies to both non-welded components (component constant amplitude S-N curve model I or model II) and to welded components (component constant amplitude S-N curve model I only).
N,N Figure 2.4.2 Component constant amplitude S-N curve, component fatigue life curve derived by the consistent version of Miner's rule, and influence of the critical damage sum DM . Highest amplitude in stress spectrum SBK , component fatigue limit SAl(, number ofcycles N after the component constant amplitude S-N curve, ~mber ofcycles N aft3the com.£?nent fatigue life curve for DM < 1 or N * for DM = 1. Itis N = N + (N *- N) . DM. This formula implies that a number ofcycles N -7 N isobtained for se:.ctra ofincreasing damage potential and the exact nu~er of cycles N = N for the constant amplitude stress spectrum as N * - N-7 O. In German the fatigue life curve is usually termed 'Gassner curve' and the constant amplitude SoN curve is usually termed 'Woehler curve'.
Rod-shaped (10) and shell-shaped (2D) components are to be distinguished. Rod-shaped (1D) components The amplitudes of the component variable amplitude fatigue strength (highest amplitude in stress spectrum) of rod-shaped (lD) components for axial stress, bending stress, shear stress and for torsional stress are, Figure 2.4.2, SBl<,zd = KSK,zd . SAK,zd, SSK,b = KSK,b . SAK,b, TSK,s = KsK,s . TAK,s , TSK,t = KSK,t . TAK,t ,
(2.4.41)
KSK,zd, ... variable amplitude fatigue strength factor, Chapter 2.4.3.1, SAK,zd ... component fatigue limit, Chapter 2.4.2.
Figure 2.4.3 Restriction of the amplitudes of the variable amplitude fatigue strength, SBK,I , or of the maximum value Sm + SBK and the minimum value Sm - SBK respectively, in relation to the yield strength, displayed in terms of the Haigh-diagram.
Except for GG, the following restrictions apply, Figure 2.4.3: SSK,zd s 0,75 Rp, SSK,b s 0,75 Rp' Kp,b, TsK,s s 0,75 fW,"t . Rp , TSK,t ~0,75 f"t' Rp' Kp,t,
(2.4.42)
1 Required total number ofcycles and required component fatigue life are corresponding denotations.
a simplified manner the variable amplitude fatigue strength can be derived on the basis ofa damage-equivalent stress amplitude. Then the assessment ofthe variable amplitude fatigue strength turns out to be an assessment ofthe fatigue limit being sufficient.
2 In
2.4 Component fatigue strength 2.4.3 Component variable amplitude fatigue strength
The amplitudes of the component variable fatigue strength (highest amplitude in stress of shell-shaped (2D) components for normal the directions x and y as well as for shear Figure 2.4.2,
amplitude spectrum) stresses in stress are,
(2.4.43)
KBI<,x" ... variable amplitude fatigue strength factor, Chapter 2.4.3.1, SAK,x, ... component fatigue limit, Chapter 2.4.2. Except for GG, the following restrictions apply, Figure 2.4.3, SBK,x s 0,75 Rp , SBK,y ::; 0,75 Rp , TBK,s ::; 0,75 fw,'t . Rp ,
Rp fw.'t
2 Assessment of the fatigue strength using nominal stresses
ka
Shell-shaped (2D) components
SBK,x = KBK,x . SAK,x, SBK,y = KBK,y . SAK,y , TBK,s = KBI<,s . TAK ,
64
(2.4.44)
yield strength, Chapter 1.2.1.1, shear strength factor, Table 1.2.5.
2.4.3.1 Variable amplitude fatigue strength factor The variable amplitude fatigue strength KBK,zd , ... , are to be derived as follows *3:
factors
Calculation for a constant amplitude spectrum
*4
Component constant amplitude S-N curve model I: horizontalfor N > ND,cr (steel and cast iron material)
slope of the component constant amplitude S-N curve for N < No,cr , Chapter 2.4.3.2. NO,cr,II number of cycles at second knee point of the component constant amplitude S-N curve, Chapter 2.4.3.2, ko,cr slope of the component constant amplitude S-N curve for N > No,cr , Chapter 2.4.3.2, f n.e factor by which the endurance limit is lower than the fatigue limit, Chapter 2.4.3.2, Table 2.4.4.
Calculation for a variable amplitude spectrum As a rule the variable amplitude fatigue strength factor is to be computed by using the elementary version of Miner's rule (not necessary for a constant amplitude stress spectrum). Somewhat more favourable results, however, may be obtained by using the consistent version of Miner's rule. Moreover, the classes of utilization can be applied as a simplified method of calculation; the so derived results approximately correspond to those obtained by the elementary version of Miner's rule. In an even more simplified manner the variable amplitude fatigue strength can be derived on the basis of a damage-equivalent stress amplitude.
Elementary version of Miner's rule based on the damage potential Using the elementary version of Miner's rule, Figure 2.4.4, the variable amplitude fatigue strength factor is to be computed directly as follows *5. The calculation applies to both component constant amplitude S-Ncurve model I and model II (2.4.53)
Assessment ofthe fatigue strength for finite life: KBK,zd = (N o.e / N) l/k cr
forN ::; No,cr .
(2.4.47)
Assessment ofthe fatigue limit = endurance limit: KBK,zd = 1
forN > No,cr.
KBK,zd = [(
1 cr -I).D + 1] k~ . ( N~cr ) :0 , N
(v zd)
M
where the damage potential is *6 *7
(2.4.48)
Component constant amplitude S-N curve model II: slopingfor N > ND,cr (non-welded aluminum alloys)
k
)kcr
'"j h i (S a,zd,i Vzd-_ k cr L.=-' -. i=l H Sa,zd,l
l
(2.4.54)
,
Assessment ofthe fatigue strength for finite life: KBK,zd = (N O,cr / N) l/k cr
for N'< No,cr.
(2.4.49)
KBK,zd = (N O,cr / N) l/kO,cr for No,cr
k", ... , but applies to
(2.4.50)
3 The following is written for axial stress, other types of stress accordingly.
(2.4.51)
4 For welded components only model I of the component constant amplitude SoN curve is of concern, not model II.
KBK.zd ,
Assessment ofthe fatigue limit: KBK,zd = 1
forN > No,cr.
Assessment ofthe endurance limit: KBK,zd = f n,e N
forN > NO,cr,II. (2.4.52)
number of cycles of the component constant amplitude S-N curve, Chapter 2.4.3.2, N required number of cycles, No,cr number of cycles at knee point of the component constant amplitude S-N curve, Chapter 2.4.3.2,
5 Direct calculation without iteration. The results obtained from the elementary version of Miner's rule approach the results obtained from the consistent version of Miner's rule on the safe side. 6 When computing the damage potential (and also in the following equations) the values ni and N according to the required total number of cycles can be replaced by the values hi and H according to the total number of cycles in the given standard type spectrum, see Chapter 2.1. 7 Instead of Alcon after Eq. (2.4.58) is here A
ele
= 11
(v zd)kcr
(2.4.55)
2.4 Component fatigue strength 2.4.3 Component variable amplitude fatigue strength
slope of the component constant amplitude S-N curve for N < ND,cr , Chapter 2.4.3.2, DM critical damage sum, Table 2.4.3, ND,cr number of cycles at knee point of the component constant amplitude S-N curve, Chapter 2.4.3.2, total number of cycles of the given spectrum, H H = H, = L hi (summed up for i = 1 toj), related number of cycles in step i, h·1 Hi = L hi (summed up for i = 1 to i) *8, total number of steps in the spectrum, j number of the step in the spectrum, Sa,zd,i stress amplitude in step i of the spectrum, Sa,zd,l stress amplitude in step i = 1 of the spectrum. If for a component constant amplitude S-N curve model I (horizontal for N > ND,cr ) a value KBK,zd < 1 is
obtained from Eq. (2.4.53), then the value to be used is KBK,zd = 1.
65
2 Assessment of the fatigue strength using nominal stresses Calculation according to the consistent version of Miner's rule *9 *10 Using the consistent version of Miner's rule the variable amplitude fatigue strength factor is to be computes! iteratively for differing values of Sa,zd,l , until a value N equal to the required total number of cycles N is obtained. The respective value of Sa,zd,l is used to derive the variable amplitude fatigue strength factor.
Component constant amplitude S-N curve model I: horizontal/or N > ND,u (Steel and cast iron material) In case of a component constant amplitude S-N curve model I ( horizontal for N > ND,cr or slope kD,o = (0) the number of cycles N to be computed for an value Sa,zd,l is (2.4.57)
s
N = {[ Akon - 1 ] . DM + I}' SAK,zd
(2.4.56)
If for a component constant amplitude S-N curve model II (sloping for N > ND,cr ) a value KBK,zd is obtained
[
. ND,cr ,
a,zd,l
where
from Eq. (2.4.53) that is smaller than the value obtained from Eq. (2.4.50) or (2.4.52), then the higher value from Eq. (2.4.50) or (2.4.52) is to be used.
Sa,zd,l )k Ak -_ [ on SAK,zd Zl =
sa Z2 =
~AK'Zd
[ a,zd,l )
cr-1 .
[ZI j Z2] -+ L Nl v=m N2
)k cr-1 kcr- 1 [S _ Sa,zd,m ,
[~a,zd'v )k
v,Sa.l
cr-1
h. [S
Stress spectrum
d.i )k
v h. S . N2=L -.:. ~ i=l H [ Sa,zd,l )
N (lg)
(2.4.58)
(2.4.59)
a.zd.l
_ [S;,Zd,V+1 )k a,zd,l a,zd,l cr m-1 Nl= L -.: ~ ~ i=l H Sa,zd,l
(lg)
2:U
)kcr
cr-1 (2.4.60)
(2.4.61)
kcr (2.4.62)
Figure 2.4.4 Elementary version of Miner's rule, component constant amplitude S-N curve model I, DM = 1.
For the summation of the term Z2, Eq. (2.4.60), it is to be observed that Sa,zd,j+l = O.
Characteristics ofthe stress spectrum according toChapter 2.1, component constant amplitude SoN curve according toChapter 2.4.3.2.
N
Table 2.4.3 Critical damage sum DM , recommended value.
Steel, GS, Aluminum alloys GGG, GT, GG
non-welded components 0,3
welded components 0,5
1,0
1,0
8 hi / H may be replaced by n, / N , N Required total number ofcycles according to the required fatigue life, N = ~ ni (summed up for 1toj), nj number ofcycles instep i according tothe required fatigue life.
number of cycles of the component constant amplitude S-N curve, Chapter 2.4.3.2, ND,cr number of cycles at knee point of the component constant amplitude S-N curve, Chapter 2.4.3.2, DM critical damage sum, Table 2.4.3, Sa,zd,i stress amplitude in step i of the spectrum, Sa,zd,l stress amplitude in step i = 1 of the spectrum, SAK,zd amplitude of the component fatigue limit, ka slope of the component constant amplitude S-N curve for N < ND,cr , Chapter 2.4.3.2, j total number of steps in the spectrum,
9 The consistent version of Miner's rule allows for the fact, that the component fatigue limit will decrease as the damage sum increases. The decrease applies tocomponent constant amplitude S-N curves model I as well as tomodel II for ND,s ~ 106 . 10 The consistent version ofMiner's rule was first developed by Haibach. A simplified version allowing for the decrease ofthe fatigue limit became
known as the modified version orthe Haibach method ofMiner's rule.
2.4 Component fatigue strength 2.4.3 Component variable amplitude fatigue strength i m H
number of the step in the spectrum, number i = m of the first step below SAK,zd, total number of cycles in the given spectrum, H = Hj = L hi (summed up for I to j), number of cycles in step i, Hi = L hi (summed up for I to i) "8.
hi
The computation is to be repeated iteratively for differing values Sa,zd,1 > SAK,zd , until a..!alue N equal to the required total number of cycles N is obtained. From the respective value of Sa,zd,1 the variable amplitude fatigue strength factor is obtained as
66
2 Assessment of the fatigue strength using nominal stresses Calculation using a class of utilization The variable amplitude fatigue strength factor KBK,zd is to be determined according to the appropriate class of utilization "12 , Chapter 5.7.
Calculation amplitude
using
a
damage-equivalent
When using a damage-equivalent stress amplitude the variable amplitude fatigue strength factor for both constant amplitude S-N curves model I and model II is KBK,zd = 1.
If a value KBK,zd < I is obtained from Eq. (2.4.63), then the value to be applied is
= 1.
(2.4.64)
Component constant amplitude S-N curve model II: slopingfor N > N D, 0' (non-welded aluminum alloys) *11
In case of a component constant amplitude S-N curve model II (sloping for N > ND,O' or slope kD,a < kD,a < (0) the number of cycles N is first to be computed for a . ' 1/3 smgle value Sa,zd,1 = SAK,zd / (fn,O' ) as follows O
N={[A
kon
-1]'D +1}.[SAK'Zd)k M S a.zd.l
with
Akon fn,O'
f
ND,a
( II a
)kal3
(2.4.65) after Eq. (2.4.58) to (2.4.62) and the explanations as before, factor by which the endurance limit is lower than the fatigue limit, Table 2.4.4.
If a value N = N* > N is obtained then the calculation of N, Eq. (2.4.65), is to be continued for differing values Sa,zd,1 > SAK,zd / ( fn,O' )1/3 until a value N equal to the required total number of cycles N is obtained. From the respective value of Sa,zd,1 the variable amplitude fatigue strength factor is obtained as KBK,zd
(2.4.69)
(2.4.63)
KBI<,zd = Sa,zd,1 / SAK,zd.
KBK,zd
stress
= Sa,zd,1 . (fn,O' )1/3 / SAK,zd
(2.4.66)
2.4.3.2 Component constant amplitude S-N curve Component constant amplitude S-N curves for nonwelded components (without surface hardening) and for welded components *13 are shown for normal stress and for shear stress in Figure 2.4.5 and 2.4.6. The particular number of cycles at the knee point ND,O' , ... and the values of slope ka, ... are given in Table 2.4.4. The component fatigue limit SAK,zd, ... is the reference fatigue strength value for calculation. It follows from Chapter 2.4.2. For S-N curves Model I the fatigue limit SAK and the endurance limit SAK,n for N = 00 are identical, while for S-N curves Model II (valid for nonwelded components of austenitic steel or of aluminum alloys) they are different by a factor fn,O' , Table 2.4.4 and Figure 2.4.5.
A lower boundary of the numbers of cycles is implicitly defined by the maximum stress being limited according to the static strength requirements, Chapter 1. For surface hardened components "14 the slope of the component constant amplitude S-N curves is more shallow. Instead of the values of slope kO' = 5 and k, = 8 for not surface hardened components, Table 2.4.4, the values that apply to surface hardened components are ka = 15 and k, = 25 ,while the number of cycles at the knee point ND,O' and ND,'t remain unchanged, see also Chapter 5.8. The component constant amplitude S-N curves for welded components are valid for the toe section and for the throat section.
If a value N = N* ~ N is obtained then the variable amplitude fatigue strength factor is (4.4.67) If a value KBK,zd < fn,O' is obtained from Eq. (2.4.67) then the value to be applied is KBK,zd = fn,O' .
(2.4.68)
II Simplified and approximate calculation. 12 Class of utilization as a characteristic of the stress spectrum. It is an approximately dam~e equivalent combination of the required total number of cycles N with the shape of a particular standard stress spectrum the frequency distribution of which is of binomial or exponential type modified by a spectrum parameter p. It provides a result that corresponds to a calculation based on the elementary version of Miner's rule.
13 With reference to nW-Recommendations and Eurocode 3.
14 Not applicable to cold rolled or shot-peened components.
2.4 Component fatigue strength 2.4.3 Component variable amplitude fatigue strength
67
2 Assessment of the fatigue strength using nominal stresses
Table 2.4.4 Number of cycles at the knee point, slope of the component constant amplitude S-N curves, and values of fu,o- and fu,t. Normal stress Component
Shear stress IND,o-
IND,o-,II Ik, IkD,o-
fu,o-
Steel and cast iron materials ( S-N curve model I ) 6 non-welded 1,0 110 115 115 ' 106 11,0 welded 13 1Aluminum alloys (S-N curve modell II non-welded 110 6 1108 0,74 15 115 6 welded 1,0 15' 10 113 1-
Component
IND,t
1
ND,t,ll
Ik, IkD;t
fu,t
Steel and cast iron materials (S-N curve model I) 6 1,0 non-welded 110 118 18 1,0 welded 110 115 1Aluminum alloys (S-N curve model II \ 6 8 non-welded 10,83 110 110 18 125 8 welded 11,0 115 1110
Sa,zd
(lg)
(Ig)
SAK,zdf--------~"-~---- II SAK.zd.IlI-----------t- ];~~~~",,""_
N (Ig)
ails bildw.
SAC SAK.zd
Nc = 6 2 '10 aila bIJdw12
T a •s
Ta . s
(lg)
(Ig)
TAK.s
+--
I
-----..:c~~-----
NDo-= 5 .'10 6 N (lg)
T AC
II
TAK,s,II 1----------+--.::...'--;~--=~s.."8
aif. bildwl6
TAK.s
Nc= . 06
N (lg) ails bildll'l5
Figure 2.4.5 Component constant amplitude S-N curve for non-welded components *14 Top: Bottom:
Normal stress S. Shear stress T.
Steel and cast iron materials, except austenitic steel, (Model I): horizontal for N > ND,cr, kD,cr = co or for N > ND,"t, k D,"t = co Aluminum alloys and austenitic steel (Model II): Sloping for N > ND cr, kD o» or for N > ND:"t, kD,~. horizontal for N > ND cr II, kD e II = co or for N > ND:"t.it" ' kD:"t:II= co.
ND'7 8 =10
N (lg)
Figure 2.4.6 Component constant amplitude S-N curve for welded components *13 Top: Bottom:
Normal stress S. Shear stress T.
Steel, cast iron materials and aluminum alloys, welded (Model I): horizontal for N > ND,cr, kD,cr = co or for N>ND,"t, kD,"t=co NC is the referencenumber of cycles correspondingto the characteristic strength values SAC and TAC. SAK,zd/ SAC = (Nc / ND,cr) 11ko = 0,736 and TAK,s / TAC = (Nc / ND,"t ) 11 kr = 0,457.
68
2.5 Safety factors
2.5 Safety factors
*1
!R25 EN .docl
Contents
Page
2.5.0
General
2.5.1
Steel
2.5.2 2.5.2.0 2.5.2.1 2.5.2.2
Cast iron materials General Ductile cast iron materials Non-ductile cast iron materials
2.5.3 2.5.3.0 2.5.3.1 2.5.3.2
Wrought aluminum alloys General Ductile wrought aluminum alloys Non-ductile wrought aluminum alloys
2.5.4
Cast aluminum alloys
2.5.5
Total safety factor
68
2 Assessment of the fatigue strength using nominal stresses
2.5.2 Cast iron materials 2.5.2.0 General Ductile and non-ductile cast tron materials are to be distinguished.
2.5.2.1 Ductile cast iron materials 69
Cast iron material with an elongation As :2: 12,5 % are considered as ductile cast iron materials, in particular all types of GS and some types of GGG. Values of elongation see Table 5.1.12. Safety factors for ductile cast iron materials are given in Table 2.5.2. Compared to Table 2.5.1 they are higher because of an additional partial safety factor jF that accounts for inevitable but allowable defects in castings *4. The factor is different for severe or moderate consequences of failure and moreover for castings that have been subject to non-destructive testing or have not.
2.5.0 General According to this chapter the safety factors are to be determined.
Table 2.5.2 Safety factors for ductile cast iron materials GS; GGG) (A,:2: 12,5%\
The safety factors are valid under the condition that the design loads are reliably determined on the safe side and that the material properties correspond to an average probability of survival of Po = 97,5 % *2.
JD
Consequences of failure severe moderatev!
I
castings not subject to non-destructive testing ~2 regular no 2,1 I 1,8 yes ~3 Inspection 1,9 I 1,7
The safety factors apply both to non-welded and welded components.
castings subject to non-destructive testing ~4 regular no 1,9 I 1,65 yes ~3 Inspection 1,7 I 1,5
2.5.1 Steel The basic safety factor concerning the fatigue strength
~1
See footnote
~1
of Table 2.5.1.
'IS
(2.5.1)
~2 Compared to Table 2.5.1 an additional partial safety factor jF = 1,4 is introduced to account for inevitable but allowable defects in castings.
This value may be reduced under favorable conditions, that is depending on the possibilities of inspection and on the consequences of failure, Table 2.5.1.
~3 Regular inspection in the sense of damage monitoring. Reduction by about 10 %.
.in = 1,5.
Compared to Table 2.5.1 an additional partial safety factor 1,25 is introduced, for which it is assumed that a higher quality of the castings is obviously guaranteed when testing. ~4
jF Table 2.5.1 Safety factors for steel *3 (not for GS) and for ductile wrought aluminum alloys (A:2: 12,5 %). Consequences of failure moderate ~1 severe
jD regular inspections
=
no
1,5
yes~2
1,35
1,3 1,2
~1
Moderate consequences of failure of a less important component in the sense of "non catastrophic" effects of a failure; for example because of a load redistribution towards other members of a statical indeterminate system. Reduction by about 15 %. ~2 Regular inspection in the sense of damage monitoring. Reduction by about 10 %.
1 Chapters 2.5 and 4.5 are identical.
2 Statistical confidenceS ; 50 %. 3 Steel is always considered as a ductile material. 4 In mechanical engineering cast. components are of standard quality for which a further reduction of the partial safety factor to jF = 1,0 does not seem possible up to now. A safety factor jF = 1,0 may be applied to high quality cast components in the aircraft industry however. Those high quality cast components have to meet special demands on qualification and checks of the production process, as well as on the extent of quality and product testing in order to guarantee little scatter of their mechanical properties.
69
2.5 Safety factors
2 Assessment of the fatigue strength using nominal stresses
2.5.2.2 Non-ductile cast iron materials
2.5.3.2 Non-ductile wrought aluminum alloy
Cast iron materials with an elongation AS < 12,5 % (for GT A3 < 12,5 %) are considered as non-ductile materials, in particular some types of GGG as well as all types of GT and GG. Values of elongation for GGG and GT see Table 5.1.12 or 5.1.13. The value for GG is AS = O.
Wrought aluminum alloys with an elongation A < 12,5 % are considered as non-ductile materials. Values of elongation see Table 5.1.22 to 5.1.30.
For non-ductile cast iron materials the safety factors from Table 2.5.2 are to be increased by adding a value Llj, Figure 2.5.1 *s: Llj
= 0,5
-JAs /50%,
(2.5.2)
AS Elongation, to be replaced by A3 for GT.
For non-ductile wrought aluminum alloys all safety factors from Table 2.5.1 are to be increased by adding a value Llj , Eq. (2.5.2).
2.5.4 Cast aluminum alloys Cast aluminum alloys are always considered as nonductile materials. All safety factors from Table 2.5.2 are to be increased by adding a value Llj , Eq. (2.5.2). Values of elongation see Table 5.1. 31 to 5.1. 38.
GG 0,5
2.5.5 Total safety factor
Llj
o
1U 12,5
Similar to an assessment of the component static strength, Chapter 1.5.5, a "total safety factor" jges is to be derived: 20 As ,A3 in %
jges =
Figure 2.5.1 Value Llj to be added to the safety factor In , defined as a function of the elongation As or A3 , respectively.
2.5.3 Wrought aluminum alloys 2.5.3.0 (;eneral Ductile and non-ductile wrought aluminum alloys are to be distinguished.
2.5.3.1 Ductile wrought aluminum alloys Wrought aluminum alloys with an elongation A"C. 12,5 % are considered as ductile materials. Values of elongation see Table 5.1.22 to 5.1.30. Safety factors for ductile wrought aluminum alloys are the same as for steel according to Table 2.5.1.
S For example the safety factor for GG is at least
in Gn
= I,S
+ O,S
= 2,0
(2.S.3)
= 1,5 from Table 2.5.2, j = O,S after Eq. (2.S.2) for AS = 0).
Jn Kt,D
i
D
,
(2.5.4)
T,D
safety factor, Table 2.5.1 or 2.5.2, temperature factor, Chapter 2.2.3.
70
2.6 Assessment
2.6 Assessment Contents
2 Assessment of the fatigue strength using nominal stresses
1R26
EN.dog Page
2.6.0
General
70
2.6.1 2.6.1.1 2.6.1.2
Rod-shaped (lD) components Individual types of stress Combined types of stress
71
2.6.2 2.6.2.1 2.6.2.2
Shell-shaped (2D) components Individual types of stress Combined types of stress
An assessment of the variable amplitude fatigue strength and an assessment of the fatigue limit or of the endurance limit are to be distinguished. In each case the calculation is the same when using the appropriate variable amplitude fatigue strength factor KBK,zd , ... , Chapter 2.4.3, and when taking
(2.6.1)
Sa,zd, I = Sa,zd , ... , in case of a constant amplitude spectrum, or 72
2.6.0 General According to this chapter the assessment of the fatigue strength using nominal stresses is to be carried out. In general the assessments for the individual types of stress and for the combined types of stress are to be carried out separately *1. The procedure of assessment applies to both non-welded and welded components. For welded components assessments are generally to be carried out separately for the toe section and for the throat section. They are to be carried out in the same way, but using the respective cross-section values, nominal stresses and fatigue classes FAT as these are in general different for the toe and throat section.
Sa,zd,l
~
Sa,zd,eff
and
N
=
ND,cr
(2.6.2)
in case of a damage-equivalent stress amplitude. Sa,zd, ... ,
constant stress amplitude for which the required number of cycles is N, Sa,zd,eff, ... , damage-equivalent stress amplitude, ND,cr number of cycles at knee point of the component constant amplitude S-N curve, Chapter 2.4.3.2.
Superposition For proportional or synchronous stress components of same type of stress the superposition is to be carried out according to Chapter 2.1. If different types of stress like axial stress,· bending stress, ... *4 act simultaneously and if the resulting stress
is multiaxial, Chapter 0.3.5 and Figure 0.0.9, both the individual types of stress and the combined types of stress are to be considered as described below *5.
Degree of utilization The assessment is to be carried out by determining the degree of utilization of the component fatigue strength. In the general context of the present Chapter the degree of utilization is the quotient of the (nominal) characteristic stress amplitude Sa,zd,l , ..., divided by the allowable (nominal) stress amplitude of the component fatigue strength at the reference point *2. The allowable stress amplitude is the quotient of the component variable amplitude fatigue strength after Chapter 2.4.3, SBI<,zd, ... , divided by the total safety factor jges . The degree of utilization is always a positive value *3.
Kinds of component Rod-shaped (lD) and shell-shaped (2D) components are to be distinguished. They can be both non-welded or welded.
4 Bending stresses intwo planes, Sa,b,y and Sa,b,z ' are different types of stress, also shear stresses in two planes, T a,s,y and T a.s.z . 5 Proportional, synchronous and non-proportional multiaxial stresses are tobe distinguished. , Chapter 0.3.5.
Only under special conditions ofproportional stresses the character ofEq. and (2.6.12) is that of a strength hypothesis from a materialmechanics point ofview. For example the extreme stresses from bending and shear will . as a rule - occur atdifferent points ofthe cross-section, so that different reference points W are to be considered. As a rule bending will be more important. More general Eq. (2.6.4) and (2.6.12) have the character of an empirical interaction formula. They are applicable for proportional stresses and approximately applicable for synchronous stresses; an improved procedure for non-welded components is given in Chapter 5.9. For non-proportional stresses they are not suitable; an approximate procedure applicable for non-proportional stresses is proposed in Chapter 5.10. (2.6.4)
1 It is essential to examine the degree of utilization not only of the combined types ofstress but also that ofthe individual types ofstress in general, and inparticular ifthese may occur separately. 2 The reference point is the critical point ofthe considered cross-section that observes the highest degree ofutilization.
the degree of utilization is the quotient of two amplitude which always are positive.
3 As
71
2.6 Assessment
2 Assessment of the fatigue strength using nominal stresses Table 2.6.1 Values of q as dependent on f W •t ~1
2.6.1 Rod-shaped (ID) components 2.6.1.1 Individual types of stress
The degrees of utilization of rod-shaped (lD) components for variable amplitude types of stress like axial, bending. shear and torsional stress are
fWt Q
aSK,zd
aSK,b
aSK,s
aSK.t =
Sa,zd,l
:5: 1,
(2.6.3)
SBK,Zd / jerf Sa,b,l SBK,b / i, T a.s, 1
GT, cast AI alloys 0,75 0,544
GG
0,85 0,759
Exceptions: For non-ductile wrought aluminum alloys (elongation q = 0,5 , for surface hardened or welded components
A < 12,5 %) q = 1.
:5: 1,
:5: 1,
TBK,s / jerf Ta,!,l
~1
Steel. GGG wrought AI alloys 0.577 0.65 0 0,264
:5: 1.
TBK,t / jerf
Sa,zd,1 • ...• characteristic stress amplitude (largest stress amplitude in the spectrum) according to type of stress. Chapter 2.1.1.1 and Eq. (2.6.1) or (2.6.2), SSK,zd •... , related amplitude of the component variable amplitude fatigue strength, Chapter 2.4.3. jges total safety factor, Chapter 2.5.5.
Rules of signs: If the individual types of stress (axial and bending, or shear and torsion, respectively) always act proportional or synchronous in phase the degrees of utilization aSK,zd and aSK,b and/or aSK,s and aSK,t are to be inserted in Eq. (2.6.6) with the same (positive) signs *7. If they act always proportional or synchronous 1800 out of phase, however. the above degrees of utilization are to be inserted in Eq. (2.6.6) with oposite signs *8 *9. If the individual types of stresses act non-proportional, that is neither proportional nor synchronous, the Eq. (2.6.4) to (2.6.6) are not applicable and the procedure proposed in Chapter 5.10 is to be applied instead.
2.6.2 Shell-shaped (2D) components 2.6.2.1 Individual types of stress
2.6.1.2 Combined types of stress
The degree of utilization of rod-shaped components for combined types of stress is *6 aSK,Sv = q' aNH + (1 - q) .
(lD)
The degrees of utilization of shell-shaped (2D) components for variable amplitude types of stress like normal stresses in the directions x and y as well as shear are
(2.6.4) asK,x =
where
aNH=1-(lsal+~s; +4.t;),
:5: 1,
(2.6.8)
SBK,X / jerf (2.6.5) aSK,y =
s.,
(2.6.6)
ta = aSK,s + aSK,t •
aSK,s
Sa,y,l
:5: 1.
SBK,y / jerf Ta,l
:5: 1.
T BK / jerf
aSK,zd,'" degrees of utilization after Eq. (2.6.3). For non-ductile wrought aluminum alloys (elongation A < 12.5 %) q = 0,5 is to be applied. For surface hardened or for welded components q = 1 is to be applied. Otherwise there is, Table 2.6.1.
q
fw,'t
./3 -(l/fw.'t) ./3-1
(2.6.7)
shear fatigue strength factor, Table 2.2.1 or 2.6.1.
6 Eq. (2.6.4) or (2.6.12) isa combination ofthe normal stress criterion (NH) and the v. Mises criterion (GH). Depending on the ductility ofthe material the combination is controlled by a parameter q as a function of tW,t according toEq. (2.6.7) and Table 2.6.1. For instance q = 0 for steel so that only the v. Mises criterion isofeffect, while q = 0,264 for GGG so that both the normal stress criterion and the v. Mises criterion are of partial influence. 7 For example a tensile axial stress and a tensile bending stress acting at the reference point that both result from the sam single external load affecting the component. 8For example an tensile axial stress and a compressive bending stress acting atthe reference point that both result from the sam single external load affecting the component. 9 Stress components acting opposingly may cancel each other inpart or completely.
72
2 Assessment of the fatigue strength using nominal stresses
2.6 Assessment
Sa,x,1 , ..., characteristic stress amplitude (largest stress amplitude in the spectrum) according to type of stress, Chapter 2.1.1.2 and Eq. (2.6.1) or (2.6.2), SB!(,x, ..., related amplitude of the component variable amplitude fatigue strength, Chapter2.4.3, jges total safety factor, Chapter 2.5.5.
2.6.1.2 Combined types of stress The degree of utilization of shell-shaped components for combined types of stresses is *7 aBK,Sv = q . aNH + (1 - q) . 1lGH:::; 1, where
(2D)
(2.6.9) (2.6.10)
aNH
=~{Isa,x +sa,yl+~~a,x
-Sa,y)2 +4.t; ),
2 2 2 1lGH = sa,x + sa,y - sa,x . sa,y + t a '
J
(2.6.11)
sa,x = aBK,x , Sa,y = aBK,y , t a = aBK,s, aBK,x ...
degrees
of utilization after Eq.
(2.6.8).
For non-ductile wrought aluminum alloys (elongation A < 12,5 %) q = 0,5 is to be applied. For surface hardened or for welded components q = 1 is to be applied. Otherwise there is, Table 2.6.1, q
13 -(lIfw,'t) 13-1
(2.6.12)
fw,'t shear fatigue strength factor, Table 2.2.1 or 2.6.1. Rules of signs: If the normal stresses Sx and Sy always act proportional or synchronous in phase the degrees of utilization aBK,x and aBK,y are to be inserted in Eq. (2.6.11) with the same (positive) signs *10. If they act always proportional or synchronous 1800 out of phase, however, the degrees of utilization aBK,x and aBK,y are to be inserted in Eq. (2.6.11) with oposite signs *11. If the individual types of stress act non-proportional, that is neither proportional nor synchronous, the Eq. (2.6.9) to (2.6.11) are not applicable and the procedure proposed in Chapter 5.10 is to be applied instead.
10 For example a tensile stress in direction x and a tensile stress in directions y that both result from the same external load affecting the component. 11 For example a tensile stress indirection x and a compressive stress in directions y that both result from the same external load affecting the component.
73
3.1 Characteristic stresses
3 Assessment of the static strength using local stresses
3 Assessment of the static strength using local stresses maximum and mirumum stresses can be positive or negative. It is assumed, that all stresses reach their extreme values simultaneously.
IU-1---=EN-'-.-'-do-'q
r-I
Elevated temperature
3.0 General According to this chapter the assessment of the static strength using local stresses is to be carried out *1. It should be observed that not necessarily the component static strength is determined by a local failure occurring at a notch. Likewise a global failure occurring ata different, unnotched or moderately notched section of the component may be determining, Figure 3.0.1.
F
Figure 3.0.1 Different locations for a static failure occurring as a local failure (A) or as a global failure (B).
3.1 Characteristic stress values Page
3.1.0
General
3.1.1 3.1.1.0 3.1.1.1 3.1.1.2 3.1.1.3
Characteristic stress values General Rod-shaped (ID) components Shell-shaped (2D) components Block-shaped (3D) components
For a long-term loading (related to the creep strength or 1% creep limit) correct results will only be obtained in case of a constant (static) tensile stress O"max,ex equally distributed over the section of concern. In all other cases of constant or variable loading the assessment will be more or less on the safe side if the values O"max,ex , . . . and O"min,ex , ... refer to a stress distribution with a stress gradient, and/or if they refer to the peak values of a variable stress history, which are of short duration only, while for the rest of time the stress is lower.
...-.;.. _._.
Contents
In case of elevated temperature the values O"max,ex , and O"min,ex , . . . are relevant for a short-term loading (related to the high temperature strength or high temperature yield strength).
If in those cases it becomes necessary to make best use
of the long-term load bearing capacity of the component (because otherwise the assessment cannot be achieved) an expert stress analysis is recommended to define the appropriate stress value to be used for the assessment. Such an analysis is beyond the scope of the present guideline, however.
73
Superposition If several stress components act simultaneously at the
74 75
3.1.0 General According to this chapter the characteristic service stress values are to be determined as elastic stresses. Relevant are the extreme maximum and minimum stresses O"max,ex and O"min,ex , ... of the individual stress components expected for the most unfavourable operating conditions and for special loads according to specification or due to physical limits *2. Both the
1 The assessment of the static strength with local stresses based on Neuber's rule and the plastic. limit load, Chapter 3.3, is an approximation that has to be regarded as provisional and therefore it should be applied with caution. Also the assessment of the static strength for welded components using structural stresses has to be regarded as provisional and therefore it is to be applied with caution, as well. 2 In general the values Gmax,ex and Gmin,ex for the assessment of the static strength are the extreme values of a stress history. For the
reference point, they are to be overlaid. For same type of stress (for example normal stress and normal stress, O"max,ex,1 , O"max,ex,2, ... ) the superposition is to be carried out at this stage, so that in the following a single stress value (O"max,ex, ... ) exists for every type of stress *3. For different types of stress (for example normal stress and shear stress, or normal stress in direction x and normal
assessment of the fatigue strength a stress spectrum is to be derived from that history consisting of stress cycles of the amplitudes Ga,i and the mean values Grn,i' Chapter 2. I. The largest amplitude of this stress spectrum is Ga,1 ' and the related mean value is Grn,1 . The related maximum and minimum values are Gmax,1 = Grn,1 + Ga,1 and Gmin,1 = Grn,1 - Ga,1 . The values Gmax,e.x and Gmin,ex may be different from the .values Gmax,1 .and Gmin, 1 . This is because extreme, very seldom occunng events are Important only for the assessment of the static strength, but hardly for the assessment of the fatigue strength. In a stress spectrum which is supposed to apply for normal service conditions they do not have to be considered therefore. 3 Stress components having different sign may cancel out each other in part or completely.
74
3.1 Characteristic stresses
stress in direction y) the superposition is to be carried out at the assessment stage, Chapter 3.6. Stress components acting opposed to each other, and which do not always occur simultaneously, are not to be overlaid however.
3 Assessment of the static strength using local stresses
/ t~·· /-
3.1.1 Characteristic stress values 3.1.1.0 General Rod-shaped (lD), shell-shaped (2D) and block-shaped (3D) as well as non-welded and welded components are to be distinguished. For welded components the local stresses are _to be 'determined as structural stresses. An assessment of the 'stailc-stiength'- ()fwelcleclcomponents using effective notch stresses is not possible up to now *4. When using local stresses it is not necessary that a well defined cross-section does exist. Hence it cannot be presupposed that nominal stresses can be determined as well.
Left: Butt weld. Right: Fillet weld. The structural stress is to be computed
with the throat thickness a.
Rod-shaped (ID) welded components For rod-shaped (I D) welded components the local stresses (structural stresses only) are generally to be determined for the weld toe and for the root of the weld separately *7. For the weld toe the local stresses are to be computed as for non-welded components, Eq. (3.1.1).. For the root of the weld equivalent structural stresses have to be computed from the structural stresses resulting from the normal and shear loadings, Figure
3.1.1.1 Rod-shaped (ID) components Rod-shapedHD) non-welded components For rod-shaped (ID) non-welded components a normal stress O'zd = 0' and a shear stress ". =" are to be considered *5. The extreme maximum and minimum stresses are
3.1.1, *8 (3.1.2) O'.L
O'max,ex , "max,ex ,
(3.1.1)
O'min,ex , "min,ex .
Stresses of different sign (O'max,ex positive, O'min,ex negative for instance) are generally to be considered separately *6. For shear and for torsion the highest absolute value is relevant.
".l "II
"wv
normal stress normal to the weld seam shear stress normal to the weld seam, shear stress parallel to the weld seam.
*9,
in analogy.
The extreme maximum and muumum values of the equivalent nominal stresses are O'max,ex,wv
and
O'min,ex,wv, ....
(3.1.3)
Stresses of different sign (O'max,ex,wv positive, O'min,ex,wv negative for instance) are generally to be considered separately. For shear and for torsion the highest absolute value is relevant.
4 See Figure 0.0.6 and 0.0.7 for definition of structural stresses and of effective notch stresses. For effective notch stresses the assessment procedure has not been developed up to now. 5 For rod-shaped (ID) components the different types of stress (axial, bending, shear and/or torsion) may also occur independent of each other. This case is not considered in the following, however, as it is supposed that (J will contain all normal stresses and t will contain all shear stresses. 6 Particularly in the case of cast iron materials with different tension and compression strength values, and moreover because of the non-linearelastic stress-strain characteristic of grey cast iron.
7 For welded components in general an assessment of the static strength is to be carried out for the toe section and for the throat section, because the cross-sectional areas may be different and because the strength behavior is evaluated in a different way. The assessment for the toe section is to be carried out as for non-welded components. The assessment for the throat section is to be carried out with the equivalent structural stress (Jwv. 8 According to DIN 18 800 part 1, page 36. The structural stress (JII (normal stress parallel to the orientation ofthe weld) is to be neglected. 9 Normally (Jwv will result mainly from (J.l. 'twv in analogy.
75
3.1 Characteristic stresses
3 Assessment of the static strength
using local stresses 3.1.1.2 Shell-shaped (2D) components
The calculation for shell-shaped (2D) components can be applied also for block-shaped (3D) components, if the stresses O"x, O"y, 't at the surface are of interest only, otherwise Chapter 3.1.1.3 applies.
(3.1.6)
Note: Independent of the value of the stresses the directions of the stresses
Shell-shaped (2D) non-welded components For shell-shaped (2D) non-welded components normal stresses in the x- and y-directions O"zd,x = o, and O"zd,y= O"y as well as a shear stress "ts = r are to be considered. The extreme maximum and minimum stresses are O"rnax.ex.x , O"rnax.ex.y , "trnax.ex , O"rnin,ex.x , O"rnin,ex.y , 'trnin,ex .
(3.1.4)
Tension stresses (positive) or compression stresses (negative) are generally to be considered separately *10 . For shear the highest absolute value is relevant.
Block-shaped (3D) welded components For certain applications block-shaped (3D) components may be welded at the surface, for example by surfacing welds. Then the calculation is to be carried out as for shell-shaped (2D) welded components, if the stresses at the surface,
Shell-shaped (2D) welded components For shell-shaped (2D) welded components, Figure 0.0.6, the local stresses (structural stresses only) are in general to be determined separately for the weld toe and for the root of the weld *7. For the weld toe the local stresses are to be computed as for non-welded components, Eq. (3.1.4). For the root of the weld an equivalent structural stresses, O"wv,x , has to be computed from the structural stresses resulting from the loading in x-direction, Eq. (3.1.2) and Figure 3.1.1. Stresses O"wv,y and"twv in analogy. The extreme maximum and minimum values of the equivalent stresses are O"max,ex,wv,x and O"min,ex,wv,y, ...
(3.1.5)
Stresses of different sign (
3.1.1.3 Block-shaped (3D) components
Block-shaped (3D) non-welded components For block-shaped (3D) non-welded components the principal stresses
10 See footnote *6. And moreover because the second normal stress 0y may reduce the degree ofutilization.
11 See footnote *6. An moreover because the second and/or third principle stress 0zand 03 may reduce the degree ofutilization.
3.2 Material properties
3.2 Material properties
1R32 EN.dog
Contents 3.2.0
General
Page 76
3.2.1 Component values according to standards 3.2.1.0 General 3.2.1.1 Component values according to standards of semi-finished products or test pieces 3.2.1.2 Component values according to the drawing 3.2.1.3 Special case of actual component values
77
3.2.2 3.2.2.0 3.2.2.1 3.2.2.2
Technological size factor General Dependence on the effective diameter Effective diameter
78
3.2.3
Anisotropy factor
80
Compression strength factor and shear strength factor 3.2.4.0 General 3.2.4.1 Compression strength factor 3.2.4.2 Shear strength factor
3 Assessment of the static strength using nominal stresses
76
Rm,N Values according to standards Component values -
3.2.4
3.2.5 3.2.5.0 3.2.5.1 3.2.5.2 3.2.5.3
81
Temperature factors General ~ormal temperature Low temperature Elevated temperature
3.2.0 General
de ff .N
-deff
(Jg)
Figure 3.2.1 Values according to standards and component values according to standards, Rm and Rp, or values specified by drawings, Rm,z and Rp,Z . Top: All kinds of material except GG, Rm ::: Rm.N, R" ::: R",N Semi-logarithmic decrease of the mechanical material properties with the effective diameter d.n- . Bottom: GG, Rm ::: or ~ Rm.N . Double-logarithmic decrease of the mechanical material properties with the effective diameter dell'.
According to this chapter the mechanical material properties like tensile strength R.n, yield strength R, and further characteristics for non-welded and welded' components are to be determined.
Values according to standards
All mechanical material properties are those of the material test specimen. Values according to standards, component values and component values according to standards are to be distinguished, Figure 3.2.1.
The values according to standards (R.n,N , Rm , Rp,N , Rp) correspond to an average probability of survival Po = 97,5 % and depend on the effective diameter deff and on the technological size factor.
Material test specimen
Component values
In the context of this guideline the material test specimen is an unnotched polished round specimen of do = 7,5 mm diameter *1.
The component values CRm , R.n.z , R, , Rp,z ) are valid for the effective diameter deff of the component, they may correspond to different probabilities of survival Po, however.
Specified values according to drawings Rm.z and
R",z.
Special case of actual component values
1 This definition is the basis of the present calculation, although specimens for tensile tests may usually have diameters different from
7,5 mm.
If specific values for a component (R.n,r , Rp,r) have been determined experimentally, they normally apply to a probability of survival Po = 50 % , and therefore they are valid only for the particular component, but not for the entirety of all those components. They may be used, for instance, for a subsequent assessment of the strength
3.2 Material properties
3 Assessment of the static strength using nominal stresses
77
of the particular component in case of a service failure, if for that purpose all safety factors are set to 1,00 in addition.
product *3 , in the case of cast iron or cast aluminum it is the value from the test piece according to the material standard.
Component values according to standards
The yield strength, Rp,N , is the guaranteed minimum value specified for the smallest size of the semi-finished product *3 or for the test piece defined by the material standard *4.
The component values according to standards
3.2.1 Component values according to standards 3.2.1.0 General The component values according to standards,
Rm
and
R, , are to be determined from the values of semifinished products or of test pieces defined by standards, Rm.N and Rp,N , or from the component value specified in the drawing, Rm,z . As a special case the experimentally determined actual component values, Rm.r and Rp,r , can be applied. For GG the yield strength is not defined and Eq. (3.2.1) is not applicable.
3.2.1.1 Component values according to standards of
Moreover there are to be considered: for compressive stresses the compression strength factor fa , Chapter 3.2.4, for shear stresses the shear strength factor f, , Chapter 3.2.4, and for elevated temperature the temperature factors Kt,m , ..., Chapter 3.2.5.
3.2.1.2 Component values according to the drawing The component value of the tensile strength, Rm, is Rm =
0,94 . Rm.z.
(3.2.2)
The component value according to the drawing Rm,z is the tensile· strength of the material specified on the drawing. As the value Rm.z is normally verified by random inspection of small samples only *5, it is assumed to have a probability of survival less than PD= 97,5 % . Eq. (1.2.2) converts the value Rm•z to a component value Rm that is expected to conform with the probability of survival of Pr, = 97,5 %. The yield strength R, corresponding to the tensile strength Rm is *6 .
R, = Kd,p
. Rp,N
Kd,m
Rm,N
. Rm,
(3.2.3)
technological size factors, Chapter 3.2.2, values of the semi-finished product or of a test pieces defined by standards, Chapter 5.1 .
semi-finished products or of test pieces The component values according to standards of the tensile strength, Rm , and of the yield strength, Rp, are Rm = Kd,m . KA ' Rm.N, R, = K
K
Rm.N, Rp.N
(3.2.1)
technological size factors, Chapter 3.2.2, anisotropy factor, Chapter 3.2.3, values of the semi-finished product or of a test piece according to standards, Chapter 5.1 .
In the case of steel or wrought aluminum alloys the tensile strength, Rm.N , is the guaranteed minimum value specified for the smallest size of the semi-finished
2 The term yield strength is used as a generalized tenn for the yield stress (of milled or forged steel as well as cast steel) and for the 0.2 proof stress (of nodular cast iron or malleable cast iron as well as aluminum alloys).
3 If different dimensions of that semi-finished product are given by the standard. 4 A probability of survival Pii = 97,5 % is assumed for the component properties according to standards Rm,N , Rp,N . This probability of survival should also apply to the values Rm ' Rp is calculated therefrom. 5 The value R m Z is checked by three hardness measurements (n=3) for exampl~, where every test has to reach or to exceed the required value. The probability of survival of the lowest of n = 3 tests may be estimated to 75 % (= I - I/(n+ 1) = 1 - 1/(3+1) = 0,75), and may be assigned to R m Z . With a likely coefficient of variation of 4% the conversion to P; = 97,5 % follows from Eq. (3.2.2). 6 A conversion proportional to R p N f R m N would not be correct since the technological size effect is more pronounced for the yield strength than for the tensile strength.
3.2 Material properties
3 Assessment of the static strength using nominal stresses
78
3.2.1.3 Special case of actual component values If only an experimental value of the tensile strength
Rm,I
is known the value of the yield strength Rp,I may be computed from Eq. (3.2.3) with Rm = Rm,I.
For milled steel there is deff,max,m = deff,max,p = 250 mm. For all other kinds of material there are no upper limit values deff,max, ... , (3.2.11)
deft:max.m = deft:max.p = 00 ,
unless otherwise specified in the material standards.
3.2.2 Technological size factor
Aluminum alloys
3.2.2.0 General The technological size factor accounts for a decrease of the material strength values usually observed with increasing dimensions of the component. It is specified as a function of the effective diameter, Figure 3.2.1. It is different for non-welded and for welded components *7
For cast aluminum alloys the technological size factors for the tensile strength and for the yield strength are as follows: For deft':::; deft:N,m = deft:N,p = 12 mm
3.2.2.1 Dependence on the effective diameter Non-welded components
:KI.m = :KI.p =
Steel and cast iron materials
(3.2.4)
for deff > 7,5 mm *8 Kd,m = 1,207' (deff/7,5 mm)-0,1922.
(3.2.5)
For stainless steel within the dimensions given in material standards there is Kd,m = Kct,p =1.
(3.2.7)
For all other kinds of steel and cast iron materials the technological size factor is: For deff s deff,N,m KcI,m = Kd,p =1, for deff,N,m < deff :s; deff,max,m *9: KcI,m
(3.2.8) . (3.2.9)
1-0, 7686·ad,m ·lg(deff /7,5mm) , 1-0, 7686·ad,m .lg(deff,N,m /7,5mm)
for deff ~ deff,max,m it is: ~m = ~m (deff,max,m).
deff deff,N,m, ad,m
(3.2.12)
1,
for 12 mm < deft' < deft:max.m =
For GG the following technological size factor applies to the tensile strength: For deff :s; 7,5 mm Kd,m = 1,207,
For wrought aluminum alloys the component values of the tensile strength, Rm , and of the yield strength, Rp, are given in Chapter 5 according to the type of material and its condition, and depending on the thickness or diameter of the semi-finished product. To these values the technological size factors Kj., = :KI.p = 1 apply.
(3.2.10)
effective diameter, Chapter 3.2.2.2 , constants, Table 3.2.1 and 3.2.2.
Considering the yield strength the values Kct,m , deff,N,m , and act,m have to be replaced by the values ~p , deff,N,p , and ad,p (except for GG).
deft:max.p =
v. = v. = 1, 1 . (d .J..~m .J..~p Ueff /7 , 5 mm) for deft'~
deft:max.m
=
deft:max.p
:KI.m = :KI.p = 0,6 . Welded components
150 mm
-0,2 ,
(3.2.13)
= 150 mm (3.2.14)
*10
For all kinds of material the technological size factor for the toe section and for the throat section of welded components is *11 KcI,m = Kct,p = 1.
(3.2.15)
For materials such as conditionally weldable steel, stainless steel or weldable cast iron the subsequent calculation is provisional and therefore it is to be applied with caution.
3.2.2.2 Effective diameter For components with a simple shape of the cross section - as far as a cross section may be defined - the effective diameter is given according to the cross section in Table 3.2.3. In general the upper limit of the effective diameter is specified in the material standards.
For the determination of the effective diameter deff two cases are to be distinguished as to the kind of material.
Table 3.2.1 Constants deff,N,m, ... , and adm, ... , for steel 7 The influence factors according toChapter 3.2.3 (KA), Chapter 3.2.4 (fer, f't) and Chapter 3.2.5 (KT m- ...) are supposed tobe valid for both non-welded and welded compon~nts. 8 Footnote an Eq. (3.2.6) cancelled. 9 0,7686 = 1 fig 20.
10 Valid for steel, cast iron material and aluminum alloys. 11 For structural steel and fine grain structural steel according to DIN 18800, part 1, page 40.
3.2 Material properties
3 Assessment of the static strength using nominal stresses
79
Table 3.2.1 Constants deff,N,m, ... , and adm' ... , for steel
Table3.2.2 Constants cleff,N,m , ..., and adm, ... , for cast iron materials
Values inthe upper row refer tothe tensile strength R m , Values inthe lower row refer to the yield strength Rp .
Values inthe upper row refer tothe tensile strength Rm , Values inthe lower row refer to the yield strength Rp .
Kinds of material -¢o1
Non-alloyed structural steel DIN-EN 10 025 Fine grain structural steel DIN 17 102 Fine grain structural steel DIN EN 10 113 Heat treatable steel, q&t DIN EN 10 083-1 Heat treatable steel, n DIN EN 10083-1 Case hardening steel, bh DIN EN 10 083-1 Nitriding steel, q&t DIN EN 10 083-1 stainless steel DIN EN 10 088-2 -¢o4 Steel for big forgings, q&t SEW 550-¢os Steel for big forgings, n SEW 550
cleff,N,m cleff,N,p
Kinds of material
inmm
ad,m ad,p -¢o2
40 40 70 40 100 30 16 -¢o3 16 16 16 16 16 40 40
0,15 0,3 0,2 0,3 0,25 0,3 0,3 0,4 0,1 0,2 0,5 0,5 0,25 0,30
-
-
250 250 250 250
0,2 0,25
Cast steel DIN 1681 Heat treatable steel casting, DIN 17205 Heat treatable steel casting, q&t, DIN 17 205, types -¢o2 No.1, 3,4 as above types -s No.2 as above types No.5, 6, 8 as above types No.7, 9 GGG DIN EN 1563 GT-¢o4 DIN EN 1562
°
0,15
q&t=quenched a. tempered, n=normalized, bh=blank hardened -e-I
Within the kinds ofmaterial there are the types ofmaterial.
-¢o2 More precise values depending on the kind of material (except for non-alloyed structural steel) see Table 5.1.2 toTable 5.1.7. -¢o2 For 30 CrNiMo 8 and 36 NiCrMo 16: deffN m = 40 values ad,m and ad,p asgiven above. ' ,
»s For 28 NiCrMoV 8 5 or 33 NiCrMo 145: deff N m = deffN p 500mm or 1000 mm resp., values ad.m and ad.~ ~s given abo~e.
~,p
inmm 100 100 300 -¢o1 300
0,15 0,3 0,15 0,3
100 100 200 200 200 200 500 500 60 60 15 15
0,3 0,3 0,15 0,3 0,15 0,3 0,15 0,3 0,15 0,15 0,15 0,15
q&t= quenched and tempered » l For GS-30 Mn 5 orGS-25 CrMo 4 there is deff,N,m = 800 mm or 500 mm respectively, values ad,m and ad,p asgiven above.
-¢o2 Material numbers see Table 5.1.11. -¢o3 Valid for strength level V I, for level V II deff,N,m = 100 mm with values ad,m and ad,p asabove.
=
deff,N,p
Case 2 Components (also forgings) made of non-alloyed structural steel, of fine grained structural steel, of normalized quenched and tempered steel, of cast steel, or of aluminum materials. The effective diameter deff is equal to the diameter or the wall thickness of the component, Table 3.2.3, case 2.
Case 1 Components (also forgings) made of heat treatable steel, of case hardening steel, of nitriding steel both nitrided or quenched and tempered, of heat treatable cast steel, of GGG, GT or GG. The effective diameters deff from Table 3.2.3, Case 1, apply. In general it is: deff= 4· V / 0, V,O
~,m
mm,
-¢o4 No technological size effect within the dimensions mentioned in the material standards. =
deff,N,m cleff,N,p
(3.2.16)
Volume and surface of the section of the component considered.
Rod-shaped (ID) components made of quenched and tempered steel The effective diameter is the diameter existing while the heat treatment is performed. In case of machining subsequent to the heat treatment the effective diameter deffis the largest diameter of the rod. In case of machining prior to the heat treatment the effective diameter deff is defined as the local diameter in question. The diameter deff according to the first sequence of machining is an estimate on the safe side.
3.2 Material properties
Aluminum alloys
Table 3.2.3 Effective diameter defi' No.
Cross section
1
~
3 Assessment of the static strength using nominal stresses
80
The anisotropy factor for cast aluminum alloys is defi' Case 1
defi' Case 2
d
d
KA = 1.
(3.2.20)
For forgings ·13, for which material standards specify the strength values as depending on the testing direction, the anisotropy factor is not to be applied: (3.2.21)
2
~
3
~
4
~
5
s[
r:fE
2s
For aluminum alloys the anisotropy factor for the strength values in the main direction of processing is
s
(3.2.22) 2s
s
2b·s
s
--
for the strength values transverse to the main direction of processing the anisotropy factor from Tab. 3.2.4 is to be applied.
Table 3.2.4 Anisotropy factor K A
b+s
.
Steel'
Rm b
b
inMpa
up to 600 from 600 from 900 above 1200 to 900 to 1200
KA
0,90
0,86
0,83
0,80
Alumtnum aIIoys:
Rm
3.2.3 Anisotropy factor The anisotropy factor allows for the fact that the strength values of milled steel and forgings are lower transverse to the main direction of milling or forging than in the main direction of processing. It is to be supposed that the specified strength values are valid for the main direction of processing. In case of multiaxial stresses, and also with shear stress, the anisotropy factor is KA = 1.
(3.2.17)
Steel and cast iron material
KA
1,00
(3.2.19)
For the strength values transverse to the main direction of processing the anisotropy factor from Table 3.2.4 is to be applied.
0,90
3.2.4 Compression strength factor and shear strength factor 3.2.4.0 (;eneral The compression strength factor allows for the fact that in general the material strength is higher in compression than in tension.
3.2.4.1 Compression strength factor For tensile stresses (axial or bending) the compression strength factor is
fa = 1.
(3.2.23)
For compression stresses (axial or bending) the tensile strength Rm and the yield strength Rp are to be replaced by the compression strength Rc,m and the yield strength in compression Rc,p:
Rc,m =fa ' Rm, Rc,F = fa . Rp , 12 With material properties depending on the direction.
0,95
(3.2.18)
For milled steel and forgings *12 the anisotropy factor in the main direction of processing is KA = 1.
up to 200 from 200 from 400 to 400 to 600
The shear strength factor allows for the fact that the material strength in shear is different from the tensile strength.
The anisotropy factor for cast iron material is KA = 1.
inMpa
(3.2.24)
3.2 Material properties
compression strength factor, Table 3.2.5, tensile strength and yield strength, see Eq. (3.2.1) to (3.2.3).
3.2.5 Temperature factors 3.2.5.0 General
The values Rc,m and Rc,p are not explicitly needed for an assessment of the static strength, as only the compression strength factor fa is needed. *13.
Table 3.2.5 Compression strength factor fa and shear strength factor f, Kinds of material
Case harden's steel Stainless steel Forging steel Other kinds of steel GS GGG GT GG Wrought aluminum Cast aluminum
3 Assessment of the static strength using nominal stresses
81
fO" for tension 1 1 1 1 1 1 1 1 1 1
fO" for compress. 1 1 1 1 1 1,3 1,5 2,5 1 1,5
f, ~l
0,577 0,577 0,577 0,577 0,577 0,65 0,75 0,85 0,577 0,75
The temperature factors allow for the fact that the material strength decreases with increasing temperature. Normal temperature, low temperature and higher temperature are to be distinguished.
3.2.5.1 Normal temperature Normal temperatures are as follows: - for fine grain structural steel from -40°C to 60°C, - for other kinds of steel from -40 DC to + lOODC, - for cast iron materials from -25 DC to + lOODC, for age-hardening aluminum alloys from -25 DC to 50 DC, - for non-age-hardening aluminum alloys from - -25°C to lOODC. For normal temperature the temperature factors are KT,m = ...
= 1.
(3.2.26)
3.2.5.2 Low temperature
~ 1 0,577 = 1 /.J3, according tov.Mises criterion,
Temperatures below the values listed above are outside the field of application of this guideline.
3.2.4.2 Shear strength factor
3.2.5.3 Elevated temperature
For shear stresses the tensile strength Rm and the yield strength Rp are to be replaced by the shear strength R, m and the yield strength in shear Rs,p: '
f, shear strength factor, Table 3.2.5 R m, Rp tensile strength and yield strength, Eq. (3.2.1) to (3.2.3).
In the field of elevated temperatures - up to 500°C for steel and cast iron materials and up to 200 °C for aluminum materials - the influence of the temperature on the mechanical properties is to be considered. In case of elevated temperature the tensile strength R m is to be replaced by the high temperature strength Rrn,T or by the creep strength Rrn,Tt . The yield strength Rp is to be replaced by the high temperature yield strength Rp,T or by the 1 % creep limit Rp,Tt *14.
The values Rs,m and Rs,p are not explicitly needed for an assessment of the strength, as only the shear strength factor f, is needed.
For the short-term values Rm,T and Rp,T as well as for the long-term values Rm,Tt and Rp,Tt the Eq. (3.2.27) to (3.2.35) apply.
13 Tensile strength and yield strength incompression are supposed to be positive, Rc,rn, Rc,p > 0, therefore for compression fO" > 1.
14 The relevant temperature factors will be applied in combination with the safety factors at the assessment stage.
also valid for welded components.
Rs,m = f, . Rm, Rs,p = f, . Rp,
(3.2.25)
3.2 Material properties
3 Assessment of the static strength using nominal stresses
82
Short-term values For GG a yield strength value is not defined and therefore the value Rp,T does not exist. Short term values of the static strength are
Hightemperarure
Rm,T = KT,m . R m , Rp,T = KT,p . R p , KT,m, Kt,p. R m, R p
yield strength Rp •T
(3.2.27)
temperature factors, Eq. (3.2.28) to (3.2.33), tensile strength and yield strength, Eq. (3.2.1) to (3.2.3).
I % creep limit Rp,Tt Rp,Tt Rp I ~'RII1'jpt
Creep Strength R;";Tt O,21--~+---+---+---+>o&..,..-..j
0,11----1-----4---'4-4-'--\-1.
Steel and cast iron materials
o
According to the temperature T the temperature factors KT,m and KT,p apply as follows: for fine grain structural steel, T > 60 °C *15: (3.2.28) KT.m = KT,p = 1 - 1,2' 10.3 . T / DC, for other kinds of steel *16, T > 100°C, Figure 1.2.2: (3.2.29) KT,m = KT,p = 1-1,7' 10,3. (T / °C -100), for GS, T> 100D C : KT,m = KT,p = 1- 1,5 . 10
(3.2.30) -3
0
Rrn.Tt
I
~'jmt
The values Rm,T and Rp,T are not explicitly needed for an assessment of the static strength, as only the temperature factors KT,m and KT,p are needed.
o
160
200
360
400
500
Tin ·C
1.2.2
OA r---,....,.--,--------,--------..., Rm,T Rm 'jm
High temperature strengtli R,.,T CreepStrength Rrn,Tt
0,3: I---t---t=""'-.;;;:c--/-'--
RIlj;TI I Rm'jmt
0,21---+---+---+--·+\----,""1
. (T / C - 100),
for GGG, GT and GG, T > 100D C, Figure 3.2.2: K T.m = Kr,p = 1- aT,m . (10 aT,m
-3.
T / DC)
2.
(3.2.31)
Constant
Eq. (3.2.28) to (3.2.31) are valid from the indicated temperature T up to 500 DC. For a temperature above 350° C they are valid only, if the relevant characteristic stress does not act on long terms.
Table 3.2.6 Constant aT,m .
o 3.2.2b
100
200300 400 Tin ·C
500
Figure 3.2.2 Temperature dependent values of the static strength of non-alloyed structural steel and of GG plotted for comparison. Safety factors after Chapter 3.5.
Kind of material
GGG
GT
GG
aT,m
2,4
2,0
1,6
Rm,T/Rm= KT,m, Rm,Tt/ Rm = KTt,m,
Rp,T/Rp=KT,p, Rp,Tt / Rp = KTt,p'
Top: Non-alloyed structural steel with Rp / Rm = Re / Rm = 0,65, Rm,T, Rp,T aswell as Rm,T1> Rp,Tt fort = 105 h, Jm= 2,0, jp =Jmt= 1,5 , Jpt= 1,0. Bottom: 00, Rm,T aswell as Rm,Tt fort = 105 h, Jm= 3,0, jmt= 2,4.
15There isan insignificant discontinuity at T = 60°C. 16 For stainless steel no values are known up to now.
3.2 Material properties
3 Assessment of the static strength using nominal stresses
83
Aluminum alloys
Long-term values
According to the temperature T the temperature factors KT,mand KT,p for aluminum alloys apply as follows:
Long term values of the static strength are
-
-
for age-hardening aluminum alloys: T > 50 DC, Figure 3.2.3 (3.2.32) Kr,m = 1 - 4,5 . 10 -3. (T / DC - 50) ;:: 0,1, Kr,p = 1 - 4,5 . 10 -3. (T / DC - 50) ;:: 0,1, for non-age-hardening aluminum alloys: T> 100°C, Figure 3.2.3 (3.2.33) Kr,m = 1 - 4,5 . 10 -3. (T / °C - 100) ~ 0,1, Kr,p = 1 - 4,5 . 10 -3 . (T / °C - 100) ~ 0,1,
Eq. (3.2.32) and (3.2.33) are valid from the indicated temperature T up to 200°C, and in general only, if the relevant characteristic stress does not act on long terms.
R""Tt ~,Tt
= KTt,m . R; , = KTt,p . ~,
KTt,m, KTt,p
Rm, R,
(3.2.34)
temperature factors, Figure 3.2.2 and 3.2.3, Eq. (3;2.35), tensile strength and yield strength; Eq. (3.2.1) to (3.2.3).
The values R""Tt and ~,Tt are not needed explicitly for an assessment of the static strength, as only the temperature factors KTt,m and KTt,p are needed.
Steel and cast iron material For GG a yield strength value is not defined and therefore the value Rp,Tt does not exist.
0,5
High temperaturc strengthRm,T Ri'D;'l'l
Depending on the temperature T and on the operation time t at that temperature the temperature factors KTt,m and KTt,p apply, Figure 3.2.2 *17
R. 'Jm CrecpStrellgth
. IR..Tt Rm,Tt
K
1
}fn7'jlllt
I
0,1 .Gw,zd,t'--""'+-~----f+----+l,o-;__+\_~
R., .jo1
6W;.d.T .00W••d
o
o
so
np
= 10(aTt,m+ bTt,m . Pm+ cTt,m . Pm )
= lO(aTt,p+b Tt,p ·Pp+cTt,p .pp2 )
, (3.2.35)
,
Pm
= 10 -4. (T / C + 273)' (C m + 19(t/ hj),
Pp
=
10 - 4. (T / C + 273) . (C m + 19(t / hj),
aTt,m, ..., Cp constants, Table 3.2.7, t operation time in hours h at the temperature T.
Higll temperature fatigueslrength
crw.>.d .
2
K Tt,m
100
150
200
1.2.3
250
Eq. (3.2.35) applies to temperatures from approximately 350°C up to 500°C, but only for stresses acting on long terms. In general they do not apply to temperatures below about 350°C *18.
100
T/'C
Figure 3.2.3 Temperature dependent values of the static strength of aluminum alloys plotted for comparison. Static strength values: Rm,T/Rm = KT,m = Rp,T/Rp = KT,p' Rm,Tt/ Rm = KTt,m = Rp,Tt / Rp = KTt,p . Rm,Tt,Rp,Tt for t = 105 h. Fatigue limit for completely reversed stress (N = 106 cycles): crW,zd / Rm = 0,30 ; crW,zd,T / crW,zd = KT,D . Safety factors according to Chapter 3.5 and 4.5:
17 Larsen-Miller-parameter P andLarsen-Miller-constant C. 18 Because the values would be unrealistic for temperatures T < 350°C, where thevalues KT,m andKT,p are relevant instead.
3.2 Material properties
Table
3 Assessment of the static strength
84
3.2.7 Constants aTt,m, ... , C p ~1
using nominal stresses
Aluminum alloys 105 hours KTt,m is given by
For aluminum alloys and t = Steel
~2
Non-
Fine grain
Heat-
alloyed
structural
structural steel
steel
treatablesteel
~3
~4
CTtm Cm
~5
- 0,994 2,485 - 1,260 20
-1,127 2,485 - 1,260 20
aTt.n cTt.n
Co Cast iron material
0,8
\
0,6
- 3,001 3,987 - 1,423 24,27
- 5,019 7,227 - 2,636 20
- 6,352 9,305 - 3,456 20
- 3,252 5,942 - 2,728 17,71
GS
GGG,GT
GG
~6
~7
~8
\\
0,4
\
0,2
o
1 % Creep limit bTt.n
1,0
R"..TI {R".
Creep strength aTt.m b Tlm
Figure 1.2.4 *19.
i RT
-100
i
~ 200
300
400
Trc
Figure 3.2.4 Temperature factor KTl,m ~ R.n.Tt/ 5 aluminum alloys and t = 10 hours.
R.n for
The given curve is the same as in Figure 3.2.3, except that the factor (1 / jm ) is different.
Creep strength aTtm bTtm CTtm Cm
-7,524 9,894 - 3,417 19,57
2,50 - 1,83
°
20
-1,46 2,36 -0,90 25
1 % Creep limit aTtn b Tln CTt.n Cn
- 10,582 8,127 - 1,607 35,76
0,12 1,52 - 1,28 18
-
<-I Approximate values, applicable from about 350 0 e to 500 o e. ~2
Not valid for stainless steel.
~3
Initially for 8t 38, Rm = 360 MPa, similar to sr37.
~4 Initially for H 52, Rm = 490 MPa, similar to 8tE 355; the absolute values Rm,Tt are the same as for St 38. ~5 Initially for e 45 N (normalized) with Rm = 620 MPa. For C 35 N, with Rm = 550 MPa the constants -3,001 and -3,252 are to be replaced by -2,949 and -3,198. The absolute values Rm,Tt are the same as for C45N. ~6
Initially for 08-C 25 with Rm
=
440 MPa.
~7
Initially for 000-40 with Rm
=
423 MPa.
~7
Initially for 00-25 with Rm = 250 MPa.
19 The temperature factor Kt,p is not defmed up to now. It may be assumed, however, as it is essential for the assessment of the static strength, that the term Rp,Tt / jpt is more or less equal to Rm,Tt / jmt , see Figure 1.2.2 (required safety factorsjpt = 1,0 andjmt = 1,5). A Larsen-Millerequation similar to Eq. (3.2.32) or (3.2.33) applicable to derive the values of KTt,m and KTt, according to temperature T and operationtime T has not been specifieffor aluminum alloys up to now.
85
3.3 Design parameters
3.3 Design parameters Contents
1R33 EN.dog Page
3.3.0
General
3.3.1 3.3.1.0 3.3.1.1 3.3.1.2
Design factors General Non-welded components Welded components
3.3.2 3.3.3 3.3.4 3.3.5
Section factors Plastic notch factors Weld factor CI.w Constant KNL
85
3 Assessment of the static strength using local stresses 3.3.1.2 Welded components For welded components the design factors are generally to be determined separately for the toe and for the root of the weld. For the toe of the weld the calculation is to be carried out as for non-welded components. For the root of the weld of rod-shaped (ID) welded components the design factors for normal stress (tension or compression) and for shear stress are
87
KSK,a = 1/ (npl,a . fJ.w · KNd , KsK,~ = 1 / (npl,~ . fJ.w ) .
88
(3.3.4)
For the root of the weld of shell-shaped (2D) welded components the design factors for normal stress (tension or compression) in the directions x and y as well as for shear are
3.3.0 General According to this chapter the design parameters are to be determined.
KSK,ax = 1 / (npl,ax . CI.w ..KNL ), KsK,cry = 1 / (npl,cry . CI.w' KNL ), KSK,~ = 1 / (npl,~ . CI.w), npl,a, ...
3.3.1 Design factors
fJ.w
(3.3.5)
section factor, Chapter 3.3.2 weld factor, Chapter 3.3.4. constant for GG, Chapter 3.3.5
3.3.1.0 General
KNL
Non-welded and welded components are to be distinguished. They can be both rod-shaped (lD), shell-shaped (2D) and block-shaped (3D).
Weld factors CI.w are given for tension, for compression, for shear and for torsion of the throat section.
3.3.1.1 Non-welded components
For certain applications block-shaped (3D) components may be welded at the surface, for example by surfacing welds. Then the calculation is to be carried out as for shell-shaped (2D) welded components, if the stresses at the surface ax, a y and 1: are of interest only.
The design factors of rod-shaped (lD) non-welded components for normal stress (tension or compression) and for shear stress are KSK,a = 1/ (npl,a . KNd, KSK;t = I / npl;t .
(3.3.1)
The design factors of shell-shaped (2D) non-welded components for normal stress (tension or compression) in the directions x and y as well as for shear are KSK, ax = 1/ (npl,a . KNd, KsK,ay = I / (npl,a . KNL), KSK,~ = 1 / npl,~ .
(3.3.2)
The design factors of block-shaped (3D) non-welded components for the principle stresses (tension or compression) in the directions 1, 2 and 3 (normal to the surface of the component) *1 are KSK,al = 1 / (npl,a . KNL), KSK,a2 = I / (npl,a . KNL), K SKa3 = 1/ KNL *', npl,a ... KNL
3.3.2 Section factors The section factors npl,a , ... allow for the influence of the stress gradient in connection with the shape of the cross section on the static strength of the component, Figure 1.3.1. They serve to make best use of the load carrying capacity by accepting some yielding as the outside fiber stress exceeds the yield strength.
An essential condition is the existence of a stress gradient of the stress a and/or 1: normal to the surface of the component, Figure 3.3.1. A stress gradient parallel to the surface is not considered for the section factor *1.
(3.3.3)
section factor, Chapter 1.3.2, constant for GG, Chapter 3.3.4 1 For the stress components ax, a y , t, a, and a2the stress gradient of interest is normal to the direction ofthestress, Figure 3.3.1. A stress gradient of a3it is not considered and np l,53 = I , because the stress gradient as defined above isparallel toa3.
86
3.3 Design parameters
3 Assessment of the static strength using local stresses For austenitic steel in the solution annealed condition according to Table 5.1.8 the section factors for normal stress (tension or compression) and for shear stress are *4 npl,a = Kp,a , npl;t = K p,~ .
(3.3.8)
For all other kinds of material the section factors for normal stress and for shear stress are *5 *6
= MIN (~E·t:ertr /R p
; Kp,a),
npl,~ = MIN (~E·t:ertr /R p
; Kp,~),
npl,a
~rlr
E
,
npl'''=R
(3.3.9)
Young's modulus, Table 3.3.1, limit value of total strain, Table 3.3.1, yield strength, Chapter 3.2, plastic notch factors.
Aluminum alloys 10 3.3.1
15
~
Rp/E
For cast aluminum alloys as well as for wrought aluminum alloy with small elongation, A '< 8 %, the section factors are *3: npl,a
Figure 3.3.1 Definition of the section factor npl,a of a notched component, for instance.
= .., = 1.
(3.3.10)
For ductile wrought aluminum alloys, A:2: 8 %, the section factors are to be determined from Eq. (3.3.9).
Top: Detail of the component. Yield strength Rp , component static strength for normal stress aSK section factor npl,a = aSK / Rp , load F. Continuous curve: Fictitious distribution of the elastically computed stress. Curve limited to Rp: Real stress distribution providing elastic ideal-plastic material behavior. Bottom: Stress-strain curve of the component (relative scales). Plastic notch factor Kp,a , limit value of total strain Sertr , Young's' modulus E.
Surface hardened components
Kinds of material
Steel
GS
GGG
GT
AI alloys
10-5. E / MPa Eertr/ % ~1 ~ 1 Sertr / % '" 5
The section factors are not applicable if the component has been surface or case hardened, see Table 2.3.5 *2: npl,a = ... = 1.
Table 3.3.1 Young's modulus E and limit values of total strain Eertr .
2,1 5
2,1 5
1,7 2 ~2
1,8 2
0,70 2 ~3
means Sertr = 0,05
~2
Valid for As < 12,5 %. For Aj z 12,5% thereis Sertr=4%.
~3
Valid for A < 12,5%. For A~ 12,5% thereis Sertr = 5 %.
(3.3.6)
Steel and cast iron material For GG as well as for types of GT or GGG with small elongation, A 3 < 8 % or A5 < 8 %, the section factors are *3: npl,a
= ... = 1.
(3.3.7) 3 Because of the low plasticity of these materials.
2 A hard surface layer - for example as a result of case hardening and particularly at notches - may observe cracks when yielding occurs because of the limited plasticity of the hardened surface layer. Possibly this rule is too far on the safe side, as npl = 1,1 is allowed for case hardened shafts according to the recent DIN 743 (launched in 2000).
4 Because of the high ductility of austenitic steel in the solution annealed condition the plastic notch factors Kp,a and Kp;r are relevant instead of the material dependent sectionfactors. 5 MIN means that thesmaller valuefrom the rightsideofthe equation is valid. 6 Section factor based on Neuber's formula.
87
3.3 Design parameters
..
3.3.3 Plastic notch factors The section factors according to Eq. (3.3.8) and (3.3.9) are limited by the plastic notch factors Kp,a and Kp,~ that depend on the plastic limit load: K
K p,a,
p,~
=
plastic limit load elastic limit load
-=--------
3 Assessment of the static strength using local stresses Table 3 3 2 Plastic notch factors K-n.o and K . Cross section Bending Torsion rectangle ~ 1 circle circular ring I-section or box
(3.3.11)
The elastic limit load for normal stress (and for shear stress) is defined as the load for which the maximum local stress exceeds the yield stress. The plastic limit load of a component may be obtained most reliable from an elastic-plastic finite element analysis. To reduce the computing effort for such an analysis a simplified elastic-ideal-plastic stress strain curve may be used and the finite element mesh may be less fine than for computing notch stresses.
~n~
~1
or plate, ~21,70=16/(3'1t), thin-walled, 1,27 = 4/1t.
~5
thin-walled, otherwisethere is p.t
= v
Kp,t
1,5 1,70 ~2 1,27 ~4
1,33 ~3
-
p5
-
~6
~4
K
Kp,b
~3
1,33=4/3.
133 1-(dlD)3 r4 ' 1-(dlD)
(3.3.14)
d, D inner and outer diameters. ~6
Kp,b = 1,5 .
1- (b 1 B)· (h 1 H)2
(3.3.15)
3
1- (b 1 B) . (h 1 H)
b, B inner and outer width, h, H inner and outer hight.
Approximately the plastic limit load may be derived as follows: Definition and plotting of the cross section which will determine the limit state, Entering the yield stresses o = ± Rp and 't = ± f~' Rp into the plotted cross section (f~ from Table 3.2.5), . Balancing the areas of the section under + Rp and Rp to obtain a similarity between these stresses and the external loading situation.
The weld factor CJ..w accounts for the effect of a weld. It applies to the root of the weld of welded components only, Table 3.3.3 *9 .
In general realization of the described procedure is not easy and the formulation of an appropriate algorithm is difficult.
Table 3.3.3 Weld factor CI..w ~1
3.3.4 Weld factor
Particular case In case of a component for which nominal stresses may be defined for the section of concern, and the corresponding stress concentration factors for tension or compression, for bending, for shear and for torsion are known *7 *8, the plastic notch factors are as follows:
= Kt,zd,
Weld quality
Type of stress
full
all
Compression
weld
Kp,~ = Kt,s,
Kp,~ Kt,zel, Kp,b,
It has to be observed, however, that the so-derived plastic notch factors only apply to the notched section considered and not to the component as a whole. Therefore other sections may have to be considered in addition, see Chapter 3.0 and Figure 3.0.1.
1,0
verified
or with
Rm > 360 MPa
Tension
10
Compression
0,95
or
0,80
1,0
not verified
partial penetration or
= Kp,t' Kt,t. stress concentration factor, Chapter 5.2, plastic notch factors, Table 3.3.2.
R m ::; 360 MPa ~2
penetration
(3.3.13)
Kp,a = Kp,b . Kt,b ,
.
Joint
back weld Kp,a
Uw
all
Tension
fillet weld all bun weld ~3
0,80
all
Shear Tension
0,55
-
055 ~I
Accordingto DIN 18800 part 1, Table 21 and Eq. (75).
~2
For aluminium alloys (independent of Rm ) the values typed in boldfaceshould be applied for the time being.
~3
Butt welds of sectional steel from St 37-2 and USt 37-2 with a product thickness t > 16 mm,
7 Usually stress concentraction factors do nor exist in combinationwith local stresses. 8 The stress concentration factors Kt.o and Kt., given in Chapter 5.12 for a substitute structure are intended to be used in Chapter 4.3.1.1 only and should not be used in the present context.
9 For the toe of a weld the calculation is to be carried out as for nonwelded components.
88
3.3 Design parameters
3.3.5 Constant K NL The Constant KNL allows for the non-linear elastic stress strain characteristic of GG in tension and compression or in bending. For all kinds of material except for GG there is K NL = 1.
(3.3.16)
For GG the values (3.3.17)
K NL = KNL,Zug
apply to the tension side of the cross section (tension or tension from bending). The reciprocal values KNL,Druck
= 1/ KNL,Zug
(3.3.18)
apply to the compression side of the cross section (compression or compression in bending). Values of the KNL,Zug and KNL,Druck from Table 3.3.4.
Table 3.3.4 Constant KNL -c- 1. Type of material
GG
GG
GG
GG
GG
GG
-10
-15
-20
-25
-30
-35
KNL,Zug
1,15
1,15
1,10
1,10
1,05
1,05
KNL,Druck
0,87
0,87
0,91
0,91
0,95
0,95
~ 1 For unnotched and slightly notched components at tension or compression there is KNL = 1.
3 Assessment of the static strength using local stresses
89
3.4 Component strength
3.4 Component strength Contents
1R34
EN.dog
Page
3.4.0 General 3.4.1 Non-welded components 3.4.2 Welded components
89
3 Assessment of the static strength using local stresses
3.4.2 Welded components For welded components the strength values are generally to be determined separately for the toe and for the root of the weld. For the toe of the weld the calculation is to be carried out as for non-welded components. For the root of the weld of rod-shaped (lD) welded components the local values of the component static strength for normal stress (tension or compression) as well as for shear stress are
3.4.0 General According this chapter the local values of the component static strength are to be determined. Non-welded and welded components are to be distinguished. They can be both rod-shaped (10), shellshaped (2D), or block-shaped (3D).
csx = fa . Rm I KSK,a , 'tSK = f~' Rml KsK,~.
(3.4.4)
For the root of the weld of shell-shaped (2D) welded components the local values of the component static strength for normal stresses (tension or compression) in the directions x and y as well as for shear stress are
3.4.1 Non-welded components crSK,x = fa . Rm I KSK,ax , crSK,y = fa . Rm I KsK,cry , TSK = f~' Rml KSK,~,
The local values of the component static strength of rodshaped (lD) components for normal stress (tension or compression) and for shear stress are *1 *2 O'sK=fa'Rm/KSK,a,
(3.4.1)
'tSK = f~ . Rm I KSK,~ . The local values of the component static strength of shell-shaped (2D) components for normal stresses (tension or compression) in the directions x and y as well as for shear stress are O'SK,x = fa . Rm I KSK,ax , O'SK,y = fa . Rm I KsK,cry , 'tSK = f~' Rml KsK,~ .
(3.4.2)
compression strength factor, Chapter 3.2.4, shear strength factor, Chapter 3.2.4, tensile strength, Chapter 3.2.1, design factor, Chapter 3.3.1. The local values of the component static strength of block-shaped (3D) components for the principal stresses (tension or compression) in the directions 1, 2 and 3 are O'l,SK = fa . Rm I KSK,a1 , 0'2,SK = fa . Rm I KSK,a2 , 0'3,SK = fa . Rm I K SK,a3 ,
(3.4.3)
compression strength factor, Chapter 3.2.4, tensile strength, Chapter 3.2.1, Rm KSK,al ... design factor, chapter 3.3.1.
fa
1 The component static strength values are different for normal stress and for shear stress, and moreover they are different due to different section factors according to the type of stress. 2 Basically the tensile strength Rm is the reference value of static strength, even if in the case of a low Rp / Rm ratio the yield strength is to be used for the assessment of the static strength, a fact that is accounted for in Chapter 1.5.5.
(3.4.5)
compression strength factor, Chapter 3.2.4, shear strength factor, Chapter 3.2.4. f~ tensile strength, Chapter 3.2.1, Rm design factor, Chapter 3.3.1. KsK, a, ... fa
For certain applications block-shaped (3D) components may be welded at the surface, for example by surfacing welds. Then the calculation is to be carried out as for shell-shaped (2D) welded components, if the stresses at the surface crx , cry and r are of interest only.
90
3.5 Safety factors
3.5 Safety factors
1R35
Contents 3.5.0 3.5.1 3.5.2 3.5.2.0 3.5.2.1 3.5.2.2 3.5.3 3.5.3.0 3.5.3.1 3.5.3.2 3.5.4 3.5.5
General Steel Cast iron materials General Ductile cast iron materials Non-ductile cast iron materials Wrought aluminum alloys General Ductile wrought aluminum alloys Non-ductile wrought aluminum alloys Cast aluminum alloys Global safety factor
EN .docl
Page 90
3 Assessment of the static strength using local stresses Table 3.5.1 Safety factors jm and jp for steel (not for GS) and for ductile wrought aluminum alloys As> 12,5 %). Consequences of failure jm ->1 ->2 severe moderate jp ->3 jmt ->S jpt ->4 high
91
92
3.5.0 General According to this chapter the safety factors are to be determined *1. The safety factors are valid under the condition that the design loads are reliably determined on the safe side and that the material properties correspond to an average probability of survival of Po = 97,5 % *2.
Probability of occurrence of the characteristic service stress values
low ->6
2,0 1,5 1,5
1,75 1,3 1,3
1,0
1,0
1,8 1,35 1,35
1,6 1,2 1,2
1,0
1,0
->1 referring tothe tensile strength Rm ortothe strength atelevated temperature RmT, ->2 referring tothe yield strength Rp ortothe hot yield strength Rp,T , ->3 referring tothe creep strength Rm,Tt, ->4 referring tothe creep limit Rp,Tt . ->S moderate consequences of failure of a less important component in the sense of "no catastrophic effects" being associated with a failure; for example because of a load redistribution towards other members of a statically undeterminate system. Reduction byapproximately IS %.
The safety factors may be reduced under favorable conditions, that is depending on the probability of occurrence of the characteristic stress values in question and depending on the consequences offailure.
->6 or only infrequent occurrences of the characteristic service stress values, for example due to anapplication ofproof loads or due to loads during anassembling operation. Reduction byapproximately 10 %.
The safety factors are valid both for non-welded and welded components.
3.5.2 Cast iron materials
The safety factors given in the following are valid for ductile and for non-ductile materials. In this respect any types of steel are ductile materials, as well as cast iron materials and wrought aluminum alloys with an elongation As~ 12,5 %, while GT, GG and cast aluminum alloys are always considered as non-ductile materials here. *3
3.5.2.0 General Ductile and non-ductile cast iron materials are to be distinguished.
3.5.2.1 Ductile cast iron materials Cast
iron
materials with an elongation % are considered as ductile, in particular all types of GS and some types of GGG (not GT and not GG). Values of elongation see Table 5.1.12. A5~12,5
3.5.1 Steel Safety factors applicable to the tensile strength and to the yield strength, to the creep strength and to the creep limit are given in Table 3.5.1.
1 The safety factors in Chapter 1.5 are the same, but with the difference, that non-ductile cast iron materials and non-ductile aluminum alloys are considered here as well. 2 Statistical confidence S = SO %. 3 All types of GT, GG and cast aluminum alloys have elongations As < 12,S % and are considered as non-ductile materials here. Wrought aluminum alloys with elongations As < 12,S % are considered asnonductile materials, too. For non-ductile materials the assessment of the static strength is to be carried outwith local stresses.
Safety factors for ductile cast iron materials are given by Table 3.5.2. Compared to Table 3.5.1 they are higher because of an additional partial safety factor jF that accounts for inevitable but allowable defects in castings. The factor is different for castings that have been subject to non-destructive testing or have not *4 .
4 In mechanical engineering. cast components areof standard quality for which a further reduction of the partial safety factor to jr = 1,0 does not seem possible up to now. A safety factor jF = 1,0 may be applied to high quality cast components in the aircraft industry however. Those high quality cast components have to meet special demands and (cont'dpage 91)
91
3.5 Safety factors
Table 3.5.2 Safety factors jm and jp for ductile cast iron materials (GS; GGG with A5~ 12,5 %) -}1 Consequences of failure severe moderate
jm
jp jmt
castings not subject to non-destructive testing-}2 high 2,8 2,45
low
2,1
1,8
2,1 1,4 2,55
1,8 1,4 2,2
1,9
1,65
1,9 1,4
1,65 1,4
castings subject to non-destructive testing -}3 high 2,5 2,2 Probability of occurrence of the characteristic service stress values
GG 0,5 Aj
o
Jpt
Probability of occurrence of the characteristic service stress values
3 Assessment of the static strength using local stresses
low
1,9
1,65
1,9 1,25 2,25
1,65 1,25 2,0
1,7
1,5
1,7 1,25
1,5 1,25
-}1 Explanatory notes for the safety factors see Table
1U 12,5
20 As ,A3 in %
Figure 3.5.1 Value L\j to be added to the safety factors jm and jp , defmed as a function of the elongation As or A3 respectively.
3.5.3 Wrought aluminum alloys 3.5.3.0 General Ductile and non-ductile wrought aluminum alloys are to be distinguished.
3.5.3.1 Ductile wrought aluminum alloys Wrought aluminum alloy with an elongation A ~ 12,5 % are considered as ductile materials. Values of elongation see Table 5.1.22 to 5.1.30. The safety factors for ductile wrought aluminum alloys are the same as for steel, Table 3.5.1.
3.5.1.
-}2
Compared to Table 3.5.1 an additional partial safety factor jF = 1,4 is introduced to account for inevitable but allowable defects in castings.
-}3
Compared to Table 3.5.1 an additional partial safety factor jF = 1,25 is introduced, for which it is assumed that a higher quality of the castings is obviously guaranteed when testing.
3.5.2.2 Non-ductile cast iron materials Cast iron materials with an elongation As < 12,5 % (A3 < 12,5 % for GT) are considered as non-ductile materials, in particular some types of GGG as well as all types of GT and GG. Values of elongation for GGG and GT see Table 5.1.12 or 5.1.13. The value for GG is As = 0 *5. For non-ductile cast iron materials the safety factors from Table 3.5.2 are to be increased by adding a value L\j, Figure 3.5.1 *6: L\j
=
0,5 -~A5 /50%.
(3.5.2)
3.5.3.1 Non-ductile wrought aluminum alloys Wrought aluminum alloy with an elongation A < 12,5 % are considered as non-ductile materials. Values of elongation see Table 5.1.22 to 5.1.30. For non-ductile wrought aluminum alloys all safety factors from Table 3.5.2 are to be increased by adding a value L\j, Figure 3.5.1 and Eq. (3.5.2).
3.5.4 Cast aluminum alloys Cast aluminum alloys are always considered as nonductile materials. Values of elongation see Table 5.1.31 to 5.1.38. For cast aluminum alloys all safety factors from Table 3.5.2 are to be increased by adding a value L\j, Figure 3.5.1 and Eq. (3.5.2).
AS Elongation, to be replaced by A3 for GT.
checks' on qualification of the production process, as well as on the quality and extent of product testing in order to guarantee little scatter of their mechanical properties. 5 For GG the values Jp and Jpt are not relevant since the yield strength and the creep limit of GO are not specified.
6 For example the safety factor Jm for GG is at least
jm
(3.S.3)
= 2,0 + O,S = 2,S .
( jm = 2,0 from Table 3.5.2, moderate consequences, nondestructively tested, low probability, ~j O,S for AS = 0 from Eq.
=
(3.S.2) ).
92
3.5 Safety factors
3.5.5 Total safety factor From the individual safety factors the total safety factor is to be derived *7:
jges
(3.5.4)
jges =
MAX(~ ~.Rm ~ ~.Rm] KT,m ' KT,p
.lm ... Kt,m ...
R p ' KTt,m ' KTt,p
n, ,
safety factors, Table 3.5.1 and 3.5.2, temperature factors, Chapter 3.2.5 *8.
Simplifications The following simplifications apply to Eq. (3.5.4): In the case of normal temperature the third and fourth term have no relevance *9, and moreover there is KT,m = K T. p =1 , for Rp / Rms 0,75 the first term has no relevance, for Rp / Rm > 0,75 the second term has no relevance * 10, for GG the second and fourth term have no relevance *11.
7 MAX means that the maximum value of the four terms in the parenthetical expression is valid. 8 Applicable to the tensile strength Rm or to the yield strength Rp to allow for the tensile strength at elevated temperature ~ T ' the hot yield strength ~,T' the creep strength Rm,Tt , or the creep limit Rp,Tt, respectively' 9 The terms containing the factors KTt,m and KTt,p must not be applied in the case of normal temperature, as they will produce misleading results. 10 If there is a ratio of the safety factorsjp I jm = 0,75. 11 Since a yield strength and a creep limit are not specified.
3 Assessment of the static strength using local stresses
93
3.6 Assessment
3.6 Assessment Contents
3 Assessment of the static strength using nominal stresses !R36 EN.dog
strength, O"SK , ..., divided by the total safety factor jges. The degree of utilization is always a positive value.
Page
3.6.0
General
3.6.1 3.6.1.1 3.6.1.2
Rod-shaped (ID) components Individual types of stress Combined types of stress
3.6.2 3.6.2.1 3.6.2.2
Shell-shaped (2D) components Individual types of stress Combined types of stress
3.6.2 3.6.2.1 3.6.2.2
Block-shaped (3D) components Individual types of stress Combined types of stress
93
94
95
Superposition For stress components of the same type of stress the superposition is to be carried out according to Chapter 3.1. If different types of stress like normal stress and shear stress act simultaneously and if the resulting state of stress is multiaxial, see Figure 0.0.9 *5, the particular
extreme maximum stresses and the extreme minimum stresses are to be overlaid as indicated in the following. 96
Kinds of component
3.6.0 General According to this chapter the assessment of the component static strength using local stresses is to be carried out. In general the assessments for the individual types of stress and for the combined stress are to be carried out separately * I *2. In general the assessments for the extreme maximum and minimum stresses (normal stresses in tension and compression and/or shear stress) are to be carried out separately. For steel or wrought aluminum alloys the highest absolute value of stress is relevant *3.
Rod-shaped (lD), shell-shaped (2D) and block-shaped (3D) components are to be distinguished. They can be both non-welded or welded
3.6.1 Rod-shaped (ID) components 3.6.1.1 Individual types of stress Rod-shaped (ID) non-welded components The degrees of utilization of rod-shaped non-welded components for the different types of stress like normal stress or shear stress are
The calculation applies to both non-welded and welded components. For welded components assessments are generally to be carried out separately for the toe and for the root of the weld as indicated in the following.
aSK,O' =
aSK,~
Degree of utilization The assessments are to be carried out by determining the degrees of utilization of the component static strength. In the context of the present Chapter the degree of utilization is the quotient of the characteristic stress (extreme stress O"max,ex, , ...) divided by the allowable static stress at the reference point *4. The allowable static stress is the quotient of the component static
I It is a general principle for an assessment of the static strength to suppose that all types of stress observe their maximum (or minimum) values atthe same time. 2 This is in order toexamine the degrees ofutilization ofthe individual types ofstress in general, and in particular if they may occur separately.
Different in the case ofcast iron materials or cast aluminium alloys with different static tension and compression strength values.
3
4 The reference point isthe critical point ofthe cross section that observes the highest degree ofutilization.
=
Cimax,ex
~
1,
(3.6.1)
CiSK / jges 'tmax,ex 'tSK / jges
s
1,
O"max,ex, , ...
extreme maximum stresses according to type of stress; the extreme minimum stresses, O"min,ex, , ..., are to be considered in the same way as the maximum stresses, Chapter 3.1.1.1,
O"SK, ...
related component static strength, Chapter 3.4.1,
jges
total safety factor, Chapter 3.5.5.
All extreme stresses are positive or negative (or zero). In general normal stresses in tension or compression are to be considered separately. For shear the highest absolute value of shear stress is relevant. 5 Only in the case ofstresses acting simultaneously the character ofEq. (1.6.4) and (1.6.12) isthat ofa strength hypothesis. If Eq. (1.6.4) and (1.6.12) are applied in other cases, they have the character ofan empirical
interaction formula only. For example the extreme stresses from bending and shear will -as arule - occur atdifferent points ofthe cross-section, so that different reference points W are to be considered. As a rule bending will be more important. Moreover see Footnote 1.
94
3 Assessment of the static strength using nominal stresses
3.6 Assessment
Rod-shaped (ID) welded components For the toe of the weld of rod-shaped (lD) welded components the calculation is to be carried out as for rod-shaped (lD) non-welded components. For the root of the weld of rod-shaped (lD) welded components the degrees of utilization for normal stress and/or shear stress follow from the equivalent nominal stresses, Chapter 3.1.1.1: . O"max,ex wv aSK, wv,e = / .'.$; 1, O"SK Jges
(3.6.2)
q
f,
O"max,ex,wv , ... Extreme maximum equivalent structural stresses; the extreme minimum stresses, Smin,ex,wv,zd .. , , are to be considered in the same way as the maximum stresses, Chapter 3.1.1.1,
All extreme stresses are positive or negative (or zero). In general normal stresses in tension or compression are to be considered separately. For shear the highest absolute value of shear stress is relevant.
Rod-shaped (ID) welded components For the toe of the weld of rod-shaped (lD) welded components the calculation is to be carried out as for rod-shaped (lD) non-welded components.
(3.6.8) aSK,wv,cr, ... degree of utilization , Eq. (3.6.2).
3.6.2 Shell-shaped (2D) components
The degrees of utilization of shell-shaped (20) nonwelded components for the types of stress like normal stress in the directions x and y as well as shear stress are
3.6.1.2 Combined types of stress
asK,crx =
O"max,ex,x ..$; 1, O"SK,x / Jges
asK,cry =
O"max,ex,y ..$; 1, O"SK,y / Jges
Rod-shaped (ID) non-welded components
(3.6.4)
where
s = aSK,cr ,
(3.6.5)
(3.6.9)
't max, ex I----I.$; 1, 'tSK / jges
For rod-shaped (lD) non-welded components the degree of utilization for combined types of stress is *6
2)'
(3.6.7)
./3-1 shear strength factor, Table 3.2.5.
Shell-shaped (2D) non-welded components
total safety factor, Chapter 3.5.5.
aNH=±{lsl +~s2 +4.t
7
*'
3.6.2.1 Individual types of stress
related component static strength values, Chapter 3.4.2,
aSK,crv = q . aNH + (l - q) . llGH.$; 1,
./3-(l/f't)
For the root of the. weld of rod-shaped (ID) welded components the degree of utilization for combined types of stress (or loadings) is *8
'tmax, ex,wv aSK,wv,'t = ..$; 1, 'tSK / Jges
O"SK, ...
For non-ductile wrought aluminum alloys (elongation A < 12,5 %) there is q = 0,5 , otherwise
O"max,ex,x, ... Extreme maximum stresses according to type of stress, Chapter 3.1.1.1; the extreme minimum stresses, O"min,ex,x , ..., are to be considered in the same way as the maximum stresses, Chapter 3.1.1.2,
(3.6.6)
t = aSK,cr ,
7Table 1.6.1 Constant q(f
t ) .
aSK,cr, .., degree of utilization, Eq. (3.6.1).
r, q
6 The applied strength hypothesis for combined types of stress is a combination ofthe normal stress criterion (NH) and the v. Mises criterion (GH). Depending on the ductility of the material the combination is controlled by a parameter q as a function off, according to Eq. (1.6.7) and Table 1.6.1. For steel isq = 0 so that only the v. Mises criterion isof effect. For GG isq = 0,759 so that both the normal stress hypothesis and the v. Mises criterion are of partial influence.
Steel, Wrought AI-alloys 0,577 0,00
GOO
GT, Cast
GG
Al-alloys
0,65 0,264
0,75 0,544
0,85 0,759
Caution: For non-ductile wrought aluminium alloys (elongation A < 12,5 %) there is q = 0,5. 8 Eq. (3.6.8) does not agree with the structure ofEq. (3.1.2) on page 74. is an approximation which has to be regarded as provisional and therefore itis tobe applied with caution. It
95
3.6 Assessment
3 Assessment of the static strength using nominal stresses
J
related static component strength, Chapter 3.4.1,
crSK,x , ...
2 2· 2,
(3.6.14)
Sx = aSK,crx ,
Total safety factor, Chapter 3.5.5. All extreme stresses are positive or negative (or zero). In general normal stresses in tension or compression are to be considered separately. For shear stress the highest absolute value is relevant.
Sy = aSK,cry , t = aSK,., asK,crx, ... degree of utilization, Eq. (3.6.9). For non-ductile wrought aluminum alloys (elongation A < 12,5 %) there is q = 0,5 , otherwise
Shell-shaped (2D) welded components
./3 -(lIf.) ./3-1 * ' 9
For the toe of the weld of shell-shaped (2D) welded components the calculation is to be carried out as for shell-shaped (2D) non-welded components. For the root of the weld of shell-shaped (2D) welded components the degrees of utilization for normal stresses in the directions x and y as well as for shear stress follow from the equivalent local stresses, Chapter 3.1.1.2: -
0"
~
1,
SK,wv,cry -
0"
s
1 ,
aSK,
a
wv.ox -
aSK,wv;t =
max,ex,wv,x / . O"SK,x Jges max,ex,wv,y / . O"SK,y Jges
(3.6.10)
(3.6.15)
f. shear strength factor, Table 3.2.5. Rules of sign: If the individual types of stress always act unidirectionally at the reference point *9, the degrees of utilization aSK,crx and asK,cry are to be inserted into Eq. (3.6.14) with equal (positive) signs (summation). If they always act opposingly, however *10, the degrees of utilization aSK,crx and aSK,cry are to be inserted into Eq. (3.6.14) with different signs. In the general case - without knowing whether the stresses act unidirectionally or opposingly *11 - the degrees of utilization are to be inserted into Eq. (3.6.14) both with equal or with different signs; then the least favorable case is relevant.
'tmax,ex,wv . ~ 1, 'tSK / J ges
O"max,ex,wv, ... extreme maximum stresses (equivalent local stresses); the extreme minimum stresses, O"min,ex,wv, ... , are to be considered in the same way as the maximum stresses, Chapter 3.1.1.1, O"SK,x ...
q
related static component strength values, Chapter 3.4.2, total safety factor, Chapter 3.5.5.
All extreme stresses are positive or negative (or zero). In general normal stresses in tension or compression are to be considered separately. For shear stress the highest absolute value is relevant.
Moreover the degrees of utilization calculated with crmin,ex,x , crmin,ex,y and 'tmin,ex,s are to be included in this comparative evaluation.
Shell-shaped (2D) welded components For the toe of the weld of shell-shaped (2D) welded components the calculation is to be carried out as for shell-shaped (2D) non-welded components. For the root of the weld of shell-shaped (2D) welded components the degree of utilization for combined types of stress (or loadings) is "8 (3.6.16)
J
2
2
2
aSK, crwv = aSK,wv,crx +aSK,wv,cry +aSK,wv,. ' aSK,wv,crx, ... degrees of utilization, Eq. (3.6.10).
3.6.2.2 Combined types of stress Shell-shaped (2D) non-welded components The degree of utilization of shell-shaped (2D) nonwelded components for combined stresses is *6 aSK,ov = q . aNH + (l - q). where
1,
(3.6.12)
9 For example tension in direction x and tension in direction y from a single loading affecting the component. 10 For example tension indirection xand compression indirection yfrom a single loading affecting the component. 11 For example, iftwo loadings vary with time ina different manner.
96 3 Assessment of the static strength
3.6 Assessment
using nominal stresses For non-ductile wrought aluminum alloys (elongation A < 12,5 %) there is q = 0,5 , otherwise
3.6.3 Block-shaped (3D) components 3.6.3.1 Individual types of stress
The degrees of utilization of block-shaped (3D) nonwelded components in terms of the principal stresses in the directions 1,2 and 3 are aSK,O'I
aSK,O'2 =1
q
/3- (lIf't) *9 /3-1 '
(3.6.23)
f't Shear strength factor, Table 3.2.5.
(J
I, max, ex <1 (Jl,SK / jges - ,
(J2,max,~x 1~
(J2,SK / Jerf
(3.6.17)
1,
aSK,O'3 = I (J3,max,ex < , 1 / . 1(J3,SK Je-r O'I,max,ex,'"
extreme maximum principal stresses; the extreme minimum principal stresses, O'I,min,ex , ..., are to be considered in the same way as the extreme maximum principal stresses, Chapter 3.1.1.3,
O'SK,1 , ...
related static component strength, Chapter 3.4.1,
Rules of sign: If the individual principal stresses always act unidirectionally at the reference point *13, the degrees of utilization aSK,O'I , aSK,cr2 and aSK,cr3 are to be inserted into Eq. (3.6.22) with equal (positive) signs (summation). If they always act opposingly, however *14, the degrees of utilization aSK,crl , aSK,cr2 and aSK,cr3 are to be inserted into Eq. (3.6.22) with different signs. In the general case - without knowing whether the stresses act unidirectionally or opposingly - the degrees of utilization are to be inserted into Eq. (3.6.22) both with equal or with different signs; then the least favorable case is relevant. Moreover the degrees of utilization calculated with O'l,min,ex , 0'2,min,ex and 0'3,min,ex are to be included in this comparative evaluation.
total safety factor, Chapter 1.5.3. All extreme principal stresses may be positive or negative (or zero). Tension and compression are generally to be considered separately.
3.6.3.2 Combined types of stress
The degree of utilization of block-shaped non-welded components for the combined principal stresses is *8 aSK,crv = q . aNH + (l - q) . aoH~ 1,
(3.6.20)
where *12 (3.6.21)
SI = aSK,O'I ,
(3.6.22)
s2 = aSK,O'2 , s3 = aSK,O'3 , aSK, 0'1, ... degrees of utilization, Eq. (3.6.17).
13 For example tension in direction 1 and tension indirection 2 from a single loading affecting the component. 12 Max means that the maximum value of the three parenthetical expression is valid.
terms
in the
14 For example tension in direction 1 and compression in direction 2 from a single loading affecting the component.
97
4.1 Characteristic service stresses
4 Assessment of the fatigue strength using local stresses
4 Assessment of the fatigue strength using local stresses *1 C"IR:-:-4l:-=EN:-:-.--=-do-'q
Stress cycle
4.0 General
Example:
According to this chapter the assessment of the fatigue strength using local stresses is to be carried out.
4.1 Parameters of the stress spectrum Contents
Page
4.1.0
General
4.1.1 4.1.1.0 4.1.1.1 4.1.1.2 4.1.1.3
Characteristic service stresses according to the kind of component General Rod-shaped (lD) components Shell-shaped (2D) components Block-shaped (3D) components
4.1.2 4.1.2.0 4.1.2.1 4.1.2.2
Parameters of the service stress spectrum General Mean stress spectrum Stress ratio spectrum
4.1.3
Adjusting a stress spectrum to match the 100 component constant amplitude S-N curve
4.1.4
Determination of the parameters of a service stress spectrum General Standard stress spectrum Class of utilization Damage-equivalent stress amplitude
4.1.4.0 4.1.4.1 4.1.4.2 4.1.4.3
Figure 4.1.1
97
stress cycle (normal stress), stress ratio a . -a . Rai= m,1 a,l , crm,i + 0' a.i t
A special case is the constant amplitude spectrum, consisting of one step i = j = 1 only. For normal stress there is O"a = O"a,i = 0"a,1, O"m = O"m,i = O"m,1 .
Superposition 98 99
102
Proportional or synchronous stresses several proportional or synchronous stress components act simultaneously at the reference point, Chapter 0.3.5, they are to be overlaid. For the same type of stress (for example unidirectional normal stresses 0"a,1, 0"m,1 and O"a,2 , 0"m,2) the superposition is to be carried out at this stage, so that in the following a single stress component (O"a, O"m ...) exists for each type of stress *3. For different types of stress (normal stress and shear stress or normal stress in x- and y-direction) the superposition is to be carried out at the assessment stage, Chapter 4.6.
If
Non-proportional stresses If several non-proportional stress components act
4.1.0 General
simultaneously at the reference point, Chapter 0.3.5, they are to be overlaid according to Chapter 5.10.
According to this chapter the parameters of the service stress spectra are to be determined (spectra for elastically determined local stresses). Spectra are applicable for N > 104 cycles approximately.
4.1.1 Characteristic service stresses according to the kind of component
Relevant are the stress spectra of the individual stress components. They are specified by a number of steps, i = I to j , giving the amplitudes O"a,i, ... and the related mean values O"m,i , ... of stress cycles, Figure 4.1.1, as well as the related numbers of cycles ni according to the required fatigue life *2.
4.1.1.0 General Rod-shaped (lD), shell-shaped (2D) and block-shaped (3D) components are to be distinguished. They may be both non-weldedor welded. For welded components the local stresses may be determined as either structural stresses or effective notch stresses. Local stresses may be applied even if nominal stresses can not be computed because a nominal cross-section can not be clearly defined.
1Chapters 4.1 and 2.1 are basically identical. 2 As a rule a stress a spectrum is to be determined for normal service conditions, see Footnote 2 on page 73. The largest amplitude 0a,1 ofa service stress spectrum with its related mean stress value am,1serves as the characteristic stress value.
3 Stress components acting opposingly can cancel each other in part or completely.
98
4.1 Characteristic service stresses
4 Assessment of the fatigue strength using local stresses
4.1.1.1 Rod-shaped (ID) components Rod-shaped (ID) non-welded components
4.1.1.2 Shell-shaped (2D) components
For rod-shaped (ID) non-welded components a local normal stress Cl"zd = cr and a shear stress 'ts = 't are to be considered *4. The respective amplitudes and mean values are
The calculation for shell-shaped (2D) components may also be applied to block-shaped (3D) components, if the stresses Cl"x, Cl"y and 't at the surface are of interest only.
Cl"a,i , 'ta,i ,
(4.1.1)
Shell-shaped (2D) non-welded components
Cl"m,i ,'tm,i·
Rod-shaped (ID) welded components For rod-shaped (lD) welded components the local stresses (structural stresses or effective notch stresses *5) are in general to be determined for the toe and the root of a weld separately *6.
Calculation with structural stresses
When performing a calculation of welded rod-shaped (ID) components with structural stresses a normal stress (normal stress) rr and a shear stress 't are to be considered. The respective amplitudes and mean values are (4.1.2)
Cl"m,i , 'tm,i .
Calculation with effective notch stresses Effective notch stresses may be applied to the toe and to the root of a weld *6. When performing a calculation of welded rod-shaped (ID) components with effective notch stresses a normal stress Cl"K and a shear stress 'tK are to be considered. The respective amplitudes and mean values are Cl"K,a,i , 'tK,a,i ,
Cl"a,x,i , Cl"a,y,i , 'ta,i ,
(4.1.4)
Cl"m,x,i , Cl"m,y,i , 'tm,i .
Shell-shaped (2D) welded components
Structural stresses are to be applied to the toe of a weld only. For the root of a weld the calculation is to be carried out with effective notch stresses *7.
Cl"a,i , 'ta,i ,
For shell-shaped (2D) non-welded components the (local) normal stresses in x- and y-direction, Cl"zdx = Cl"x and Cl"zdy = Cl"y, as well as a shear stress 'ts = 't are to be considered. The respective amplitudes and related mean values are
(4.1.3)
For shell-shaped (2D) welded components, Figure 0.0.6 and 0.0.7, the local stresses (structural stresses or effective notch stresses) are in general to be determined for the toe and the root of a weld separately *6.
Calculation with structural stresses Structural stresses are to be applied to the toe of a weld only. For the root of a weld the calculation is to be carried out with effective notch stresses *7 • When performing a calculation of welded shell-shaped (2D) components with structural stresses, the normal stresses in the directions x and y , Cl"x and Cl"y , as well as a shear stress 't are to be considered. The respective amplitudes and mean values are Cl"a.x.i » Cl"a.y.i » 'ta,i,
(4.1.5)
Cl"m,x,i, Cl"m,y,i, 'tm,i·
Calculation with effective notch stresses
Cl"K,m,i , 'tK,m,i .
4 Rod-shaped (10) components may be subject to normal stresses resulting from tension-compression and from bending and to shear stresses resulting from shear and torsion. The case that these stresses may occur separate from each other, is not considered here, however, as both tension-compression stresses and bending stresses as well as both shear stresses and torsion stresses are supposed to be contained in cr or in 't, respectively. 5 Definition of structural stresses and of effective notch stresses see Figure 0.0.6 and Figure 0.0.7, Chapter 5.4 and 5.5 6 For welded components separate assessments of the fatigue strength for both the toe and the root of the weld are to be carried out. Both assessments are of the same kind, but in general the respective stresses and fatigue classes FAT are different. 7 An alternative is an assessment of the throat section using nominal stresses.
When performing a calculation of welded shell-shaped (2D) components with effective notch stresses, the normal stress in the direction of the maximum effective notch stress, Cl"K , as well as the shear stress, 'tK , are to be considered. The respective amplitudes and mean values are Cl"K,a,x,i , Cl"K,a,y,i , 'tK,a,i,. Cl"K,m,x,i, Cl"K,m,y,i, 'tK,m,i·
(4.1.6)
99
4.1 Characteristic service stresses
4.1.1.3 Block-shaped (3D) components
4 Assessment of the fatigue strength using local stresses O"m,i N
Block-shaped (3D) non-welded components For block-shaped (3D) non-welded components the (local) principal stresses in the directions 1, 2 and 3, O"I,zd = 0"1 , 0"2,zd = 0"2 and 0"3,zd = 0"3 , are to be considered. The respective amplitudes and related mean values are (4.1.7) O"I,a,i , 0"2,a,i , 0"3,a,i, O"I,m,i , 0"2,m,i, 0"3,m,i· Caution: Independent of the particular values of the principle stresses the directions 1 and 2 are defined here to be parallel to the free surface, the direction 3 to point normally to the surface into the interior of the component.
n'I
H
h·I
j Vzd
mean value in step i, total number of cycles corresponding to the required fatigue life (required total number of cycles), N = Lni (summed up for 1 to j), related number of cycles in step i, N, = Lni (summed up for 1 to i), total number of cycles of a given spectrum, H = Hj = Lhi (summed up for 1 to j) *11, related number of cycles in step i, Hi = Lhi (summed up for 1 to i), step, i = 1 to j, total number of steps, step for the smallest amplitudes, damage potential.
The damage potential is defined by *12,
Block-shaped (3D) welded components For certain applications block-shaped (3D) components may be welded at the surface, for example by a surfacing welds. Then the calculation can be carried out as for shell-shaped (2D) welded components, if the stresses o"x, O"y and 't are of interest only.
Ye =
ke
J.
L
h· [ O"ai )kcr. I. - ' -
i=1 H
(4.1.10)
0" a,I
where k, is the exponent ofthe component S-N curve. O"a,i /O"a,I and hi / H describe the shape of stress spectrum. The amplitudes O"a,i are always positive, the mean values O"m.i may be positive, negative, or zero.
4.1.2 Parameters of the stress spectrum 4.1.2.0 General
A stress spectrum describes the stress cycles contained in the stress history of concern *8.
As a rule a restriction to the following kinds of stress spectra is possible: Mean stress spectra and stress ratio spectra (with the fluctuating stress spectra as a special case), Figure 2.1.2 *13.
If the stress cycles show variable amplitudes a stress
spectrum is to be determined for every stress component *9. The constant amplitude stress spectrum may be regarded in the following as a special case *10, for which i = 1 and O"a = O"a,i = 0"a,1 .
(4.1.8)
4.1.2.1 Mean stress spectrum
A constant mean stress applies to all steps of a mean stress spectrum: O"m,i = O"m·
(4.1.11)
N= N = nj = nl
Parameters of stress spectrum are: 0"a,1 O"a,i
characteristic (largest) stress amplitude equal to the amplitude in step 1 of the stress spectrum, amplitude in step i, O"a,i > 0, O"a,i+1/ O"a,i s 1,
8 In the following all variables and equations are presented for the local stress o only, but written with the appropriate indices they are valid for all other types ofstress as well. normal
9 In this case anassessment ofthe variable amplitude fatigue strength is tobe carried out. lOin this case an assess~nt ofthe fatigue limit isto be carried out for type I SoN curves if N= N ;:: ND,cr.,.2r an assessment ofthe endurance limit for type II SoN curves if N = N ;:: NDcr II , respectively, oran assessment for finite life based on the constant amplitude SoN curve (formally similar.20 an assessment ~ the variable amplitude fatigue strength) if N = N < ND,cr or N= N ;:: ND,cr, II for Typ I orTyp II SoN curves, respectively. ND,cr orND,cr, II isthe number ofcycles at the fatigue limit ofthe component constant amplitude SoN curve, Chapter 2.4.3.2.
2.1.2.2 Stress ratio spectrum
A constant stress ratio applies to all steps of a stress ratio spectrum:
Res,i = Res ,
(4.1.12)
11 The values N -total number ofcycles required -and II -total num~ ofcycles ofa given spectrum - are different ingeneral. The terms ni IN and hi I H are equivalent. 12 The damage potential is a characteristic for the shape of a stress spectrum. The values kcr = 5for normal stress and k't = 8for shear stress are valid for non-welded components. The values kcr = 3 and ~ = 8 are valid for welded components. The term hi IH may be replaced by ni IN . 13 A mean stress spectrum, for example, results from a static load with dynamic loads superimposed, a fluctuating stress spectrum, for example, results for a crane hook when lifting variable loads.
100
4.1 Characteristic service stresses
4 Assessment of the fatigue strength
using local stresses
4.1.3 Adjusting a stress spectrum to match the component constant amplitude S-Ncurve This chapter mainly applies to stress spectra the steps of which do not have the same stress ratio.
A mean stress spectrum, for example, has different amplitudes Ga,i ' and constant mean stress values Gm,i = Gm ' and consequently the individual steps have different stress ratios Ra,i . On the other hand the component constant amplitude S-N curve, Chapter 4.4.3.2, is derived for a constant stress ratio Ra . To allow the proper application of Miner's rule, Chapter 4.4.3.1, all steps of a spectrum, however, must have or must be converted to that stress ratio Ra,i = Ra, Chapter 5.6.1.
4.1.4 Determination of the parameters of a stress spectrum
'.. '.-H'
= 106
4.1.4.0 General
1
20'a,l
If the stress spectrum of a component under consideration is not known, or in case of high demands on its accuracy, the parameters of the stress spectrum are to be determined by calculation, by simulation, or by measurement. The determination of the stress spectrum from a stress history has to be realized according to the rainflow cycle counting procedure or in the sense of this procedure.
"I"
20'a,1
O'roin =
0
6 -H=10
From a measured and graphically presented continuous stress spectrum a stepped stress spectrum may be obtained according to Chapter 5.6.2.
Figure 4.1.2 Stress spectra *14.
extrapolated to the required total number of cyclesN.
In case of existing experiences - dependent on the component and its application - the determination of the parameters of a stress spectrum may be simplified by applying a standard stress spectrum, a class of utilization or a damage-equivalent stress amplitude.
where
4.1.4.1 Standard stress spectrum
Top: Mean stress spectrum. Midle: Stress ratio spectrum. Bottom: Fluctuating stress spectrum. Example: The presented stress spectra are. standard type stress spectra, basically defined by a binomial frequency distribution, a coefficient p = 1/3 , a total number of cyclesH = 106 , and
Ra = (Gm,i - Ga,i) / (Gm,i + Ga,i)
(4.1.13)
Gm,i / Ga,i = (1 + Ra) / (l - Ra).
(4.1.14)
or
Special case: Fluctuating stress spectrum
A constant stress ratio of zero applies to all steps of a fluctuating stress spectrum: Ra,i =Ra = 0,
(4.1.15)
Gm,i / Ga,i = 1.
(4.1.16)
Standard stress spectra are used to describe the shape of typical stress spectra. Standard stress spectra having a binomial or an exponential frequency distribution, and modified by the spectrum parameter p , are presented in Figure 4.1.3. In addition, damage potentials v, according to Eq. (4.1.10) and Figure 4.1.1 are given in the graphical presentations. (These apply to an exponent of the component constant amplitude S-N curve k, = 5 and a total number of cycles H = 106 ). Parameters of a so derived stress spectrum
or Ga,l N
or Ga,i / Ga,l and hi , i = 1 to j, according to the shape of the standard stress spectrum Sm,i mean values, i = 1 to j.
Vcr
14 To derive the steps of a spectrum see chapter 5.6.2.
characteristic (largest) stress amplitude equal to the amplitude in step 1 of the stress spectrum, required total number of cycles,
101
4.1 Characteristic service stresses
4 Assessment of the fatigue strength using local stresses Table 4.1.1 Damage potential v, and v- for standard stress spectra having a binomial or exponential frequency distribution, modified by the spectrum parameter p, a total number of cycles H = 106 , for nonwelded and welded components, for normal stress and shear stress (exponents of the constant amplitude S-N curve k, and k, ). welded non-welded Expon, binom. I expon. binom. normal stress
p Vcr
ka= 5 Step i
°
P 1 2 3 4 5 6 7 8
1 0,950 0,850 0,725 0,575 0,425 0,275 0,125
1,0
h·I
Ga i / Ga I
1
1/3
2/3
1 0,967 0,900 0,817 0,717 0,617 0,517 0,417
1 0,983 0,950 0,908 0,858 0,808 0,758 0,708
2~3
1/6 1/3 1/2 2/3 5/6 1
2 2 16 18 280 298 2720 3018 20000 23000 92000 115000 280000 395000 604982 1000000
k, 0,399 0,452 0,527 0,627 0,743 0,869 1
°
1/6 1/3 1/2 2/3 5/6 1
p
8
0,267 0,366 0,483 0,608 0,737 0,868 1
=3 0,155 0,286 0,426 0,569 0,712 0,856 1
shear stress
Vt
1
4
aa,i aa,l
°
H-1
k,
0,196 0,297 0,430 0,570 0,713 0,856 1
0,326 0,400 0,499 0,615 0,739 0,868 1
=8 0,275 0,330 0,438 0,573 0,713 0,856 1
0,326 0,400 0,499 0,615 0,739 0,868 1
k, = 5 0,196 0,297 0,430 0,570 0,713 0,856 1
2/3
0,5 1/3
Analytical relationship: For standard stress spectra (p = 1/6, 1/3, 1/2, 2/3, with spectrum parameters p > 5/6) there is
°
[
Step i P
1 2 3 4 5 6 7 8
Ga
°
1 0,875 0,750 0,625 0,500 0,375 0,250 0,125
i/
hi
Gal
1/3
2/3
1 0,917 0,833 0,750 0,667 0,583 0,500 0,417
1 0,958 0,917 0,875 0,833 0,792 0,750 0,708
a.l
p
(4.1.17)
a,l p=o
H·1
2 2 10 12 64 76 340 416 2000 2400 11000 13400 61600 75000 924984 1000000
Figure 4.1.3 Standard stress spectra Top: Binomial distribution. Bottom: Exponential distribution (straight line distribution). Spectrum parameter p, total number of cycles H = Hj = ~ hi = 106, number of steps j = 8 , damage potential Vcr for an exponent k cr = 5 of the component constant amplitude S-N curve.
= p + (1- p) .[:a,i)
: a,i )
Application: In case of existing experiences about the shape of the stress spectrum a suitable standard stress spectrum may be applied to assess the variable amplitude fatigue strength in two ways: -
Application of the damage potential v.,; Eq. (4.1.10) for an assessment of the variable amplitude fatigue strength according to the elementary version of Miner's rule, Chapter 4.4.3.1.
-
Application of the data on Ga,i / Ga,1 and hi of the steps i = 1 to j from Figure 4.1.3 for assessing the variable amplitude fatigue strength according to the consistent version of Miner's rule, Chapter 4.4.3.1.
The appropriate standard stress spectrum has to be specified separate from this guideline.
102
4.1 Characteristic service stresses
4.1.4.2 Class of utilization *15
A class of utilization is an approximately damageequivalent combination of different shapes of stress spectra and of specific figures of the required total numbers of cycles, Figure 4.1.4, see also Chapter 5.7.
4 Assessment of the fatigue strength using local stresses
question. In particular it is defined by the shape of the stress
cra.
WL
cra,1 Cl'a,cJt ~~......,-,...----i
....--~~--
ND,Q' N
Iii'
Figure 4.1.5 Damage-equivalent stress amplitude
Figure 4.1.4 Spectra corresponding to the same class of utilization
Component constant amplitude S-N. curve WL, number of cycles at the knee point ND cr, component variable amplitude fatigue life curve LL. Characteristic stress amplitude 0"a,1, required total number ofcycles. The damage-equivalent stress amplitude O"a,eff is. assigned to ND,O" and hence itallows an assessment ofthe variable amplitude fatigue strength to be performed asan assessment ofthe fatigue limit.
Example: Welded component, stress spectra with binomial distribution, stress. All three stress spectra are approximately damageequivalent and correspond to the same class of utilization B5, Table 5.7.4.
spectrum, the required total number of cycles and the characteristic (largest) stress amplitude, Figure 4.1.5.
N
normal
Parameters of the so derived stress spectrum Parameters of a so derived stress spectrum 0"a,1 B
O"m
characteristic (largest) stress amplitude equal to the amplitude in step 1 of the stress spectrum, class of utilization (a combination of the shape of the stress spectrum and the required total number of cycles), mean stress *16.
Analytical relationship: See Chapter 5.7. Application: In case of existing experiences about the shape of stress spectrum and the required total number of cycles a FEM-class of loading may be applied to the assessment of the variable amplitude fatigue strength, Chapter 2.4.3.1. The appropriate class of utilization has to be specified separate from this guideline.
4.1.4.3 Damage-equivalent stress amplitude
The damage-equivalent stress amplitude is a constant stress amplitude with an assigned number of cycles equal to the number of cycles at the knee point of the component constant amplitude S-N curve, ND CJ • It is damage-equivalent to the stress spectrum in
O"a,eff
damage-equivalent stress amplitude
O"m
related mean value.
Analytical relationship: Based on the elementary version of Miner's rule the damage-equivalent stress amplitude is obtained as d7 1 j 0"a.eff "" k n' ·crak
(4.1.18)
(N / ND,cr )11ks . Vcr . 0"a,1 , exponent of the component constant amplitude S-N curve ND,O"
j, i, n, ... VO"
number of cycles at the knee point of the component constant amplitude S-N curve, see (4.1.9), damage potential, Eq. (4. 1.10).
Application: In case of existing experiences about the damaging effect of the stress spectrum a damageequivalent stress amplitude O"a,eff may be applied. It allows an assessment of the variable amplitude fatigue strength to be performed as an assessment of the fatigue limit, Chapter 2.6. The damage-equivalent stress amplitude has to be specified separate of this guideline.
15 Following DIN 15018. 17 Eq. (4.1.18) is based on a critical damage sum DM = 1, Chapter 16 The determination ofan individual mean stresses crm,i is not possible.
4.4.3.1.
103
4.2 Material parameters
4.2 Material properties *1
1R42
EN.dog
Contents
4.2.0
Page
47
General
4.2.1 Component values according to standards 4.2.1.0 General
Fatigue strength factors for normal stress and for shear stress
4.2.3 4.2.3.0 4.2.3.1 4.2.3.2 4.2.3.3
Temperature factor General Normal temperature Low temperature Elevated temperature
48
4.2.1.2 Welded components For the base material of welded components the material fatigue strength for completely reversed stress are the same as for non-welded components. Steel and cast iron materials
4.2.0 General According to this chapter the material fatigue strength values (component values according to standards) are to be determined, These are the material fatigue limit for completely reversed normal stress, aW,zd , and shear stress, "Cw,s ' as well as further characteristics *2
4.2.1 Component standards
values
fw,cr fatigue strength factor for completely reversed normal stress, Chapter 4.2.2, fW,"t fatigue strength factor for completely reversed shear stress, Chapter 4.2.2, R m tensile strength, Chapter 3.2.1.1. Caution: For non-welded wrought and cast aluminum alloys the fatigue limit is different from the endurance limit associated with N ~ No.e.n =ND,"t,n= lOS cycles.
4.2.1.1 Non-welded components 4.2.1.2 Welded components
4.2.2
4 Assessment of the fatigue strength with local stresses
according
to
4.2.1.0 General The determination of the material fatigue strength is different for non-welded and for welded components.
For the toe and the root of the weld of professionally welded components from weldable structural steel *5 specific values of the fatigue strength apply independent of the kind of material. These are for completely reversed normal stress at N ~ ND,cr = 5' 106 cycles and for completely reversed shear stress at N ~ ND,"t = 1 . lOS cycles *6, Chapter 5.5, aW,zd = aw,w = 92 MPa, "Cw,s = "Cw,w = 37 MPa.
(4.2.3)
Caution: For other kinds of material (conditionally weldable steel, stainless steel, weldable cast iron material) these values are to be considered as provisional and are to be applied with caution.
Aluminum alloys 4.2.1.1 Non-welded components
For non-welded components the values according to standards of the material fatigue strength for completely reversed normal stress and shear stress *3 and for a number of cycles N = 106 *4 are aW,zd = fw,cr . Rm , rw., = fW,"t' aW,zd,
I
(4.2.1)
aW,zd = aw,w = 33 MPa, "Cw,s = "Cw,w = 13 MPa.
Chapters 2.2 and 4.2 are identical.
2 An influence offrequency on the material fatigue strength values is not considered up to now although it might be ofimportance for aluminum alloys. 3 For the tensile strength according to standards, Rm , a probability of survival Po = 97,5 % ispresumed. That probability should also apply to the values crW,zd and "tW,s computed from Rm . Moreover Eq. (1.2.1) applies here too:
crw zd = Kd m. KA . crw zd N, "tw~ = Kd:n· KA'"tW s'N', "
(2.2.2)
"
technological size factor as for the tensile strength, Chapter 3.2.2. anisotropy factor, Chapter 3.2.3, KA crW,zd,N, ... semi-finished product fatigue strength value according to standards, Chapter 5.1. Kd,m
For the toe and the root of the weld of professionally welded components from aluminum alloys *5 specific values of the fatigue strength apply in analogy to steel independent of the kind of material. These are for completely reversed normal stress at N ~ ND,cr = 5 . 106 cycles and for completely reversed shear stress at N ~ ND,"t = 1 . 108 cycles *6, Chapter 5.5, (4.2.4)
Caution: These values are provisional and are to be applied with caution *7 .
4 The values crW.zd and "tw.s correspond tothe fatigue limit which isequal to the endurance limit of steel and cast iron material, but not of aluminum alloys, however, Figure 4.4.5 and Chapter 5.1.0.
5 Weld imperfections occurring with normal production standards are allowable. 6 The values crw.w and "tw.w correspond tothe fatigue limit which is equal tothe endurance limit ofwelded steel and cast iron material aswell as of welded aluminum alloys, Figure 4.4.6 and Chapter 5.1.0.
7 Values derived from an average relation of0,36 ofthe FAT classes for aluminum alloys and for structural steel, Chapter 5.4.
104
4.2 Material parameters
4.2.2 Fatigue strength factors for normal stress and for shear stress The fatigue strength factor for completely reversed normal stress, fw,O" , is the quotient of the axial fatigue strength value for completely reversed stress divided by the tensile strength, Table 4.2.1. The fatigue strength factor for shear stress, fw,~ , considers that the material fatigue strength is lower for shear stress than for normal stress, Table 4.2.1.
4 Assessment of the fatigue strength with local stresses For normal temperature the temperature factor is KT,D'" 1.
(4.2.5)
4.2.3.2 Low temperature Temperatures below the values listed above are outside the field of application of this guideline.
4.2.3.3 Elevated temperature Table 4.2.1 Fatigue strength factors for completely reversed normal stress, fw,O" , and shear stress, fw,~ ~1. Kind of material
fw,O"
Case hardening steel Stainless steel Forging steel Steel other than these GS GGG GT GG Wrought aluminum alloys Cast aluminum alloys
0,40 ~2 0,40 ~4 0,40 ~4 0,45 0,34 0,34 0,30 0,30 0,30 ~5 0,30 ~5
fw,~
0,577
~2 ~3
0,577 0,577 0,577 0,577 0,65 0,75 0,85 0,577 0,75
fw 0" and fw ~ are valid fora number of cycles N = 106 • fw' ~ is equal 'to f~ , Table 3.2.5. ~2 Bla'nk-hardened. The influence of the carburization on the component fatigue strength is to be considered by the surface treatment factor, Kv, Chapter 4.3.4. ~3 0,577 = 1//3, according tothe v. Mises criterion. Also valid for welded components. ~4 Preliminary values. ~5 fW,O" does not correspond tothe endurance limit for N = co here!
In the field of elevated temperatures - up to SOO°C for steel and cast iron materials and up to 200°C for aluminum materials - the influence of the temperature on the fatigue strength is to be considered. For elevated temperature the fatigue strength values for completely reversed normal stress and shear stress are
't:W,s
~1
temperature factor, Eq. (4.2.7) to (4.2.11), material fatigue strength value for completely reversed normal stress, Chapter 4.2.1.1 and 4.2.1.2. material fatigue strength value for completely reversed normal stress, Chapter 4.2. 1. 1 and 4.2.1.2.
According to the temperature T the temperature factor KT,D is for fme grain structural steel, T KT,D"'I-1O-3'T/oC,
> 60 DC: (4.2.7)
for other kinds of steel *7, T> 100°C, Figure 4.2.1: (4.2.8) KT,D = 1-1,4' 10- 3. (T / °C-100), for GS, T> 100°C: KT,D = 1- 1,2 . 10 -3. (T / °C- 100),
4.2.3 Temperature factor 4.2.3.0 General
(4.2.6)
-
The temperature factor considers that the material fatigue strength for completely reversed stress decreases with increasing temperature.
for GGG, GT and GG, T > 100°C, Figure 4.2.1: KT,D'" 1- aT,D' (10 - 3. T / 0C)2, (4.2.10) for aluminum alloys, T > 50°C: KT,D = 1- 1,2' 10 -3. (T / °C - 50)2, Figure 3.2.3 in the Chapter 3.2,
Normal temperature, low temperature and elevated temperature are to be distinguished.
aT,D Constant, Table 4.2.2.
4.2.3.1 Normal temperature Normal temperatures are as follows: for fine grain structural steel from -40°C to 60°C, - for other kinds of steel from -40°C to + 100°C, for cast iron materials from -25°C to + 100°C, - for age-hardening aluminum alloys from -25°C to 50°C, - for non-age-hardening aluminum alloys from -25°C to 100°e.
Table 4.2.2 Constant aT,D *8. Kind of material aT,D
8
(4.2.9)
GGG 1,6
GT 1,3
GG 1,0
Forstainless steel novalues are known up to now.
(4.2.11)
105
4.2 Material parameters
4 Assessment of the fatigue strength
with local stresses Rm,T R m 'jm
High temperature strength Rm,T
I
I Rp I Rp'R m ' jp
o4 I~-+--''r-~:-- Rp,T ,
High temperature yieldstreilgth Rp,T 1 % creep limit Rp;Tt . Rp,Tt It p '1
0,3t----K:--+---",;:t-''':--tt--r---,.-J
R p . Rm ' jpt
Creep Strength R,.,Tt
0,2 m ........."'f-...,...,..,..,.,..,~=--+~-fu~-1
Rm,T~
1
R';;"""' jmt 0;1
o
o
100
ZOO
2.2.1.
300 400 Tin "C
500
Creep$trengthR,.;Tt Rm,Tt I Rm 'jmt
0,1 t====J=::='=b--L....,,=-1-..+1
o
o
100
Z,2.1b
200
300 400 Till 'c
500
Figure 4.2.1 Temperature dependent values of the static strength and of the fatigue strength plotted for comparison. Safety factorsj according to Chapter 3.5 or 4.5, respectively. Rm,TI Rm = KT,m,
Rm,Tt l Rm = KTt,m,
Rp,T I Rp = KT,p, Rp,Tt l Rp = KTt,p'
Rm,T, Rp,T as well as Rm, Tt, Rp,Tt
5
for t = 10 h.
Fatigue strength value at elevated temperature : crW,zd,T I crW,zd = KT,D· Top: Non-alloyed structural steel, as in the Figure 3.2.2, Rp I Rm = n, I R m = 0,65 , crW,zd I Rm = 0,45, Jm = 2,0, Jp = jmt = 1,5, Jpt = 1,0, in = 1,5 . Bottom: GG, as in Figure 3.2.2, crW,zd I Rm = 0,30, Jm = 3,0, Jrnt = in
= 2,4 .
Eq. (4.2.7) to (4.2.10) apply to steel and cast iron materials from the indicated temperature T up to 500°C. Eq. (4.2.11) applies to aluminum alloys up to 200°C. The values CYW,zd,T and 1:W,s,T are not explicitly needed for an assessment of the fatigue strength, as only the temperature factor KT,D is used. For elevated temperature, and in particular when the mean stress Sm, i:- 0 , the fatigue strength in terms of the maximum stress may be higher than the static strength so that the assessment is governed by the static strength.
106
4.3 Design parameters
4 Assessment of the fatigue strength using local stresses KwK,crx =
4.3 Design parameters
(4.3.2)
1R43 EN.dog
Content
=_1_'(1+_1_.(_1_ _ 1)) ncr,x Kf KR,cr
Page
4.3.0
General
4.3.1 4.3.1.0 4.3.1.1 4.3.1.2
Design factors General Non-welded components Welded components
4.3.2 4.3.2.0 4.3.2.1 4.3.2.2
Kt-K f ratios General Computation of Kj-K, ratios Kj-K, ratio for superimposed notches
4.3.3 4.3.4 4.3.5 4.3.6 4.3.7
Roughness factor Surface treatment and coating factor Constant KNL,E Fatigue classes (FAT) Thickness factor
106
w K
: ,O"Y1= ncr,y
107 108
'(1+~.(_1 Kf
KR,cr
1 K y .K s .KNL,E '
-1)1 )
K y .K s .KNL,E
KwK,~ =
~ n1, {1+ ~f K~, -I)J Ky l Ks -(
>
109 110
III 112
The design factors of block-shaped non-welded components for the principle stresses in the directions 1, 2 and 3 (normal to the surface) are *2 KWK,crl =
(4.3.3)
~ n:,1 {1+ ~f -(K~,o -I)) >KYKS\N~E K WK,cr2 =
4.3.0 General According to this chapter the design parameters are to be determined in terms of design factors.
1
=_1 .(1+-2-.(_1 -1)] n cr,2 Kf K R,« KWK,cr3 =
++ ~f
4.3.1 Design factors 4.3.1.0 General Non-welded and distinguished.
welded
components
are
to
be
4.3.1.1 Non-welded components Rod-shaped (lD), shell-shaped (2D) and block-shaped (3D) non-welded components are to be distinguished. The design factors of rod-shaped (lD) non-welded components for normal stress and for shear stress are ·1 KWK,cr =
(4.3.1)
~ n1 {I+ ~f K~,o -I)) >K y >KS\N~E 0
-(
-(
K~o -I)) KYKS\N~E >
Kt-K f ratio, Chapter 4.3.2, constant, Table 4.3.1, if no better estimate is available, KR,cr, ... roughness factor, Chapter 4.3.3, Ky surface treatment factor, Chapter 4.3.4, Ks coating factor, Chapter 4.3.4, constant for GG, Chapter 4.3.5. KNL,E ncr, .., Kf
Table 4.3.1 Constant K,
.
Kind of material
Steel wrought Al-alloys
GS
GGG
GT cast Al-alloys
GG
Kf
2,0
2,0
1,5
1,2
1,0
'
KWK,~ =
=_1
n,
'(1+~.(_1 -1))' 1 x, Ky.K s KR,~
The design factors of shell-shaped (2D) non-welded components for normal stresses in the directions x and y as well as for shear stress are
A better estimate of K f may be obtained from stress concentration factors Kt,cr and Kt,~ of a substitute structure, Chapter 5.12, and the Kt-K f ratios, Chapter 4.3.2.1: Kf~Kt:cr=Kt,cr/ncr or Kf~Kf,~=Kt,~/n~.
1 About the
purpose ofthe constant Kf see Footnote 1 inChapter 2.3.
2 The Kt-Kf ratio in direction 3 normal to the surface, ",,3. , is not contained in Eq. (4.3.3) since a stress gradient normal tothe surface isnot considered.
107
4.3 Design parameters
4,3.1.2 Welded components For the base material of welded components the design factors are to be computed as for non-welded components.
4 Assessment of the fatigue strength using local stresses FAT ft Kv Kg KNL,E
fatigue class, Chapter 4.3.6, thickness factor, Chapter 4.3.7, surface treatment factor, Chapter 4.3.4 *5, coating factor, Chapter 4.3.4; constant for GG, Chapter 4.3.5.
The design factors for the toe and for the root of a weld are in general to be determined separately, since the local stresses and the fatigue classes (FAT) may be different.
The fatigue classes FAT are in general different for normal stresses in the directions x and y as well as for shear stress.
Rod-shaped (lD), shell-shaped (2D) and block-shaped (3D) welded components are to be distinguished. The calculation can be carried out with structural stresses or with effective notch stresses.
For certain applications block-shaped (3D) components may be welded at the surface, for example by surfacing welds. Then the design factors are to be calculated as for shell-shaped (2D) welded components.
Calculation with structural stresses
Calculation with effective notch stresses
Steel and cast iron material
Steel and cast iron material as well as aluminum alloys
The design factors of rod-shaped (lD) welded components made of steel or of cast iron materials *3 for normal stress and for shear stress are, KWK,cr = 225 / (FAT' ft' Kv KNL,E), KWK,~ = 145/ (FAT' ft' Ko ),
(4.3.4)
The design factors of shell-shaped (2D) welded components for normal stresses in the directions x and y as well as for shear stress are KWK,crx = 225 / (FAT' ft' Ky' KNL,E), KwK,cry = 225 / (FAT' ft' Kv KNL,E), KwK,~ = 145/ (FAT' ft' Ko ).
(4.3.5)
The design factors of rod-shaped (lD) welded components made of ~ steel, of cast iron materials l'' , and of a1uminum alloys for normal stress and for shear stress are *6, KWK,crK = 1/ (Kv Kg' KNL,E), KWK,~K = 1/ !Ky' Kg).
For shell-shaped (2D) welded components, as a rule, only the effective notch stress in direction of the maximum effective notch stress and the corresponding shear stress are to be considered. The design factors are as before KWK,crK = 1 / (Ko . Kg . KNL,E ), KWK,~K = 1/ (Ky' Kg),
Aluminum alloys The design factors of rod-shaped (lD) welded components from aluminum alloys *4 for normal stress and for shear stress are, KWK,cr = 81 / (FAT' ft' Ky' Kg), 52 / (FAT' ft' Ky' Ks).
(4.3.6)
KwK,~ =
The design factors of shell-shaped (2D) welded components for normal stresses in the directions x and y as well as for shear stress are KWK,sx = 81 / (FAT' ft' Ky' Kg), KwK,sy = 81 / (FAT' ft' Ky' Kg), KwK,~ = 52/ (FAT' fi' Ky' Kg),
(4.3.8)
Kv Ks KNL,E
(4.3.9)
surface treatment factor, Chapter 4.3.4 *5, coating factor, Chapter 4.3.4, constant for GG, Chapter 4.3.5
For certain applications block-shaped (3D) components may be welded at the surface, for example by surfacing welds. Then the design factors are to be calculated as for shell-shaped (2D) welded components.
(4.3.7)
To some part the FAT values where derived with reference to the IIW recommendations and Eurocode 3 (Ref. /9/, /81). Moreover the design factors are supposed tobe valid, however, not only for weldable structural ste~1 but also for other kinds of steel (conditionally weldable steel, stainless steel) and weldable cast iron materials). 3
To some part the FAT values where derived with reference tothe IIW reco~endations (Ref. /91). Moreover the design factors are supposed to be v.ahd, however, for all weldable aluminum alloys, except the aluminum alloys 5000, 6000 and 7000. Numerical values see Footnote 7 on page 103.
4
5 As a rule
Ky is not relevant for welded components, that is Ky = I.
principle for steel: KWK,crK = 225 / (FAT ... ) where FAT = 225, 145 / (FAT ... ) where FAT = 145; aluminum alloys accordingly, Weld quality conforming tonormal production standard. In combination with effective notch stresses the thickness factor ft is not applied, since the thickness effect isaccounted for by the stress analysis.
6 On
and
K~K,~K =
108
4.3 Design parameters
4 Assessment of the fatigue strength
using local stresses 3
4.3.2 Kt-Kr ratios
GG~V
400
//'~~it//
800
4.3.2.0 General
The Kj-K, ratios nO", ... allow for an influence on the fatigue strength resulting from the design (contour and size) of a non-welded component. Condition for the application of a Kj-K; ratio is a stress gradient normal to the direction of stress as shown in Figure 3.3.1 *7.
/ /
Kt-Kr ratios for normal stress 1,1
The Kt-Kr ratio for normal stress, Ocr, Figure 4.3.1, is to be computed from the related stress gradient GO" after Eq. (4.3.13) to (4.3.15). ;;;;
0,1 rnm"
1
there is
n 0" = 1 +G 0" . mm Itl
(4.3.13)
-(a o -0,5+
r
for 0,1 mm" 1 <00"
;;;;
Rm ) bo ·MPa
,
1 mm" 1 there is
n 0" = 1 +.~ G 0" . mm . 10
(
- ao+
(
- ao+
r
ao, bo
1/
~/10,80
/
/
G S:/
-:
1/0,85
800
-: 400
//'
800
Stah~ 1200
-:V
V /{;!~ ,,-/ ./J ~ /I/;;/ I / / / /
400
j
{III ill II 1/ Iff;
/
/
110,95
/v /
//
1~ /II til
~(f;
,
2/ do =
r
0,267-
! 2
5
10
(4.3.14)
,
Figure 4.3.1 Kt-Kr ratios Ocr for normal stress.
for 1 mrrr ! < GO";;;; 100 mm" 1 there is
n0" = 1 +~G 0" -rnm l O
IIV~
.
\ I I 1,01 .0,01 0,02 0,05 0,1 0,2 0,5
R)
m bo . MPa
/ 1 10,75 V/ /V
1
1,02
v
~/1/
~/I//il /
1,04
V, ~ [GGG-: ., ',.I "/V 7'"" i
1/0.65'
/ / 1 10,70
1,4
4.3.2.1 Computation of Kt-Kr ratios
ForG 0"
/2.·~ 900
2
1,2
100 MP;---:: 350
~m in
R)
m bo·MPa
The diagram may be extended up to GO"; 100 mm -1.
(4.3.15)
,
constants, Table 4.3.2.
Indicated numerical values 1/0,65 to 1/0,95: Difference of the fatigue limit for completely reversed stress in tension-compression and in bending, valid for the material test specimen of the diameter do = 7,5 mm. Not included in the figure 4.3.1:
Table 4.3.2 Constants Kind of material
Stainless steel
aa
0,40 2400
bo
Kind of material
aa bo
Stainless steel. Threshold values forGO" = 1 mm -1 : largest value. n-, = 1,27 for Rm = 400 MPa and smallest value: "cr = 1,14 for Rm = 1070 MPa.
aa and bo .
Other kinds of steel 0,50 2700
GS
GGG
0,25 2000
0,05 3200
GT
GG
-0,05 -0,05 3200 3200
Wrought Al-allovs
Al-allovs
0,05 850
-0,05 3200
Cast
7 A stress gradient in direction of stress is supposed not to cause any effect. This restriction concerns block-shaped (3D) components only.
Wrought aluminum alloys: Threshold values forGO" = 1 mm -1 : largest value:"cr = 1,69 for Rm = 95 MPa and smallest value:"cr = 1,18 for Rm = 590 MPa. Cast aluminum alloys: Threshold values for: GO" = 1 mm -1 : largest value: "cr = 2,02 for Rm = 130 MPa and smallest value: "cr = 1,88 for Rm = 330 MPa.
For surface hardened components *8 (components with thermal or with chemo-thermal surface treatment) the KcK r ratios are lower than for non surface hardened components *9 *10.
8 Does not apply to cold rolled or shot peened surfaces. See the summary of special features of the fatigue strength of surface hardened components, Chapter 5.8
109
4.3 Design parameters
Kt-K, ratios for shear stress The Kj-K. ratio for shear stress, n, , is to be computed from the related stress gradient G, according to Eq. (4.3.13) to (4.3.15), after having replaced a by 't and the tensile strength Rm by fw" . Rm , where fw" is the fatigue strength factor for shear stress, Table 4.2.1.
The related stress gradients normal to the direction of stress , G a and G, necessary to compute the KcK r ratios, are to be determined from the stress amplitudes for normal stress, ()a , and for shear stress, 't a , at the reference point and a point below the reference point, Figure 4.3.2 * 11, G a=_l- . ",,"aa =_1 . (1- a2a),
",,"s
",,"s
a la
(4.3.16)
G, =_1_ . ",,"'t a =_1 '(1- 't2a) ,
'tla ala, 'tla a2a, 't2a ",,"s
",,"s
",,"s
The point below the surface is to be chosen such that the maximum values of Ga and G, being calculated. If stress amplitudes below the surface (as in Figure 4.3.2 provided by an FE analysis, e.g.) are not available, an approximate computation of the related stress gradients for normal stress and for shear stress is as follows: With the radius r at the reference point (influence of the contour) and the dimension d (influence of a loading in bending or torsion) there is *12
Related stress gradients
a la
4 Assessment of the fatigue strength using local stresses
'tla
stress amplitudes at the reference point, stress amplitudes in a distance ",,"s below, distance between the reference point and the neighboring point below the surface, Figure 4.3.2.
G a = 2 / r + 2 / d,
G, = 4.3.2.2
1/ r
(4.3.17)
+ 2 / d.
Kt-K, ratio for superimposed notches
For superimposed notches - for example a boring located in a groove, the partial K-K; ratios of which are n 1 and n2 according to the related stress gradients G I and G 2 - a most favorable Kj-K, ratio n is to be computed for a related stress gradient G=Gl+ G 2
'
(4.3.24)
If the distance of notches is 2 r or above (where r is the larger one of both radii) *13 a superposition is not to be considered. If a value of a radius is missing, a fictitious radius may be estimated fromEq. (4.3.17)(for example r:::o 2/G a ) .
4.3.3 Roughness factor Figure 4.3.2 Stress amplitudes at the reference point and below the surface.
The roughness factors KRcr or KR" accounts for the influence of the surface roughness on the fatigue strength of the component. The roughness factors valid for polished surface is KR,cr = KR" = 1.
(4.3.25)
For a rolling skin, a forging skin or the skin of castings an average roughness value R, = 200 urn applies. ratio for a crack originating inthe hardened surface layer is lower because the tensile strength Rm ofthe hard surface layer is higher than the tensile strength Rm ofthe core material according tothe material standard.
The roughness factors for normal stress, Figure 4.3.3, and for shear stress are *14 (4.3.26)
The Kt - Kf ratio for a crack origklating i!!,.the core material is lower because the related stress gradient Oa (or 0, ) in the core material has decreased from its maximum value atthe surface.
KR" = 1- f w" . aR,cr . 19 (R, /um) . Ig(2Rm1Rm, N, miJ,
9 The Kt - Kf
The tensile strength of the surface layer may be estimated approximately as Rm = (3,3 . HV) MPa , where HV is the Vickers hardness number. As this equation, however, was not specifically established for hardened surface layers, itistobe applied with caution. In particular the fatigue strength value aw zd ofthe hardened surface layer must not be derived from that estimate of the tensile strength (aW,zd* fW,a' Rm)· 10
11 For Eq. (4.3.16) the tangent at al. is approximately replaced by the secant. If no stress gradient exists, then na = n, = I . In general a stress gradient normal to the direction ofstress and normal tothe surface does exist for the stress components ax , ay , t , at and cr2 . A stress gradient in direction ofstress isnot considered, that is"cr,3 = I.
KR,cr = 1- aR,a . 19 (Rz / urn) . Ig(2Rm / Rm,N,min ),
aR,cr R,
constant, Table 4.3.4, average roughness of the surface of the component in um, according to DIN 4768, tensile strength, Chapter 3.2.1.1, Rm Rm,N,min constant, Table 4.3.4, fatigue strength factor for shear stress, fw" Table 4.2.1.
110
4.3 Design parameters
1,0
Table 4.3.4 Constant aR,oo and minimum tensile strength, Rm,N,min , of the kind of material considered.
....
;:::--::1-
~ ;:::: r-...
1,6
...>:1'\.,
GS
GGG
GT
GG
0,22
0,20
0,16
0,12
0,06
~ 25
Rm,N,min inMPa
400
400
400
350
100
~
Kind of material
J.Q.o
aR,oo
Wrought aluminum alloys 0,22
Cast aluminum alloys 0,20
20o
Rm,N,min inMPa
133
133
3,2
~
~ r-
f"
~'" ~
~
r-.,
0,7
Steel
t--..
R ~ "-'~
i'
0,6 0,5 0,4 300 2.3.3a
1,0
.., = == e
Kind of material aR,oo
l-
~ ~ r-, :----- I--...
0,8
"~
500 700 1000 2000 RminMPa
~---r---'-
KR,11
--l"
' 0
II
0,8
Without a surface treatment there is
k y = 1.
0, 1l----l-·----''Y-,~;:X;;rl---H
600 800 IOOO GS, ('..GG, GT
Rut in .MPa fiir
•
'.
100
4.3.4 Surface treatment factor and coating factor The surface treatment factor, Kv , allows for the influence of a treated surface layer on the fatigue strength of the component.
O9 l-...---+---+-~-..;;j0 ,8 83
400
4 Assessment of the fatigue strength using local stresses
!
300 400 in MPa fiir cc
200
(4.3.28)
For components with surface treatment ·8 the surface treatment factor depends on whether a crack origin is to be expected at the surface or in the core. Essential factors of influence are the ratio of the fatigue limits of the surface layer and of the core material, as well as the ratio of the local stress values on the surface and in the core just below the surface layer.
Figure 4.3.3 Roughness factor KR,oo .
Upper and lower limits of the surface treatment factors for steel and cast iron materials are given in Table 4.3.5. A definite value is to be determined by the user *15.
Top: Steel. Bottom: Cast iron material with skin, steel with rolling skin for comparison
The coating factor Ks allows for the influence of a surface coating on the fatigue strength of a component made of an aluminum alloy.
Z.3.3b
Rm
• 14
For steel and cast iron materials there is For surface hardened components '8 and an expected crack origin at the surface the roughness factor is less favorable (smaller) than for components not surface hardened, because of the higher tensile strength Rm of the hardened surface layer *10. 12 For shell-shaped (2D) componen~ Goo,x , rxan.!Goo,y
, ry. For block-shaped (3D) components Goo,l, q and Goo,2 , r2 " 13 The
Ks = 1.
(4.3.29)
For aluminum alloys without coating there is Ks = 1.
(4.3.30)
For aluminum alloys with coating there is Ks < 1.
(4.3.31)
Ks for example after Figure 4.3.4 (provisional values).
value 2r is likely to be on the safe side.
14 In particular residual stresses as a result of manufacturing and ofa surface treatment are determining the influence of the surface on the component fatigue limit, rather than the surface roughness. According to the current state of knowledge, however, improved regulations to allow for the surface effect are not yet developed, so the traditional equations based on aroughness value have tobe accepted for the time being.
15 Provided that the procedures ofthe surface treatment can be applied to components ofaluminum alloys, the Ko -values for cast iron. material may approximately be taken into account.
1 r
III
4.3 Design parameters
4 Assessment of the fatigue strength using local stresses
Ks
Table 4.3.5 Upper and lower limits of the surface treatment factor for steel and cast iron materials ?1?2.
--...,J. .. r
0.9 0.8
1""-__
~._-~.j .j -W-W I I i I! i I .Lu.u
I II
I
0,7
Surface treatment
unnotched components
notched components
0;1
1,20 - 2,00 (1,50 - 2,50)
(1,80)
Mechanical treatment Cold rolling 1,10 - 1,25 (1,20 - 1,40) Shot peening 1,10 - 1,20 (1,10 - 1,30) Thermal treatment 1,20 - 1,50 Inductive hardening (1,30 - 1,60) Flame-hardening
1,30 - 1,80 (1,50 - 2,20) 1,10-1,50 (1,40 - 2,50) 1,50 - 2,50 (1,60 - 2,80)
Depth of case 0,9 ... 1,5 nun Surface hardness 51 to 64 HRC
Cast iron materials Nitriding 1,10 (1,15) Case hardening 1,1 (1,2) Cold rolling 1,1 (1,2) 1,1 (1,1) Shot peening Inductive hardening, 1,2 (1,3) Flame-hardening
1,3 (1,9) 1,2 (1,5) 1,3 (1,5) 1,1 (1,4) 1,5 (1,6)
1 Concerning typical component values and further kinds of treatments, see also FVA·worksheet "Schwingfestigkeitssteigerung (increasing the fatigue strength)". ? 2 The given values typically apply to the component fatigue limit. Values applying to the variable amplitude fatigue strength are in general somewhat lower.
The values are valid for specimens of 30 to 40 nun diameter; values in parenthesis for specimens of 8 to 15 nun diameter. 3 For unnotched or slightly notched components .
'+1;
L.LLL~.!.J. i. II ,I
!I I !
rn rr
10
1
100
Thickness of layer in /lID
Figure 4.3.4 Influence of anodic coating on the fatigue limit (at 106 cycles) of a component from aluminum alloys as a function of the layer thickness (after Wilson). Provisional values.
4.3.5 Constant KNL,E The constant KNL,E accounts for the non-linear elastic stress strain behavior of GG when loaded in tensioncompression or bending. For all kinds of material except for GG there is KNL,E = KNL,E
?
?
i I I i 111.1 I--·-Ti-t.-i-i.. t·i~
I
0.2
o.t o
"1---
2.3.•
1,10 - 1,50 (1,20 - 2,00)
Carbo-nitriding Depth of case 0,2 ... 0,8 nun Surface hardness 670 to 750 HV 10
L..LJ._l.~.
: -r-_-.t i l.....ll···Tr !i
I
0."
Surface hardness 700 to 1000 HV 10
Depth of case 0,2 ... 0,8 nun Surface hardness 670 to 750 HV 10
. ,l_LLU+ i I , I. II : . __---.4_,__
0,6
Steel Chemo-thermal treatments Nitriding 1,10-1,15 1,30 - 2,00 Depth of case 0,1...0,4 nun (1,15 - 1,25) (1,90 - 3,00) Case hardening
--+-.llllif
~
?3
I
ffi-rTf1
for GG after Table 4.3.6.
Table 4.3.6 Kind of material KNL,E ?
(4.3.32)
1.
Constant KNL,E GG -10
I GG -15
1,075
?
1.
I
GG GG -20 -25 1,05
I
GG GG -30 -35 1,025
1 For unnotched or slightly notched components in tension-compression 1.
KNL,E =
4.3.6 Fatigue class (FAT) Calculation with structural stresses The fatigue classes (FAT) for structural stresses allow for the influence of the toe of a weld on the fatigue strength *16 (For the root of a weid a fatigue class FAT for structural stresses is not applicable up to now; only effective notch stresses are applicable).
16 Fatigue classes for structural stresses do not depend on the of design of a component, because the influence of design on the fatigue strength is allowed for when computing structural stresses, see Chapter 5.5 (This is different from computing nominal stresses, Chapter 2.3.)
112
4.3 Design parameters
A complete catalogue of the fatigue classes of structural stresses according to the IIW-Recommendations is given in Chapter 5.4.2 *17.
Calculation with effective notch stresses Effective notch stresses are applicable for the toe and for the root of a weld and do not require a fatigue classes to be considered as the fatigue strength values given by Eq. (4.3.8) or (4.3.9) are those determined for effective notch stresses (normal stress or shear stress, respectively) *18.
4.3.7 Thickness factor When using structural stresses for the calculation of transversely loaded welds the thickness factor ft accounts for the influence of the sheet metal thickness on the fatigue strength *19. The thickness factor ft is of no effect, however, -
if the calculation uses effective notch stresses, if there is no weld, if there is no transversely loaded weld, or if the sheet metal thickness is t < 25 mm.
In these cases the thickness factor is (4.3.33)
For a transversely loaded weld and a sheet metal thickness t > 25 mrn the thickness factor is a function of the sheet metal thickness t (in mrn):
it = (25 mm / t)
n.
(4.3.34)
n after Table 4.3.7.
17 All fatigue classes for structural stresses given in the IIWRecommendations are considered except those for the base material. Considered are for steel FAT::; 140 for normal stress and FAT:::;; 100 for shear stress, or for aluminum alloys FAT::; 50 for normal stress and FAr::; 36 for shear stress. The calculation for the base material of welded components is to be carried out as for non-welded components. 18 The generally applicable fatigue strength values do not depend on the design of a component nor on the shape of the weld, because all these influences on the fatigue strength are considered when computing effective notch stresses. Chapter 5.5 (This is different from computing nominal stresses or structural stresses, see Chapter 5.5). 19 'Thethickness factor is supposed to be valid for steel, but also for aluminum alloys
4 Assessment of the fatigue strength using local stresses Table 4.3.7 Exponent n for the thickness factor. Type of the welded joint cruciform joints, transverse T-joints, plates with transverse attachments - as welded - toe ground transverse butt welds, - as welded butt welds ground flush, base material, longitudinal welds or attachments, - as welded or ground
n
0,3 0,2 0,2 0,1
113
4.4 Component strength, 4.4.1 Fatigue limit for completely reversed stress
4.4 Component strength
1R44 EN.dog
Content
Page
4 Assessment of the fatigue strength using local stresses aWK
= aW,zd I KwK,cr ,
aW,zd,1:W,s
4.4.0
General
4.4.1
Component fatigue limit for completely reversed stress
4.4.2 4.4.2.0 4.4.2.1
4.4.2.2 4.4.2.3 4.4.2.4
Component fatigue limit according to mean stress General Mean stress factor Calculation for type of overloading F2 Calculation for type of overloading FI Calculation for type of overloading F3 Calculation for type of overloading F4 Individual or equivalent mean stress Residual stress factor Mean stress sensitivity
113 KWK,cr ...
114
115 116 117 118
4.4.3
Component variable amplitude fatigue 119 strength 4.4.3.0 General 4.4.3.1 Variable amplitude fatigue strength factor 120 Calculation for a constant amplitude spectrum Calculation for a variable amplitude spectrum Elementary version of Miner's rule based on the damage potential Calculation according to the consistent version of Miner's rule 121 Calculation using a class of utilisation 123 4.4.3.2 Component constant amplitude S-N curve
4.4.0 General According to this chapter the component fatigue strength is to be calculated as follows: - Step 1: component fatigue limit for completely reversed stress in considering the design factor, Chapter 4.4.1, - Step 2: component fatigue limit in considering the mean stress factor, Chapter 4.4.2, - Step 3: component variable amplitude fatigue strength in considering the variable amplitude fatigue strength factor, Chapter4.4.3.
4.4.1 Component fatigue limit for completely reversed stress According to this chapter the component fatigue limit for completely reversed stress is to be calculated in considering the design factor.
(4.4.1)
1:WK = 1:w,s I KWK;t ,
material or weld specific fatigue limit for completely reversed stress, Chapter 2.2.1 design factor, Chapter 4.3.1
Eq. (4.4.1) is based on the fatigue limit for completely reversed stress, Eq. (4.2.1), (4.2.3) or (4.2.4), and on the design factor, Eq. (4.3.1), (4.3.4), (4.3.6) or (4.3.8). It applies to non-welded components for calculations with local stresses and to welded components both for calculations with structural stresses or with effective notch stresses *2. The component fatigue limits of shell-shaped (2D) components for completely reversed normal stresses in the directions x and y as well as for shear stress are aWK,x = aW,zd I KWK,crx ,
(4.4.2)
awK,y = aW,zd I KWK,cry ,
1:WK = 1:w,s I KwK,s , aW,zd, 'tw,s KwK,crx,...
material or weld specific fatigue limit for completely reversed stress, Chapter 2.2.1 design factor, Chapter 4.3.1
Eq. (4.4.2) is based on the fatigue limit for completely reversed stress, Eq. (4.2.1), (4.2.3) or (4.2.4), and on the design factor, Eq. (4.3.2), (4.3.5), (4.3.7) or (4.3.9). It applies to non-welded components for calculations with local stresses and to welded components both for calculations with structural stresses or with effective notch stresses. The component fatigue limits of block-shaped (3D) components for completely reversed principal stresses in the directions 1, 2, and 3 are al,WK = aW,zd l KWK,crl ,
(4.4.3)
a2,WK = aW,zd l KWK,cr2, a3,WK = aW,zd l KWK,cr3,
aW,zd,1:W,s K WK, I ...
material or weld specific fatigue limit for completely reversed stress, Chapter 2.2.1 design factor, chapter 4.3.1
Eq. (4.4.3) is based on the fatigue limit for completely reversed stress, Eq. (4.2.1), and on the design factor, Eq. (4.3.3). It applies to non-welded components. For certain applications block-shaped (3D) components may be welded at the surface, for example through surfacing welds. Then the calculation is to be carried out as for shell-shaped (2D) welded components.
Caution: See the comment in the second paragraph of Chapter 4.4.2. Rod-shaped (lD), shell-shaped (2D) and block-shaped (3D) components are to be distinguished. The component fatigue limits of rod-shaped (lD) components for completely reversed normal stress and shear stress are *I
1 The component fatigue limits for completely reversed stress are different for normal stress and for shear stress, and moreover because of different stress gradients or different weld characteristics depending on the type of stress. 2 Structural stresses crWK, ... or effective notch stresses crWK,K . The index K is to be added where appropriate.
--r I
114 4.4 Component strength 4.4.2 Component fatigue limit according to mean stress
4.4.2 Component fatigue limit according to mean stress 1R442 EN.dog 4.4.2.0 General According to this chapter the amplitude of the component fatigue limit is to be determined according to a given mean stress and, where appropriate, in considering a multiaxial state of stress. Comment: For non-welded components of austenitic steel, or of wrought or cast aluminum alloys the component fatigue limit is different from the component endurance limit for N = 00 , Chapter 4.4.3.2. Observing the specific input values the calculation applies to non-welded components (with local stresses) and to welded components (with structural stresses or effective notch stresses) *1. An improved procedure for non-welded components of steel to compute the component fatigue limit in the case of synchronous multiaxial stresses is given in Chapter 5.9. In combination with a stress spectrum the indicated stress ratio R, , ... commonly refers to step I of the stress spectrum (maximum amplitude), Ra,I, ... *2 *3. The mean stress factor, Figure 4.4.1, allows for the influence of the mean stress on the fatigue strength. Without mean stress the mean stress factor is KAK,cr
= KAK;t = 1.
(4.4.4)
The residual stress factor accounts for the influence of the residual stress on the fatigue strength. For nonwelded components the residual stress factor for normal stress and for shear stress is K E,cr = KE;r
= 1.
(4.4.5)
Rod-shaped (10), shell-shaped (2D) and block-shaped (3D) components are to be distinguished.
4 assessment of the fatigue strength with nominal stresses Rod-shaped (ID) components The mean stress dependent amplitudes of the component fatigue limit of rod-shaped (10) components for normal stress and for shear stress are 0'AK = KAK,cr . KE,cr . O'WK , 1:AK
=
KAK,cr, .. , KE,cr,
.
O'WK,
.
(4.4.6)
KAK;t . KE,~ . 1:WK ,
mean stress factor, Chapter 4.4.2.1, residual stress factor, Chapter 4.4.2.3, component fatigue limit for completely reversed stress, Chapter 4.4.1.
Eq. (4.4.6) applies' to non-welded and to welded components. Shell-shaped (2D) components The mean stress dependent amplitudes of the component fatigue limit of shell-shaped (2D) components for normal stress in the directions x and y as well as for shear stress are 0'AK,x = KAK.,x . KE,cr . O'WK,x ,
= KAK.,y . KE,cr = KAK.,~ . KE,~
0'AK,y 1:AK KAK.,x, ... KE,cr, '"
O'WK,x' .. ,
(4.4.7)
. O'WK,y , . 1:WK ,
mean stress factor, Chapter 4.4.2.1, residual stress factor, Chapter 4.4.2.3, component fatigue limit for completely reversed stress, Chapter 4.4.1.
Eq. (4.4.7) applies to non-welded and to welded components. Block-shaped (3D) components The mean stress dependent amplitudes of the component fatigue limit of block-shaped (3D) components *4 for principal stresses in the directions I, 2 and 3 are O'I,AK = KAK.,crl . KE,cr . O'I,WK , O'2,AK
= KAK.,cr2
(4.4.7)
. KE,cr . 0'2, WK ,
O'3,AK = KAK.,cr3 . KE,cr . O'3,WK , KAK.,crl , ... KE,cr,
.
O'I,WK, ..
mean stress factor, Chapter 4.4.2.1, residual stress factor, Chapter 4.4.2.3, component fatigue limit for completely reversed stress, Chapter 4.4.1.
1 Struktural stresses crWK' ... or effective notch stresses crWK.,K . In the following the missing index K is to be added where appropriate. 2 This definition is necessary only for mean stress spectra, not for stress ratio spectra or for fluctuating stress spectra, for which the stress ratios of all steps are identical. 3 For more details see Chapter 5.6.
4 For certain applications block-shaped (3D) components may be welded at the surface, for example by surfacing welds. Then the calculation may be carried out as for shell-shaped (2D) components.
i I
115 4.4 Component strength 4.4.2 Component fatigue limit according to mean stress
Figure 4.4.1 Amplitude of the component fatigue strength as a function of mean stress or stress ratio (Haigh diagram), described in four fields of mean stress Example: Normal stress, types of overloading FI and F2. Given:
Component fatigue strength for completely reversed
4 assessment of the fatigue strength with nominal stresses
R :-= "
Q
@
(M~=O)
CD
stress crwK ' service stress amplitude cra , stress ratio Derived:
(M~=MQ/3)
Ra ,
(M~=O)
®
Amplitudes of the component fatigue limit oAK for the types of overloading FI and F2.
Type of overloading The mean stress factor, KAK,cr or KAK,~, depends on the type of overloading, Fl to F4. It distinguishes the way how the stress may increase in the case of a possible overload in service (not by crash). Therefore it is to be determined in the sense of a safety of operation in service, that is for normal stress as follows: - Type Fl: the mean stress am remains the same, - Type F2: the stress ratio Rcr remains the same, - Type F3: the minimum stress amin remains the same, - Type F4: the maximum stress a max remains the same. For shear stress a is to be replaced by L. Intermediate types of overloading are possible. Dependent on the type of overloading the amplitude of the component fatigue limit is different, Figure 4.4.1.
Shear stress: *5: Field I: Field II: - 1S; R~S; 0 Field III: 0 < R~ < 0,5 Field IV: R~~ 0,5
(not existing), (lower boundary changed), (unchanged), (unchanged).
4.4.2.1 Mean stress factor The mean stress factor for normal stress, KAK,cr , or shear stress, KAK,1: , depends on the mean stress and on the mean stress sensitivity.
Calculation for the type of overloading F2
*6
In case of a possible overload in service the stress ratio
Rcr remains the same. Normal stress:
Fields of mean stress In determining the mean stress factor, KAK,cr , ... , four fields of mean stress are to be distinguished. These depend on the stress ratio Rcr or on the mean stress am respectively, see Chapter 4.4.2.2.
Field I:
n, > 1:
KAK,cr=
1/ (1 - Ma),
(4.4.9)
(4.4.10)
Normal stress: Field I: Rcr > I, field of fluctuating compression stress, where Rcr = + or - 00 is the zero compression stress. Field II: -00 S; Rcr S; 0, where R, < -1 is the field of alternating compression stress, R, = -1 is the completely reversed stress, R; > -1 is the field of alternating tension stress. Field III: 0 < Rcr < 0,5, field of fluctuating tension stress, where R, = 0 is the zero tension stress. Field IV: R, stress.
~
0,5, field of high fluctuating tension
5 The fatigue limit diagram (Haigh diagram) for normal stress shows increasing amplitudes for R < -1 (compression mean stress). For negative mean stress the fatigue limit diagram (Haigh diagram) for shear stress is the same as for positive mean stress and symmetrical to ~m = O. Practically it is restricted to the fields of positive mean stress or a stress ratio R~ 2:- 1 , as the mean stress in shear is always regarded to be positive, ~m 2: 0 . 6 The type of overloading F2 is described first because it is of primary practical importance. (4.4.11)
Using the term crm / cra instead of (1 + Rcr ) / (1 - Rcr ) avoids numerical problems, when the stress ratio becomes Ra = - 00.
116
4 assessment of the fatigue strength with nominal stresses
4.4 Component strength 4.4.2 Component fatigue limit according to mean stress
Field III, Q< n, < 0,5:
Field IV
I+M cr /3 K
AK,cr -
Field IV, K
I+M cr M ' I+~. crm 3 ca
n,
AK,cr -
n, M;
am aa
~
(4.4.12) (4.4.17)
0,5:
3+M cr ( \2 3· 1 + Mcrl
(4.4.13)
'
am KE,cr aWK
M,
stress ratio *8, Chapter 4.4.2.2, mean stress sensitivity, Chapter 4.4.2.4, mean stress *8, Chapter 4.4.2.2, stress amplitude.
mean stress *8, Chapter 4.4.2.2, residual stress factor, Chapter 4.4.2.3, component fatigue limit for completely reversed stress, Chapter 4.4. I, mean stress sensitivity, Chapter 4.4.2.4.
Shear stress:
For KAK,'[ Field I is not existing and Field II is restricted to positive mean stresses ~ tm = Om / (KE,' . 0WK) ~ 1 / (1 + M'[) . For positive mean stresses the same equations are valid if Sm is replaced by t m and M, is replaced by M'[ .
°
Shear stress:
For KAK,'[ Field I is not existing and Field II is restricted to positive mean stresses R'[ ~ -I . For positive mean stresses, or R'[ ~ -I , the same equations are valid if M, is replaced by M'[
Calculation for the type of overloading F3
In case of a possible overload in service the minimum stress amin remains the same. Calculation for the type of overloading Fl
Normal stress:
In case of a possible overload in service the mean stress am remains the same.
-2
For smin = crmin / (KE,a . crWK) < - - - there is *9 I-M cr
Normal stress:
Field I
(4.4.18)
For sm= crm / (KE,a . crWK) < -1 / (l -M cr ) there is *9 (4.4.14)
Field II for - 2 /(1 -
Field II for -I / (l - M cr )
~
sm
s
1 / (l
Mcr)~
Smin
~
° there is
1-M cr .Smin.,zd I+M cr
+ M cr ) there is
(4.4.19)
(4.4.15)
Field III Field III for
°< Smin < -
2
3
(4.4.16)
KAK, cr =
Field IV Or equivalent mean stress, equivalent minimum stress, equivalent maximum stress, Chapter 4.4.2.2.
8
9 In the following the abbreviation sm= crm I accordingly tosmin , smax , tm , ... .
(KE.cr . 0"Wl()
applies
.
3+M
cr there is (I+M cr ) 2
1+ M cr /3 M cr ---·s· I+M cr 3 mm
--~~-----
I+M cr /3
(4.4.20)
117 4.4 Component strength 4.4.2 Component fatigue limit according to mean stress K
-
3+M cr
AKa - (1 + M cr)2 O"min
(4.4.21)
'
minimum stress *8, Chapter 4.4.2.2, residual stress factor, Chapter 4.4.2.3, component fatigue limit for completely reversed stress, Chapter 4.4.1, mean stress sensitivity, Chapter 4.4.2.4.
KE,a
O"WK
M,
Shear stress: For KAK" Field I is not existing and Field II is restricted to positive mean stresses, that is - 1 :::; tmin = 'tmin I (KE,t . 'tWK ) :::; O. For positive mean stresses, 'tm 2: 0 , the same equations are valid if Smin is replaced by tmin and Mcr is replaced by M,
Calculation for the type of overloading F4 In case of a possible overload in service the maximum stress O"max remains the same.
Normal stress:
For Smax= CY max I (KE,a . CYWK) < 0 there is *9 KAK,a =
1 I (1 - M, ),
4 assessment of the fatigue strength with nominal stresses
Shear stress: For shear stress the type of overloading F4 ('tmax remaining constant) can practically not being realized.
4.4.2.2 Individual or equivalent mean stress In each case Ra , O"min , and O"max are determined by mean stress and stress amplitude. The mean stress may be taken either as the individual mean stress according to type of stress or as an equivalent mean stress from the individual mean stresses of all types of stress. Individual mean stress As a rule the individual mean stress O"m is used to determine O"min , O"max and Ra . For normal stress the respective equations are (4.4.26) O"min = O"m - O"a , O"max = O"m + O"a , Ra = O"min I O"max , O"a O"min O"max Ra
stress amplitude, minimum stress, maximum stress, stress ratio.
For shear stress
0"
is to be replaced by t
.
(4.4.22) Equivalent mean stress *10,
for 0:::; smax :::; 2 I (I + M a ) there is KAK.
.o
I-M cr ,smax = ---.,;;---:,:;:::;.:. 1- M cr '
(4.4.23)
Field III
2 4 . 3 +M cr for - - - < Smax <-
1+ M cr
3
(I + M cr
?
there is
O"min,v = O"m,v - O"a , O"max,v = O"m,v + O"a, Ra,v = O"min,v l O"max,v,
I+M cr 13 M cr l+M --3-, smax
cr KAK.,a = - - - - : ; : . . . - - - - - -
I-M cr 13
In the case "bending and torsion which is typical for numerous applications in machine design, and in similar cases, where normal stresses are combined with shear stresses, the variables O"min,v , O"max,v and Ra,v are to be used. They are derived from an equivalent mean stress O"m,v , to be computed as a function of the respective individual mean stress values, Eq. (4.4.28). For normal stress there is
(4.4.24)
Field IV
O"a Ra,v O"min,v O"max,v
individual stress amplitude, equivalent stress ratio, equivalent minimum stress, equivalent maximum stress.
For shear stress
(4.4.25) maximum stress *8, Chapter 4.4.2.2, residual stress factor, Chapter 4.4.2.3, component fatigue limit for completely reversed stress, Chapter 4.4.1, mean stress sensitivity, Chapter 4.4,2.4.
(4.4.27)
0"
is to be replaced by r .
The equivalent mean stress, Eq. (4.4.27), for normal stress is O"m,v = q . O"m,v,NH + (1 - q) . O"m,v,GH,
(4.4.28)
where q=
.J3 -(lIf-c) .J3-1
(4.4.29)
'
118 4.4 Component strength 4.4.2 Component fatigue limit according to mean stress
4 assessment of the fatigue strength with nominal stresses High residual stresses are to be assumed in case of welding without residual stress reducing precautions.
q
Material dependent parameter after Table 4.6.1
am , Tm Individual mean stresses,
Moderate residual stresses are to be assumed in case of welding with residual stress reducing precautions, for example by observing a suitable weld sequence. Low residual stresses are to be assumed in case of welding with subsequent stress-relief heat treatment, or if residual stresses may evidentially be excluded.
Eq. (4.4.31) and (4.4.32).
For shear stress there is Tm,v = f w,<
.
(4.4.30)
am,v,
4.4.2.4 Mean stress sensitivity
Rod-shaped (ID) components
The mean stress sensitivity M, or M. , in connection with the mean stress factor, describes to what extent the mean stress affects the amplitude of the component fatigue strength, Figure 4.4.1.
For rod-shaped (ID) components the equivalent mean stress after Eq. (4.4.28) is to be computed only if am~ O.
For non-welded components the mean stress sensitivity for normal stress and for shear stress, applicable in case of normal or elevated temperature, is
fw,<
shear strength factor, Table 4.2.1.
M, = aM . 10. 3 For shell-shaped (2D) components the equivalent mean stress after Eq. (4.4.28) is to be computed only if am,y = 0 and am,x ~ 0 (or in reverse). It is am
=
am,x
(or am = am,y),
(4.4.32)
am,x, ... individual mean stresses, Chapter 4.1.1.2.
4.4.2.3 Residual stress factor The residual stress factor for non-welded components is KE,cr = KE;[ = 1.
(4.4.33) .
For welded components of structural steel and of aluminum alloys the residual stress factor is different for high, moderate or low residual stresses. It is given for normal stress and for shear stress in Table 4.4.1, see also Chapter 5.5. Table 4.4.1 Residual stress factor KE,cr, K E;[ and mean stress sensitivity Mcr , M. for welded components. Residual stress high moderate low
M
KE,cr
Ma
K E;[
1,00 1,26 1,54
0 0,15 0,30
1,00 1,15 1,30
fw.· M cr
fw,. = 0,577,
1> 1 For Shear Stress there is M. = Table 4.2.1.
.
Rm / MFa + bM,
(4.4.34)
M. = fw,< • Ma: '
Shell-shaped (2D) components
• 1>1
0 0,09 0,17
"
10 The equivalent mean stress applies to rod-shaped and shell-shaped components as indicated, but not to block-shaped components.
aM, bM constants, Table 4.4.2, fw ,< shear fatigue strength factor, Table 4.2.1. For components that have been surface hardened *11 the mean stress sensitivity is greater because of the tensile strength Rm of the hardened surface is higher than that of components not surface hardened. For welded components the mean stress sensitivity for normal stress and for shear stress, applicable in case of normal or elevated temperature, is dependent on the intensity of the residual stress, but independent of the tensile strength R; of the base material. Values are given in Table 4.4.1, see also Chapter 5.5. Table 4.4.2 Constants aM and bM . Kind of material aM bM
Steel 1>1
GS
GGG
GT
GG
0,35 - 0,1
0,35 0,05
0,35 0,08
0,35 0,13
0 0,5
Kind of material
Wrought aluminum alloys 1,0 - 0,04
aM bM
Cast aluminum alloys 1,0 0,2
1> 1 also stainless steel.
11 Not applicable to components being cold rolled or shot-peened.
4.4 Component fatigue strength 4.4.3 Component variable amplitude fatigue strength
4.4.3 Component variable amplitude fatigue strength 1R443 EN.dog
119
4 Assessment of the fatigue strength using local stresses Except for GG, the following restrictions apply, Figure 4.4.3: crSK ~
4.4.3.0 General
'tBK
According to this chapter the amplitude of the component variable amplitude fatigue strength is to be derived from the stress spectrum and the component constant amplitude S-N curve, Chapter 4.4.3.2. The variable amplitude fatigue strength factor KBK•a , ... , to be calculated depends on the stress spectrum, that is on the required total number of cycles *1 and on the shape of the stress spectrum, as well as on the component constant amplitude S-N curve, and in addition it depends on the type of stress (normal stress or shear stress).
Rp
Observing the specific input values the calculation applies to both non-welded components (component constant amplitude S-N curve model I or model II) and to welded components (component constant amplitude S-N curve model I only). Rod-shaped (lD), shell-shaped (2D) and block-shaped (3D) components are to be distinguished.
(4.4.42)
, ,
yield strength, Chapter 1.2.1.1, plastic notch factors, Table 1.3.2, shear strength factor, Table 1.2.5.
Kp,o , K p,.
f. 4
N,
'!Ii.
Component fatigue life curve
N Component s-N curve
2
It has to be distinguished, whether - in case of a constant amplitude spectrum - an assessment of the fatigue limit (or endurance limit) or of the fatigue strength for finite life is intended, or whether - in case of a variable amplitude spectrum - an assessment of the variable amplitude fatigue strength is intended *2. The calculation for a constant amplitude stress spectrum is a special case of the more general case of calculation for a variable amplitude stress spectrum. In any case the way of calculation is the same, but the variable amplitude fatigue strength factors are different.
0,75 Rp . Kp,o
s 0,75 f.' Rp' Kp,.
lOB 2.••2
N,
'!Ii
Figure 4.4.2 Component constant amplitude S-N curve, component fatigue life curve derived by the consistent version of Miner's rule, and influence of the critical damage sum DM . Highest amplitude in stress spectrum GSK, component fatigue limit GAJ(, number of cycles N after the component constant amplitude S-N curve, number of cyclesN after the component fatigue life curve for DM < 1 or N' for DM = 1. It isN = N + (N' - N) DM. This formula implies that a number of cycles N -7 N is obtaine~ for spectra of increasing damage potential and a nu~er of cycles N = N for the constant amplitude stress spectrum as N' - N -7 O. In German the fatigue life curve is usually termed 'Gassner curve' and the constant amplitude S-N curve is usually termed' Woehler curve'.
Rod-shaped (ID) components The amplitudes of the component variable amplitude fatigue strength (highest amplitude in stress spectrum) of rod-shaped (lD) components for normal stress and for shear stress are, Figure 4.4.2, crSK 'tSK
= KsK,o . c AK , = KsK,•. 'tAK,
KSK,o , ... crAK,...
(4.4.41)
variable amplitude fatigue strength factor, Chapter 4.4.3.1, component fatigue limit, Chapter 4.4.2.
1 Required total number of cy~les and required component fatigue life are corresponding denotations. 2 In a simplified manner the variable amplitude fatigue strength can be derived on the basis of a damage-equivalent stress amplitude. Then the assessment ofthe variable amplitude fatigue strength turns out to be an assessment of the fatigue limit.
Figure 4.4.3 Restriction of the amplitudes of the variable amplitude fatigue strength, or of the maximum value crrn,1 + crBK,1 and the minimum value crrn,1 - crBK,1 respectively, in relation to the yield strength, displayed in terms of the Haigh-diagram.
4.4 Component fatigue strength 4.4.3 Component variable amplitude fatigue strength Shell-shaped (2D) components The amplitudes of the component variable fatigue strength (highest amplitude in stress of shell-shaped (2D) components for normal the directions x and y as well as for shear Figure 4.4.2,
O"AK,x, ...
4 Assessment of the fatigue strength using local stresses Calculation for a constant amplitude spectrum
amplitude spectrum) stresses in stress are,
O"BK,x = KBK,crx· O"AK,x, O"BK,y = KBK,cry . 0"AK,y , 'tBK = KBK,'t . 'tAK, KBK,crx , ...
120
Component constant amplitude S-N curve model I: horizontal for N > No,cr (steel and cast iron material) Assessment ofthe fatigue strength for finite Life: -)lIk KBK,cr= (No,cr/N cr forN:<:;No,cr. (4.4.47)
(4.4.43)
Assessment ofthe fatigue limit = endurance Limit:
variable amplitude fatigue strength factor, Chapter 4.4.3.1, component fatigue limit, Chapter 4,4-.2.
Except for GG, the following restrictions apply, Figure 4.4.3, O"BK,x :<:;0,75 Rp' Kp,crx, O"BK,y :<:; 0,75 Rp . Kp,cry, 'tBK :<:; 0,75 f't' R p' Kp,'t,
KBK,cr = I
forN > No,cr.
Assessment ofthe fatigue strength for finite Life: KBK,cr = (N D,« I N) IIk cr for Nz; No,cr. (4.4.49)
(4.4.44)
KBK,cr = (N D,« I N)lIk o,cr for No,cr
yield strength, Chapter 1.2.1.1, Kp,crx, ... plastic notch factors, Chapter 3.3.2, f't shear strength factor, Table 1.2.5.
(4.4.50)
Assessment ofthe fatigue Limit: KBK,cr = I
forN > No,cr.
Block-shaped (3D) components
Assessment ofthe endurance Limit:
The amplitudes of the component variable amplitude fatigue strength (highest amplitude in stress spectrum) of block-shaped (3D) components for the principal stresses in the directions I, 2 and 3 are, Figure 4.4.2,
KBK,cr = f n,e
KBK,crl , ... O"l,AK, ...
(4.4.45)
variable amplitude fatigue strength factor, Chapter 4.4.3.1, component fatigue limit, Chapter 4.4.2.
Except for GG, the following restrictions apply, Figure 4.4.3: O"l,BK O"Z,BK
s 0,75 Rp . Kp,crl , s 0,75 Rp . Kp,crz,
(4.4.48)
Component constant amplitude S-N curve model II: sloping for N > Nn,cr (non-welded aluminum alloys)
Rp
O"l,BK = KBK,crl . O"l,AK, O"Z,BK = KBK,crZ . O"z,AK , 0"3,BK = KBK,cr3 . 0"3,AK,
*4
(4.4.46)
(4.4.51)
forN > NO,cr,ll. (4.4.52)
N
number of cycles of the component constant amplitudeS-N curve, Chapter 4.4.3.2, N required number of cycles, No,cr number of cycles at knee point of the component constant amplitude S-N curve, Chapter 4.4.3.2, ka slope of the component constant amplitude S-N curve for N < No,cr, Chapter 4.4.3.2. No.e.n number of cycles at second knee point of the component constant amplitude S-N curve, Chapter 4.4.3.2, ko,cr slope of the component constant amplitude S-N curve for N > No,cr , Chapter 4.4.3.2, f n.e factor by which the endurance limit is lower than the fatigue limit, Chapter 4.4.3.2, Table 4.4.4.
0"3,BK :<:; 0,75 Rp ,
Calculation for a variable amplitude spectrum
Rp
yield strength, Chapter 1.2.1.1, Kp,crl , Kp,crz plastic notch factors, Chapter 3.3.2 f't shear strength factor, Table 1.2.5.
4.4.3.1 Variable amplitude fatigue strength factor The variable amplitude fatigue strength KBK,cr, ... , are to be derived as follows *3:
factors
3 The following is written for axial stress, KBK,o , k,; ... , but applies to other types of stress accordingly. For effective notch stresses the index K is to be added. 4 For welded components model 1 of the component constant amplitude S-N curve is of concern only, not model II.
As a rule the variable amplitude fatigue strength factor is to be computed by using the elementary version of Miner's rule (not necessary for a constant amplitude stress spectrum). Somewhat more favourable results, however, may be obtained by using the consistent version of Miner's rule. Moreover, the classes of utilization can be applied as a simplified method of calculation; the so derived results approximately correspond to those obtained by the elementary version of Miner's rule. In an even more simplified manner the variable amplitude fatigue strength can be derived on the basis of a damage-equivalent stress amplitude.
4.4 Component fatigue strength 4.4.3 Component variable amplitude fatigue strength
121
4 Assessment of the fatigue strength
using local stresses
Calculation using the elementary version of Miner's rule based on the damage potential The variable amplitude fatigue strength factor is to be computed directly as follows *5. Both for model I and for model II of the component constant amplitude S-N curve the elementary version of Miner's rule yields, Figure 4.4.4, (4.4.53-)
K BK,cr -[( (v zd1)ka
I)-D
M
k
a
. hi [Ga,i )k
J
L=' - -
i=1 H
H h·I
j
Ga,i Ga,1
Ga,l
1\r,11•• 1
+f r~·· J:..
where the damage potential is *6 *7 _ Vcr -
l1 a
(lg)
Figure 4.4.4 Elementary version of Miner's rule, component constant amplitude S-N curve model I, DM = 1.
a
,
(4.4.54)
slope of the component constant amplitude S-N curve for N < No,a , Chapter 4.4.3.2, critical damage sum, Table 4.4.3, number of cycles at knee point of the component constant amplitude S-N curve, Chapter 4.4.3.2, total number of cycles of the given spectrum, H = H, = L: hi (summed up for i = 1 to j), related number of cycles in step i, Hi = L: hi (summed up for i = 1 to i) *8, total number of steps in the spectrum, number of the step in the spectrum, stress amplitude in step i of the spectrum, stress amplitude in step i = 1 of the spectrum.
If for a component constant amplitude S-N curve model I (horizontal for N > No,a ) a value KBl<,cr < 1 is obtained from Eq. (4.4.53), then the value to be used is
(4.4.56) If for a component constant amplitude S-N curve model II (sloping for N > NO,a ) a value KBK,cr is obtained from Eq. (4.4.53) that is smaller than the value obtained from Eq. (4.4.50) or (4.4.52), then the higher value from Eq. (4.4.50) or (4.4.52) is to be used.
5 Direct calculation without iteration. The results from the elementary version ofMiner's rule approach the results from the consistent version of Miner's rule on the safe side. 6 When computing the d~ge potential (and also in the following equations) the values ni and N according toth.:..;equired total number of cycles can be replaced by the values hi and H according to the total number ofcycles inthe given standard type spectrum, see Chapter 4.1. 7 Instead ofAJcon after Eq. (4:4.57) and (4.4.63) ishere A ele = I / (va) ke .
N
(4.4.55)
8 hi / H may also be replaced by n, / N , N Required total number ofcycles according tothe required fatigue life, N = Eni(summed up for I toj), ni number ofcycles instep i according tothe required fatigue life.
Characteristics ofthe stress spectrum according toChapter 4.1, component constant amplitude S-N curve according toChapter 4.4.3.2. Table 4.4.3 Critical damage sum DM, recommended values.
Steel, GS, Aluminum alloys GGG,GT,GG
non-welded components 0,3
welded components 0,5
1,0
1,0
Calculation according to the consistent version of Miner's rule *9 *10 Using the consistent version of Miner's rule the variable amplitude fatigue strength factor is to be computed iteratively for differing values of Ga,l , until a value N equal to the required total number of cycles N is obtained. The respective value of Ga,1 is used to derive the variable amplitude fatigue strength factor. Component constant amplitude S-N curve model I: horizontal for N > ND,a (Steel and cast iron material) In case of a component constant amplitude S-N curve model I ( horizontal for N > No,a or slope kD,o = (0) the number of cycles N to be computed for a value Sa,1 is (4.4.57) a N = {[ Akon -1] . DM + I}' [G AI< . NO,a,
)k
G a.l
where
9 The consistent version of Miner's rule allows for the fact, that the component fatigue limit will decrease asthe damage sum increases. The decrease applies tocomponent constant amplitude S-N curves model Ias well astomodel IIfor N D,s 2': 10 6 . 10 The consistent version ofMiner's rule was first developed byHaibach. simplified version allowing for the decrease ofthe fatigue limit became known as the modified version orthe Haibach method ofMiner's rule. A
4.4 Component fatigue strength 4.4.3 Component variable amplitude fatigue strength
Akon
= (
aaI a~
ka - I )
[
ZI J. Z2 ] . NI + v~m N2 '
k-I ( )k -I ( ) k-I ( )k -I ( )
ZI = a AK
a
a a,m
_
a a.l
Z2 =
a a,v
m-J
a
a a,v+!
_
a
(4.4.60)
a a,1
hi (aa,i
L -=-' -
)k
a a,1
i=1 H
N2 = v hi (aa,i
L-=-' -
i=1 H
(4.4.59)
a a.I
a a.l
Nl =
a
(4.4.58)
a
)k a
In case of a component constant amplitude S-N curve model II (sloping for N > No,a or slope kD,a < kD,a < (0) the number of cycles N is first to be computed for a single value aa,1 = a AK / (fn,a )1/3 as follows {[
Akon - I ] , DM + I}'
(aa
a
AK ) k a.l
N D:" / 3 ([n,,,)
with
(4.4.65)
Akon
after Eq. (4.4.58) to (4.4.62) and the explanations as before, factor by which the endurance limit is lower than the fatigue limit, Table 4.4.4.
(4.4.62)
aa,1
fn,a
N
number of cycles of the component constant amplitude S-N curve, Chapter 4.4.3.2, N D,« number of cycles at knee point of the component constant amplitude S-N curve, Chapter 4.4.3.2, DM critical damage sum, Table 4.4.3, stress amplitude in step i of the spectrum, stress amplitude in step 1 of the spectrum, component fatigue limit, slope of the component constant amplitude S-N curve for N < No, a , Chapter 4.4.3.2, j total number of steps in the spectrum, i number of the step in the spectrum, m number i = m of the first step below a AK , H total number of cycles in the given spectrum, H = Hj = L: hi (summed up for 1 to j), h·I number of cycles in step i, Hi = L: hi (summed up for I to i) '8. The computation is to be repeated iteratively for differing values a a,I > a AK , until a value N equal to the required total number of cycles N is obtained. From the respective value of aa,1 the variable amplitude fatigue strength factor is obtained as
(4.4.63)
If a value KSK,a < I is obtained from Eq. (4.4.63), then the value to be applied is KSK,a = 1.
Component constant amplitude S-N curve model II: sloping for N > ND,a (non-welded aluminum alloys) *11
(4.4.61)
,
= aa,1 / aAK·
4 Assessment of the fatigue strength using local stresses
N=
For the summation of the term Z2, Eq. (4.4.60), it is to be observed that aaj+! = O.
KSK,a
122
(4.4.64)
If a value N = N* > N is obtained then the calculation of N, Eq. (4.4.65), is to be continued fqr differing values aa,1 > a AK / ( fn,a )1/3 until a value N equal to the required total number of cycles N is obtained. From the respective value of aa,1 the variable amplitude fatigue strength factor is obtained as KSK,a = aa,1 . (fn,a
)1/3/ aAK
(4.4.66)
If a value N = N *:s N is obtained then the variable amplitude fatigue strength factor is
(4.4.67) If a value KSK,a < fn,a is obtained from Eq. (4.4.67) then the value to be applied is KSK,a = fn,a .
(4.4.68)
Calculation using a class of utilization The variable amplitude fatigue strength factor KSK,a is to be determined according to the appropriate class of utilization *12 , Chapter 5.7.
Calculation using a damage-equivalent stress amplitude When using a damage-equivalent stress amplitude the variable amplitude fatigue strength factor for both constant amplitude S-N curves model I and model II is KSK,a = 1.
(4.4.69)
12Class ofutilization asa characteristic ofthestress spectrum. It isan approximately damage equivalent combination oftherequired total number ofcycles N with theshape ofa particular standard stress spectrum thefrequency distribution ofwhich is ofbinomial orexponential type modified bya spectrum parameter p. It provides a result that corresponds toa calculation based ontheelementary version ofMiner's II Simplified and approximate calculation.
rule
4.4 Component fatigue strength 4.4.3 Component variable amplitude fatigue strength 4.4.3.2 Component constant amplitude S-N curve Component constant amplitude S-N curves for nonwelded components (without surface hardening) and for welded components *13 are shown for normal stress and for shear stress in Figure 4.4.5 and 4.4.6. The particular number of cycles at the knee point No,cr , ... and the values of slope kcr, ... are given in Table 4.4.4. The component fatigue limit crAK , ... is the reference fatigue strength value for calculation. It follows from Chapter 4.4.2. For S-N curves Model I the fatigue limit crAK and the endurance limit o AK,II for N = 00 are identical, while for S-N curves Model II (valid for nonwelded components of austenitic steel or of aluminum alloys) they are different by a factor fII,cr , Table 4.4.4 and Figure 4.4.5. A lower boundary of the numbers of cycles is implicitly defined by the maximum stress being limited according to the static strength requirements, Chapter 1. For surface hardened components "14 the slope of the component constant amplitude S-N curves is more shallow. Instead of the values of slope kcr = 5 and k, = 8 for not surface hardened components, Table 4.4.4, the values that apply to surface hardened components are kcr = 15 and k, = 25 , while the number of cycles at the knee point No,cr and No,~ remain unchanged, see also Chapter 5.8. The component constant amplitude S-N curves for welded components are valid for the toe section and for the throat section.
13 With reference to IIW-Recommendations and Eurocode 3.
14 Not applicable to cold rolled or shot-peened components.
123
4 Assessment of the fatigue strength using local stresses
4.4 Component fatigue strength 4.4.3 Component variable amplitude fatigue strength
124
4 Assessment of the fatigue strength using local stresses
Table 4.4.4 Number of cycles at the knee point, slope of the component constant amplitude S-N curves, and values of flI,cr and flI,<'
Normal stress Component
Shear stress IND,cr
IND,cr,II Ik, IkD,cr
flI,cr
Steel and cast iron materials (S-N curve model I ) 6 non-welded 110 1,0 115 16 welded 15 . 10 11,0 13 1Aluminum alloys (S-N curve modell II non-welded 1106 1108 /5 /15 0,74 15 . 106 1welded 1,0 13 1-
Component
IND,<,II Ik, IkD,< IflI,<
IND,<
Steel and cast iron materials (S-N curve model I ) non-welded 11,0 11086 118 1welded 11,0 110 15 11Aluminum alloys (S-N curve model II ) non-welded 1106 1108 18 125 10,83 8 welded 110 15 1- 11,0 1-
(lg)
1
O"AC 1 - - - - - - - - - " " O"AK f--------~l!ji,.~-----
O"AK,1I f-----'--------~:-
(JAK I---------+~------
~~-='T':;~~
ND,D =10 6 aifa bild'W13
N (lg)
N (lg)
!Iifa bildll'JI
(Ig) TAK f--------~""_=~----TAK,1I
f----------l-~'~--.:~~~
2 '10
Steel and cast iron materials, except austenitic steel, (Model I): horizontal for N > NO,a, kO,a = co or for N > NO,~, k O,~ = co
horizontal for N > NO,a,lI, kO,a,1I = co or for N > N0, ~,II ' kO, ~,II = co.
N (lg)
etra bild,,14
Normal stress a. Shear stress t.
Aluminum alloys and austenitic steel (Model II): sloping for N > NO a, kO a, or for N > NO:~, kO:~'
Nn,T =10 8
N (lg)
Figure 4.4.5 Component constant amplitude S-N curve for non-welded components *14 Top: Bottom:
I----------+--~~---
Nc = 6
ND,T =10 6 Bifa bildwl7
TAK
Figure 4.4.6 Component constant amplitude S-N curve for welded components *13 Top: Bottom:
Normal stress a. Shear stress t;
Steel, cast iron materials and aluminum alloys, welded (Model I): horizontal for N > NO a, kO a = co or for N > NO' ~, k ~ = co NC is the reference number of cycles
D
corresponding to the characteristic strength values a AC and ~ AC. aAK / aAC = (Nc / NO,a ) 11ko = 0,736 and
~AK / ~AC
=
(Nc / NO,~) 11kr = 0,457.
125
4.5 Safety factors
4.5 Safety factors
*1
IR25 EN .docl
Contents
Page
4.5.0
General
4.5.1
Steel
4.5.2 4.5.2.0 4.5.2.1 4.5.2.2
Cast iron materials General Ductile cast iron materials Non-ductile cast iron materials
4.5.3 4.5.3.0 4.5.3.1 4.5.3.2
Wrought aluminum alloys General Ductile wrought aluminum alloys Non-ductile wrought aluminum alloys
4.5.4
Cast aluminum alloys
4.5.5
Total safety factor
68
4 Assessment of the fatigue strength using local stresses
4.5.2 Cast iron materials 4.5.2.0 General Ductile and non-ductile cast iron materials are to be distinguished.
4.5.2.1 Ductile cast iron materials 69
Cast iron materials with an elongation A5 ~ 12,5 % are considered as ductile cast iron materials, in particular all types of GS and some types of GGG. Values of elongation see Table 5.1.12. Safety factors for ductile cast iron materials are given in Table 4.5.2. Compared to Table 4.5.1 they are higher because of an additional partial safety factor jp that accounts for inevitable but allowable defects in castings *4. The factor is different for severe or moderate consequences of failure and moreover for castings that have been subject to non-destructive testing or have not.
4.5.0 General According to this chapter the safety factors are to be determined. The safety factors are valid under the condition that the design loads are reliably determined on the safe side and that the material properties correspond to an average
Table 4.5.2 Safety factors for ductile cast iron materials (GS; GGG) (A5~ 12,5 %).
I
Jo
probability of survival of Po = 97,5 % *2.
Consequences of failure Severe moderate? 1
I
castings not subject to non-destructive testing ?2
The safety factors apply both to non-welded and welded components.
regular inspection
no yes?3
I I
2,1 1,9
I I
1,8 1,7
castings subject to non-destructive testing ?4
4.5.1 Steel The basic safety factor concerning the fatigue strength is
Jo =
(4.5.1)
1,5.
regular inspection
I I
1,9 1,7
I
I
1,65 1,5
? 1 See footnote? I of Table4.5.1. ?2 Compared to Table 4.5.1 an additional partial safety factor = 1,4 is introduced to account for inevitable but allowable defects in castings.
This value may be reduced under favorable conditions, that is depending on the possibilities of inspection and on the consequences of failure, Table 4.5.1.
jF
Table 4.5.1 Safety factors for steel *3 (not for GS) and for ductile wrought aluminum alloys (A~ 12,5 %).
jp
?3 Regular inspection in the senseof damage monitoring. Reduction by about10 %. ?4 Compared to Table 4.5.1 an additional partial safety factor = 1,25 is introduced, for which it is assumed that a higher quality ofthecastings isobviously guaranteed when testing.
Consequences of failure moderate ?1 severe
jo regular inspections
no yes ?3
I I
no yes?2
1,5 1,35
1,3 1,2
? 1 Moderate consequences of failure of a less important component in the sense of "non catastrophic" effects of a failure; for example because of a load redistribution towards other members of a statical indeterminate system. Reduction by about 15 %. ? 2 Regular inspection in the sense of damage monitoring. Reduction by about 10 %.
1 Chapters 4.5 and2.5 are identical.
2
Statistical confidence S = 50 % .
3 Steel is always considered as a ductile material. 4 In mechanical engineering cast components are of standard quality for which a further reduction of the partial safety factor to jF = 1,0 does not seempossible up to now. A safety factor jF = 1,0 may be applied to high quality cast components in the aircraft industry however. Those high quality cast components, have to meet special demands on qualification and checks of the production process, as well as on the extent of quality and product testing in order to guarantee little scatter of their mechanical properties.
126
4.5 Safety factors
4 Assessment of the fatigue strength using local stresses
4.5.2.2 Non-ductile cast iron materials
4.5.3.2 Non-ductile wrought aluminum alloy
Cast iron materials with an elongation As < 12,5 % (for GT A3 < 12,5 %) are considered as non-ductile materials, in particular some types of GGG as well as all types of GT and GG. Values of elongation for GGG and GT see Table 5.1.12 or 5.1.13. The value for GG is As = O.
Wrought aluminum alloys with an elongation A < 12,5 % are considered as non-ductile materials. Values of elongation see Table 5.1.22 to 5.1.30.
For non-ductile cast iron materials the safety factors from Table 4.5.2 are to be increased by adding a value ~j, Figure 4.5.1 *s:
~j
=
0,5 -~ As /50%,
(4.5.2)
AS Elongation, to be replaced by A3 for GT.
For non-ductile wrought aluminum alloys all safety factors from Table 4.5.1 are to be increased by adding a value Aj , Eq. (4.5.2).
4.5.4 Cast aluminum alloys Cast aluminum alloys are always considered as nonductile materials. All safety factors from Table 4.5.2 are to be increased by adding a value 4i , Eq. (4.5.2). Values of elongation see Table 5.1. 31 to 5. 1.38.
GG
0,5
~.---GGG-,----r~1
4.5.5 Total safety factor
GT
~j
Similar to an assessment of the component static strength, Chapter 3.5.5, a "total safety factor" .lges is to be derived:
o
10 12,5
20 As, A3 in %
.
_ In
Jges-~ ,
T,O
Figure 4.5.1 Value ~j to be added to the safety factor Jn , defined as a function of the elongation As or A3 , respectively.
4.5.3 Wrought aluminum alloys 4.5.3.0 General Ductile and non-ductile wrought aluminum alloys are to be distinguished.
4.5.3.1 Ductile wrought aluminum alloys Wrought aluminum alloys with an elongation A~ 12,5 % are considered as ductile materials. Values of elongation see Table 5.1.22 to 5.1.30. Safety factors for ductile wrought aluminum alloys are the same as for steel according to Table 4.5.1.
S For example the safety factor for GG is at least
Jn = (Jn
1,5
+ 0,5
= 2,0
(4.5.3)
= 1,5 from Table 4.5.2, j = 0,5 after Eq. (4.5.2) for AS = 0).
safety factor, Table 4.5.1 or 4.5.2, temperature factor, Chapter 4.2.3.
(4.5.4)
1 I
127 4.6 Assessment
4.6 Assessment Contents
4 Assessment of the fatigue strength using local stresses 1R46 EN.doq
Page
4.6.0
General
127
4.6.1 4.6.1.1 4.6.1.2
Rod-shaped (lD) components Individual types of stress Combined types of stress
128
4.6.2 4.6.2.1 4.6.2.2
Shell-shaped (2D) components Individual types of stress Combined types of stress
4.6.3 4.6.3.1 4.6.3.2
Block-shaped (3D) components Individual types of stress Combined types of stress
129
fatigue strength after Chapter 4.4.3, GBK , ... , divided by the total safety factor jges. The degree of utilization is always a positive value *4. An assessment of the variable amplitude fatigue strength, an assessment of the constant amplitude fatigue strength for finite life, or an assessment of the fatigue limit or of the endurance limit are to be distinguished. In each case the calculation is the same when using the appropriate variable amplitude fatigue strength factors KBK,o , ... , Chapter 2.4.3, and when taking G a,l
=
G a , ... ,
in case of a constant amplitude spectrum, or Ga , l = Ga,eff
4.6.0 General According to this chapter the assessment of the fatigue strength using local stresses is to be carried out. In general the assessments for the individual types of stress and for the combined types of stress are to be carried out separately *1. The procedure of assessment applies to both non-welded and welded components. For welded components the assessment is to be carried out with structural stresses or effective notch stresses *2. Assessments are generally to be carried out separately for the toe and for the root of a weld. They are to be carried out in the same way, but using the respective local stresses and fatigue classes FAT as these are in general different for the toe and the root of a weld.
Degree of utilization The assessment is to be carried out by determining the degree of utilization of the component fatigue strength. In the general context of the present Chapter the degree of utilization is the quotient of the (local) characteristic stress amplitude Ga,l> ... , divided by the allowable (local) stress amplitude of the component fatigue strength at the reference point *3. The allowable stress amplitude is the quotient of the component variable amplitude
1 It is essential to examine the degree of utilization not only of the combined types of stress but also of the individual types of stress in general, and in particular if these may occur separately. 2 The additional index K marking effective notch stresses is to be added to the stress symbols where appropriate. 3 The reference point is the critical point of the considered component that observes the highest degree of utilization.
(4.6.1)
(4.6.2)
in case of a damage-equivalent stress amplitude. Ga ,
characteristic constant amplitude stress for which the required number of cycles is N, ... , damage-equivalent stress amplitude.
... ,
Ga"eff,
Superposition For proportional or synchronous stress components of same type of stress the superposition is to be carried out according to Chapter 4.1. If different types of stress like normal stress and shear stress act simultaneously and if the resulting stress is multiaxial, Chapter 0.3.5 and Figure 0.0.9, both the individual types of stress and the combined types of stress are to be considered as described below *5.
Kinds of component Rod-shaped (10), shell-shaped (2D) and block-shaped (3D) components are to be distinguished. They can be both non-welded or welded.
4 As the degree of utilization is the quotient of two amplitude which always are positive. 5 Proportional, synchronous and non-proportional multiaxial stresses are to be distinguished. , Chapter 0.3.5. Only under special conditions of proportional stresses the character of Eq. (4.6.4), (4.6.9) and (4.6.14) is that of a strength hypothesis from a material-mechanics point of view. For example the extreme stresses from bending and shear will - as a rule - occur at different points of the crosssection, so that different reference points W are to be considered. As a rule bending will be more important. More general the Eq. (4.6.4), (4.6.9) and (4.6.14) have the character of an empirical interaction formula. They are applicable for proportional stresses and approximately applicable for synchronous stresses; an improved procedure for non-welded components is given in Chapter 5.9. For non-proportional stresses the Eq. (4.6.4), (4.6.9) and (4.6.14) are not suitable; an approximate procedure applicable for non-proportional stresses is proposed in Chapter 5.10.
128
4 Assessment of the fatigue strength using local stresses
4.6 Assessment
Table 4.6.1 Values of q as dependent on f w ,< ~1
4.6.1 Rod-shaped (ID) components 4.6.1.1 Individual types of stress The degrees of utilization of rod-shaped (ID) components for variable amplitude types of stress like normal stress and shear stress are ~
I,
(4.6.3)
f w< q ~1
A
GT, cast Al alloys 0,75 0,544
Steel, GGG wrought Al alloys 0,577 0,65 0 0,264
GG
0,85 0,759
Exceptions: For non-ductile wrought aluminum alloys (elongation < 12,5 %) q = 0,5 , for surface hardened or welded components
q = I.
4.6.2 Shell-shaped (2D) components O"a,1 , ... characteristic stress amplitude (largest stress amplitude in the spectrum) according to type of stress, Chapter 4.1.1.1 and Eq. (4.6.1) or (4.6.2), O"SK, ... related amplitude of the component variable amplitude fatigue strength, Chapter 4.4.3, jges total safety factor, Chapter 4.5.5.
4.6.2.1 Individual types of stress The degrees of utilization of shell-shaped (2D) components for variable amplitude types of stress like normal stress in the directions x and y as well as shear are aSK,crx
0'., x, I
=
0' BK,x
4.6.1.2 Combined types of stress The degree of utilization of rod-shaped components for combined types of stress is *6 aSK,Sv = q' aNH + (l - q) . aoH
s
1,
(ID)
/
O'.,y,]
aSK,cry = 0' BK,y
/
~
1,
~
1,
(4.6.8)
j erf j erf
(4.6.4)
where aNH =1 {Isal + aoH
~s; + 4· t; ).
(4.6.5)
=Js; +t; , (4.6.6)
Sa= aSK,cr ,
aSK,cr, ... degrees
of utilization after Eq.
(4.6.3).
For non-ductile wrought aluminum alloys (elongation A < 12,5 %) q = 0,5 is to be applied. For surface hardened or for welded components q = 1 is to be applied. Otherwise there is, Table 4.6.1,
q fw,'t
J3 -(l/fw"t) J3 -1
(4.6.7)
shear fatigue strength factor, Table 4.2.1 or 4.6.1.
0"a,x,1,... characteristic stress amplitude (largest stress amplitude in the spectrum) according to type of stress, Chapter 4.1.1.2 and Eq. (4.6.1) or (4.6.2), O"SK,x, ... related amplitude of the component variable amplitude fatigue strength, Chapter 4.4.3, jges total safety factor, Chapter 4.5.5.
4.6.1.2 Combined types of stress The degree of utilization of shell-shaped components for combined types of stresses is *6 aSK,crv = q . aNH + (l - q) . aoH~ 1, where
(2D)
(4.6.9) (4.6.10)
aNH =1{lsa,x
J
2
+Sa,yl+~(Sa,x -Sa,y)2 +4.t;), 2
2
aoH = sa,x + sa,y - sa,x . sa,y + t a ' sa,x = aSK,crx , 6 Eq. (4.6.4), (4.6.9) and (4.6.14) is a combination ofthe normal stress criterion (NH) and the v. Mises criterion (GH). Depending on the ductility ofthematerial thecombination is controlled bya parameter q as a function of fw,< according to Eq. (4.6.7), (4.6.12) or (4.6.17) and Table 4.6.1. For instance q = 0 forsteel sothat only thev. Mises criterion is of effect, while q = 0,264 for GGG so that both the normal stress criterion and thev.Mises criterion areof partial influence.
(4.6.11)
sa,y= aSK,cry , ta = aSK,"t , aSK,crx, ... degrees of utilization after Eq. (4.6.8) .
129 4 Assessment of the fatigue strength using local stresses
4.6 Assessment
For non-ductile wrought aluminum alloys (elongation A < 12.5 %) q = 0,5 is to be applied. For surface hardened or for welded components q = 1 is to' be applied. Otherwise there is, Table 4.6.1, q f w"
(4.6.12)
J3 -1
shear fatigue strength factor, Table 4.2.1 or 4.6.1
Rules of signs: If the normal stresses ax and a y always act proportional or synchronous in phase the degrees of utilization aSK,ax and aSK,cry are to be inserted in Eq. (4.6.11) with the same (positive) signs. If they act always proportional or synchronous 1800 out of phase, however, the degrees of utilization aSK,ax and aSK,cry are to be inserted in Eq. (4.6.11) with opposite signs *7 . If the individual types of stress act non-proportional, that is neither proportional nor synchronous, the Eq. (4.6.9) to (4.6.11) are not applicable and the procedure proposed in Chapter 5.10 is to be applied instead.
4.6.3 Block-shaped (3D) components
~
1,
~
1,
~
1,
(4.6.13)
(J I BK / j erf
aSK,a2 =
(J 2,0,1 (J 2,BK / j erf (J 3,0,1
aSK,a3 = (J3 BK / jerf
(4.6.14)
,I ,I
aoH = 1/ 2 "2\(Sa,1 -Sa,2) +(Sa,2
(4.6.15)
2
-Sa,3) +(Sa,3 -Sa,l)
2) ,
(4.6.16)
Sa,I = aSK,al , Sa,2 = aSK,a2 , Sa,3 = aSK,a3 , aSK,al ... degrees of utilization after Eq.
(4.6.13).
For non-ductile wrought aluminum alloys (elongation A < 12,5 %) q = 0,5 is to be applied. For surface hardened or for welded components q = 1 is to be applied. Otherwise there is, Table 4.6.1, q fw"
The degrees of utilization of block-shaped (3D) components for the principle stresses in the directions 1, 2 and 3 are
= q . aNH + (1 - q) . aGH~ 1,
aNH = MAX (Isa,d Sa,21 Sa,31) ,
*8
4.6.3.1 Individual types of stress
(J l,a,1
The degree of utilization of block-shaped (3D) components for combined types of stresses is *6 *9 aSK,sv
J3-(l/fw,)
aSK,al =
4.6.3.2 Combined types of stresses
J3-(l/fw,)
(4.6.17)
J3 -1 shear
fatigue
strength
factor,
Tab.
4.2.1.
Rules of signs: If the principle stresses al , a2 and a3 always act proportional or synchronous in phase the degrees of utilization aSK,al , aSK,a2 and aSK,a3 are to be inserted in Eq. (4.6.16) with the same (positive) signs. If they act always proportional or synchronous 1800 out of phase, however, the respective degrees of utilization aSK,aI , aSK,a2 and aSK,a3 are to be inserted in Eq. (4.6.16) with opposite signs *12. If the individual principle stresses act non-proportional (that is in a nonconstant direction), the Eq. (4.6.14) to (4.6.16) are not applicable and the procedure proposed in Chapter 5.10 is to be applied instead.
al,a,l , ... characteristic stress amplitude (largest stress amplitude in the spectrum) ofthe particular principle stress, Chapter 4.1.1.3 and Eq. (4.6.1) or (4.6.2), al,SK, ... related amplitude of the component variable amplitude fatigue strength, Chapter 4.4.3, jges total safety factor, Chapter 4.5.5.
7 For example normal stresses iii thedirections x and ythatresult from the same single external load affecting the component. 8 Sometimes block-shaped (3D) components may be welded at the surface, for example by surfacing welds. Then assessment can becarried out as for shell-shaped (2D) welded components, if the stresses ax, ay and, areofinterest only.
9 MAX means themaximum ofthevalues
inparenthesis to bevalid.
130
4.6 Assessment
4 Assessment of the fatigue strength using local stresses
131
5.1 Material tables
5 Appendices
IRT51
EN. dog
5.1 Material tables Contents 5.1.0 5.1.1 5.1.2
Page General Material tables for steel and cast iron materials Material tables for for aluminum alloys
131 132 132/ 142
5 Appendices
fw,o-
Fatigue strength factor for completely reversed normal stress, Table 2.2.1.
Material fatigue strength for completely reversed shear stress -Cw,s = fW,t' crW,zd, (2.2.1) (5.2) fW,t Shear fatigue strength factor, Tab. 2.2.1. Material fatigue strength for completely reversed bending stress c W,b = ncr(do) . crW,zd, no-(do) Kj-Kj ratio, Eq.(2.3.14)
5.1.0 General No responsibility can be taken for the mechanical material properties indicated in the material tables below, see page 3 "Terms of liability". The newest versions of the standards are decisive. The data given are not to be used for selecting the material in design since this would require additional material properties to be considered that are not contained in the tables below.
*5,
(5.3) with do = 7,5 mm.
Material fatigue strength for completely reversed torsional stress -CW,t = nldo)' -cw,s, (5.4) nldo) Kt-Kfratio, Eq.(2.3.14) *5, with do = 7,5 mm. Material fatigue strength for zero-tension axial stress (amplitude) crSch,zd = crW,zd / (1 + Mo- ), Mean stress sensitivity, Eq. (2.4.34)
(5.5)
The tables *I contain mechanical properties according to standards Rm,N , ... . They apply in the case of steel to the smallest dimension of a semi-finished product *2, in the case of cast iron materials and cast aluminum alloys for the test piece. In the case of wrought aluminum alloys the tables give component values Rm= Rm.N, ... , of the semi-finished product indicated. Properties according to standards, component values and component properties according standards are to be distinguished, as explained in the Chapters 1.2,2.2, 3.2 or 4.2.
M,
Rm,N or Rm are the minimum value, the guaranteed value or the lower boundary of the specified range of the tensile strength. The minimum value or the guaranteed value ofthe yield strength are Rp,N or R, *3 *4.
For aluminum alloys (constant amplitude S-N curve model II, Figure 2.4.4 and Table 2.4.4) crW,zd, ..., is the fatigue limit, while the endurance limit crW,II,zd, ..., is achieved at a number of cycles N = ND, II,o- = ND,II;, = 108 . It is lower than crW,zd or -cw,s by a factor fII, or fn,t :
The material fatigue strength values in the tables for completely reversed loading, crW,zd,N , or for zerotension loading, crSch zd N ' ..., are intended for information only, because they can be computed as described below and are not necessary for the assessment therefore. All following equations are supposed to be valid for a material test specimen of the diameter do = 7,5 mm independent of the real dimension of the semi-finished product or of the raw casting (index N left out, e.g. crW,zd instead of crW,zd,N , etc.)
*6.
Comment: The values crw, zd , ... , Eq. (5.1)6to (5.5), apply to a number of cycles N = ND,s = ND,t = 10 .
For steel and cast iron materials (constant amplitude S-N curve modell, Figure 2.4.4 and Table 2.4.4) crW,zd, ..., is the fatigue limit = endurance limit. Example: Quenched and tempered steel, - fw,o- = 0,45 (Tab. 2.2.1), - fatigue limit crW,zd = fw,o- . Rm = 0,45 Rm .
0-
_ fILo- = (108/106 ) 1/15 = 0,74 (kD,o-= 15 for normal stress) and _ fILt = (108/106 ) 1/25 = 0,83 (kD,t = 25 for shear stress). Example: -
fw,o- = 0,30 (Tab. 2.2.1), fILo- = 0,74, Endurance limit crW,II,zd = fILo- . fw,o- . Rm= = 0,74 . 0,30 . Rm = 0,22 . Rm .
Material fatigue strength for completely reversed normal stress crW.zd = fw,o- . Rm ,
(2.2.1) (5.1)
I Kinds of material (e.g. non-alloyed structural steel) and types of material within the kind ofmaterial (e.g. St37-2) are distinguished.
2
Ifdifferent dimensions ofa semi-finished product are given.
3 For the values Rm,N ' Rp,N, Rm ' Rp , an average probability of survival PO = 97,5 % is supposed that should also apply to the further values crW,zd,N ' "" crW,zd , "', derived therefrom.
4 Rp stands both for the yield stress R,
orthe 0.2 proofstress RpO,2 .
5 Eq. (5.3) for bending (and Eq. (5.4) for torsion in analogy) results from a combination ofthe following equations: - Eq. (2.4. I) (crW,b in the meaning ofa component value SWK,b ) - Eq. (2.3.1) (KWK,b = K(b), - Eq. (2.3. 10) (Kt,b = I ; ncr(r) = I ; K(b = 11 ncr(d) ), - Eq. (2.3.14) (ncr(d) with d = do = 7,5 mrn for the material in question, - Eq. (2.3.17) (Ocr (do) = 2/ do = 0,267 mrn -I ).
Eq. (5.5) follows from Eq. (2.4.10) with Rzrl = 0 orSm,zd / Sa,zd = I, respectively.
6
132 5.1 Material tables
5 Appendices
5.1.1 Material tables for steel and cast iron materials
5.1.2 Material tables for aluminum alloys
The tables 5.1.1 to 5.1.14, from page 132 on, contain mechanical properties according to standards, Rm.N, ... , for the following kinds of material: for rolled steel (nonalloyed structural steel, weldable fine grain structural steel, quenched and tempered steel, case hardening steel, nitriding steel and stainless steel), for forging steel and for cast iron materials (cast steel, heat treatable steel castings, nodular cast iron (GGG), malleable cast iron (GT) and cast iron with lamellar graphite (GG)). From these and according to Chapter 1.2.1 or 3.2.1 the component properties according to standards Rrn are to be computed under observation of the technological size factor according to the diameter or width of the semifinished product or of the raw casting, respectively. The fatigue limit values endurance limit as well.
O"W.zd.N. ..,
correspond to the
Table 5.1.21 on page 142 gives a survey of the aluminum materials. The tables 5.1.22 to 5.1.30, from page 143 on, contain component properties according to standards, R.ll , ..., for wrought aluminum alloys according to the type of material and its condition. They are valid for the indicated dimensions. The tables 5.1.31 to 5.1.38, from page 172 on, contain material properties according to standards, Rrn•N , ... , for cast aluminum alloys according to the type of material and its condition, from which - and according to Chapter 1.2.1 or 3.2.1 - the component properties according to standards, Rm , ... , are to be computed under observation of the technological size factor according to the width of the raw casting. The fatigue limit values O"W.zd , O"W.zd.N , ... , are different from those of the endurance limit, however, see page 131.
Table 5.1.1 Mechanical properties in MPa for non-alloy structural steels, after DIN EN 10 025 (1994-03-00) Type of material
Type of material, after DIN 17 100
S185 S235JR S235JRGI S235JRGlC S235JRG2 S235JRG2C S235JO S235JOC S235J2G3 S235J2G4 S235J2G3C S275JR S275JRC S275JO S275JOC S275J2G3 S275J2G4 S275J2G3C S355JR S355JO S355JOC S355J2G3 S355J2G4 S355J2G3C S355K2G3 S355K2G4 E295 E335 E360
St 33 St 37-2 USt 37-2 UQSt 37-2 RSt 37-2 RQSt 37-2 St 37-3 U QSt 37-3 U St 37-3 N QSt 37-3N St 44-2 QSt 44-2 St 44-3 U QSt 44-3 U St 44-3 N QSt 44-3N St 52-3 U QSt 52-3 U St 52-3 N QSt 52-3 N
St 50-2 St 60-2 St 70-2
Material No. 1.0035 1.0037 1.0036 1.0121 1.0038 1.0122 1.0114 1.0115 1.0116 1.0117 1.0118 1.0044 1.0128 1.0143 1.0140 1.0144 1.0145 1.0141 1.0045 1.0553 1.0554 1.0570 1.0577 1.0569 1.0595 1.0596 1.0050 1.0060 1.0070
c- 1.
Rm.N
s,.N <>2
O"W,zd,N
O"Sch,zd,N
O"W,b,N
310 360
185 235
140 160
138 158
155 180
80 95
90 105
430
275
195
185
215
110
125
510
355
230
215
255
130
150
490 590 690
295 335 360
220 265 310
205 240 270
245 290 340
125 155 180
145 170 200
<> 1 Effective Diameter del(N = 40 mm. c- 2 Re.N / Rrn,N < 0,75 for all types ofmatenal hsted.
'tW.s.N
'tW.I,N
133
5.1 Material tables
5 Appendices
Table 5.1.2 Mechanical properties in MFa for weldable fine grain structural steels in the normalized condition, after DIN 17102 (1983-10-00) ~1. Type of material
Material No.
Rm,N
Re,N
()W,zd,N
()Sch,zd,N
()W,b,N
1:W,s,N
1:W,t,N
~2
ad,rn
ad,p
~3
~3
StE StE StE StE
255 285 315 355
1.0461 1.0486 1.0505 1.0562
360 390 440 490
255 285 315 355
160 175 200 220
160 170 190 205
180 195 220 245
95 100 115 125
105 115 130 145
0,33 0,31 0,28 0,26
0,41 0,38 0,35 0,30
StE StE StE StE
380 420 460 500
1.8900 1.8902 1.8905 1.8907
500 530 560 610
380 420 460 500
225 240 250 275
210 220 230 245
250 265 280 300
130 140 145 160
145 155 165 180
0,26 0,24 0,23 0,22
0,34 0,31 0,30 0,31
~ 1 Effective Diameter for the tensile strength deff,N ~ 2 Re,N / ~N ~
= 70 mm, for the yield strength deff,N = 40 mm.
< 0,75 up to and including StE 355, Re,N / ~N > 0,75 from StE 380 on.
3 More specific values for the individual types of material compared to the average values given in Table 1.2.1 and 3.2.1.
Table 5.1.3 Mechanical properties in MFa for weldable fine grain structural steels in the normalized condition, after DIN EN 10 113 (1993-04-00) -c- 1. Type of material S 275 N S 275 NL S 355 N S 355 NL S 420N S 420 NL S460N S 460 NL S275M S 275 ML S 355M S 355 ML S420M S 420 ML S460M S 460 ML ~
Rrn,N
1.0490 1.0491 1.0545 1.0546 1.8902 1.8912 1.8901 1.8903 1.8818 1.8819 1.8823 1.8834 1.8825 1.8836 1.8827 1.8838
370
275
165
160
185
95
470
355
210
200
235
520
420
235
215
550
460
245
360
275
450
ad,rn
ad,p
~3
~3
110
0,30
0,30
120
140
0,25
0,28
260
135
150
0,23
0,30
225
275
140
160
0,00
0,22
160
158
180
95
105
0,30
0,30
355
205
190
225
115
130
0,25
0,28
500
420
225
210
250
130
145
0,23
0,30
530
460
240
220
265
140
155
0,00
0,22
Re,N
()W,zd,N
()Sch,zd,N
()W,b,N
1:W,s,N
1:W,t,N
~2
I Effective Diameter for the tensile strength deff,N
~ 2 Re,N / ~N ~
Material No.
= 100 mm, for the yield strength deff,N = 30 mm.
< 0,75 up to and including S 275 NL, Re,N / ~N > 0,75 from S 355 Non.
3 More specific values for the individual types of material compared to the average values given in Table 1.2.1 and 3.2.1.
134 5 Appendices
5.1 Material tables
Table 5.1.4 Mechanical properties in MFa for quenched and tempered steels in the quenched and tempered condition, after DIN EN 10 083-1 (1996-10-00) -¢-1. Notes? 1 to -¢-4 see next page. Type of material, after DIN EN 10 027-1 C22E C22R C22 C25E C25R C25 C30E C30R C30 C35E C35R C35 C40E C40R C40 C45E C45R C45 C50E C50R C50 C55E C55R C55 C60E C60R C60 28Mn6 38Cr2 38CrS2 46Cr2 46CrS2 34Cr4 34CrS4 37Cr4 37CrS4 41Cr4 41CrS4 25CrMo4 25CrMoS4 34CrMo4 34CrMoS4 42CrMo4 42CrMoS4 50CrMo4 36CrNiMo4 34CrNiM06 30CrNiMo8 -¢- 1 36NiCrMo16?1 51CrV4
Type of material, after DIN 17200 Ck 22 Cm22 C 22 Ck 25 Cm25 C25 Ck 30 Cm30 C 30 Ck 35 Cm35 C 35 Ck40 Cm40 C40 Ck45 Cm45 C45 Ck 50 Cm50 C 50 Ck 55 Cm55 C 55 Ck60 Cm60 C60 28Mn6 38 Cr 2 38 CrS 2 46 Cr 2 46 CrS 2 34 Cr4 34 CrS 4 37 Cr4 37 CrS 4 41 Cr 4 41 CrS 4 25 CrMo4 25 CrMoS 4 34 CrMo 4 34 CrMoS 4 42 CrMo 4 42 CrMoS 4 50 CrMo4 36 CrNiMo 4 34 CrNoMo6 30 CrNiMo 8 50 CrY 4
Material No.
1.1151 1.1149 1.0402 1.1158 1.1163 1.0406 1.1178 1.1179 1.0528 1.1181 1.1180 1.0501 1.1186 1.1189 1.0511 1.1191 1.1201 1.0503 1.1206 1.1241 1.0540 1.1203 1.1209 1.0535 1.1221 1.1223 1.0601 1.1170 1.7003 1.7023 1.7006 1.7025 1.7033 1.7037 1.7034 1.7038 1.7035 1.7039 1.7218 1.7213 1.7220 1.7226 1.7225 1.7227 1.7228 1.6511 1.6582 1.6580 1.6773 1.8159
R,N
crW,zd,N
crSch,zd,N
crW,b,N
LW,s,N
LW,t,N
ad,rn
llci,p
?2
-¢-3
-¢-3
?3
?3
?3
?4
?4
340 225
210
250
130
145
0,19
0,43
370 250
225
275
145
160
0,29
0,40
600
400 270
245
295·
155
175
0,26
0,37
630
430 285
255
310
165
185
0,20
0,39
650
460 295
260
320
170
190
0,12
0,36
700
490 315
275
345
180
205
0,16
0,36
750
520 340
290
365
195
215
0,21
0,35
800
550 360
305
390
210
230
0,19
0,35
850
580 385
320
415
220
245
0,18
0,34
800 800
590 360 550 360
305 305
390 390
210 210
230 230
0,30 0,37
0,38 0,52
900
650 405
335
435
235
260
0,41
0,54
900
700 405
335
435
235
260
0,33
0,49
950
750 430
345
460
245
270
0,32
0,46
1000
800 450
360
480
260
285
0,30
0,44
900
700 405
335
435
235
260
0,33
0,49
1000
800 450
360
480
260
285
0,30
0,44
1100
900 495
385
525
285
315
0,32
0,43
1100 900 495 1100 900 495 1200 1000 540 1250 1050 565 1250 1050 565 1100 900 495
385 385 410 420 420 385
525 525 570 595 595 525
285 285 310 325 325 285
315 315 340 355 355 315
0,28 0,32 0,33 0,36 0,28 0,28
0,38 0,38 0,39 0,42 0,32 0,33
Rm,N
500 550
135 5 Appendices
5.1 Material tables
Table 5.1.5 Mechanical properties in MPa for quenched and tempered steels in the normalized condition, after DIN EN 10 083-1 (1996-10-00) -9-1. Type of material, after DIN EN 10 027-1 C22E C22R C22 C25E C25R C25 C30E C30R C30 C35E C35R C35 C40E C40R C40 C45E C45R C45 CSOE C50R C50 C55E C55R C55 C60E C60R C60 28Mn6
Type of material, after DIN 17200
Material No.
Ck22 Cm22 C 22 Ck 25 Cm25 C 25 Ck 30 Cm30 C 30 Ck 35 Cm35 C 35 Ck40 Cm40 C40 Ck45 Cm45 C45 Ck50 Cm50 C 50 Ck 55 Cm55 C 55 Ck60 Cm60 C60 28Mn6
1.1151 1.1149 1.0402 1.1158 1.1163 1.0406 1.1178 1.1179 1.0528 1.1181 1.1180 1.0501 1.1186 1.1189 1.0511 1.1191 1.1201 1.0503 1.1206 1.1241 1.0540 1.1203 1.1209 1.0535 1.1221 1.1223 1.0601 1.1170
Rn,N
Re,N
crW,zd,N
CJSch,zd,N
CJW,b,N
't W,s,N
'tW,I,N
-9-2
~m
ad,p
-9-3
-9-3
430
240
195
185
215
110
125
0,08
0,19
470
260
210
200
235
120
140
0,10
0,18
510
280
230
215
255
135
150
0,10
0,19
550
300
250
225
275
145
160
0,10
0,19
580
320
260
235
285
150
170
0,09
0,19
620
340
280
250
305
160
180
0,10
0,20
650
355
295
260
320
170
190
0,10
0,19
680
370
305
270
335
175
195
0,09
0,20
710
380
320
280
350
185
205
0,09
0,19
630
345
285
250
310
165
185
0,07
0,17
-9- 1 Effective diameter deff,N = 16 rom. -9- 2 Re,N / Rm,N < 0,75 for all types of material listed. -9- 3 More specific values for the individual types of material compared to the average values given in Table 1.2.1 and 3.2.1.
Notes referring to Table 5.1.4: -9- 1 Effective diameter deff,N;= 40 rom for 30 CrNiMo 8 and 36 NiCrMo 16, deff,N = 16 rom for all other types of material listed. -9- 2 Re,N / Rm,N < 0,75 up to and including 46 Cr 2, 46 CrS 2; Re,N / Rm,N > 0,75 from 34 Cr 4, 34 CrS 4 on. -9- 3 The fatigue strength values of the sulphur bearing steels 38 CrS 2 to 42CrMoS 4 are lower than the values listed for 28 Cr 2 to 42 CrMo 4. -9- 4 M ore specific values for the individual types of material compared to the average values given in Table 1.2.1 and 3.2.1.
136
5 Appendices
5.1 Material tables
Table 5.1.6 Mechanical properties in MPa for case hardening steels in the blank hardened condition -:> 1, after DIN EN 10 084 (1998-06-00) (selected types of material only) -:>2. Type of material -:>3 ClOE C15E C16E 17Cr3 28Cr4 * 16MnCr5 * 20MnCr5 * 18CrMo4 * 18CrMoS4 * 22CrMoS3-5 * 20MoCr3 20MoCr4 16NiCr4 10NiCr5-4 * 18NiCr5-4 * l7CrNi6-6 * l5NiCr13 * 20NiCrMo2-2 * l7NiCrMo6-4 * 20NiCrMoS6-4 * 18CrNiMo7~6
* *
14NiCrMo13-4 -:> 1 Values after
DIN EN
Material No.
Rm,N
Re,N -:> 4 -:> 5
O'W,zd,N
O'Sch,zd,N
O'W,b,N
1: W,s,N
1:W,t,N
1.1121 1.1141 1.1148 1.7016 1.7030 1.7131 1.7147 1.7243 1.7244 1.7333 1.7320 1.7321 1.5714 1.5805 1.5810 1.5918 1.5752 1.6523 1.6566 1.6571 1.6587 1.6657
500 800 800 800 900 1000 1200 1100 1100 1100 900 900 1000 900 1200 1200 1000 1100 1200 1200 1200 1200
310 545 545 545 620 695 850 775 775 775 620 620 695 620 850 850 695 775 850 850 850 850
200 320 320 320 360 400 480 440 440 440 360 360 400 360 480 480 400 440 480 480 480 480
185 270 270 270 295 320 365 340 340 340 295 295 320 295 365 365 320 340 365 365 365 365
220 345 345 345 385 430 510 470 470 470 385 385 430 385 510 510 430 470 510 510 510 510
115 185 185 185 210 230 280 255 255 255 210 210 230 210 280 280 230 255 280 280 280 280
130 205 205 205 230 255 305 280 280 280 230 230 255 230 305 305 255 280 305 305 305 305
10084 Appendix
F ("tensile strength values after quenching and tempering at
ad,rn -:> ad,p
6
0,56 0,68 0,68 0,37 0,33 0,44 0,48 0,52 0,52 0,28 0,33 0,33 0,30 0,61 0,37 0,37 0,300,52 0,37 0,37 0,37 0,37
200°C") given for information only.
-c- 2 Effective diameter deff,N = 16 mm, -c- 3 Only up to 40 mm diameter, types of material marked by * up to 100 mm diameter, however. -:> 4 Re,N after DIN 17210 (Draft 1984-10-00), fitted. -:> 5 Re,N / ~,N < 0,75 for all types of material listed. -:> 6 More specific values for the individual types of material compared to the average values given in Table 1.2.1
and
3.2.1.
Table 5.1. 7 Mechanical properties in l\1Pa for nidriding steels in the quenched and tempered condition, after DIN EN 10 085 (2001-07-00) -:>1. Type of material
24CrMo13-6 31CrMo12 32CrAIMo7-1O 3lCrMoV5 33CrMoV12-9 34CrAINi7-1O 41CrAlMo7-1O 40CrMoV13-9 34CrAIMo5-1O
Material No.
Rm,N
Re,N -:>2
O'W,zd,N
O'Sch,zd,N
O'W,b,N
1: W,s,N
1:W,t,N
ad,rn -:>3
ad,p -:>3
1.8516 1.8515 1.8505 1.8519 1.8522 1.8550 1.8509 1.8523 1.8507-:>4
1000 1030 1030 1100 1150 900 950 950 800
800 835 835 900 950 680 750 750 600
450 465 465 495 520 405 430 430 360
360 370 370 385 395 335 345 345 305
480 495 495 525 550 435 460 460 390
260 270 270 285 300 235 250 250 210
285 295 295 315 330 260 275 275 230
0,22 0,21 0,21 0,31 0,30 0,17 0,23 0,23 0,00
0,26 0,27 0,27 0,36 0,35 0,17 0,24 0,24 0,00
-:> 1 Effective diameter deff,N = 40 mm. -:> 2 Re,N / ~N > 0,75 for all types of material listed. -:> 3 More specific values for the individual types of materiaI compared to the average values for the kind of material given in Table 1.2.1 and 3.2.1. -:> 4 Only up to 100 mm diameter.
137 5 Appendices
5.1 Material tables
Table 5.1.8 Mechanical properties in MFa for stainless steels, after DIN EN 10 088-2 (1995-08-00) (selected types of material only) v I v 2 Type of material
Type of material, after DIN / SEW
Mate- Kind of rial product v3 No.
Rm,N
R,N
CJW,zd,N
CJSch,zd,N
CJW,b,N
'"CW,.,N
'"CW,t,N
450 400 430 450
250 210 240 260
180 160 170 180
170 155 165 170
205 180 195 205
105 90 100 105
120 110 115 120
Martensitic steeIs 'ill th e h eat treate d con d" inon, stan dar d oualiti qua ities. X20Cr13 X20Cr 13 1.4021 P(75) QT650 650 QT750 750 X4CrNiMo16-5-1 P(75) 1.4418 QT840 840
450 550
260 300
230 260
290 330
150 175
170 195
680
335
280
410
195
220
430 380 340
335 310 285
460 410 370
245 220 195
275 245 220
240 220 210 200 210 230
215 200 190 185 190 210
270 245 235 225 235 260
140 125 120 115 120 135
160 145 140 135 140 155
. tl ie annealed con diition, . F emtic stee 1s ill stan dar d qualiHIes,
X2CrNi12 X6CrAl13 X6Crl7 X6CrMo17-1
X6CrAI13 X6Cr17 X6CrMo 17 1
1.4003 1.4002 1.4016 1.4113
P(25) P(25) P(25) H(12)
P ecipitation .. h ar demng . martensitic steeIs ill . tll e heat treate d condition, special X5CrNiCuNb16-4 1.4542 P(50) P1070 1070 1000 P950 950 800 P850 850 600
qualities.
-
, ' anneaIed condiition, Austemtic steeIs 'ill t h e soiution oualiti stan dar d qua ities. C(6) X10CrNi18-8 X12CrNi 177 1.4310 600 250 X2CrNiNI8-1O X2CrNi 18 10 P(75) 550 270 1.4311 X5CrNil8-10 X5CrNi 18 10 P(75) 520 220 1.4301 X6CrNiTi18-1O X6CrNi 18 10 P(75) 500 200 1.4541 X6CrNiMoTil7-12-2 X6CrNiMoTi 1722 1.4571 P(75) 520 220 X2CrNiMoN17-13-5 X2CrNiMoN17135 1.4439 P(75) 580 270
v I The fatigue strength values are provisional values. v 2 An effective diameter deff,N is not required, as there is no technological size effect within the dimensions covered by the standard. v 3 Kind of product: P(2S) hot rolled plates up to 25 mm thickness, H(12) hot rolled strip up to 12 mm thickness, C(6) cold r~l1ed strip up to 6 mm thickness, QT650 heat treated to a tensile strength of650 MPa, PI070 hot rolled plate with a tensile strength of 1070 MPa.
138
5 Appendices
5.1 Material tables
Table 5.1.9 Mechanical properties in MFa of steels for bigger forgings, after SEW 550 (1976-08-00) <, I <,2. Type of material
Material No.
Rn,N
R,N
O"W,zd,N
O"Sch,zd,N
O"W,b,N
1: W,s,N
1:W,t,N
<,3
ad,p <03
~,m
Quenched and tempered condition. Ck22 Ck 35 Ck45 Ck 50 Ck60 20Mn5 28Mn6 20 MnMoNi 45 22 NiMoCr 47 24 CrMo 5 34 CrMo4 42 CrMo 4 50 CrMo 4 32 CrMo 12 34 CrNiMo 6 30 CrNiMo 8 28 NiCrMoV 85<>' 2 33 NiCrMo 145<0
1.1151 1.1181 1.1191 1.1206 1.1221 1.1133 1.1170 1.6311 1.6755 1.7258 1.7220 1.7225 1.7228 1.7361 1.6582 1.6580 1.6932 1.6956
410 490 590 630 690 490 590 580 560 640 690 740 780 880 780 880 780 930
225 295 345 365 390 295 390 420 400 410 460 510 590 685 590 685 635 785
165 195 235 250 275 195 235 230 225 255 275 295 310 350 310 350 265 315
155 185 215 280 240 185 215 210 205 230 240 255 265 290 265 290 225 260
185 215 260 275 300 215 260 255 245 280 300 320 340 380 340 380 290 340
95 115 135 145 160 115 135 135 130 150 160 170 180 205 180 205 155 185
105 130 155 165 180 130 155 150 145 165 180 190 200 225 200 225 170 200
0,00 0,00 0,00 0,00 0,00 0,00 0,26 0,18 0,00 0,24 0,23 0,34 0,23 0,27 0,19 0,19 0,22 0,35
0,16 0,22 0,19 0,25 0,27 0,22 0,31 0,23 0,00 0,26 0,30 0,37 0,30 0,33 0,26 0,22 6,26 0,37
1.1151 1.1181 1.1191 1.1206 1.1221
410 490 590 620 680
225 275 325 345 375
165 195 235 250 270
155 180 215 220 220
185 215 260 270 295
95 115 135 145 155
105 130 155 160 175
0,00 0,00 0,00 0,00 0,00
0,16 0,19 0,16 0,15 0,14
Normalized condition. Ck22 Ck 35 Ck45 Ck 50 Ck60 <> I <> 2
The fatigue strength values are provisional values. Effective diameter deff,N = 500 nun for 28 NiCrMoV 8 5 und deff,N = 1000 nun for 33 NiCrMo 145, deff,N = 250 nun for all other types of material listed.
<> 3
More specific values for the individual types of material compared to the average values for the kind of material given in Table
1.2.1
and 3.2.1.
139 5 Appendices
5.1 Material tables Table 5.1.10 Mechanical propertiesin:MFafor steelcastingsfor general applications, after DIN 1681 (1985-06-00) ~ 1.
Type of material GS-38 GS-45 GS-52 GS-60 ~
Material No.
Rm,N
1.0420 1.0446 1.0552 1.0558
380 450 520 600
Re,N
~
2
200 230 260 300
crW,zd,N
crSch,zd,N
crW,b,N
L W,s,N
130 150 175 205
125 130 145 160
150 180 205 235
75 90 100 120
. LW,t,N
90 105 125 140
1 Effective diameter deff,N = 100 mm. ~ 2 Re,N / ~N < 0,75 for all types of material listed.
Table 5.1.11 Mechanical properties in:MFafor quenched and tempered steel castingsfor general applications, after DIN 17205 (1992-04-00). A'If-hardened and tempered condiinon (LV) ~ 1
Type of material
Material No.
Rm,N
GS-30 Mn 5 ~1 GS-25 CrMo 4 ~ 1 GS-34 CrMo 4 GS-42 CrMo 4 GS-30 CrMoV 6 4
1.1165 1.7218 1.7220 1.7225 1.7725
520 550 650 700 650
GS-35 CrMoV 10 4 GS-25 CrNiMo 4 GS-34 CrNiMo6 GS-30 NiCrMo 8 5 GS-33 NiCrMo 7 4 4
1.7755 1.6515 1.6582 1.6570 1.6740
800 700 800 800 800
~
2
crW,zd,N
crSch,zd,N
crW,b,N
LW,s,N
LW,t,N
260 300 380 400 400
175 185 220 240 220
145 150 175 185 175
205 215 250 270 250
100 110 130 135 130
125 130 150 160 150
650 400 550 600 600
270 240 270 270 270
205 185 205 205 205
305 270 305 305 305
155 135 155 155 155
185 160 185 185 185
Liquid-hardened and temperedcondition, strength level V I (upperline) or V II (line below) ~ 3. 100 GS-30 Mn 5 1.1165 175 145 205 520 400 (No. J) ~4 240 185 270 135 700 550 120 GS-25 CrMo 4 1.7218 205 160 235 600 450 145 (No.2) 255 195 285 750 600 145 255 195 285 GS-34 CrMo 4 1.7220 750 600 165 (No, 3) 290 215 320 850 700 265 200 295 155 GS-42 CrMo 4 1.7225 780 650 305 225 340 175 (No.4) 800 900 165 290 215 320 GS-30 CrMoV 64 1.7725 850 700 175 (No.5) 305 225 340 900 750
125 160 140 175 175 195 180 205 195 205
165 205 135 155 165 195 165 205 165 205
195 235 160 185 195 225 195 235 195 235
GS-35 CrMoV 10 4
1.7755
(No.6)
GS-25 CrNiMo 4
1.6515
(No.7)
GS-34 CrNiMo 6
1.6582
(No.8)
GS-30 NiCrMo8 5
1.6570
(No. 9) ~5
GS-33 NiCrMo 7 4 4 (No. 9) ~5 ~ 1 Effective diameter defT,N
= 800
1.6740
850 1050 700 800 850 900 850 1050 850 1050
Re,N
700 850 550 650 700 800 700 950 700 950
290 355 240 270 290 340 290 355 290 355
215 250 185 205 215 225 215 250 215 250
mm for GS-30 Mn 5 and defLN = 500 mm for GS-25 CrMo 4, defLN
320 390 270 305 320 370 320 390 320 390 = 300
mm for all other materials listed.
~ 2 Air-hardened condition: Re,N / ~N ::;; 0,75 for all types of material listed.
Liquid-hardened condition: Re,N / ~N > 0,75 for all types of material listed. ~
3 Effective diameter deff,N
=
100 mm for type of material-No.2 (strength level VII only) and for type of material-No. 1, 3, 4 (strength levels VI and VII);
deff,N = 200 mm for type of material-No. 2 (strength level VI only) and for type of material-No. 5,6,8 (strength levels VI and VII); deff,N ~
=
500 mm for type ofmaterial-No.7, 9 (strength levels VI and VII);
4 Numbers indicating types of material for Table 1.2.2 and 3.2.2.
-c- 5 The mechanical properties for GS-30 NiCrMo 8 5 and GS-33 NiCrMo 74 4-are the same.
140
5 Appendices
5.1 Material tables
Table 5.1.12 Mechanical properties in MPa for spheroidal graphit cast irons, after DIN EN 1563 (1997-08-00) or after DIN 1693/01 (1973-10-00) (namings given in brackets) {ol. Type of material EN-GJS-350-22-LT (GGG-35.3) EN-GJS-350-22-RT EN-GJS-350-22 EN-GJS-400-18-LT (GGG-40.3) EN-GJS-400-18-RT EN-GJS-400-18 EN-GJS-400-15 (GGG-40) EN-GJS-450-1 0 EN-GJS-500-7 (GGG-50) EN-GJS-600-3 (GGG-60) EN-GJS-700-2 (GGG-70) EN-GJS-800-2 (GGG-80) EN-GJS-900-2
Material No. EN-JS1015 (0.7033) EN-JS1014 EN-JS 1010 EN-JS1025 (0.7043) EN-JS1024 EN-JS1020 EN-JS1030 (0.7040) EN-JS1040 EN-JS1050 (0.7050) EN-JS1060 (0.7060) EN-JS1070 (0.7070) EN-JS1080 (0.7080) EN-JS1090
Rm,N
RpO,2,N
350
220
400
{o 2
As
{o3
1:W,t,N
1: W,s,N
CYW,zd,N
CYSch,zd,N
CYW,b,N
22
120
100
160
75
110
240
18
135
110
185
90
120
400
250 250 250
15
135
110
185
90
120
450 500
310 320
10 7
155 170
125 135
205 225
100 110
135 150
600
370
3
205
160
265
135
180
700
420
2
240
180
305
155
205
800
480
2
270
200
340
175
235
900
600
2
305
220
380
200
260
{o 1 Effective diameter deff,N = 60 mm. {o 21)J0,2,N / ~,N < 0,75 for all types of material listed. {o3 Elongation in %. For non-ductile materials, A 5 < 12,5%, the assessment ofthe static strength is to be carried out by using local stresses, Chapter 1.0, and all safety factors are to be increased by adding a value 6.j, Eq. (2.5.2), ... , see Chapters 2.5, 3.5 or 4.5 , respectively.
Table 5.1.13 Mechanical properties for malleable cast irons see next page.
Table 5.1.14 Mechanical properties in MPa for grey cast irons, after DIN EN 1561 (1997-08-00) or after DIN 1691 (1985-05-00) (namings given in brackets) {> 1. Type of material EN-GJL-100 (GG-10) {>4 EN-GJL-150 (GG-15) EN-GJL-200 (GG-20) EN-GJL-250 (GG-25) EN-GJL-300 (GG-30) EN-GJL-350 (GG-35) {> 1 Effective diameter deff,N
Material No. EN-JL 1010 (0.6010) EN-JL1020 (0.6015) EN-JL1030 (0.6020) EN-JL1040 (0.6025) EN-JL1050 (0.6030) EN-JL1060 (0.6035) =
{o2 Rm,N
RpO,I,N
3
CYW,zd,N {o
CYW.b.N
1: W.s,N
1:W,t,N
100
-
30
20
45
25
40
150
100
45
30
70
40
60
200
130
60
40
90
50
75
250
165
75
50
110
65
95
300
195
90
60
130
75
115
350
230
105
70
150
90
130
20 mm.
{> 2 After supplement 1 of the standard; not to be used for an assessment of strength. {o3 0W,zd,N / Rrn,N = 0,30; different from DIN EN 1561. {o 4 Not to be used for load carrying components.
CYSch,zd,N
141 5 Appendices
5.1 Material tables Table 5.1.13 Mechanical properties in MPa for malleable cast irons, after DIN EN 1562 (1997-06-00) or after DIN 1692 (1982-01-00) (namings given in brackets) ~ 1. Type of material
Material No.
Rm,N
RpO.2,N
~
2
A 3 ~3
O"W,zd,N
O"Sch,zd,N
O"W,b,N
'tW,s,N
'tW,t,N
Black heart malleable (non-decarburized) cast irons. EN-JMlllO (- )
300
-
6
90
75
130
70
100
(- )
EN-GJMB-350-1O (GTS-35-1O)
EN-JMl130 (0.8135)
350
200
10
105
85
150
80
115
EN-GJMB-450-6 (GTS-45-06)
EN-JMl140 (0.8145)
450
270
6
135
105
190
100
145
EN-GJMB-500-5
EN-JMl150
500
300
5
150
115
210
115
160
(-)
(-)
EN-GJMB-550-4 (GTS-50-04)
EN-JM1160 (0.8155)
550
340
4
165
125
230
125
175
EN-GJMB-600-3
EN-JM1l70
600
390
3
180
135
250
135
190
(-)
(-)
EN-GJMB-650-2 (GTS-65-02)
EN-JMl180 (0.8165)
650
430
2
195
145
265
145
205
EN-GJMB-700-2 (GTS-70-02)
EN-JM1l90 (0.8170)
700
530
2
210
155
285
160
220
EN-GJMB-800-1
EN-JM1200
800
600
1
240
170
320
180
250
(-)
(-)
EN-GJMB-300-6
White heart malleable (decarburized) cast irons. EN-JM1010 (0.8035)
350
-
4
105
85
150
80
115
EN-GJMW-360-12 EN-JM1020 (GTW-S 38-12) (0.8038)
360
190
12
110
85
155
80
120
EN-GJMW-400-5 (GTW-40-05)
EN-JM1030 (0.8040)
400
220
5
120
95
170
90
130
EN-GJMW-450-7 (GTW-45-07)
EN-JM1040 (0.8045)
450
260
7
135
105
190
100
145
EN-GJMW-550-4
EN-JM1050
550
340
4
165
125
230
125
175
(-)
(-)
EN-GJMW-350-4 (GTW-35-04)
~
1 Effective diameter deff,N = 15 mm.
-c- 2 Table on top: R pO,2,N / Rm,N ~
< 0,75; except for GTS-70-02 there is
R pO,2,N / Rm,N
> 0,75; Table below: R pO,2,N / Rm,N < 0,75 throughout.
3 Elongation in %. For non-ductile materials, A5 < 12,5%, the assessment of the static strength is to be carried out by using local stresses, Chapter 1.0, and all safety factors are to be increased by adding a value t.j , Eq. (2.5.2), ... , see Chapters 2.5,3.5 or 4.5 , respectively.
Table 5.1.14 Mechanical properties for grey cast irions see previous page.
142
5.1 Material tables Table 5.1.21. Survey of the Aluminum materials. Table
Kind of material
5.1.22
Wrought Strips, sheets, plates Aluminum alloys Strips, sheets
5.1.23
Semi-finished product / Type of casting
5 Appendices
IRT51Al-a.do~ Material standard (Edition) DIN EN 485-2
(03/95)
DIN 1745 T. 1
(02/83)
5.1.24
Cold drawn rods / bars and tubes
DIN EN 754-2
(08/97)
5.1.25
Rods / bars
DIN 1747 T. 1
(02/83)
5.1.26
Extruded rods / bars, tubes and profiles
DIN EN 755-2
(08/97)
5.1.27
Extruded profiles
DIN 1748 T. 1
(02/83)
5.1.28
Forgings
DIN EN 586-2
(U/94)
5.1.29
Die forgings
DIN 1749 T. 1
(12/76)
5.1.30
Hand forgings
DIN 17606
(12/76)
DIN EN 1706
(06/98)
DIN EN 1706
(06/98)
5.1.31 5.1.32
Cast Sand castings Aluminum alloys Permanent mould castings
5.1.33
Investment castings
DIN EN 1706
(06/98)
5. 1.34
High pressure die castings
DIN EN 1706
(06/98)
5.1.35
Casting alloys for general applications
DIN 1725 T. 2
(02/86)
5. 1.36
Alloys with special mechanical properties
DIN 1725 T. 2
(02/86)
5. 1.37
Alloys for special applications
DIN 1725 T. 2
(02/86)
5.1.38
Alloys for high pressure die castings
DIN 1725 T. 2
(02/86)
Tables 5.1.22 to 5.1.38 give the respective values of elongation: For non-ductile materials, A < 12,5%, the assessment of the component static strength is to be carried of using local stresses, Chapter 1.0, and all safety factors are to be increased by adding a value ~j , see Eq. (2.5.2), ... in Chapter 2.5, 3.5 or 4.5, respectively.
Attention: The fatigue limit values GW,zd, ... given in the Table 5.1.22 to 5.1.38 refer to the knee point of the S-N curve at N = ND,O' = ND,< = 106 cycles. The endurance limit values GW,Il,zd , ... refer to a number of N = ND,O'.II = ND.< ,II = 108 cycles, and are lower than the fatigue limit by a factor fIl,O' or fIl,< (see also page 131): -
fIl,O' = (108 / 106 ) fIl,< = (108 / 106 )
1/15 1/25
= 0,74 (kD,O' = 15 for normal stress), = 0,83 (kD,< = 25 for shear stress).
143
5.1 Material tables
5 Appendices
Table 5.1.22 Mechanical properties in MPa for wrought aluminum alloys, strips, s h eets, pJates, I aft er DIN EN 485-2 (03/95) (selected types 0 f matenial onlly), Material
Condition
EN AW-2014
T3
AlCu4SiMg
T4 T451 T451 T42
T6 T651 T651
T62 EN AW-2017A
T4 T451
AICu4MgSi(A) T451
T42
EN AW-2024
T4
AICu4Mgl
T3 T351
T351
T42
T8 T851 T851 T62 -c-
Nom, thickness inmm from to 1,5 <: 0,4 6,0 1,5 1,5 <: 0,4 6,0 1,5 12,5 6,0 12,5 40,0 40,0 100,0 6,0 <:0,4 12,5 6,0 25,0 12,5 1,5 <: 0,4 6,0 1,5 12,5 6,0 12,5 40,0 40,0 60,0 60,0 80,0 80,0 100,0 100,0 120,0 12,5 <: 0,4 25,0 12,5 1,5 <: 0,4 6,0 1,5 12,5 6,0 12,5 40,0 40,0 100,0 100,0 120,0 120,0 150,0 3,0 <:0,4 12,5 3,0 25,0 12,5 1,5 <: 0,4 6,0 1,5 1,5 <:0,4 3,0 1,5 6,0 3,0 12,5 6,0 12,5 40,0 40,0 80,0 80,0 100,0 100,0 120,0 120,0 150,0 6,0 <: 0,4 12,5 6,0 25,0 12,5 1,5 <:0,4 6,0 1,5 12,5 6,0 12,5 25,0 25,0 40,0 12,5 <:0,4 25,0 12,5
Rm
Re
crW,zd
crSch,zd
crW,b
~W,s
~W,t
395 400 395 395 400 400 395 395 400 400 440 440 450 460 450 435 420 410 440 450 390 390 390 390 385 370 350 390 390 390 425 425 435 435 440 440 430 420 400 380 360 425 425 420 460 460 460 455 455 440 435
245 245 240 240 250 250 250 230 235 235 390 390 395 400 390 380 360 350 390 395 245 245 260 250 240 240 240 235 235 235 275 275 290 290 290 290 290 290 285 270 250 260 260 260 400 400 400 400 395 345 345
120 120 120 120 120 120 120 120 120 120 130 130 135 140 135 130 125 125 130 135 115 115 115 115 115 110 105 115 115 115 130 130 130 130 130 130 130 125 120 115 110 130 130 125 140 140 140 135 135 130 130
85 90 85 85 90 90 85 85 90 90 95 95 95 95 95 95 90 90 95 95 85 85 85 85 85 85 80 85 85 85 90 90 95 95 95 95 95 90 90 85 80 90 90 90 95 95 95 95 95 95 95
140 140 140 140 140 140 140 140 140 140 150 150 155 160 155 150 145 145 150 155 135 135 135 135 135 130 125 135 135 135 145 145 150 150 150 150 150 145 140 135 130 145 145 145 160 160 160 155 155 150 150
70 70 70 70 70 70 70 70 70 70 75 75 80 80 80 75 75 70 75 80 70 70 70 70 65 65 60 70 70 70 75 75 75 75 75 75 75 75 70 65 60 75 75 75 80 80 80 80 80 75 75
85 85 85 85 85 85 85 85 85 85 95 95 95 100 95 95 90 90 95 95 85 85 85 85 85 80 75 85 85 85 90 90 95 95 95 95 90 90 85 85 80 90 90 90 100 100 100 95 95 95 95
A{>1 %
1 Elongation A for gaugelengthof 50 mm, or (with*) Elongation A5 for gaugelength of 5 x specimen diameter
14 14 14 14 14 10* 7* 14 14 12* 6 7 7 6* 5* 4* 4* 4* 7 6* 14 15 13 12* 10* 8* 4* 14 15 12* 12 14 12 14 14 13 11* 8* 7* 5* 5* 15 12 8* 5 6 5 4* 4* 5 4*
Hardness number HB III
112 110 110 112 112 111 110 III III
133 133 135 138 135 131 126 123 133 135 110 110 III
110 108 105 101 109 109 109 120 120 123 123 124 124 122 120 115 110 104 119 119 118 138 138 138 137 136 129 128
144
5.1 Material tables
5 Appendices
Table 5.1.22 Continued, page 1 of 7. Material
EN AW-4006
Condition
H12
AISi1Fe H14 T4
EN AW-4007
O1H111
AISi1, 5Mn H12
EN AW-5049
O/H111
AI Mg2MnO,8
Hl12
H12
H14
H16
H18 H22/H32
H241H34
H26/H36
H28/H38
Nom. thickness inmm from to 0,2 0,5 0,5 1,5 1,5 3,0 0,2 0,5 0,5 1,5 1,5 3,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 0,5 ~0,2 1,5 0,5 3,0 1,5 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 100,0 12,5 ~6,0 25,0 12,5 40,0 25,0 80,0 40,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 40,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 25,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 0,2 0,5 0,5 1,5 1,5 3,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 40,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 25,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 0,2 0,5 0,5 1,5 1,5 3,0
Rm
Re
crW,zd
crSch,zd
crW,b
1W,S
1W,t
120 120 120 140 140 140 120 120 120 120 110 110 110 110 110 140 140 140 190 190 190 190 190 190 210 200 190 190 220 220 220 220 220 220 240 240 240 240 240 240 265 265 265 265 290 290 290 220 220 220 220 220 220 240 240 240 240 240 240 265 265 265 265 290 290 290
90 90 90 120 120 120 55 55 55 55 45 45 45 45 45 110 110 110 80 80 80 80 80 80 140 120 80 80 170 170 170 170 170 170 190 190 190 190 190 190 220 220 220 220 250 250 250 130 130 130 130 130 130 160 160 160 160 160 160 190 190 190 190 230 230 230
35 35 35 40 40 40 35 35 35 35 35 35 35 35 35 40 40 40 35 35 35 35 35 35 65 60 55 55 65 65 65 65 65 65 70 70 70 70 70 70 80 80 80 80 85 85 85 65 65 65 65 65 65 70 70 70 70 70 70 80 80 80 80 85 85 85
35 35 35 40 40 40 35 35 35 35 30 30 30 30 30 40 40 40 50 50 50 50 50 50 55 50 50 50 55 55 55 55 55 55 60 60 60 60 60 60 65 65 65 65 70 70 70 55 . 55 55 55 55 55 60 60 60 60 60 60 65 65 65 65 70 70 70
50 50 50 55 55 55 50 50 50 50 45 45 45 45 45 55 55 55 75 75 75 75 75 75 80 75 75 75 85 85 85 85 85 85 90 90 90 90 90 90 100 100 100 100 105 105 105 85 85 85 85 85 85 90 90 90 90 90 90 100 100 100 100 105 105 105
20 20 20 25 25 25 20 20 20 20 20 20 20 20 20 25 25 25 35 35 35 35 35 35 35 35 35 35 40 40 40 40 40 40 40 40 40 40 40 40 45 45 45 45 50 50 50 40 40 40 40 40 40 40 40 40 40 40 40 45 45 45 45 50 50 50
30 30 30 35 35 35 30 30 30 30 25 25 25 25 25 35 35 35 45 45 45 45 45 45 50 45 45 45 50 50 50 50 50 50 55 55 55 55 55 55 60 60 60 60 65 65 65 50 50 50 50 50 50 55 55 55 55 55 55 60 60 60 60 65 65 65
A~l
%
4 4 5 3 3 3 14 16 18 21 15 16 19 21 25 4 4 5 12 14 16 18 18 17* 12 10* 12* 14* 4 5 6 7 9 9* 3 3 4 4 5 6* 2 3 3 3 1 2 2 7 8 10 11 10 9* 6 6 7 8 10 8* 4 4 5 6 3 3 4
Hardness number HB 38 38 38 45 45 45 35 35 35 35 32 32 32 32 32 44 44 44 52 52 52 52 52 52 62 58 52 52 66 66 66 66 66 66 72 72 72 72 72 72
80 80 80 80 88 88 88 63 63 63 63 63 63 70 70 70 70 70 70 78 78 78 78 87 87 87
145
5.1 Material tables
5 Appendices
Table 5.1.22 Continued, page 2 of 7. Material
EN AW-5052
Condition
OIHIlI
AI Mg2,5
HIl2
Nom.thickness inmm from to 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 80,0 12,5 <: 6,0 12,5 40,0 80,0
40,0
H12
H14
H16
H18 H22IH32
H24/H34
H26IH36
H28IH38
EN AW-5251
OIHIlI
AlMg2
H12
Hl4
H16
0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 0,2 0,5 1,5 0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 0,2 0,5 1,5 0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 6,0 0,2 0,5
0,5 1,5 3,0 6,0 12,5 40,0 0,5 1,5 3,0 6,0 12,5 25,0 0,5 1,5 3,0 6,0 0,5 1,5 3,0 0,5 1,5 3,0 6,0 12,5 40,0 0,5 1,5 3,0 6,0 12,5 25,0 0,5 1,5 3,0 6,0 0,5 1,5 3,0 0,5 1,5 3,0 6,0 12,5 50,0 0,5 1,5 3,0 6,0 12,5 25,0 0,5 1,5 3,0 6,0 12,5 0,5 1,5
A~1
Rm
Re
crW,zd
crSch,zd
crW,b
~W,s
~W,t
170 170 170 170 165 165 190 170 170
65 65 65 65 65 65 110 70 70
50 50 50 50 50 50 55 50 50
45 45 45 45 45 45 50 45 45
65 65 65 65 65 65 75 65 65
30 30 30 30 30 30 30 30 30
40 40 40 40 40 40 45 40 40
12 14 16 18 19 18* 7 10* 14*
210 210 210 210 210 210 230 230 230 230 230 230 250 250 250 250 270 270 270 210 210 210 210 210 210 230 230 230 230 230 230 250 250 250 250 270 270 270 160 160 160 160 160 160 190 190 190 190 190 190 210 210 210 210 210 230 230
160 160 160 160 160 160 180 180 180 180 180 180 210 210 210 210 240 240 240 130 130 130 130 130 130 150 150 150 150 150 150 180 180 180 180 210 210 210 60 60 60 60 60 60 150 150 150 150 150 150 170 170 170 170 170 200 200
65 65 65 65 65 65 70 70 70 70 70 70 75 75 75 75 80 80 80 65 65 65 65 65 65 70 70 70 70 70 70 75 75 75 75 80 80 80 50 50 50 50 50 50 60 60 60 60 60 60 65 65 65 65 65 70 70
55 55 55 55 55 55 60 60 60 60 60 60 60 60 60 60 65 65 65 55 55 55 55 55 55 60 60 60 60 60 60 60 60 60 60 65 65 65 45 45 45 45 45 45 50 50 50 50 50 50 55 55 55 55 55 60 60
80 80 80 80 80 80 85 85 85 85 85 85 95 95 95 95 100 100 100 80 80 80 80 80 80 85 85 85 85 85 85 95 95 95 95 100 100 100 65 65 65 65 65 65 75 75 75 75 75 75 80 80 80 80 80 85 85
35 35 35 35 35 35 40 40 40 40 40 40 45 45 45 45 45 45 45 35 35 35 35 35 35 40 40 40 40 40 40 45 45 45 45 45 45 45 30 30 30 30 30 30 35 35 35 35 35 35 35 35 35 35 35 40 40
50 50 50 50 50 50 55 55 55 55 55 55 55 55 55 55 60 60 60 50 50 50 50 50 50 55 55 55 55 55 55 55 55 55 55 60 60 60 40 40 40 40 40 40 45 45 45 45 45 45 50 50 50 50 50 55 55
4 5 6 8 10 9* 3 3 4 4 5 4* 2 3 3 3 1 2 2 5 6 7
%
10
12 12* 4 5 6 7 9 9* 3 4 5 6 3 3 4 13 14 16 18 18 18 3 4 5 8 10 10* 2 2 3 4 5 1 2
Hardness number HB 47 47 47 47 46 46 55 47 47 63 63 63 63 63 63 69 69 69 69 69 69 76 76 76 76 83 83 83 61 61 61 61 61 61 67 67 67 67 67 67 74 74 74 74 81 81 81 44 44 44 44 44 44 58 58 58 58 58 58 64 64 64 64 64 71
71
146
5.1 Material tables
5 Appendices
Table 5.1.22 Continued, page 3 of 7. Material
AlMg2 continued
Condition
H16 H18
H221H32
H241H34
H26/H36
H281H38
EN AW-5154A
OlHlll
AIMg3,5(A)
H112
H12
H14
H18 H19 H221H32
H241H34
H261H36
H28/H38
Nominal thickness inmm from 1,5 3,0 0,2 0,5 1,5 0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 6,0 0,2 0,5 1,5 3,0 0,2 0,5 1,5 0,2 0,5 1,5 3,0 6,0 12,5 ~6,0
12,5 40,0 0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 0,2 0,5 0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 0,2 0,5 1,5
Rm
Re
crW,zd
crSch,zd
crW,b
"tW,s
"tW,t
230 230 255 255 255 190 190 190 190 190 190 210 210 210 210 210 230 230 230 230 255 255 255 215 215 215 215 215 215 220 215 215 250 250 250 250 250 250 270 270 270 270 270 270 310 310 310 330 330 250 250 250 250 250 250 270 270 270 270 270 270 290 290 290 290 310 310 310
200 200 230 230 230 120 120 120 120 120 120 140 140 140 140 140 170 170 170 170 200 200 200 85 85 85 85 85 85 125 90 90 190 190 190 190 190 190 220 220 220 220 220 220 270 270 270 285 285 180 180 180 180 180 180 200 200 200 200 200 200 230 230 230 230 250 250 250
70 70 75 75 75 55 55 55 55 55 55 65 65 65 65 65 70 70 70 70 75 75 75 65 65 65 65 65 65 65 65 65 75 75 75 75 75 75 80 80 80 80 80 80 95 95 95 100 100 75 75 75 75 75 75 80 80 80 80 80 80 85 85 85 85 95 95 95
60 60 65 65 65 50 50 50 50 50 50 55 55 55 55 55 60 60 60 60 65 65 65 55 55 55 55 55 55 55 55 55 60 60 60 60 60 60 65 65 65 65 65 65 75 75 75 75 75 60 60 60 60 60 60 65 65 65 65 65 65 70 70 70 70 75 75 75
85 85 95 95 95 75 75 75 75 75 75 80 80 80 80 80 85 85 85 85 95 95 95 80 80 80 80 80 80 85 80 80 95 95 95 95 95 95 100 100 100 100 100 100 110 110 110 120 120 95 95 95 95 95 95 100 100 100 100 100 100 105 105 105 105 110 110 110
40 40 45 45 45 35 35 35 35 35 35 35 35 35 35 35 40 40 40 40 45 45 45 35 35 35 35 35 35 40 35 35 45 45 45 45 45 45 45 45 45 45 45 45 55 55 55 55 55 45 45 45 45 45 45 45 45 45 45 45 45 50 50 50 50 55 55 55
55 55 60 60 60 45 45 45 45 45 45 50 50 50 50 50 55 55 55 55 60 60 60 50 50 50 50 50 50 50 50 50 55 55 55 55 55 55 60 60 60 60 60 60 70 70 70 75 75 55 55 55 55 55 55 60 60 60 60 60 60 65 65 65 65 70 70 70
%
to 3,0 4,0 0,5 1,5 3,0 0,5 1,5 3,0 6,0 12,5 25,0 0,5 1,5 3,0 6,0 12,5 0,5 1,5 3,0 4,0 0,5 1,5 3,0 0,5 1,5 3,0 6,0 12,5 50,0 12,5 40,0 80,0 0,5 1,5 3,0 6,0 12,5 40,0 0,5 1,5 3,0 6,0 12,5 25,0 0,5 1,5 3,0 0,5 1,5 0,5 1,5 3,0 6,0 12,5 40,0 0,5 1,5 3,0 6,0 12,5 25,0 0,5 1,5 3,0 6,0 0,5 1,5 3,0
A?1
3 3 1 2 2 4 6 8 10 12 12* 3 5 6 8 10 3 4 5 7 2 3 3 12 13 15 17 18 16* 8 9 13* 3 4 5 6 7 6* 2 3 3 4 5 4* 1 1 1 1 1 5 6 7 8 10 9* 4 5 6 7 8 7* 3 3 4 5 3 3 3
Hardne ss number HB 71 71 79 79 79 56 56 56 56 56 56 62 62 62 62 62 69 69 69 69 77 77 77 58 58 58 58 58 58 63 59 59 75 75 75 75 75 75 81 81 81 81 81 81 94 94 94 100 100 74 74 74 74 74 74 80 80 80 80 80 80 87 87 87 87 93 93 93
147
5.1 Material tables
5 Appendices
..
T a ble 5122 Contmued, page 4 0 f 7 Material
EN AW-5454
Condition
O1H111
AIMg3Mn
Hl12 HI2
H14
H221H32
H24/H34
H26/H36
H28/H38 EN AW-5754
O/HU1
AI Mg3
HIl2
H12
H14
H16
H18
Nominalthickness inmm from to 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 80,0 12,5 40,0 120,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 40,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 25,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 40,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 25,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 0,2 0,5 0,5 1,5 1,5 3,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 100,0 12,5 ?: 6,0 25,0 12,5 40,0 25,0 80,0 40,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 40,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 25,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 0,2 0,5 0,5 1,5 1,5 3,0
Rm
Re
crW,zd
crSch,zd
crW,b
'tW,s
vw..
A
215 215 215 215 215 215 220 215 215 250 250 250 250 250 250 270 270 270 270 270 270 250 250 250 250 250 250 270 270 270 270 270 270 290 290 290 290 310 310 310 190 190 190 190 190 190 210 200 190 190 220 220 220 220 220 220 240 240 240 240 240 240 265 265 265 265 290 290 290
85 85 85 85 85 85 125 90 90 190 190 190 190 190 190 220 220 220 220 220 220 180 180 180 180 180 180 200 200 200 200 200 200 230 230 230 230 250 250 250 80 80 80 80 80 80 140 120 80 80 170 170 170 170 170 170 190 190 190 190 190 190 220 220 220 220 250 250 250
65 65 65 65 65 65 65 65 65 75 75 75 75 75 75 80 80 80 80 80 80 75 75 75 75 75 75 80 80 80 80 80 80 85 85 85 85 95 95 95 55 55 55 55 55 55 65 60 55 55 65 65 65 65 65 65 70 70 70 70 70 70 80 80 80 80 85 85 85
55 55 55 55 55 55 55 55 55 60 60 60 60 60 60 65 65 65 65 65 65 60 60 60 60 60 60 65 65 65 65 65 65 70 70 70 70 75 75 75 50 50 50 50 50 50 55 50 50 50 55 55 55 55 55 55 60 60 60 60 60 60 65 65 65 65 70 70 70
80 80 80 80 80 80 85 80 80 95 95 95 95 95 95 100 100 100 100 100 100 95 95 95 95 95 95 100 100 100 100 100 100 105 105 105 105 110 110 110 75 75 75 75 75 75 80 75 75 75 85 85 85 85 85 85 90 90 90 90 90 90 100 100 100 100 105 105 105
35 35 35 35 35 35 40 35 35 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 50 50 50 50 55 55 55 35 35 35 35 35 35 35 35 30 30 40 40 40 40 40 40 40 40 40 40 40 40 45 45 45 45 50 50 50
50 50 50 50 50 50 50 50 50 55 55 55 55 55 55 60 60 60 60 60 60 55 55 55 55 55 55 60 60 60 60 60 60 65 65 65 65 70 70 70 45 45 45 45 45 45 50 45 45 45 50 50 50 50 50 50 55 55 55 55 55 55 60 60 60 60 65 65 65
12 13 15 17 18 16* 8 9* 13* 3 4 5 6 7 6* 2 3 3 4 5 4* 5 6 7 8 10 9* 4 5 6 7 8 7* 3 3 4 5 3 3 3 12 14 16 18 18 17* 12 10* 12* 14* 4 5 6 7 9 9* 3 3 4 4 5 5* 2 3 3 3 1 2 2
%
Hardness number HB 58 58 58 58 58 58 63 59 59 75 75 75 75 75 75 81 81 81 81 81 81 74 74 74 74 74 74 80 80 80 80 80 80 87 87 87 87 93 93 93 52 52 52 52 52 52 62 58 52 52 66 66 66 66 66 66 72 72 72 72 72 72
80 80 80 80 88 88 88
148
5.1 Material tables
5 Appendices
Table 5.1.22 Continued, page 5 of 7. Material
EN AW-5754 AlMg3 continued
Condition
HI8 H22/H32
H24/H34
H26/H36
H28/H38
EN AW-5083
O/Hll1
AI Mg4,5MnO,7
H112 H116"}
HI2
HI4
H16
H22/H32
H24/H34
Nominal thickness inmm from to 0,2 0,5 0,5 1,5 1,5 3,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 40,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 25,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 0,2 0,5 0,5 1,5 1,5 3,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 50,0 50,0 80,0 80,0 120,0 120,0 150,0 12,5 <:6,0 40,0 12,5 80,0 40,0 3,0 <: 1,5 6,0 3,0 12,5 6,0 40,0 12,5 80,0 40,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 40,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 25,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 4,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 40,0 0,2 0,5 0,5 1,5 1,5 3,0 3,0 6,0 6,0 12,5 12,5 25,0
Rm
Re
crW,zd
crSch,zd
crW,b
ToW,S
vw.r
290 290 290 220 220 220 220 220 220 240 240 240 240 240 240 265 265 265 265 290 290 290 275 275 275 275 275 275 270 260 255 275 275 270 305 305 305 305 285 315 315 315 315 315 315 340 340 340 340 340 340 360 360 360 360 305 305 305 305 305 305 340 340 340 340 340 340
250 250 250 130 130 130 130 130 130 160 160 160 160 160 160 190 190 190 190 230 230 230 125 125 125 125 125 125 115 110 105 125 125 115 215 215 215 215 200 250 250 250 250 250 250 280 280 280 280 280 280 300 300 300 300 215 215 215 215 215 215 250 250 250 250 250 250
85 85 85 65 65 65 65 65 65 70 70 70 70 70 70 80 80 80 80 85 85 85 85 85 85 85 85 85 80 80 75 85 85 80 90 90 90 90 85 95 95 95 95 95 95 100 100 100 100 100 100 110 110 110 110 90 90 90 90 90 90 100 100 100 100 100 100
70 70 70 55 55 55 55 55 55 60 60 60 60 60 60 65 65 65 65 70 70 70 65 65 65 65 65 65 65 65 65 65 65 65 70 70 70 70 70 75 75 75 75 75 75 80 80 80 80 80 80 80 80 80 80 70 70 70 70 70 70 80 80 80 80 80 80
105 105 105 85 85 85 85 85 85 90 90 90 90 90 90 100 100 100 100 105 105 105 100 100 100 100 100 100 100 95 95 100 100 100 110 110 110 110 105 115 115 115 115 115 115 120 120 120 120 120 120 130 130 130 130 110 110 110 110 110 110 120 120 120 120 120 120
50 50 50 40 40 40 40 40 40 40 40 40 40 40 40 45 45 45 45 50 50 50 45 45 45 45 45 45 45 45 45 50 50 45 55 55 55 55 50 55 55 55 55 55 55 60 60 60 60 60 60 60 60 60 60 55 55 55 55 55 55 60 60 60 60 60 60
65 65 65 50 50 50 50 50 50 55 55 55 55 55 55 60 60 60 60 65 65 65 60 60 60 60 60 60 60 60 60 60 60 60 70 70 70 70 65 70 70 70 70 70 70 75 75 75 75 75 75 80 80 80 80 70 70 70 70 70 70 75 75 75 75 75 75
A
1 2 2 7 8 10 11 10 9* 6 6 7 8 10 8* 4 4 5 6 3 3 4 11 12 13 15 16 15* 14* 12* 12* 12 10* 10* 8 10 12 10* 10* 3 4 5 6 7 6* 2 3 3 3 4 3* 1 2 2 2 5 6 7 8 10 9* 4 5 6 7 7 7*
Hardness number HB 88 88 88 63 63 63 63 63 63 70 70 70 70 70 70 78 78 78
78 87 87 87 75 75 75 75 75 75 73 70 69 75 75 73 89 89 89 89 83 94 94 94 94 94 94 102 102 102 102 102 102 108 108 108 108 89 89 89 89 89 89 99 99 99 99 99 99
149
5.1 Material tables
5 Appendices
Table 5.1.22 Continued, page 6 of 7. Material
Condition
Nom.thickness
Rm
Re
crW,zd
crSch,zd
crW,b
~W,s
~W,t
280 280 280 280 100 100 100 100 100 100 125 105 100 195 195 195 195 200 200 200 200 200 200 240 240 240 240 240 240 270 270 270 270 290 290 290 185 185 185 185 185 185 220 220 220 220 220 220 250 250 250 250 110 110 110 110 110 110 95 95 95 95 95 95 260 260 260 260
110 110 110 110 70 70 70 70 70 79 75 70 70 85 85 85 85 85 85 85 85 85 85 90 90 90 90 90 90 100 100 100 100 105 105 105 85 85 85 85 85 85 90 90 90 90 90 90 100 100 100 100 60 60 60 60 60 60 60 60 60 60 60 60 95 95 95 95
80 80 80 80 60 60 60 60 60 60 60 60 60 65 65 65 65 65 65 65 65 65 65 70 70 70 70 70 70 75 75 75 75 80 80 80 65 65 65 65 65 65 70 70 70 70 70 70 75 75 75 75 55 55 55 55 55 55 55 55 55 55 55 55 75 75 75 75
130 130 130 130 90 90 90 90 90 90 95 90 90 100 100 100 100 100 100 100 100 100 100 110 110 110 110 110 110 120 120 120 120 125 125 125 100 100 100 100 100 100 110 110 110 110 110 110 115 115 115 115 80 80 80 80 80 80 80 80 80 80 80 80 110 110 110 110
60 60 60 60 40 40 40 40 40 40 45 40 40 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 55 55 55 55 60 60 60 50 50 50 50 50 50 50 50 50 50 50 50 55 55 55 55 35 35 35 35 35 35 35 35 35 35 35 35 55 55 55 55
80 80 80 80 55 55 55 55 55 55 55 55 55 60 60 60 60 60 60 60 60 60 60 65 65 65 65 65 65 70 70 70 70 75 75 75 60 60 60 60 60 60 65 65 65 65 65 65 70 70 70 70 50 50 50 50 50 50 50 50 50 50 50 50 70 70 70 70
m mm
EN AW-5083 AI Mg4,5MnO,7 continued
H26/H36
EN AW-5086
OlHlIl
AlMg4
H1I2
H1I6
H12
H14
H16
H18 H22/H32
H24/H34
H261H36
EN AW-6082
T4 T451
AISiMgMn T451 T42
T6 T651 T62
from 0,2 0,5 1,5 3,0 0,2 0,5 1,5 3,0 6,0 12,5 2: 6,0 12,5 40,0 2: 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 0,2 0,5 1,5 0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 6,0 12,5 0,2 0,5 1,5 3,0 2:0,4 1,5 3,0 6,0 12,5 40,0 2: 0,4 1,5 3,0 6,0 12,5 40,0 2: 0,4 1,5 3,0 6,0
to 0,5 360 1,5 360 3,0 360 4,0 360 0,5 240 1,5 240 3,0 240 6,0 240 12,5 240 150,0 240 12,5 250 40,0 240 80,0 240 3,0 275 6,0 275 12,5 275 50,0 275 0,5 275 1,5 275 3,0 275 6,0 275 12,5 275 40,0 275 0,5 300 1,5 300 3,0 300 6,0 300 12,5 " 300 25,0 300 0,5 325 1,5 325 3,0 325 4,0 325 0,5 345 1,5 345 3,0 345 0,5 275 1,5 275 3,0 275 6,0 275 12,5 275 40,0 275 0,5 300 1,5 300 3,0 300 6,0 300 12,5 300 25,0 300 0,5 325 1,5 325 3,0 325 4,0 325 1,5 205 3,0 205 6,0 205 12,5 205 40,0 205 80,0 205 1,5 205 3,0 205 6,0 205 12,5 205 40,0 205 80,0 205 1,5 310 3,0 310 6,0 310 12,5 310
AV
1
%
2" 3 3 3 11 12 13 15 17 16* 8 9* 12* 8 9 10 9* 3 4 5 6 7 6* 2 3 3 3 4 3* 1 2 2 2 1 1 1 5 6 7 8 10 9* 4 5 6 7 8 7* 2 3 3 3 12 14 15 14 13* 12* 12 14 15 14 13* 12* 6 7 10 9
Hardness number HB 106 106 106 106 65 65 65 65 65 65 69 65 65 81 81 81 81 81 81 81 81 81 81 90 90 90 90 90 90 98 98 98 98 104 104 104 80 80 89 80 80 80 88 88 88 88 88 88 96 96 96 96 58 58 58 58 58 58 57 57 57 57 57 57 94 94 94 91
150
5.1 Material tables
5 Appendices
Table 5.1.22 Continued, page 7 of 7. Material
Condition
Nom.thickness
Rm
Re
crW,zd
crSch,zd
crW,b
~W,s
~W,t
295 295 275 275 280 280 280 280 275 275 275 275 320 320 320 320 350 350 350 350 350 340 330 330 400 400 450 450 450 430 410 525 540 540 545 540 540 530 525 495 490 460 410 360 500 500 490 460 460 475 475 475 455 440 430
240 240 240 230 205 205 205 205 200 200 200 200 210 210 210 210 280 280 280 280 280 270 260 260 350 350 370 370 370 350 330 460 460 470 475 460 470 460 440 420· 390 360 300 260 425 425 415 385 385 390 390 390 360 340 340
90 90 85 85 85 85 85 85 85 85 85 85 95 95 95 95 105 105 105 105 105 100 100 100 120 120 135 135 135 130 125 160 160 160 165 160 160 160 160 150 145 140 125 110 150 150 145 140 140 145 145 145 135 130 130
70 70 65 65 70 70 70 70 65 65 65 65 75 75 75 75 80 80 80 80 80 80 75 75 90 90 95 95 95 90 90 105 110 110 110 110 110 105 105 100 100 95 90 80 105 105 100 95 95 100 100 100 95 95 95
110 110 100 100 105 105 105 105 100 100 100 100 115 115 115 115 125 125 125 125 125 120 120 120 140 140 155 155 155 150 145 175 180 180 180 180 180 180 175 170 165 160 145 130 170 170 165 160 160 160 160 160 155 150 150
50 50 50 50 50 50 50 50 50 50 50 50 55 55 55 55 60 60 60 60 60 60 55 55 70 70 80 80 80 75 70 90 95 95 95 95 95 90 90 85 85 80 70 60 85 85 85 80 80 80 80 80 80 75 75
65 65 60 60 65 65 65 65 60 60 60 60 70 70 70 70 75 75 75 75 75 75 75 75 85 85 95 95 95 95 90 110 115 115 115 115 115 110 110 105 105 100 90 80 105 105 105 100 100 100 100 100 95 95 95
A-}I
in mm
EN AW-6082 AlSiMgMn continued
T651 T62 T61 T6151
T6151
EN AW-7020
T4 T451
AI Zn4,5Mg1 T6 T651 T62 T651
EN AW-7021 AIZn5,5Mg1,5 EN AW-7022 AIZn5Mg3Cu
EN AW-7075 AIZn5,5MgCu
T6 T6 T6 T651 T6 T651 T62
T651 T62
T76 T7651 T73 T7351 T7351
from 12,5 60,0 100,0 150,0 20,4 1,5 3,0 6,0 12,5 60,0 100,0 150,0 20,4 1,5 3,0 6,0 20,4 1,5 3,0 6,0 12,5 40,0 100,0 150,0 21,5 3,0 >3,0 12,5 25,0 50,0 100,0 20,4 0,8 1,5 3,0 6,0 12,5 25,0 50,0 60,0 80,0 90,0 100,0 120,0 21,5 3,0 6,0 21,5 3,0 6,0 12,5 25,0 50,0 60,0 80,0
to 60,0 100,0 150,0 175,0 1,5 3,0 6,0 12,5 60,0 100,0 150,0 175,0 1,5 3,0 6,0 12,5 1,5 3,0 6,0 12,5 40,0 100,0 150,0 175,0 3,0 6,0 12,5 25,0 50,0 100,0 200,0 0,8 1,5 3,0 6,0 12,5 25,0 50,0 60,0 80,0 90,0 100,0 120,0 150,0 3,0 6,0 12,5 3,0 6,0 12,5 25,0 50,0 60,0 80,0 100,0
%
8* 7* 6* 4* 10 11 11 12 12* 10* 9* 8* 11 12 13 14 7 8 10 10 9* 8* 7* 6* 7 8 8 8* 7* 5* 3* 6 6 7 8 8 6* 5* 4* 4* 4* 3* 2* 2* 7 8 7 7 8 7 6* 5* 5* 5* 5*
Hardness number HB 89 89 84 83 82 82 82 82 81 81 81 81 92 92 92 92
104 104 104 104 104 101 98 98 121 121 133 133 133 127 121 157 160 161 163 160 161 158 155 147 144 135 119 104 149 149 146 137 137 140 140 140 133 129 126
151
5.1 Material tables
5 Appendices
Table 5.1.23 Mechanical properties in MFa for wrought aluminum alloys, strips and sheets with a thickness from 0,35 mm on, after DIN 1745 T. I (1983-02-00) (selected types of material only). Material DIN notation A1Mg2,5 W17 F21
No. 3.3523 .10 .24
G21
.25
F23
.26
G23
.27
F25
.28
G25
.29
F27
.30
G27 A1Mg3 W19 W19
.31 3.3535 .10 .10
F19
.07
F20
.07
F21
.07
F22
.24
G22
.25
F24
.26
G24
.27
F27
.28
G27
.29
F29 A1Mg2MnO,8 W19 W19
.30 3.3527 .10 .10
F19
.07
F20
.07
Thickness inmm from to 0,35 3,0
F21
.07
F22
.24
022
.25
F24
.26
G24
.27
F27
~
1 see page153
.28
~
crW,zd
crSch,zd
crW,b
~W,s
~W,t
A5
AlO
%
%
~1
~1
Hardness Condo number HB ~2 50 w
60
50
45
65
30
40
20
17
210
160
65
55
80
35
50
10
8
65
kg
210
130
65
55
80
35
50
12
10
65
rg
230
180
70
60
85
40
55
5
4
73
kg
230
150
70
60
85
40
55
10
8
73
rg
250
210
75
60
95
45
55
4
3
80
kg
250
180
75
60
95
45
55
7
6
80
rg
270
240
80
65
100
45
60
3
2
85
kg
270
210
80
65
100
45
60
6
5
85
rg
190
80
55
50
75
35
45
20
17
50
w
190
80
55
50
75
35
45
18
-
50
w
190
80
55
50
75
35
45
12
-
50
wg
200
120
60
50
75
35
45
10
-
60
wg
210
140
65
55
80
35
50
12
-
60
wg
220
165
65
55
85
40
50
9
7
65
kg
220
130
65
55
85
40
50
14
12
65
rg
240
190
70
60
90
40
55
5
4
73
kg
240
160
70
60
90
40
55
10
8
73
rg
265
215
80
65
100
45
60
4
3
80
kg
265
190
80
65
100
45
60
7
6
80
rg
290
250
85
70
105
50
65
3
2
85
kg
190
80
55
50
75
35
45
20
17
50
w
190
80
55
50
75
35
45
18
-
50
w
190
80
55
50
75
35
45
12
-
50
wg
-
200
120
60
50
75
35
45
10
-
60
wg
210
140
65
55
80
35
50
12
-
60
wg
220
165
65
55
85
40
50
9
7
65
kg
220
130
65
55
85
40
50
14
12
65
rg
240
190
70
60
90
40
55
5
4
73
kg
240
160
70
60
90
40
55
10
8
73
rg
265
215
80
65
100
45
60
4
3
80
kg
10
0,35
3,0
0,35
10
0,35
3,0
0,35
10
0,35
3,0
0,35
10
0,35
3,0
0,35
10
0,35
3,0
0,35
4,0
0,35
3,0
0,35
4,0
0,35
3,0
0,35
3,0
0,35
3,0
0,35
3,0
0,35
3,0
0,35 6,0
6,0
50
-
-
25
50
-
-
10
25
3
-
5,0
10
0,35
10
0,35
10
0,35
3,0
0,35
10
0,35
3,0
0,35
10
0,35
3,0
0,35
4,0
0,35
3,0
0,35
4,0
0,35
3,0
0,35
4,0
0,35
3,0
0,35
3,0
0,35
3,0
0,35
6,0
-
-
6,0
50
-
.
25
50
-
Rp
170
0,35
10
Rm
25
-
-
6,0
10
0,35
3,0
0,35
10
0,35
3,0
0,35
10
0,35
3,0
0,35
10
0,35
3,0
0,35
10
0,35
3,0
0,35
10
2 kg = coldrolled, rg = recrystallization annealed, w = softannealed, wg = hot rolled.
152
5.1 Material tables
5 Appendices
Table 5.1.23 Continued, page 1 of2. Material DIN notation AlMg2MnO,8 G27 F29 AlMg2,7Mn F22 F22
No. .29 .30 3.3537 .07 .07
Thickness inmm from to 0,35 3,0 0,35
10
0,35
3,0
0,35
10
4,0
-
25 G25 G25
.25 .25
G27
.27 .27
AlMg4Mn 3.3545 W24 .10 W24 .10 F28 G28 G30 AlMg4,5Mn W28 F28 G31 G35 AlMgSil W F21
-
.25 .27 .27 3.3547 .10 .07 .25 .27 3.2315 .10 .51
-
-
-
4,0
6,0
-
-
-
-
6,0
50
-
-
1,0
6,0
-
-
1,0
6,0
-
-
1,0
6,0
0,35
3,0
0,35
50
-
-
4,0 2,0
50
-
65
100
45
60
7
6
290
250
85
70
105
50
65
3
2
85
kg
215
100
65
55
80
35
50
17
-
55
wg
215
100
65
55
80
35
50
12
-
55
wg
245
180
75
60
90
40
55
10
-
75
rg
245
180
75
60
90
40
55
8
-
75
rg
270
200
80
65
100
45.
·60
9
-
85
rg
270
200
80
65
100
45
60
7
-
85
rg
240
310
70
60
90
40
55
18
-
65
w
240
95
70
60
90
40
55
17
-
60
w
275
200
85
65
100
50
60
7
-
80
kg
275
190
85
65
100
50
60
12
-
80
rg
300
230
90
70
110
50
65
8
-
90
rg
275
125
85
65
100
45
60
17
15
70
w
275
125
85
65
100
45
60
12
-
70
wg
310
205
95
75
110
55
70
10
-
85
rg
345
270
105
80
125
60
75
6
5
100
rg
-
:S: 85
-
-
-
-
-
18
15
35
w
10
0,35
3,0
205
110
60
55
80
35
50
16
14
65
ka
3,0 20
205
110
60.
55
80
35
50
14
12
65
ka
275
200
85
65
100
50
60
14
12
85
wa
275
200
85
65
100
50
60
12
-
85
wa
315
255
95
75
115
55
70
10
8
95
wa
295
245
90
70
110
50
65
9
-
95
wa
295
240
90
70
110
50
65
8
-
90
wa
-
:S: 80
-
.
-
-
-
18
15
40
w
-
:S: 80
-
-
-
-
-
17
14
40
w
205
110
60
55
80
35
50
14
12
60
ka
-
205
110
60
55
80
35
50
12
10
60
ka
12 3,0
290
240
85
70
105
50
65
10
8
90
wa
290
240
85
70
105
50
65
9
-
90
wa
3,0
0,35
10
F29
80
3,0
0,35
F29
190
0,35
.71
F21
265
0,35
3,0
F21
-¢>1
Hardness Condo number HB ~2 rg 80
6,0
3,0
AlMglSiCu W W
%
3,0
0,35 3,0
60
-
-
0,35
20
-
-
2,0
100
.10
0,35
3,0
.10
0,35 6,0
6,0 -
.72
t'"1
AlO
1,0
0,35
F30
A5
1,0
.71
.72
'tW,t
40
F28
F30
'tW,s
6,0
.51
.72
crW,b
12
F21
F32
crSch,zd
12
0,35 3,0
F28
~
.24
6,0
6,0 1,0
crW,zd
50
-
Rp
25
4,0 6,0
G27
-
Rm
.51
0,35
.51
0,35 3,0
.71
0,35
.71
0,35 3,0
12 3,0 3,0
3,0
12
2 ka = naturallyaged, kg = coldrolled, rg = recrystallization annealed, w = softannealed, wa = artificially aged, wg = hot rolled.
153
5.1 Material tables
5 Appendices
Table 5.1.23 Continued, page 2 of2. Material DIN notation No. AlCuMgI 3.1325 W .10 F40 .51
Thickness inmm from to 0,35 3,0 0,35 12 0,35 3,0 0,35
F39 F39
.51 .51
AlCuMg2 3.1355 W .10 F44 .51
-
12
-
0,35
0,35 0,35
AlCuSiMn 3.1255 W .10 F40 .51 F40 F39 F46
.51 .51 .71
AlZn4,5Mg1 3.4335 W .10 F35 .71 F34
.71
AlZnMgCuO,5 3.4345 F45 .71 F45 .71 .71
-
1,5
25
.71
AlZnMgCu1,5 3.4365 F53 .71 F53 .71 F53
.71
F48 F48
.71
A5
AIO
~I
%
-}1
Hardness Condo number .;..2 HB w 50
-
s 140
-
-
-
-
-
13
II
395
265
120
85
140
70
85
13
II
100
ka
390
265
115
85
135
70
85
13
-
100
ka
385
245
115
85
135
65
85
12
-
95
ka
-
s 140
-
-
-
-
-
13
II
55
w
440
290
130
95
150
75
95
13
II
110
ka
-
-
-
-
-
13
-
55
w
-
~
140
140
70
85
12
-
105
ka
400
250
120
90
140
70
85
II
-
100
ka
390
250
115
85
135
70
85
8
-
100
wa
460
400
140
95
160
80
100
7
-
125
wa
-
s 140
-
-
-
-
-
15
13
45
w
3,0 15
350
275
105
80
125
60
75
10
8
105
wa
-
340
270
100
80
120
60
75
9
-
105
wa
60 -
450
370
135
95
155
80
95
8
-
125
wa
-
-
50
100
-
-
1,5
25
-
-
1,5 0,35
6,0
25
-
450
370
135
95
155
80
95
7
-
125
wa
50 100
430
350
130
95
150
75
95
5
-
110
wa
-
-
410
330
125
90
145
70
90
3
-
100
wa
100
-
200 -
530
450
160
105
180
90
110
8
-
140
wa
6,0
12 530
450
160
105
180
90
110
5
-
140
wa
530
450
160
105
180
90
110
3
-
140
wa
-
500
430
150
105
170
85
105
2
-
130
wa
63 -
480
410
145
100
165
85
100
2
-
130
wa
480
390
145
100
165
85
100
2
-
130
wa
-
-
-
12
25
-
50
.71
-
.71
63 -
75 -c-
~W,t
90
-
25 F50
~W,s
120
50
6,0 -
O'W,b
250
-
-
O'Sch,zd
400
-
25
50
F41
3,0 12 3,0 12
12
25 F43
-
-
15
O'W,zd
60
6,0 -
0,35
Rp
3,0
3,0
12 0,35
Rm
50
75 100
1 The elongation As is to be usedfor the assessment.
.;.. 2 ka = naturallyaged, w = soft annealed, wa = artificially aged.
154
5.1 Material tables
5 Appendices
Table 5.1.24 Mechanical properties in MPa for wrought aluminum alloys, cold drawn rods / bars and tubes, after DIN EN 754-2 (1997-08-00). Material, EN notation DIN notation No. EN AW-2007 AlCu4PbMgMn 3.1645
EN AW-2011 AlCu6BiPb 3.1655 EN AW-2011A AlCu6BiPb(A) EN AW-2014 AlCu48iMg 3.1255
EN AW-2014A AlCu48iMg(A)
EN AW-2017A AlCu4Mg8i(A) 3.1325
EN AW-2024 AlCu4Mgl 3.1355
EN AW-2030 AlCu4PbMg
EN AW-3003 AlMnlCu 3.0517
Condition
Rods/ Bars D; 8 ~ 1
Tubes e~ I
mm
mm
von T3
-
30 T351 T3510 T3511 T3
-
40 50 T8 0 Hill T3 T351 T3510 T3511 T4
T451 T4510 T4511 T6 T651 T6510 T6511 0 HIll T3 T351 T3510 T3511 0, Hill T3
T351 T3510 T3511 T6 T651 T8 T851 T3
-
HI4 H16 HI8
von
to
-
-
-
40 50 80
-
-
80
-
80
-
80
-
80 80
-
80 80
-
-
-
80 80
-
-
-
5
-
20
20 -
-
5 20
-
-
20 20
-
20
-
20
-
20
20
Rp
crW,zd
crsch,zd
crW,b
'tW,s
'tW,t
A
A50
~2
~2
MPa
MPa
MPa
MPa
MPa
MPa
MPa
%
%
370 340 370 370 370
240 220 250 240 240
110 100 110 110 110
85 80 85 85 85
130 120 130 130 130
65 60 65 65 65
80 75 80 80 80
7 6 7 5 5
320 300 280 310 290 370 370 <240
270 250 210 260 240 270 275 < 125
95 90 85 95 85 110 110 70
75 70 70 75 70 85 85 60
115 110 105 110 105 130 130 90
55 50 50 55 50 65 65 40
70 70 65 70 65 80 80 55
10 10 10 10 8 8 8 12
8 6 8 6 10
380 380 380
290 290 290
115 115 115
85 85 85
135 135 135
65 65 65
85 85 85
8 6 6
6 4 4
380 380 380 380
220 240 220 240
115 115 115 115
85 85 85 85
135 135 135 135
65 65 65 65
85 85 85 85
12 12 10 10
10 10 8 8
380 380 380
135 135 135
95 95 95
155 155 155
80 80 80
95 95 95
8 6 6
6 4 4
5
-
5 3 3 8
-
20
-
-
20
450 450 450
-
80
-
20
<240
< 125
<70
<60
<90
40
55
12
10
-
80 80
-
20
-
-
20
400 400 400
250 250 250
120 120 120
90 90 90
140 140 140
70 70 70
85 85 85
10 8 8
8 6 6
10 -
80
-
<250 <240 425 425 440 420 425 420
< 150 < 140 310 290 290 270 310 290
<75 <70 130 130 130 125 130 125
<60 <60 90 90 95 90 90 90
<90 >90 145 145 150 145 145 145
<45 <40 75 75 75 75 75 75
< 55 < 55 90 90 95 90 90 90
12 12 10 9 10 10 8 8
10 10 8 7 8 8 6 6
-
80 80 80 80 30 80 80
425 425 455 455 370 340 370 370
315 315 400 400 240 220 240 240
130 130 135 135 110 100 110 110
90 90 95 95 85 80 85 85
145 145 155 155 130 120 130 130
75 75 80 80 65 60 65 65
90 90 95 95 80 75 80 80
5 4 4 3 7 6 5 5
4 3 3 2 5
95 95 130 130 160 160 180 180
35 35 110 110 130 130 145 145
30 30 40 40 50 50 55 55
25 25 35 35 45 45 45 45
40 40 50 50 65 65 70 70
15 15 25 25 30 30 30 30
25 25 30 30 40 40 40 40
25 25 6 6 4 4 3 3
-
30 T351 T3510 T3511 0, HIli
to 30 80
Rm
-
-
10 80
-
80
-
-
-
20
-
5
5 20
-
20
-
-
-
-
80
-
(D) (8) (D) (8) (D) (8)
40 10 15 5 10 3
-
-
-
-
-
-
20
-
20 10
-
5
-
3
-
-
3 3 16 10 4 4 3 3 2 2
155
5.1 Material tables
5 Appendices
Table 5.1.24 Continued, page I of 2. Material EN notation DIN notation No. EN AW-3103 AlMnI 3.0515
Condition
0, HIll H14
H18 0,H111 H14 EN AW·5005A AlMg1(C) 3.3315 EN AW-5019 AlMg5 3.3555
EN AW-5251 AlMg2 3.3525
EN AW·5052 AlMg2,5 3.3523
EN AW-5154A AlMg3,5(A)
EN AW-5754 AlMg3 3.3535
EN AW·5083 AlMg4,5MnO,7 3.3547
Tubes e -e- I
mm
mm
von
H16
EN AW-5005 AlMg1(B)
Rods/ Bars D;8~ I
H18 0, HIll H12, H22, H32 H14, H24, H34 H16, H26, H36 0, HIll H12, H22, H32 H14, H24, H34 H16, H26, H36 H18, H28, H38 0, HIll H12, H22, H32 H14, H24, H34 H16, H26, H36 H18, H28, H38 0, HIll
~~?
(D) (8) (D) (8) (D) (8) (D) (8) (D) (8)
~~?
(D) (8) (D) (8) (D) (8)
-
(D) (8) (D) (8) (D) (8) (D) (8)
~~?
(D) (8) (D) (8) (D) (8)
~~?
(D) (8) (D) (8)
~~?
H14, H24, H34 H18, H28, H38 0, HIll
(D) (8) (D) (8)
H14, H24, H34 H18, H28, H38 0, H111
(D) (8) (D) (8)
H12, H22, H32 H14, H24, H34
(D) (8)
~~? ~~? -
to 80 60 40 10 15 5 10 3 80 60 40 10 15 2 80 60 40 25 25 10
von
·
·
to 20
· 10
-
5
-
3
-
20
-
5
-
3
· 20
· 10
Rp
O"W,zd
O"sch,zd
O"W,b
'tW,s
'tW,t
A
A50
~2
~2
MPa
MPa
MPa
MPa
MPa
MPa
MPa
%
%
95 95 130 130 160 160 180 180 100 100 140 140 185 185 250 250 270 270 300 300 300 320
35 35 110 110 130 130 145 145 40 40 110 110 155 155 110 110 180 180 210 210 220 260
30 30 40 40 50 50 55 55 30 30 40 40 55 55 75 75 80 80 90 90 90 95
25 25 35 35 45 45 45 45 30 30 40 40 50 50 60 60 65 65 70 70 70 75
40 40 50 50 65 65 70 70 40 40 55 55 70 70 95 95 100 100 110 110 110 115
15 15 25 25 30 30 30 30 15 15 25 25 30 30 45 45 45 45 50 50 50 55
25 25 30 30 40 40 40 40 25 25 35 35 45 45 55 55 60 60 65 65 65 70
25 25 6 6 4 4 3 3 18 18 6 6 4 4 16 16 8 8 4 4 4 2
20 20 4 4 3 3 2 2 16 16 4 4 2 2 14 14 7 7 3 3 3 2 15 15 4
·
-
·
· ·
5 3 -
·
-
·
-
-
·
-
80 60
· ·
20
150 150 180
60 60 110
40 40 45
60 60 70
25 25 30
35 35 40
17 17 5
·
-
45 45 55
200 200 200 220
160 160 160 180
60 60 60 65
50 50 50 55
75 75 75 85
35 35 35 40
45 45 45 50
5 5 4 3
·
-
-
· ·
240 240 170 170 210
200 200 65 65 160
70 70 50 50 65
60 60 45 45 55
90 90 65 65 80
40 40 30 30 35
55 55 40 40 50
2 2 20 20 7
2 2 17 17 5
5
230
180
70
60
85
40
55
5
250
200
75
60
95
-
-
· 30 5
-
20 3 80 60 40
-
25
-
15
·
10
-
80 60 25
-
10
-
80 60 25 5 10 3 80 60 30
-
-
·
-
Rm
-
·
·
-
10
-
3
-
· 5 5
·
-
-
-
·
-
·
-
· -
· · ·
20
-
5
-
-
-
-
-
270
-
-
-
220
-
·
-
-
80
-
10
85 85 200
60 60 80
5
310
240
95
-
-
-
20
-
-
10
-
-
20
·
10 5
300
-
-
3
-
-
-
-
·
-
-
-
·
200 200 260
20
180 180 240 240 280 280 270 270 280
-
-
-
-
-
·
.
-
-
-
-
65
-
-
-
-
100
45
60
70
110
-
-
-
·
2
14 14 4
55
70
3
110
90
3
-
16 16 5
75
235
2
4
-
45 45 60
75 75 95
70 70 90 90 105 105 100 100 105
3
.
-
35 35 45
50 50 65
45 45 60 60 70 70 65 65 70
-
4 4 3 2
-
-
-
-
-
-
·
-
-
-
-
-
-
-
55
55 55 70 70 85 85 80 80 85
-
-
-
-
80 80 180 180 240 240 110 110 200
-
-
45
-
-
.
-
·
·
.
-
-
-
-
-
-
2
·
-
-
30 30 40 40 50 50 45 45 50
40 40 55 55 65 65 60 60 65
16 16 4 4 3 3 16 16 6
14 14 3 3 2 2 14 14 4
50
65
4
3
-
-
.
-
-
-
-
156
5.1 Material tables
5 Appendices
Table 5.1.24 Continued, page 2 of2. Material, EN notation DIN notation No. EN AW-5086 AlMg4 3.3545
EN AW-6012 AlMgSiPb 3.0615 EN AW-6060 AlMgSi 3.3206
Condition
EN AW·6262 AlMglSiPn
0, HIlI H12, H22, H32 H14, H24, H34 H16, H26, H36 T4 T6 T4
0, HIll T4 T6 T6
T4
EN AW-6082 AlSilMgMn 3.2315
EN AW-7020 AlZn4,5Mgl 3.4335 EN AW-7022 AlZn5Mg3Cu 3.4345 EN AW-7049A AlZn8MgCu EN AW-7075 AlZn5,5MgCu 3.4365
mm
~~?
(D) (S)
·
-
to 80 60 30
-
von
-
to 20
-
10 -
Rm
Rp
A
A50
-¢o2
-¢o2
MPa
MPa
MPa
%
%
240 240 270
95 95 190
70 70 80
60 60 65
90 90 100
40 40 45
55 55 60
16 16 5
14 14 4
230
90
70
110
50
65
3
2
95
75
115
·
-
3
320
260
-5
~W,t
MPa
-
-
~W,s
MPa
20 20
crW,b
MPa
295
-
crsch,zd
MPa
5
-
crW,zd
-
-
·
-
200 310
100 260
60 95
65 65 65 160
40 40 40 65
-
-
-
-
-
-
-
-
-
-
55
2
1
-
70
·
50 75
75 110
35 55
45 70
10 8
8 5
35 35 35 55
50 50 50 80
25 25 25 35
30 30 30 50
15 12 15 12
13 10 13 10
-
-
-
80 80
-
80
-
5
-
80
-
20 20
130 130 130 215
80
-
20
< 150
< 110
<45
<40
<60
<25
<35
16
14
80 80 80
-
20 20 5 20 10 10
205 290 290 290 345 360 150 150 150 220 230 275 < 140
110 240 240 240 315 330 75 75 75 190 195 240
-
60 85 85 85 105 110 45 45 45 65 70 85 <40
55 70 70 70 80 80 40 40 40 55 60 65 <40
80 105 105 105 125 130 60 60 60 85 85 100 < 55
35 50 50 50 60 60 25 25 25 40 40 50 < 25
50 65 65 65 75 80· 35 35 35 50 55 60 < 35
16 10 10 10 4 4 15 12 15 10 10 5 15
14 8 8 8 3 3 13 10 13 8 8 3 13
·
-
·
-
-
-
50 50 80
-
5
-
-
-
-
80 80
-
T66 T832
-
0, HlIl T4 T6 0, HIll T4 T6
-
80
-
5 20 20 20 5 20
-
80 80 80
-
20 20 20
150 230 < 160
90 190 < 110
45 70 <50
40 60 <45
60 85 <65
25 40 <30
35 55 <40
16 9 15
14 7 13
-
80 80
-
20
(D) (S)
80 50
-
-
205 310 310 310 350 350
110 255 255 240 280 280
60 95 95 95 105 105
55 75 75 75 80 80
80 110 110 110 125 125
35 55 55 55 60 60
50 70 70 70 75 75
4 10 8 10 10 10
12 9 7 9 8 8
-
80
-
20
460
380
140
95
155
80
100
8
6
·
T6
EN AW-6063A AlMgO,7Si(A)
mm
-
T8 T9 EN AW-6063 AlMgO,7Si
Tubes e -¢o 1
von
T6 EN AW-6061 AlMglSiCu 3.3211
Rods! Bars D;S -¢ol
T6
T6 T6 T6, T651O, T6511
0, HIll T6 T651
T651O, T6511 T73 T7351
-
-
-
-
-
·
-
-
-
-
-
-
·
·
·
·
·
.
-
5 20 20
500 530 530 < 165
175 175 175 <85
115 115 115 <65
195 195 195 < 100
100 100 100 < 50
120 120 120 <60
7 6 7 10
5 4 5 8
80 80
·
20
-
-
· ·
· · · ·
20
540 540 540
485 485 485
160 160 160
110 110 110
180 180 180
95 95 95
115 115 115
7 5 5
6 4 4 8 6 6
· · · · · · -
5 20 20
-
80
T73511
5
-
590 590 590 <275
80
-
5
·
· · · ·
T73510
·
·
80 80
-
5
·
·
·
·
·
·
·
.
-
20
385 385 385
135 135 135
95 95 95
155 155 155
80 80 80
95 95 95
10 8 8
·
·
·
·
-
20
455 455 455
·
·
·
·
-
~
1 D diameter of roundrods, S gaugeof squareor hexagonal rods, S thickness of rectangular rods, e wall thickness of tubes.
~
2 The elongation A is to be usedfor the assessment.
-
.
.
.
157
5.1 Material tables
5 Appendices
Table 5.1.25 Mechanical properties in MFa for wrought aluminum alloys, rods / bars, after DIN 1747 T. I (1983-02-00) (selected types of material only). Material DIN notation
Rods/ Bars No.
D~1
S~2
rom
rom
AlMg3 F18 W18 F25 AlMg5 F25 W25
3.3535 .08 .10 .26 3.3555 .08 .10
aile
F26 F28 AlMg2MnO,8 F20 W18
Rm
R"
(JW,zd
O'Sch.zd
Q"W.b
'tW,s
'tw.t
A, %
A IO %
~4
~4
Hdn Condo ~5 no.
aile
S~ 3 mm aile
180
80
55
50
70
30
40
14
12
45
P
aile 20 aile
aile 10 aile
aile 5 aile
180 250 250
80 180 110
55 75 75
50 60 60
70 95 95
30 45 45
40 55 55
16 4 13
14 3 11
45 75 60
P,Z Z P
aile
aile
aile
250
110
75
60
95
45
55
14
12
60
.24 .26 3.3527 .08 .10
60 35 aile
60 25 aile
15 10 aile
255 280 200
145 200 100
75 85 60
65 70 50
95 105 75
45 50 35
60 65 45
10 6 13
8 5 11
70 80 50
w p,z Z Z P
aile
aile
aile
180
80
55
50
70
30
40
16
14
45
w p,z
F25 AlMg4,5Mn F27 W27
.26 3.3547 .08 .10
20 aile
10 aile
5 aile
250 270
180 140
75 80
60 65
95 100
45 45
55 60
4 12
3 10
75 65
Z
aile
aile
aile
270
110
80
65
100
45
60
12
10
AlMgSiO,5 F13 F22
3.3206 .51 .71
aile
aile
aile
130
65
40
35
50
25
30
15
13
-
50
-
50
-
50
215
160
65
55
80
35
50
12
10
.72
-
50
-
50
-
50
145
195
45
40
55
25
35
10
8
3.2315 .51 .71
-
80
-
80
-
50
205
110
60
55
80
35
50
14
12
-
60
-
60
-
50
275
200
85
65
100
50
60
12
13
F31
.72
-
60
-
60
-
50
310
260
95
75
110
55
70
10
8
F30 F27 AlCuMgl F38 F40 F36 F33 AlCuMg2 F44 F47 F40 AlCuSiMn F44 F46 F43 AlZn4,5Mgl F35 F35 F35 AlZnMgCuO,5 F46 F49 F47 AlZnMgCul,5 F51 F52 F51 F50
.72 .72
60 200
200 250 50
60 200
200 250 50
50 100 100 200 - 20
300 270 380
240 200 260
90 80 115
70 65 85
110 100 135
50 45 65
65 60 85
8 6 10
-
w P, Z 45 ka p, Z 70 wa P,Z 75 wa, p,z 65 ka, p,z 80 wa p,Z 95 wa p,z 95 wa,p 95 wa,p 110 ka,z
80 200 250 50
30 70 200 30
400 360 330 440
270 220 200 310
120 110 100 130
90 80 75 95
140 130 120 150
70 60 55 75
85 80 75 95
10 7 6 10
8
30 70
100 200 50
60 150 30
470 400 440
330 260 360
140 120 130
100 90 95
160 140 150
80 70 75
100 85 95
8 6 8
6
60
100 200 50
60 150 30
460 430 350
400 350 280
140 130 105
95 95 80
160 150 125
80 75 60
100 95 75
7 6 10
6
60
100 250 50
60 200 30
350 350 460
290 270 380
105 105 140
80 80 95
125 125 160
60 60 80
75 75 100
10 7 .7
8
60
80 200 50
50
50 150 30
490 470 510
420 400 440
145 140 155
100 100 105
165 160 170
85 80 90
105 100 105
7 7 7
50 80 150
520 510 500
460 450 440
155 155 150
105 105 105
175 170 170
90 90 85
110 105 105
7 7 5
F25 AlMgSil F21 F22
~
3.1325 .51 .51 .51 80 .51 200 3.1355 .51 .51 .51 100 3.1255 .71 .71 .71 100 3.4335 .71
-
80 200 250 50
80 200
-
100 200 50
100
-
100 200 50
100
100 250 50
100
80 200 50
80
.71 .71 100 3.4345 .71 .71
-
-
.71 80 3.4365 .71 .71 .71 . 80 .71 120
80 120 200
80 120
80 120 200
-
-
.
50 80
HB
1 D diameterof roundrods, ~ 2 S gaugeof squareor hexagonal rods, ~ 3 S thickness of rectangular rods. 4 The elongation A, is to be usedfor the assessment. ~ 5 Condition: ka = naturallyaged, p = extruded, w = softannealed, wa = artificially aged, Z = extruded and drawn. ~
8
-
8
7
-
8
6 6
6 6 5
-
P
60
110 110 110 115
ka,p ka,p ka, p ka, Z
120 ka, p 105 ka,p 120 wa,z 125 wap 120 wa,p 100 wa,z 105 wa, p 100 wa, p 125 wa,z 130 wa,p 130 wa, p 140 wa,z 140 wa, p 140 wa, p 140 wa,p
158
5.1 Material tables
5 Appendices
IRT51Al-b.doJ
Table 5.1.26 Material properties in MFa for wrought aluminum alloys, extruded rods / bars, tubes and profiles after DIN EN 755A W-2 (1997-08-00). Material notation
Condition
Rods/Bars D
Rm
Rp
O'W,zd
O'sch,zd
O'W,b
~W,s
~W,t
A
Rods/BarsS
Tubese EN-notation
Profiles e
DIN-notation No.
v3 mm
v 1 AW-2007 AICuMgPb
3.1645
T4 T4510 T4511
250
110
85
130
65
80
v5 8
200 200
340
220
100
80
120
60
75
8
-
-
>200 >200
250 250
330
210
100
75
120
55
75
7
-
200 60
275
125
85
65
100
50
60
14
75 60 25
310
230
95
75
110
55
70
8
eP
-
D
>75
200
295
195
90
70
110
50
65
6
200 60
275
125
85
65
100
50
60
14
75 60 25
310
230
95
75
110
55
70
8
D S
eR eP
D S
eR eP
D S
eR eP
AW-2011
T4
D
AICuBiPb
S
3.1655
eR eP
T6
D S
eR
S
eR eP
AW-2011A
-
T4
D S
eR eP
T6
D S
eR
AW-2014A
T4 T4510 T4511
-
-
-
-
30
-
-
-
295
195
90
70
110
50
65
6
200 200 20
<250
<135
<75
<60
<95
<45
<55
12
370
230
110
85
130
65
80
13
410
270
125
90
145
70
90
12
D S
D S
eR
-
-
eP
-
D eR
>25 >25 >25
eP
-
D
>75 >75
S
S
-
all
25 25 20 25 20 25 75 75 75
-
-
150 150
D
>150 >150
-
S
eR eP
-
10 390
250
115
85
135
70
85
10
350
230
105
80
125
60
75
8
-
eP
eR
v 1 to 6 see page 159.
>80 >80
200
eP
and
80 80 25
-
eR
3.1255
-
-
>75
eP AICuSiMn
bis
D eR 0 HIll
von
eP
S
AW-2014
%
v4 370
v 2
159
5.1 Material tables
5 Appendices
Table 5.1.26 Continued, page 1 of 9 Material notation
Condition
Rods/Bars D Rods/BarsS Tubes e Profiles e
EN-notation DIN-notation No.
Rm
Rp
crW,zd
crsch,zd
crW,b
~W,s
~W,t
~3
mm c- I
continued AW-2014 AICuSiMn 3.1255
~2
T6 T6510 T6511
and AW-2014A
-
AW-2017A AlCuMg1 3.1325
0 Hili
T4 T4510 T4511
von D S eR eP D S eR eP D S eR eP D S eR eP D S eR eP D S eR eP D
Is
eR eP D
Is
eR eP D
IseR eP D
IseR eP D
IseR AW-2024 AlCuMg2 3.1355
0 Hill
eP D S eR eP
>25 >25 >25 >75 >75 >150
>150
-
%
bis 25 25 10 25 75 75
~4
415
~5
370
125
90
145
~
70
90
6 7
460
415
140
95
160
80
100
7
465
420
140
95
160
80
100
7
430
350
130
95
150
75
95
6
420
320
125
90
145
75
90
5
75 150
150 200
200
>200
250
>200
250
>10
40
450
400
135
95
155
80
95
6
200
<250
<135
<75
<60
< 95
< 45
< 55
12
380
260
115
85
135
65
85
12
400
270
120
90
140
70
85
10 10
390
260
115
85
135
70
85
9
370
240
110
85
130
65
80
8
360
220
110
80
130
60
80
7
<250
<150
<75
<60
<95
< 45
< 55
12
-
>25 >25 >10
-
-
200 20
-
25 25 10 30 75 75 75
-
>75 >75
150
>150
200
>150
200
-
150
-
>200
250
>200
250
-
. -
-
200
200 30 all
1 Sequence and material notation after DIN EN 755AW-2, page 2, 2 The values "F" are for information only. ~ 3 D diameter of round rods, S gauge of square or hexagonal rods, e wall thickness of tubes and profiles. -e- 4,,<" for R",and R, means, that only upper bound values ofR", and R, are given in DIN EN 755AW-2, whereas lower bound values are required for an assessment of strength. ~ 5 Elongation referring to an initial length of the specimen of 5,65x (section of specimen) 1/2, ~ 6 open = open profil, hollow = hollow profil.
-c-
A
160
5.1 Material tables
5 Appendices
Table 5.1.26 Continued, page 2 of 9 Rods/Bars D Rods/BarsS Tubese Profiles e
Material notation Condition EN-notation DIN-notation No.
Rm
Rp
crW,zd
crsch,zd
crW,b
'tW,s
'tW,t
~3
%
mm ~1
continued AW-2024 AlCuMg2 3.1355
AW-2030
-
AW-3003 AlMnCu 3.0517
T3 T3510 T3511
T4 T4510 T4511
F
H112 0
H111 AW-3103 AlMn1 3.0515
F
H112 0
H111 AW-5005
-
F
H112
0
H111 AW-5005A AlMg1 3.3315
F
H112
0
H111 AW-5051A AlMg1,8 3.3326
F
H112
0
H111
~
von
~2
T8 T8510 T8511
-
A
1 to 6 seepage 159.
D S
eR eP D S eR eP D S eR eP D S eR eP D S eR eP D S eR eP D S eR eP D S eR eP D S eR eP D S eR eP D S eR eP D S eR eP D S eR eP D S eR eP D S eR eP D S eR eP
-
bis 50 50
-
-
>50 >50
100 100
-
-
-
>100 >100
-
>15 >200 >200 -
-
450
310
135
95
155
80
95
8
440
300
130
95
150
75
95
8
420
280
125
90
145
75
90
8
400
270
395
290
120 125 120
90 90 85
140 145 140
70 75 70
85 90 85
8 8 8
455
380
135
95
155
80
95
5
370
250
110
85
130
65
80
8
340
220
100
80
120
60
75
8
330
210
100
75
120
60
75
7
95
35
30
25
40
15
25
25
95
35
30
25
40
15
25
25
100
40
30
30
40
15
25
18
100
40
. 30
30
40
15
25
20
100
40
30
30
40
15
25
18
100
40
30
30
40
15
25
20
all
150
50
45
40
60
25
35
16
all all all
150
60
45
40
60
25
35
16
all
150
50
45
40
60
25
35
18
all all
150
60
45
40
60
25
35
18
-
200 200 30 50 250 250 15
-
>80 >80
150 150 30 50 80 80 25 30 200 200
-
-
>200 >200
250 250
-
-
~5
~4
-
-
all
all all all all
all all all all
all all all all
all all
-
all
all all all all
all all
-
-
161
5.1 Material tables
5 Appendices
Table 5.1.26 Continued, page 3 of 9 Material notation
Condition
Rods/Bars D Rods/BarsS Tubese
EN-notation No.
F H1l2
D S
eR
eP
F H1l2
D S eR
0
D
HIll
S
F H1l2
F H1l2
Hlll
D S eR D S eR D S eR
F H1l2
D S eR
eP 0
D
HIll
S
eR
eP F H1l2
3.3555
D S eR
eP 0
Hlll
D S eR
eP F 0 Hlll
D S eR
eP D S eR
eP ~
40
16
160
60
50
45
65
30
40
17
170
70
50
45
65
30
40
15
170
70
50
45
65
30
40
17
200
85
60
50
75
35
45
16
200
85
60
50
75
35
45
18
200
85
60
50
75
35
45
16
·
1 to 6 see page 159.
-
·
D S eR
3.3547
30
eP
eP
AlMg4,5Mn
65
-
eP
AW·5083
45
D S eR
eP 0
AlMg5
50
-
~5
all
all
eP
AW-5019
60
-
Hlll
AlMg3 3.3535
160
-
0
AW-5754A
all aLL
-
eP
AlMg2,7Mn 3.3537
-
D
eR
AW-5454
A
%
S
eP
-
'tW,t
~4
Hlll
3.3523
-
'tW,s
bis
0
eP
AW-5154A
O"W,b
von
all all aLL
eR
AlMg2,5
O"sch,zd
mm ~2
3.3525
AW-5052
O"W,zd
~3
~1
AW-5251
Rp
Profiles e
DIN-notation
A IMg2MnO,3
Rm
-
all aLL
all all all aLL
all
.
200 200 25 25
-
200 200 25
-
200 200 25
200
85
60
50
75
35
45
18
·
-
·
150 150 25
180
80
55
45
70
30
40
14
>150 >150
250 250
180
70
55
45
70
30
40
13
150 150 25
180
80
55
45
70
30
40
17
200 200 30
250
110
75
60
95
45
55
14
200 200 30
250
110
75
60
95
45
55
15
200 200 all
270
110
80
65
100
45
60
12
260
100
8B
65
95
45
60
12
-
· >200 >200
-
25
200 200 25 25
25
-
-
30
-
all
250 250
-
162
5.1 Material tables
5 Appendices
Table 5.1.26 Continued, page 4 of 9 Material notation
Condition
Rm
Rods! Bars D
Rp
Cl"W,zd
Rods r Bars S
Cl"sch,zd
Cl"W,b
~W,s
~W,t
A
Tubese Profiles e
EN-notation
-¢-3
DIN-notation
%
mm
No.
-¢-1 continued AW-5083
-¢-2 -¢-6 H1l2
AUvIg4,5Mn
3.3547 AW-5086 AUvIg4Mn
von D S eR
D S eR
-
eP
-
D
· -
eP
F H1l2
3.3545
D S
eR eP
0 Hlli
D S
eR eP
AW-61OIA
T6
AW-6101B
T6
-
D S eR eP
E-AUvIgSiO, 5 3.3207
T7
S
eR eP
AW-6005
-
T6
D
S
-
eR eP D
S
eR eP D
S
eR T4 open T4 hollow T6 open
-
eP eP
-¢-6 eP
-¢-6 T6 hollow
->25 >25
>50 >50 >5
-
T6
AUvIgSiO,7 3.3210
D
S
eR eP D
S
eR eP D
S
eR T4 open T4 hollow T6 open
eP eP
-¢-6 eP
-¢-6 T6 hollow -¢-1 to 6 see page 159.
125
80
65
100
45
60
-¢-5 12
240
95
70
60
90
40
55
12
240
95
70
60
90
40
55
18
200
170
60
50
75
35
45
10
215
160
65
55
80
35
50
8
170
120
50
45
65
30
40
12
25 25 5
270
225
80
65
100
45
60
10
50 50 5
270
225
80
65
100
45
60
8
100 100 10
260
215
80
65
95
45
60
8
25
180
90
55
45
70
30
40
15
270 260 250 255 250
225 215 200 215 200
80 80 75 75 75
65 65 60 65 60
100 95 95 95 95
45 45 45 45 45
60 60 60 60 60
8
270
225
80
65
100
45
60
10
-
150 150 all all
15 15 15 15 15 15 15
·
-
-
-
10
5
>5
10
>10 -
25 5 15 25 25 5
>5 AW-6005A
-¢-4 270
bis 200 200 all all 250 250 all all 200 200 all
· -
>25 >25
8
·
270
225
80
65
100
45
60
8
-
50 50 5
>50 >50 >5
100 100 10
260
215
80
65
95
45
60
8
-
25
180
90
55
45
70
30
40
15
270 260 250 255 250
225 215 200 215 200
80 80 75 75 75
65 65 60 65 60
100 95 95 95 95
45 45 45 45 45
60 60 60 60 60
8
-
-
·
·
-
10
5
>5
10
>10
25 5
>5
15
-
I
163
5.1 Material tables
5 Appendices
Table 5.1.26 Continued, page 5 of 9 Material notation
Condition
Rods/Bars D Rods/BarsS Tubese
Rm
Rp
O"W,zd
O"sch,zd
O"W,b
~W,s
~W,t
A
Profiles e
EN-notation
{>3
DIN-notation
%
rom
No.
{>1 AW-6106
{> 2 -{> 6 T6
AW-6012
T6 T6510 T6511
-
D S eR eP
AlMgSiPb 3.0165
D S eR eP
D S eR eP
AW-6018
-
T6 T6510 T6511
D S eR eP
AW-6351
0
-
Hill
-
AW-6060
T5 T5 T6 T6 T4
A lMgSiO,5 3.3206
-
>150 >150
-
eP
-
D S eR
eP eP
{>6 eP
-{>6 D S eR eP
T5
-
>150 >150
D S eR open hollow open hollow
bis
-
D S eR
eP
T4
von
D S eR eP
-
>5
-
>5 T6
D S eR eP
-
>3 T64
D S eR eP
T66
D S eR eP
-
>3 AW-6061
0
AlMg1SiCu
Hill
3.3211
D S eR eP
{> 1 to 6 see page 159.
-
-{>5
-{>-4
250 310
200 260
75 95
60 75
95 110
45 55
60 70
8 8
200 200
260
200
80
65
95
45
60
8
150 150 30
310
260
95
75
110
55
70
8
200 200
260
200
80
65
95
45
60
8
200 200 25
< 160
< 110
<50
<45
< 65
<30
<40
14
205
110
60
55
80
35
50
14
270
230
80
65
100
45
60
8
290 300 120
250 255 60
85 90 35
70 70 35
105 110 50
50 50 20
50 65 30
8 10 16
160
120
50
45
60
30
40
8
140 190
100 150
40 55
40 50
55 75
25 35
35 45
8 8
170 180
140 120
50 55
45 45
65 70
30 30
40 40
8 12
215
160
65
55
80
35
50
8
195 < 150
150 < 110
60 <45
50 <40
75 <60
35 <25
45 < 35
8 16
10
150 150 30 30
-
30
-
all
200 200 25 25 5
5 25 150 150 15 25 150 150 15 5 25 150 150 15 3 25 50 50 15 15 150 150 15 3 25 200 200 25 25
164
5.1 Material tables
5 Appendices
Table 5.1.26 Continued, page 6 of 9 Condition
Material notation
Rods/ Bars D
Rm
Rp
crW,zd
crsch,zd
crW,b
tw,s
tW,t
A
Rods r Bars S
Tubese Profiles e
EN-notation
~3
DIN-notation No. ~
continued
von
~2 ~6
T4
D S
AW-6061
eR
AlMg1SiCu
eP
3.3211
T6
D S
eR
-
-
>5 eP
-
>5 AW-6261
0
D
Hill
-
-
S
-
-
T4
eR eP D
-
S
eR eP
T6
D S
>5
10
-
5 25
-
5
-
-
>5 eP
T5 open
eP ~6
T5 hollow T6 open
.
-
HilI T4
D S
eR eP D S
eR T5
-
. -
S
eR eP
-
>3
~
I to 6 see page 159.
80
65
95
45
60
8
< 170
< 120
< 50
<45
< 65
<30
<40
8 10 .9 10 14
180
100
55
45
70
30
40
14
290
245
85
70
105
50
65
8
100
45 45 45 45 45 50 50 50 45
60 60 60 60 60 65 65 65 60
9 8 9 8 9 9 8 9 8 8 8 9
60
10
< 130
-
<40
<35
< 50
< 25
<30
18
150 150 10 25 200 200 25
130
65
40
35
50
25
30
14
120
65
35
35
50
20
30
12
200 200 25 3 25
175
130
55
45
70
30
40
8
160
110
50
45
65
30
40
7
200 200 25 25 200 200 25
eP
240
45
-
D
260
95
10
>150 >150 >10
IS
65
>5
-
40
80
-
5 25 5
.
30
240
>5
-
70
260
-
~6
0
45
65 65 60 65 65 70 70 70 65
10
-
AW-6063
55
80 80 75 80 80 85 85 85 80
-
-
110
230 220 210 230 220 245 235 245 230
>5
T6
180
270 260 250 270 260 290 280 290 270
eP
T6 hollow AW-6262
>5 >25
~5
~4
10
-
-
>20 eR
bis 200 200 25 25 200 200 5 25 5 25 100 100 10 100 100 10 25 20 100 20 100 5 10 5
-
>20
-
%
mm
I
100 95 95 100 95
lOS 105
lOS
-
-
165
5.1 Material tables
5 Appendices
Table 5.1.26 Continued, page 7 of 9 Material notation
Condition
Rods/Bars D Rods/BarsS
Rm
Rp
crW,zd
crsch,zd
crW,b
'tW,s
'tW,t
A
Tubese Profiles e
EN-notation
~3
DIN-notation No.
1 continued -c-
mm von
~2 ~6
T6
AW-6063 -
D
-
S eR
-
eP D
-
S eR
T66
eP D
S eR eP
>150 >150
-
>10
-
>10 T64
D
S eR
AW-6063
0, Hll1
-
eP D
S eR
T4
eP D
S eR eP D
S eR
T5
eP D
S eR eP
-
-
-
>150 >150 >10
eP
-
-
D
-
150 150
eP D
AW-6463
-
T4
S eR
T5
eP D
S eR
T6
eP D
S eR
AW-6081
-
T6
S eR
T6 open T6 hollow ~
eP D
1 to6 seepage 159,
eP eP ~6
-
-
65
55
80
35
50
10
195
160
60
50
75
35
45
8 10
245
200
75
60
90
40
55
8 10
225
180
70
55
85
40
50
8 8
180 < 150
120
-
55. < 45
45 <40
70 <60
30 < 25
40 < 35
12 16
150
90
45
40
60
25
35
12
140
90
40
40
55
25
35
10
200
160
60
50
'75
35
45
7
190 230
150 190
60 70
50 60
75 85
35 40
45 55
6 7
220
160
65
55
85
40
50
7
220
180
65
55
85
40
50
5
125
75
40
35
50
20
30
14
150
110
45
40
60
25
35
8
195
160
60
50
75
35
45
10
275
240
85
65
100
50
60
8
275
240
85
65
100
50
60
8
10
S eR
S eR
-
170
-
200 200 25 25 150 150 25 10 200 200 25
D
215
-
15 200 200 25 150 150 10 25 200 200 25
-
~5
-
-
>150 >150 >10
~4
-
25 200 200 25 10 25
-
>10 T6
%
bis 150 150 25 10 200 200
-
50 150 150
50 150 150 25 50 250 250 25 25 15
166
5.1 Material tables
5 Appendices
Table 5.1.26 Continued, page 8 of 9 Material notation
Condition
Rm
Rods/Bars D Rods r Bars S
Rp
crW,zd
crsch,zd
crW,b
~W,s
~W,t
A
Tubese Profiles e
EN-notation
->3
DIN-notation
%
mm
No.
->1 AW-6082
von
->2 ->6
AlMgSiI
S
-
3.2315
eR
-
0, HIll
D
-
all
-
200 200 25 25 5
->6
>5
5 15
D
-
all all
eP D S
T4
eR
-7003
T5 T5 T6 T6 T5
open hollow open hollow
-
eP eP
->6 eP
S
eR T6
eP D S
eR eP D S
eR -7005
T6
-
-
eP D S
<30
<40
->5 14
205
110
60
55
80
35
50
14
270
230
80
65
100
45
60
8
290 310 310
250 260 260
85 95 95
70 75 75
105 110 110
50 55 55
65 70 70
8 10 10
350
290
105
80
125
60
75
10
340
280
100
80
120
60
75
10
350
290
105
80
125
60
75
10
all all
50 50 10
-
10
150 150 25 25 50 50 15
-
40
200 200
340
270
100
80
120
60
75
10
50 50 15
350
290
105
80
125
60
75
10
200 200
340
275
100
80
120
60
75
10
80 80 30
490
420
145
100
165
85
105
7
470
400
140
100
160
80
100
7
eR eP D S
eR eP D S
eR eP D
S
eR eP
-> 1 to 6 see page 159.
< 65
>50 >50
3.4335
T6, T6510 T6511
<45
eR
AIZn4,5Mg1
-7022 AlZn5Mg3Cu 3.4345
< 50
-
>50 >50 >10 >10-
< 110
eP D S eP D S
T6
-
-
->4 < 160
-
eR -7020
bis 200 200 25
>50 >50
>80 >80
-
40
30
200 200
167
5.1 Material tables
5 Appendices
Table 5.1.26 Continued, page 9 of 9 Material notation
Condition
Rods/ Bars D RodslBarsS Tubese
A IZnMgCu 0,5
3.4345
Rp
Cl"W,zd
Cl"sch,zd
Cl"W,b
'tW,s
'tW,t
A
Profiles e
EN-notation
?3
DIN-notation No. ? 1 -7049A
Rm
%
mm
?2 T6, T6510, T6511
von D S eR
eP D S eR
eP D S eR
eP D S eR
eP ·7075
0
AIZnMgCu1,5
Hill
D S eR
T6 T6510 T6511
D S eR
3.4365
eP
eP D S eR
-
-
150 . 150
-
-
>150 >150
180 180
>25 >25 >25 5
200 200 10
D S eR
500
170
110
185
95
115
5
520
430
155
105
175
90
110
5
450
400
35
95
55
80
95
3
<275
< 165
<100
< 65
<100
< 50
<60
10
540
480
180
110
180
95
115
7
110
185
95
115
530
470
180
105
175
90
110
6
25 200 200
530 470
460 400
180 160
105 110
175 160
90 80
110 100
6 5
485
420
145
100
165
85
100
7
475
405
145
100
160
80
100
7
-
-
-
D S eR
>25 >25 >25
eP
-
-
D S eR
>75 >75 >5 -
eP D S eR
-
100 100 25 5
>100 >100
150 150
-
560
185
eP
eP
125
500
25 25 25 25 75 75 50
5
105
560
100 100 10 -
-
200
8 6 7
150 150
eP
115
60
-
>150 >150
185
-
25 25 5
>100 >100 -
530
?5 5
-
-
D S eR D S eR
? 1 to 6 see page 159.
125 125
>125 >125
?4 610
30
>100 >100
eP
eP
T73 T73510 T73511
-
bis 100 100 30
8 470 470 485 470
390 400 420 400
140 140 145 145
100 100 100 100
160 160 165 160
80 80 85 80
100 100 105 100
6 7 8 7
440
360
130
95
150
75
100
6
-
-
168
5.1 Material tables
5 Appendices
Table 5.1.27 Material properties in MFa for wrought aluminum alloys, extruded profiles after DIN 1748 T. I (1983-02-00) (selected types of material only). Material
Wall
Rm
Rp
crW,zd
crSch,zd
crW,b
"tW,s
"tW,t
thi'*Y ess DIN notation AlMg3 F18 AlMg5 F25 AlMg2MnO,3 F15 AlMg2MnO,8 F20 AlMg4,5Mn F27 AlMgSiO,5 F13 F22 F25 AlMgSiO,7 F26 F27 AlMgSil F21 F28 F31 AlCuMg1 F38 AlCuMg2 F44 AlCuSiMn F45 AlZn4,5Mg1 F35 AlZnMgCuO,5 F49 AlZnMgCul,5 F53
No. 3.3535.08 3.3555.08 3.3525.08 3.3527.08 3.3547.08 3.3206.51 .71 .72 3.3210.71 .71 3.2315.51 .71 .72 3.1325.51 3.1355.51 3.1255.71 3.4335.71 3.4345.71 3.4365.71
mm any to 10 any any any any any to 10 r
J
'0
any to 10 to 20 2 to 30 2 to 30 2 to 30 3 to 30 2 to 30 2 to 30
180 250 150 200 270 130 215 245 260 270 205 275 310 380 440 450 350 490 530
80 110 60 100 140 65 160 195 215 225 110 200 260 230 315 400 290 420 460
55 75 45 60 80 40 65 75 80 80 60 85 95 115 130 135 105 145 160
50 60 40 50 65 35 55 60 65 65 55 65 75 85 95 95 80 100 105
70 95 60 75 100 50 80 90 95 100 80 100 110 135 150 155 125 165 180
30 45 25 35 45 25 35 40 45 45 35 50 55 65 75 80 60 85 90
40 55 35 45 60 30 50 55 60 60 50 60 70 85 95 95 75 105 110
A5
AlO
% -¢>2
% -¢>2
14 13 14 13 12 15 12 Y 't
12 11 12 11 10 13
lOY't
8 8 14 12 10
io 10 7 10 7 7
lOY't
8 Y 't 6 6 12 10 8 8 8 6 8 6 6
Hardness No. HB 45 55 40 50 65 45 70 75 85 90 65 80 95 95 120 135 105 140 150
Con-
dW~n
p p P p p
ka wa wa wa wa ka wa wa ka ka wa wa wa wa
-¢> I The material condition assigned to a profile is determined by the maximum thickness of its wall or web plate. -¢>2 The elongation A5 is to be used for the assessment. -¢> 3 ka = naturally aged, p = extruded, wa = artificially aged. -¢>4 For profiles where the diameter ofthe circumscribing circle is larger than 250 mm the elongation A5 is 8% minimum or AIO is 6 % minimum. -¢>5 For solid sections with 6 mm to 10 mm thickness ofthe web plate and for hollow sections up to 10 mm wall thickness. -¢>6 For solid.sections up to 6 mm thickness of the web plate.
169
5.1 Material tables
5 Appendices
Table 5.1.28 Material properties in MPa for wrought aluminum alloys, forgings after DIN EN 586AW-2 (1994-11-00). Material
Product
EN AWAW2014 AI Cu4SiMg
Forgings, any kind Die forgings
Condition
Section size I
Testing direction
Rm
Rp
crW,zd
crSch,zd
crW,b
'tW.s
'tW,t
A %
T4
IS 150
L
370
270
110
85
130
65
80
11
IS 50
L orT L orT L orLT orST L orLT orST L orLT orST L
440 430 440 430 440 430 420 420 420 410 410 410 400 420
380 370 370 360 380 370 360 370 360 350 360 350 340 260
130 130 130 130 130 130 125 125 125 125 125 125 120 125
95 95 95 95 95 95 90 90 90 90 90 90 90 90
150 150 150 150 150 150 145 145 145 145 145 145 140 145
75 75 75 75 75 75 75 75 75 70 70 70 70 75
95 95 95 95 95 95 90 90 90 90 90 90 85 90
6 3 6 3 8 4 3 7 4 3 6 3 2 8
T6 50 < IS 100
Hand forgings
T652
IS75
75<15150
150 < I S 200 EN AWAW2024 AlCu4Mgl EN AWAW5083 AlMg4,5MnO,7 EN AWAW5754 AlMg3 EN AWAW6082 AlSilMgMn EN AW·7075 AI Zn5,5MgCu
Forgings, any kind
T4
IS 100
Forgings, any kind
H112
IS 150
L orT
270 260
120 110
80 80
65 65
100 95
5 45
60 60
12 10
Forgings, any kind
Hil2
IS 150
L
180
80
55
50
70
30
40
15
Forgings, any kind
T6
IS 100
L orT
310 290
260 250
95 90
75 70
110 105
55 50
70 65
6 5
Die forgings
T6
IS 50
L orT L orT L orT L orT L orLT or ST L orLT or ST L orLT orST L orLT or ST
510 480 500 470 455 420 445 410 490 480 470 470 460 445 450 440 430 420 410 395
430 410 425 400 385 360 375 350 415 400 390 385 375 370 370 360 350 350 340 330
155 145 150 140 135 125 135 125 145 145 140 140 140 135 135 130 130 125 125 120
105 100 105 100 95 90 90 100 100 100 100 100 95 95 95 95 95 90 90 85
170 165 170 160 155 145 140 165 165 160 160 160 160 155 155 150 150 145 145 140
90 85 85 80 80 75 80 70 85 85 80 80 80 75 80 75 75 75 70 70
105 100 105 100 95 90 95 90 105 100 100 100 100 95 95 95 95 90 90 85
7 4 6 4 6 4 6 3 6 4 3 6 4 3 6 4 3 6 4 3
50 < 15100 T73
IS 50 50
Hand forgings
T652
1< 75
75 < IS 150
T7352
1575
75 < IS 150
~1
L: LT: T: ST:
~1
Direction parallel to the main grain flow, Direction parallel to larger cross section dimension (width), Direction not parallel to the main grain flow, Direction parallel to smaller cross section dimension (thickness) (usually forging direction).
170
5.1 Material tables
5 Appendices
Table 5.1.29 Material properties in MFa for wrought aluminum alloys, die forgings after DIN 1749 T. 1 (1976-12-00) (Selected types of material only). Material DIN notation No. A1Mg3 F18 3.3535 .08 A1Mg5 F24 3.3555 .08 A1Mg4,5Mn F27 3.3547 .08
Thickness
Testingdirect.
n,
100 100 100
L L L
180 240 270 260 215 275 200 275 260 310 290 380 420 440 430 440 430 350 480 470 470 460 500 480 490 470 450 420 440 410
F22 3.3206 .61 F28 3.2316 .61 F20 3.2315 .41 F28 .61
100 100 100 100 100
A1CuMgl
F31 F38
A1CuMg2 A1CuSiMn
3.1325 .41 F42 3.1355 .41 F44 3.1255 .61
L L L L
T .62
L
T 100 100 50
L L L
T
A1Zn4,5Mgl F35 3.4335 .61 A1ZnMgCuO,5 F48 3.4345 .61
>50 to 100 100 75
L
T L L
T F47 A1ZnMgCul,5 F50 3.4366 .61
>75 to 100 50
L
T L
T F49 F34
.63 .63
>50 to 100 50
L
T L
T F44
>50 to 100
CYW,zd
CYSch,zd
CYW,b
'tw,s
'tw,t
~I
T A1MgSiO,5 A1MgSiO,8 A1MgSil
n,
L
T
80 100 120 110 160 200 100 220 200 260? 250 230 260 380 370 370 360 280 410 400 400 390 420 410 410 400 380 360 370 350
~1
L Direction parallelto the main grainflow, T Direction not parallelto the main grainflow,
~2
Condition ka = naturallyaged, s = forged, wa = artificially aged.
55 70 80 80 65 85 60 85 80 95 90 115 125 130 130 130 130 105 145 140 140 140 150 145 145 140 135 125 130 125
45 60 65 65 55 65 50 65 65 75 70 85 90 95 95 95 95 80 100 100 100 95 105 100 100 100 95 90 95 90
70 90 100 95 80 100 75 100 95 110 105 135 145 150 150 150 150 125 165 160 160 160 170 165 165 160 155 145 150 145
30 40 45 45 35 50 35 50 45 55 50 65 75 75 75 75 75 60 85 80 80 80 85 85 85 80 80 75 75 70
40 55 60 60 50 60 45 60 60 70 65 85 90 95 95 95 95 75 100 100 100 100 105 100 105 100 95 90 95 90
A5 %
14 12 12 10 12 8 12 6 5 6 5 10 8 6 3 6 3 10 6 3 6 3 6 4 6 4 6 4 6 3
Hardness HB 45 55 65 65 75 60 75
Cnd. ~2
s s s wa wa ka wa wa
120
ka ka wa
95 135
wa wa
130 135 130 120 115
wa
171
5.1 Material tables
5 Appendices
Table 5.1.30 Material properties in MFa for wrought aluminum alloys, hand forgings after DIN 17 606 (1976-12-00) (selected types of material only). Material DIN notation AlMg3 F18 AlMg4,5Mn F27
No. 3.3535.08 3.3547.08
AlMgSil
3.2315 Al
AlCuMgl AlCuMg2 AlCuSiMn
F20 F28 F31 F38 F42 F44
3.1355.61 3.1255.61
Rm
100 100
L L LT L L L L L L LT ST L LT ST L LT ST L L LT ST L LT ST L LT ST L LT ST L LT ST L LT ST L LT ST
180 270 260 200 275 310 380 420 440 430 420 420 420 410 410 410 400 350 480 470 460 470 460 450 460 450 440 490 480 470 460 450 440 450 440 420 420 410 400
100 100 100 100 100 75
.61
>75 to 150
F41
.61
>150 to 200
3A335.61 3A345.61
100 75
F47
.61
>75 to 150
F46
.61
>150 to 200
AlZnMgCul,5 F49
~2
3.1325 Al
Testingd~ft.
F42
AlZn4,5Mgl F35 AlZnMgCuO,5 F48
~1
.61 .62
Thickness
3A365 .61
75
F46
.61
>75 to 150
F45
.63
75
F42
.63
>75 to 150
Rp
crW,zd
crSch,zd
crW,b
tW,s
tW,t
A5 %
80 120 110 100 220 260 230 260 380 370 370 370 360 360 360 350 350 370 410 400 380 400 390 370 390 360 360 420 410 390 380 370 370 380 370 360 350 350 340
55 80 80 60 85 95 115 125 130 130 125 125 125 125 125 125 120 105 145 140 140 140 140 135 140 135 130 145 145 140 140 135 130 135 130 125 125 125 120
45 65 65 50 65 75 85 90 95 95 90 90 90 90 90 90 90 80 100 100 95 100 95 95 95 95 95 100 100 100 95 95 95 95 95 90 90 90 90
70 100 95 75 100 110 135 145 150 150 145 145 145 145 145 145 140 125 165 160 160 160 160 155 160 155 150 165 165 160 160 155 150 155 150 145 145 145 140
L: Directionparallelto the main grainflow, LT: Direction parallelto largercrosssection dimension (width), ST: Direction parallelto smallercrosssectiondimension (thickness) (usuallyforging direction). Condition ka = naturally aged, s = forged, wa = artificially aged.
30 45 45 35 50 55 65 75 75 75 75 75 75 70 70 70 70 60 85 80 80 80 80 80 80 80 75 85 85 80 80 80 75 80 75 75 75 70 70
40 60 60 45 60 70 85 90 95 95 90 90 90 90 90 90 85 75 100 100 100 100 100 95 100 95 95 105 100 100 100 95 95 95 95 90 90 90 85
14 12 10 12 6 6 10 8 8 4 3 7 4 3 6 3 2 10 6 4 3 6 3 2 6 4 3 6 4 3 6 4 3 6 4 3 6 4 3
Hardness HB 45 65 65 65 75 90 95 105 120 120 120 120 120 120 120 120 120 90 135 135 135 130 130 130 130 130 130 135"" 135 135 135 135 135 120 120 120 115 115 115
Cnd. ~2
s s ka wa wa ka ka wa
wa
wa wa
wa
wa
172
5.1 Material tables
5 Appendices
Table 5.1.31 Material properties in MPa for cast aluminum alloys, sand castings, test pieces cast separately, after DIN EN 1706 (1998-06-00). Material EN notation AC-21000 AC-21100
DIN notation AI Cu4MgTi AI Cu4Ti
AC-41000
AI Si2MgTi
Condition
Rm,N
T4 T6
300 300 280 140 240 140 220 230 250 ISO 220 ISO 220 160 220 230 ISO ISO ISO ISO 140 230 170 230 ISO 135 ISO ISO 140 140 160 160 190
T64 F
T6 AC-42000 AC-42100 AC-42200 AC-43000
AI Si7Mg AISi7MgO,3 AI Si7MgO,6 AI SiIOMg(a)
F
T6 T6 T6 F
T6 AC-43 100
AI SiIOMg(b)
F
T6 AC-43200
AI SiIOMg(Cu)
AC-43300 AC-44000 AC-44100 AC-44200 AC-45000 AC-45200
AI Si9Mg AISill AISiI2(b) AI SiI2(a) AI Si6Cu4 AI Si5Cu3Mn
AC-45300
AI Si5CulMg
AC-46200 AC-46400 AC-46600 AC-47000 AC-51000 AC-5ll00 AC-51300 AC-51400 AC-71000
AI Si8Cu3 AI Si9CulMg AI Si7Cu2 AI SiI2(Cu) AI Mg3(b) AI Mg3(a) AI Mg5 AIMG5(Si) AlZn5Mg
F
T6 T6 F F F F F
T6 T4 T6 F F F F F F F F
T1
Rp,N
crW,zd,N
crSch,zd,N
crW,b,N
~W,s,N
~W,t,N
A50 %
200 200 180 70 180 80 180 190 210 80 180 80 180 80 180 190 70 70 70 90 70 200 120 200 90 90 90 80 70 70 90 100 120
90 90 85 40 70 40 65 70 75 45 65 45 65 50 65 70 45 45 45 45 40 70 50 70 45 40 45 45 40 40 50 50 55
60 60 55 30 50 30 45 50 50 35 45 35 45 35 45 50 35 35 35 35 30 50 35 50 35 30 35 35 30 30 35 35 40
130 130 125 65 lOS 65 100 lOS 110 70 100 70 100 75 100 105 70 70 70 70 65 105 75 lOS 70 60 70 70 65 65 75 75 85
65 65 65 30 55 30 50 50 55 35 50 35 50 35 50 50 35 35 35 35 30 50 40 50 35 30 35 35 30 30 35 35 45
100 100 95 50 80 50 75 80 85 50 75 50 75 55 75 80 50 50 50 50 50 80 60 80 50 45 50 50 50 50 55 55 65
5 3 5 3 3 2 I 2 I 2 I 2 I I 1 2 6 4 5 I I
Hardness HBS 90 95 85 50 85 50 75 75 85 50 75 50 75 50 75 75 45 50 50 60 60 90 80 100 60 60 60 50 50 50 55 60 60
173
5.1 Material tables
5 Appendices
Table 5.1.32 Material properties in MFa for cast aluminum alloys, permanent mold castings, test pieces cast separately, after DIN EN 1706 (l998~06-00). Material DIN notation EN notation AC-21000 Al Cu4MgTi AC-21100 Al Cu4Ti AC-41000 Al Si2MgTi
Cnd.
T4 T6 T64 F
T6 AC-42000 Al Si7Mg AC-42100 Al Si7MgO,3 AC-42000 Al Si7MgO,6 AC-43000 Al Sil0Mg(a) AC-43100 Al SilOMg(b) AC-43200 Al Sil0Mg(Cu) AC-43300 Al Si9Mg AC-44000 AC-44100 AC-44200 AC-45000 AC-45100
Al Al Al Al Al
Sill Si12(b) Si12(a) Si6Cu4 Si5Cu3Mg
AC-45200 Al Si5CulMn AC-45300 Al Si5CulMg AC-45400 AC-46200 AC-46300 AC-46400
Al Al Al Al
Si5Cu3 Si8Cu3 Si7Cu3Mg Si9Cu1Mg
AC-46600 Al Si7Cu2 AC-47000 Al Si12(Cu) AC-48000 Al Si12CuNiMg AC-51000 AC-51100 AC-51300 AC-51400 AC-71000
Al Al Al Al Al
Mg3(b) Mg3(a) Mg5 MG5(Si) Zn5Mg
F
T6 T64 T6 T64 T6 T64 F T6 T64 F T6 T64 F T6 T6 T64 F F F F T4 T6 F T6 T4 T6 T4 F F F T6 F F T5 T6 F F F F Tl
Rm,N
320 330 320 170 260 170 260 240 290 250 230 290 180 260 240 180 260 240 180 240 290 250 170 170 170 170 270 320 160 280 230 280 230 170 180 170 275 170 170 170 275 150 150 180 180 210
Rp,N
200 220 180 70 180 90 220 200 210 180 240 210 90 220 200 90 220 200 90 200 210 180 80 80 80 100 180 280 80 230 140 210 110 100 100 100 235 100 90 185 240 70 70 100 110 130
crW,zd,N
95 100 95 50 80 50 80 70 85 75 95 85 55 80 70 55 80 70 55 70 85 75 50 50 50 50 80 95 50 85 70 85 70 50 55 50 85 50 50 60 85 45 45 55 55 65
crSch,zd,N
65 65 65 35 55 35 55 50 60 50 65 60 40 55 50 40 55 50 40 50 60 50 35 35 35 35 55 65 35 55 50 55 50 35 40 35 55 35 35 45 55 35 35 40 40 45
crW,b,N
140 145 140 75 115 75 115 105 130 110 140 130 80 115 105 80 115 105 80 105 130 110 75 75 75 75 120 140 75 125 105 125 105 75 80 75 120 75 75 90 125 70 70 80 80 95
~W,s,N
70 75 70 40 60 40 60 55 65 55 70 65 40 60 55 40 60 55 40 55 65 55 40 40 40 40 60 70 35 65 50 65 50 40 40 40 60 40 40 45 65 35 35 40 40 45
~W,t,N
105 110 105 60 90 60 90 80 100 85 105 100 60 90 80 60 90 80 60 80 100 85 60 60 60 60 90 105 55 95 80 95 80 60 60 60 95 60 60 70 95 50 50 60 60 70
%
Hardness HBS
8 7 8 5 5 2,5 1 2 4 8 3 6 2,5 1 2 2,5 1 2 1 1 4 6 7 5 6 1 2,5 <1 1 <1 3 <1 6 1 1 1 1,5 1 2 <1 <1 5 5 4 3 4
95 95 90 50 85 55 90 80 90 80 100 90 55 90 80 55 90 80 55 80 90 80 45 55 55 75 85 110 70 90 85 110 75 75 80 75 105 75 55 90 100 50 50 60 65 65
A50
174
5.1 Material tables
5 Appendices
Table 5.1.33 Material properties in MPa for cast aluminum alloys, investment castings, test pieces cast separately, after DIN EN 1706 (1998-06-00). Material EN notation
Cnd.
Rm,N
Rp,N
crW,zd,N
crSch,zd,N
crW,b,N
'tW,s,N
'tW,t,N
A50 %
Hardness HBS
T4 F T6 T6 T6 F F F
300 150 240 260 290 150 160 170
220 80 190 200 240 80
90 45 70 80 85 45 50 50
60 35 50 55 60 35 35 35
130 70 105 115 130 70 75 75
70 35 55 60 65 35 35 40
100 50 80 90 100 50 55 60
5 2 1 3 2 4 1 3
90 50 75 75 85 50 60 55
DIN notation
AC-21000 AC-42000
AI Cu4MgTi AI Si7Mg
AC-42100 AC-42200 AC-44100 AC-45200 AC-51300
AI Si7MgO,3 AI Si7MgO,6 AI SiI2(b) AI Si5Cu3Mn AlMg5
80
95
Table 5.1.34 Material properties in MPa for cast aluminum alloys, high pressure die castings after DIN EN 1706 (1998-06-00), without obligation, for information only. Material EN notation AC-43400 AC-44300 AC-44400 AC-46000 AC-46100 AC-46200 AC-46500 AC-47 100 AC-51200
Cnd.
Rm,N
Rp,N
crW,zd,N
crSch,zd,N
crW,b,N
'tW,s,N
'tW,t,N
A50 %
hardness HBS
F
240 240 220 240 240 240 240 240 200
140 130 120 140 140 140 140 140 130
70 70 65 70 70 70 70 70 60
50 50 45 50 50 50 50 50 45
105 105 100 105 105 105 105 105 90
55 55 50 55 55 55 55 55 45
80 80 75 80 80 80 80 80 70
1 1 2 <1 <1 1 <1 1 1
70 60 55 80 80 80 80 70 70
DIN notation AI SilOMg(Fe) AI SiI2(Fe) AI Si9 AI Si9Cu3(Fe) AI Si11Cu2(Fe) AI Si8Cu3 AI Si9Cu3(Fe)(Zn) AI SiI2Cul(Fe) AlMg9
F F F F F F F F
175
5.1 Material tables
5 Appendices
Table 5.1.35 Material properties in MPa for cast aluminum alloys, alloys for general applications, sand castings and permanent mould castings, after DIN 1725 T. 2 (1986-02-00). Material DIN ~o:ation
G-AlSiI2
Material No.
Rp,N
O'W,zd,N
O'Sch,zd,N
O'W,b,N
'tW,s,N
'tW,t,N
~2
70 (70) 80 (70)
45 (40) 45 (40)
35 (30) 35 (30)
70 (65) 70 (65)
35 (30) 35 (30)
50 (50) 50 (50)
170 (150) 170 (160)
80 (80) 80 (80)
50 (45) 50 (50)
35 (35) 35 (35)
75 (70) 75 (75)
40 (35) 40 (35)
60 (50) 60 (55)
150 (140) 180 (160) 160 (150) 220 (200)
80 (80) 90 (90) 80 (70) 180 (170)
45 (40) 55 (50) 50 (45) 65 (60)
35 (30) 40 (35) 35 (35) 45 (45)
70 (65) 80 (75) 75 (70) 100 (90)
35 (30) 40 (35) 35 (35) 50 (45)
50 (50) 60 (55) 55 (50) 75 (70)
3.2381 Perm. mould c. .02 as-cast condit. 3.2381 Perm. mould c. .62 wa
180 (180) 240 (220)
90 (90) 210 (190)
55 (55) 70 (65)
40 (40) 50 (45)
80 (80) 105 (100)
40 (40) 55 (50)
60 (60) 80 (75)
3.2383 Sand castings .01 as-cast condit. 3.2383 Sand castings .61 wa
170 (150) 220 (200)
90 (80) 180 (180)
50 (45) 65 (60)
35 (35) 45 (45)
75 (70) 100 (90)
40 (35) 50 (45)
60 (50) 75 (70)
3.2383 Perm. mould c. .02 as-cast condit. 3.2383 Perm. mould c. .62 wa
200 (180) 240 (220)
100 (100) 210 (190)
60 (55) 70 (65)
45 (40) 50 (45)
90 (80) 105 (100)
45 (40) 55 (50)
3.2163 .01 3.2163 .02 3.2151 .01 3.2151 .02
160 (140) 180 (160) 160 (140) 180 (160)
100 (100) 110 (100) 100 (100) 120 (110)
50 (40) 55 (50) 50 (40) 55 (50)
35 (30) 40 (35) 35 (30) 40 (35)
75 (65) 80
35 (30) 40 (35) 35 (30) 40 (35)
GAlSil2g GKAlSil2 GKAlSil2g
3.2581 .02 3.2581 .45
GAlSiI2(Cu) GKAlSiI2(Cu) GAlSilOMg GAlSilOMg wa GKAlSilOMg GKAlSilOMg wa GAlSiIOMg(Cu) GAlSiIOMg(Cu) wa GKAlSiIOMg(Cu)I GKAlSiIOMg(Cu) wa GAlSi9Cu3 GKAlSi9Cu3 GAlSi6Cu4 GKAlSi6Cu4
3.2583 .01 3.2583 .02 3.2381 .01 3.2381 .61
~2
Condition~
delivered I Sand castings as-cast condit. Sand castings annealed and quenched Perm. mould c. as-cast conddit. Perm. mould c. annealed and quenched Sand castings as-cast condit. Perm. mould c. as-cast condit. Sand castings as-cast condit. Sand castings wa
Rm,N
150 (140) 150 (140)
3.2581 .01 3.2581 .44
~I
Casting process
Sand castings as-cast condit. Perm. mould c. as-cast condit. Sand castings as-cast condit. Perm. mould c. as-cast condit.
wa = artificially aged Upper line: values for test pieces cast separately, line below (in brackets): values for test pieces cast integrally or taken from the casting.
(75)
75 (659 80 (75)
%
Hardness HB
5 (3) 6 (5)
45 (45) 45 (45)
6
50 (50) 50 (50)
A50
(3)
6 (4)
(I)
50 (50) 55 (55) 50 (50) 80 (75)
2 (2) I (I)
60 (60) 85 (80)
I I (0,5)
55 (55) 80 (75)
70 (60) 80 (75)
I (0,5) I (0,5)
65 (60) 85 (80)
55 (50) 60 (55) 55 (50) 60 (55)
I (0,5) I (0,5) I (0,5) I (0,5)
65 (60) 70 (65) 60 (60) 75 (65)
I (l)
2 (I)
2 (2) I
(1)
176
5.1 Material tables
5 Appendices
Table 5.1.36 Material properties in MPa for cast aluminum alloys, alloys with particular mechanical properties, sand castings, permanent mould castings and investment castings, after DIN 1725 T. 2 (1986-02-00). Material ~11' notation
GAlSilI GAlSill
Material no.
Casting process Condition~
Rm,N
Rp,N
crW,zd,N
crSch,zd,N
crW,b,N
'tW,s,N
'tW,t,N
A50 %
Hardness HB
~2
3.2211 .01 3.221I .81
delivered 1 Sand castings As-cast condit. Sand castings annealed
150 (140) 150 (140)
70 (70) 70 (70)
45 (40) 45 (40)
35 (30) 35 (30)
70 (65) 70 (65)
35 (30) 35 (30)
50 (50) 50 (50)
6 (5) 8 (7)
45 (45) 45 (40)
3.221I .02 3.2211 .82
Perm.mould c. As-cast condit. Perm.mould c. Annealed
170 (150) 170 (150)
80 (80) 80 (80)
50 (45) 50 (45)
35 (35) 35 (35)
75 (70) 75 (70)
40 (35) 40 (35)
60 (50) 60 (50)
7 (6) 9 (8)
45 (45) 45 (40)
3.2373 .61
Sand castings Wa
230 (220)
190 (180)
70 (65)
50 (45)
100 (100)
50 (50)
80 (75)
2 (2)
75 (75)
3.2373 .62
Perm.mould c. Wa
250 (240)
200 (190)
75 (70)
50 (50)
110 (105)
55 (55)
85 (80)
4 (3)
80 (80)
3.2371 Sands .61 Wa
230 (230)
190 (190)
70 (70)
50 (50)
105 (105)
50 (50)
80 (80)
2 (2)
75 (75)
3.2371 .62
Perm.mould c. Wa
250 (250)
200 (200)
75 (75)
50 (50)
1I0 (1I0)
55 (55)
85 (85)
5 (3)
80 (80)
3.2371 .63
Investm. casts. Wa
260 (230)
200 (190)
80 (70)
55 (50)
1I5 (105)
60 (50)
90 (80)
3 (3)
80 (70)
3.1841 .63
Sand castings Ta
280 (240)
180 (160)
85 (70)
55 (50)
125 (105)
65 (55)
95 (80)
5 (3)
85 (80)
3.1841 .61
Sand castings Wa
300 (250)
200 (180)
90 (75)
60 (50)
130 (110)
70 (55)
100 (85)
3 (2)
95 (90)
3.1841 .64
Perm.mould c. Ta
320 (260)
180 (170)
95 (80)
65 (55)
140 (1I5)
70 (60)
105 (90)
8 (4)
90 (85)
3.1841 .62
Perm.mould c. Wa
330 (280)
220 (200)
100 (85)
65 (55)
145 (125)
75 (65)
110 (95)
7 (3)
95 (90)
3.1371 .41
Sand castings Ka
300 (240)
220 (180)
90 (70)
60 (50)
130 (125)
70 (55)
100 (80)
5 (3)
90 (85)
3.1371 .42
Perm.mould c. Ka
320 (280)
220 (200)
95 (85)
60 (50)
130 (125)
70 (65)
105 (95)
8 (5)
95 (90)
3.1371 .45
Investm. casts. Ka
300 (270)
220 (180)
90 (80)
60 (55)
130 (120)
70 (60)
100 (90)
5 (3)
90 (85)
g
GKAlSill GKAlSill g
GAlSi9Mg wa GKAlSi9Mg wa GAlSi7Mg wa GKAlSi7Mg wa GFAlSi7Mg wa GAlCu4Ti ta GAlCu4Ti wa GKAlCu4Ti ta GKAlCu4Ti wa GAlCu4TiMg ka GKAlCu4TiMg ka GFAlCu4TiMg ka ~I ~2
ka
=
naturally aged, ta
=
partially aged, wa = artificially aged.
Upper line: values for test pieces cast separately, line below (in brackets): values for test pieces cast integrally or taken from the casting.
177
5.1 Material tables
5 Appendices
Table 5.1.37 Material properties in MPa for for cast aluminum alloys, alloys for particular applications, sand castings, permanent mould castings and investment castings, after DIN 1725 T. 2 (1986-02-00). Material DIN notation
Rp,N
crW,zd,N
crSch,zd,N
crW,b,N
'tW,s,N
'tW,t,N
A50 %
Hardness HB
140 (130) 150 (150) 150 (140) 140 (130) 200 (180)
70 (60) 70 (70) 90 (80) 80 (70) 120 (120)
40 (40) 45 (45) 45 (40) 40 (40) 60 (55)
30 (30) 35 (35) 35 (30) 30 (30) 40 (40)
65 (65) 70 (70) 70 (65) 65 (60) 90 (80)
30 (30) 35 (35) 35 (30) 30 (30) 45 (40)
50 (45) 50 (50) 50 (50) 50 (45) 70 (60)
3 (3) 5 (4) 3 (3) 3 (3) 2 (2)
50 (45) 50 (50) 60 (55) 50 (45) 65 (60)
3.3241 Penn. mould c. .02 as-cast condit. 3.3241 Penn. mould c. .62 wa
150 (140) 220 (220)
80 (80) 120 (120)
45 (40) 65 (65)
35 (30) 45 (45)
70 (65) 100 (100)
35 (30) 50 (50)
50 (50) 75 (75)
4 (4) 3 (3)
50 (50) 65 (65)
3.3241 Investment c. .63 wa
200 (180)
120 (120)
60 (55)
40 (40)
90 (80)
45 (40)
70 (60)
2 (2)
60 (55)
160 (140) 180 (150) 160 (140) 180 (150) 140 (130) 160 (140) 260 (190)
100 (90) 100 (100) 110 (l00) 110 (100) 100 (90) 120 (100) 240 (180)
50 (40) 55 (45) 50 (40) 55 (45) 40 (40) 50 (40) 80 (55)
35 (30) 40 (35) 35 (30) 40 (35) 30 (30) 35 (30) 55 (40)
75 (65) 80 (70) 75 (65) 80 (70) 65 (60) 75 (65) 115 (85)
35 (30) 40 (35) 35 (30) 40 (35) 30 (30) 35 (30) 60 (45)
55 (50) 60 (50) 55 (50) 60 (50) 50 (45) 55 (50) 90 (65)
3 (2) 4 (2) 2 (1) 2 (1) 1 (0,5) 1,5 (I) I (0,5)
55 (50) 60 (55) 60 (55) 65 (60) 55 (55) 60 (60) 90 (90)
'tW,s,N
'tW,t,N
A50 %
Hardness HB
Material No.
~1
G-
AlMg3 GK-
AlMg3 GF-
AlMg3 G-
AlMg3Si G-
AlMg3Si wa GK-
AlMg3Si GK-
AlMg3Si wa GF-
AlMg3Si wa G-
AlMg5 GK-
AlMg5 G-
AlMg5Si GK-
AlMg5Si G-
AlSi5Mg GK-
AlSi5Mg GK-
AlSi5Mg wa ~1 ~2
3.3541 .01 3.3541 .02 3.3541 .09 3.3241 .01 3.3241 .61
Casting process, Condition as delivered~ I Sand castings as-cast condit. Penn. mould c. as-cast condit. Investment c. as-cast condit. Sand castings as-cast condit. Sand castings wa
Rm,N
3.3561 .01 3.3561 .02 3.3261 .01 3.3261 .02 3.2341.0 1 3.2341 .02 3.2341 .62
Sand castings as-cast condit. Penn. mould c. as-cast condit. Sand castings as-cast condit. Penn. mould c. as-cast condit. Sand castings as-cast condit. Penn. mould c. as-cast condit. Penn. mould c. wa
~2
wa = artificially aged Upper line: values for test pieces cast separately, line below (in brackets): values for test pieces cast integrally or taken from the casting.
Table 5.1.38 Material properties in MPa for cast aluminum alloys, high pressure casting alloys after DIN 1725 T. 2 (1986-02-00). Material DIN nataion
Material No.
GO-
3.2163 .05
GO-
3.2585 .05
AlSi9Cu3 2)
AlSi12 GO-
AlSiI2(Cu) GO-
AlSilOMg GO-
AlMg9
3.2982 .05 3.2381 .05 3.3292 .05
Casting process, Condition as delivered High press. c as-cast condition High press. c as-cast condition High press. c as-cast condition High press. c as-cast condition High press. c as-cast condition
Rm,N
Rp,N
crW,zd,N
crSch,zd,N
crW,b,N
240
140
70
50
105
55
80
0,5
80
220
140
65
45
100
50
75
1
60
220
140
65
45
100
50
75
I
60
220
140
65
45
100
50
75
1
70
200
140
60
45
90
45
70
I
70
178
5.2 Stress concentration factors
5.2.1.1 Round bars with groove or shoulder fillet
5.2 Stress concentration factors lR52 EN.dog
Content
Page
5.2.0
General
5.2.1 5.2.1.0 5.2.1.1 5.2.1.2 5.2.1.3 5.2.1.4
Round bars General Round bars with Round bars with Round bars with Round bars with
5 Appendices
178
groove or shoulder fillet multiple grooves relief groove collar (narrow shoulder)
5.2.2 Flat bars 5.2.2.0 General 5.2.2.1 Flat bars with notches or shoulder fillets on both sides 5.2.2.2 Flat bars with notch on one side 5.2.2.3 Flat bars with multiple notches 5.2.2.4 Flat bars with transverse hole 5.2.2.5 Flat bars with notches on both sides or with transverse hole, bending in plane 5.2.2.6 Flat bars with narrow shoulder
The stress concentration factors for round bars with a groove or shoulder fillet in tension, in bending and in torsion are to be computed after Petersen from the equation below, or are to be taken from the Figures 5.2.1 to 5.2.6, r> 0, diD < 1: (5.2.2)
180
K, = 1 + - - ; = = = = = = = = = = = d +C{ D
181
r, t, d, D
A'~+2B'~{1+2·~r
A,B,C,z
~r
Constants, Table 5.2.1, See Figure 5.2.1 to 5.2.6.
..
182 183 184 185
5.2.0 General
Table 5 2 1 Constants ABC , , , z for round bars Groove Shoulder fillet
A B C z
tension 0,22 1,37
bending 0,2 2,75
torsion 0,7 10,3
tension 0,62 3,5
-
-
-
-
torsion 3,4 19 1 2
bending 0,62 5,8 0,2 3
-
Stress concentration factors for round bars and for flat bars are to be determined from the following equations and figures. Stress concentration factors are used together with Kj-K, ratios for computing fatigue notch factors, Chapter 2.3.2.1. Stress concentration factors are combination with nominal stresses *1.
applicable
in
Stress concentration factors may be determined by the. user if he has more detailed knowledge at his disposal.
5.2.1 Round bars 5.2.1.0 General
Stress concentration factors are given for round bars in tension (load F), in bending (bending moment M, ) and in torsion (torsion moment M t ) *2. The related nominal stresses are nd 2 ,
Szd = 4 F I Sb = 32 Mbl nd 3 , Tt = 16 Mtl nd 3 .
(5.2.1)
The diameter d is shown in the respective figures.
1 Sometimes the nominal stress may be defined in a different way, for example see Figure 5.2.20. 2 In the following tension or compression or tension-compression are mentioned as tension throughout. Stress concentration factors for shear are not available. Therefore no formula for the nominal shear stress is contained in Eq. (5.2.1)
1~~~~ 0.4
0.5
0.6
0.7
0.8
0.9
,
dID
Figure 5.2.1 Stress concentration factors for round bars with groove in tension, r > 0, diD < 1. 1 Kt,zd = 1 +---;=========== r r r 022·-+274·-· ( 1+2·-) , t ' d d
2
(5.2.3)
179
5.2 Stress concentration factors
5 Appendices
t
rl
--
0.06
F
0.2
J'-n-f-1'-¥iffl'rHLH O.25
'>,,+--+--¥->L-,H 0.07
0.06
-+---¥---,+-,oY-Hi-i o,09 0.1
-l-~+-¥-.'--lh14tj-...,hf-l..lrl°·3
-t--t-r-h~,.f-;,L71Ifirt--TH 0.15
-l-,.y+~H¥-'<'1L+-+-It-I-+-A-J°·4 0.5
0.2
h"'-l7"-7f-r-,>"17'n-f--7'f--rtiO,25 0.3
h"71,.7'J;..
¥..".LIi7'S~~"1--7"f-7£.:;f'Y-tiO.4
~lf-t--7"<-i7-S-~~~----H'-M ~,5
-r"..,>-S1~-+:""'::"'''''''''7'''!>'''-7''f:r-t-i
o.s I
2.5
is>f3....-;7'''b..-s-f'O--f,,L-h7L+i5
b....g~;,...f;;;....o::::~rt---7""':;ti 1.5
-±::::"'M'---::p...-c=::~n;"::"-¥-A-110
-i'7-::$1;:"=::=-+=""...f"::-"-:j;;.;$;:;.
~,5
I~~~ 0.4
0.5
0.6
0.7
0.8
0.9
~~~~~t]10
I
0.5
0.6
0.7
0.6
diD
0.9
1
diD
Figure 5.2.2 Stress concentration factors for round bars with groove in bending, r> 0, d / D < 1. 1 (5.2.4) Kt,b== 1 +r========== 2 r r o,20· -rt + 5' 5 .-. 1+ 2 . d ( d)
Figure 5.2.4 Stress concentration factors for round bars with shoulder fillet in tension, r > 0, diD < 1. 1 (5.2.6) 1< '~,zd == 1 +--,========= 2 r r r 062·-+ 7·-· ( 1+2·-) , t d d
t
GMt
MtC
0,06
0.05
'f-l'-H'HO,07
0,06
0,08
-t--+--f--HCf11-iO,09
0,07 0.08 0.09 0,1
Kt,t
t--t--t--H'--loLf--MHIH
0.1
4
3
~2:t,.....::::~~~+?<::+~1
2
1 0.4
1.5 2
~;;~~i~t~~~~,5
1~ 0.5
0.6
0.7
0.6
0.9
0.4
1
10
0.5
0.6
0.7
0.8
1< '~,t
==
1 1 +r=========
r r o,70· -rt + 20' 6 .-. 1+ 2· - ) d ( d
(5.2.5)
1
diD
diD
Figure 5.2.3 Stress concentration factors for round bars with groove in torsion, r > 0, d / D < 1.
0.9
Figure 5.2.5 Stress concentration factors for round bars with shoulder fillet in bending, r > 0, diD < 1. (5.2.7)
2
~==l+-;============= ,b
062. E+1l6'.!.'(1+2 . .!.)2 , t ' d d
+02.(E)3 ' t
d D
180
5.2 Stress concentration factors
5 Appendices FormD The stress concentration factors for round bars with relief groove, type D, Kt,F , Figure 5.2.8, are to be computed by superposition of the stress concentration factors for round bars with groove and with shoulder fillet *4:
GMt
MtC r
Kt,t
K, F = (KtU - K, A.>' ~Dl-d - + K,'A, (5.2.9) , , , D-d
4
.04 .05 .06 .07 .08
3
.~; ,2
2
4°,3
l' 0.5 1,5 2.5 1 0.4
° 0.5
0.6
0.7
0.8
0.9
Kt,U Stress concentration factor of the round bar with groove, Figure 5.2.1 to 5.2.3. Kt,A Stress concentration factor of the round bar with shoulder fillet, Figure 5.2.4 to 5.2.6. D 1 Smaller diameter, d Reduced diameter, D Larger diameter.
1
dID 5.2.8
Figure 5.2.6 Stress concentration factors for round bars with shoulder fillet in torsion, r > 0, d / D < 1. (5.2.8)
Figure 5.2.8 Round bar with relief groove, type D.
K, = 1 +-,============ .t
3.4f+38Hl+2~r +l.O.(f)'
d D
5.2.1.5 Round bars with collar (narrow shoulder) The stress concentration factors for the round bars with bolt head in tension, Figure 5.2.9, are approximately the same as for the flat bars with shoulder head, Figure 5.2.26 (d = b, D= B).
5.2.1.2 Round bars with multiple grooves Stress concentration factors for round bars with multiple grooves in tension, in bending and in torsion are to be determined as for flat bars with multiple notches, Chapter 5.2.2.3. .
5.2.1.3 Round bars with relief groove FormB Stress concentration factors for round bars with relief groove, type B, Figure 5.2.7, are to be determined as for the round bars with shoulder fillet with the diameters d and D, Figure 5.2.4 to 5.2.6, *3. The fatigue strength of type B is lower than that of type D.
Figure 5.2.9 Round bar with "bolt head". The stress concentration factors for the round bars with collar, Figure 5.2.10, in tension, in bending and in torsion, ~,zd,L,' ~,b,L,' ~,t,L' are to be computed from Eq. (5.2.10):
~L = 1 + (K, - 1)' ,
K, L ,
K, Figure 5.2.7 Round bars with relief groove, type B.
3 11 is assumed that the additional small shoulder does not influence the stress concentration factor considerably as fl / r ~ 5 .
Kt,b,LlD
-1 ,
(5.2.10)
K t ,b,Ll D= 2 -1
Stress concentration factor of a collar with values L / D and d / D according to type of stress, Stress concentration factor of the shoulder fillet with values d / D according to type of stress, Figure 5.2.4, 5.2.5 or 5.2.6.
4 Different from type B it is accepted, that the additional small shoulder does influence the stress concentration factor considerably as f3 / r ~ 2 .
181
5.2 Stress concentration factors
5 Appendices
Stress concentration factor in bending for the actual value LID from Figure 5.2.24 (D = B, d = b), referring to the diagram providing the closest approximation ofB lb. ~b,UD=2 Stress concentration factor in bending for the value LID = LIB from Figure 5.2.24 (D = B, d = b), referring to the diagram as before.
K "'1,b,UD
0,2 -tJ--r--:o11 0,25 jL.,t44W~-r--~717''11
0,3 0,4
4
IhW~-r-l7-n"i;i""t1 0,5
1,5 \L.,...:::j,.4-7Fr-t--1:r-::PA1t,5
Figure 5.2.10 Round bar with collar.
2b"'~-+--;7h-f:7:?1""---:t1S !---=~,...-1$~~:P""'-:Y'11
10
1 . 0,4 0,5 0,6 0,7 0,8 0,9 1,0
biB
5.2.2 Flat bars 5.2.2.0 General
Figure 5.2.11 Stress concentration factors for flat bars with notches on both sides in tension, r> 0, biB < 1 .
Stress concentration factors are given for flat bars in tension (load F) and in bending (bending moment M, )
~zd = 1 + r = = = = = = = = =
'5
r r o,22· -rt + 17' .-. 1+ 2 . - ) ( b b
The related nominal stresses are normally to be computed according to the following equations: Szd = F I (s . b), Sb = 6 Mb I (s . b2 ) .
(5.2.11)
Otherwise the equations to compute the nominal stresses are presented with the diagrams in question. The dimensions sand b are shown in the figures.
MJ t--~
Bt'-S;),.~. .. ,
Thickness s
The stress concentration factors for flat bars with notches or shoulder fillets on both sides in tension and in bending are to be computed from the equations below, or read from the Figures 5.2.11 to 5.2.14, r> 0, diD < 1, thickness s: 1
K, = 1 + - - - ; = = = = = = = = 2 r r r A·-+2B·-· 1+2·A,B r, t, b, B
b (
Constants, Table 5.2.2, See Figures 5.2.11 to 5.2.14.
5
= 0,2
' r:k'
1---+7''-1;;:)'
t-7''-hH'-r*'''''rt--f-.Jf+.A-I
1,5 f-:;;.f-:;>""V"74rr:7"f--t"7'H2
2,5
2
1"'75""''-:rl7'''T-""7I''-'7'j7"--t1 5
1
~~~~JI0 ....
bIB
6..2.12
Figure 5.2.12 Stress concentration factors for flat bars with notches on both sides in bending, r > 0, biB < 1. 1
A B
Tension 0,22 0,85
Bending 0,2 2,1
.
0,4 0,5 0,6 0,7 0,8 0,9 1,0
~b = 1 + r = = = = = = = = =
Table 5.2.2 Constants A and B for flat bars Notch on both sides Shoulder fillet
0;25 0,3
3~,.y"----V"7lf7';>'t7,,*;t11
(5.2.12)
b)
r
"""'"""""71rTTlrxr--m/ t
Kt b
5.2.2.1 Flat bars with notches or shoulder fillets on both sides
t
(5.2.13)
2
r r r 020·-+42·-· ( 1+2·-) , t ' b b
(5.2.14)
2
Tension Bending 0,5 0,5 2,5 6 5 In the following tension or compression or tension-compression are mentioned as tension throughout. .
182
5.2 Stress concentration factors
-
5.2.2.2 Flat bar with notch on one side
~ +--+., F
F
. B-·- b
__
5 Appendices
r/t=
-r-r-rr-,.,....,...".,
0,08 0.09 0 1
Thickness s r
5
'
Stress concentration factors for flat bars with a notch on one side in bending according to Figure 5.2.15. .. ..... 3,8 _.&~b 3,6
,- .::rrnnTMb( r=0,04 ~r/b
)
i
I
3,4
Thickne ss s
..
3,2
3,0
.
0,08
.;...-t-1 I
2,8 2,6
0,1~
2,4
5.2.H
1,& 1,6 1,4
Figure 5.2.13 Stress concentration factors for flat bars with shoulder fillet in tension, r > 0, b / B < 1. 1 ~ zd == 1 +---;=========
r r r 05·-+5·_· 1+2·, t b b
(
, it'
1,2 1,0
:
, I
0,4 0,6
I
I
I
i I-
1,01,21,41,61,& 2,02,2 2,42,62,M 3,0 . . - "BIb
5:2.15
(5.2.15)
2
Figure 5.2.15 Stress concentration factors for flat bars with a notch on one side in bending, after Sors.
J
5.2.2.3 Flat bars with multiple notches
~
r/t==
MJ ~ )Mb-r--r---rTTTTl Thickness s
0,2
2,0
0,4 0,5 0,6 0,7 0,8 0,9 1,0 bIB
I
I .
2,2
l~~~~Jj
! r
Stress concentration factors for flat bars with multiple notches in tension according to Figure 5.2.16. For a large number of notches arranged in a row on one side of a flat bar the effective depth t' of an equivalent single notch is to be computed with a release factor y from Figure 5.2.17:
5 1-+--1-,.-+---,t--t
Kt,b
t' == y' t .
(5.2.17)
Figure 5.2.17 approximately applies for both tension and bending. With the effective depth t' of a single notch the stress concentration factors are to be determined from Figure 5.2.11 and 5.2.12.
I.~~
0,4 0,5 0,6 0.7 0,8 0,9 I,D
6.2.14
.
)
IB
Figure 5.2.14 Stress concentration factors for flat bars with shoulder fillet in bending, r> 0, b / B < 1. 1
(5.2.16)
r r r 05·-+12·-· 1+2·, t b b
(
2
J
183
5.2 Stress concentration factors
5 Appendices 5.2.2.4 Flat bars with transverse hole
5.2.16
--
F
F
Stress concentration factors for flat bars with a circular or slotted transverse center hole for different types of stress are given in Figure 5.2.18 to 5.2.20.
-- 1trt
3,8
J4,ro
--
--
F
F
c::r--
r-
2,4
2,4 2,2 I-
tl r-= 4
1..-
hH0'1-n~
ec limit case (b)
r:::l ~
2,0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7
1,,2
rib
5.2.18
2,° 2
4
6
10 12 14 16 18 20 22
8
e/r
Figure 5.2.16 Stress concentration factors for flat bars with multiple notches in tension. The stress concentration factor is valid for the first (or last) notch in the row, after Peterson (Ref. Durelli, Lake and Phillips), photoelastic study. Nominal stress: S d
F s.(B-r)
z
bl
Thickness s I'
2,6
p
...;.+-
\c\\es 1 nO c\\" ol.~ . 5 (\o\c\\oS~
F --
21
-'2r
3,0
m.s\\l)
D-
N-
3,4
2,8
3,2 r t I I 01 notch 3,0 1.(\~
I +--
3,2
B I r = 18, Thickness s
2.8 2,6
F
3,6
(5.2.18)
Figure 5.2.18 Stress concentration factors for flat bars with a circular or slotted transverse center hole in tension, after Peterson (Ref. Frocht and Leven), photoelastic study. In addition circular hole after Peterson (Ref. Howland), elastic analysis. hole: t / r = 1; limit value for b / r - 0: Kt,z = 2. Nominal stress: Szd
F s.(B-2t) .
(5.2.19)
b/2
1,0
Y
I I I
0,8
V
ll\rJ\lrw ,
1./
0,4
0,2
o 0
II
2
MJ
I I I I I I
1/
0,6
1111'"'' r TT1 1
J...-t
3
4
5
6
7
8
9 10 bIt
Figure 5.2.17 Release factor y for an infinite number of notches in a row, after Peterson (Ref. Neuber), elastic analysis.
2t- .
Thickness s
1,4 1,2
C
tb
2r
J 'f = i.SO'b·~FG·~'S. '"t""';:tD~.±:.~.±j H:::.+-.i-+-,.f4I--,f....:,:.=, l~~:::" 1 (1'= 30')f-" 1.O~:!7"-P:-~~4~~~~""":'~..J o 0.1 0,2 0,3 0,4 0,5 06 0,7 0& 09 1,0 ;Y'
1/ I ""''Kt.b,F
rIb
Figure 5.2.19 stress concentration factors for flat bars with a circular or slotted transverse center hole in bending, after Peterson (Ref. Procht and Leven), photoelastic study. Hole: t / r = 1; limit value for b / r - 0: Kt,z = 2. Nominal stress (at reference point G): Sb G
,
Mb =--------.::::----(1-(2t1B)3).s.B 2/6
(5.2.20)
184
5.2 Stress concentration factors
-F
B
F
-I-,K.t',i -I-
b
Thickness s
zd
ee
==~!J
0 I81- !"-B/b== 1 2 Kt,zd 3, 6 3, 4 'V/ 3,2
SZd,,,,, II ' F,
tr
~~ g'~
"
°
2, 8
I-
2, 61-
f",
i'-...
"
2, "I
°
2, 0
5.2.20
S I
2,8 2,6
01 , 0,2 0,3 0,4 0,5
I
1'\
'"
I.....
2r I s ==
r-,
0
.......
.....
2,2
ac tts K.t,zd,C -- Szd,Ac
2,4
3,0
2,4
I,..,,:~'-
3,
5 Appendices
r-,
2,0
r-,
1,8 r-,
1,6
~
0,25 r-... 0,5 ....... 1 1,5 1'-.,2
I"C'"
1,4
r-
oc--
1,2
I"-- I"--r-
r-
rib
1'°0
Figure 5.2.20 Stress concentration factors for flat bars with excentric hole in tension, after Peterson (Ref.: Sjoestroem), elastic analysis. Any B / b ; transverse hole: B / b = I. Nominal stresses (away from or at the notched section): F
(5.2.21)
s·(B+b) ,
~I-(r/bf
0,] 0,2 0,3 0,4 0,5 0,6 0,7
2r 18 Figure 5.2.22 Stress concentration factors for flat bars with transverse hole in bending in plane, after Peterson, photoelastic study; strain measurements, 2r / s = 0 after Peterson (Ref.: Howland), elastic analysis. . Nominal stress: Sb -
6M b
K'b~:: 2,4
5.2.2.5 Flat bars with notches on both sides or with transverse hole, bending in plane
Stress concentration factors for flat bars with notches on both sides or with transverse hole in bending in plane are given in Figure 5.2.21 to 5.2.23.
.
(5.2.22)
(B-2r).s2
~Jb m~ (
s-···
1\
2,2 2,0 1,8
._ ....
I.....
0
1,6 1,4 1,2
3,0 2,8 2,6
B
b
=~ ~: --
MJ
2,4 1\
2,2
1\'
2,0
s
I
I
1 1 I
,'\I I,,,·
I,~
1,8 1,6
"
I'
1,4 1-1"--1-
== ~~$' 15'!~ Bib oc
'1.'/"0 0 .... I'Sro-
::;;: 2.00' ...... 1,50
,o~ to-
1,2
1'°0
]'°0
2
3
4
5
-~
0,04
0,08
0,12 rib
Figure 5.2.21 Stress concentration factors for flat bars with notches on both sides in bending in plane, after Peterson (Ref.: Goodier, G. H. Lee and Neuber), elastic analysis, (B - b) » s , r> O.
6 7 2rls
Figure 5.2.23 Stress concentration factors for broad flat bars with transverse hole in bending in plane, after Peterson (Ref.: Goodier and Reissner), elastic analysis, bending moment per unit of length m, in N. Nominal stress: Sb = 6 mb/ s2 .
(5.2.23)
185
5.2 Stress concentration factors
5 Appendices
5.2.2.6 Flat bars with narrow shoulder Stress concentration factors for flat bars with narrow shoulder in bending after Figure 5.2.24.
Figure 5.2.24 stress concentration factors for flat bars with narrow shoulder in bending, after Peterson (Ref.: Leven and Hartman), photoelastic study. B / b = 1,25; 2 and 3.
00\
3,0 2,8
...
Bib == 1,25
,
2,6
I / II
/ 1 / fI ' /
2,4 2,2
v-:
.., ..... ".
f/
1,8
v
1.,..00 foo-
w..
--
2,8
0,02=
...... l - 0,025 I - -O,~
.....
-
'/ "..
1/ I......
'10=
'~,zd,L
=
1+ (T<
~"t,zd
_
I)'
'
Kt,b,LlB
K
1,00
-I
_ -1'
3,0
O,03~
il 1/
2,2
/
2,0
0,15
1,6 I 1 v
/'
1,8
62-
05~
1,2
1,°
LIB 2,0
1'1 0,05'
. . . 9,°16
.....
9,0,g
-
-P'\= I I o 15
02=
.-
1,4
O'g:.M= " -1,0=
_-
f-- r-
l - I-"
6,080,1= I
./
,
,..-
/ /' r/ ......-
2,4
0,05 0,06
I
1,0
'I V »:
2,6
-d,04-
--':"[(f -bd4
vf"'"
B/b=3
2,8
,
"
I
05~
;;..--
o's:M.= , -1,0-
0
1,0
LIB 2,0
Stress concentration factors for flat bars with shoulder head and concentrated compression loads at the specified positions according to Figure 5.2.25.
(5.2.24)
t,b,LlB-2
stress concentration factor for the "narrow" shoulder and values L / Band B / b, T< Stress concentration factor for the "broad" '~,zd shoulder in tension and values b / B after Figure 5.2.13, T< Stress concentration factor for the "narrow" '~,b,UB shoulder and values L / B in bending after Figure 5.2.24 (diagram that is closest to the value BIb in question). K, b UB=2 stress concentration factor in bending for ,, L / B = 2 after Figure 5.2.24 (Diagram as before) T< '~,zd,L
--
l-
~I-
Stress concentration factors for flat bars with narrow shoulder in tension may be approximately computed from Eq. (5.2.24): T<
_f-
-
LIB 2,0
° "
~
0'8~ I
'/ . /
1,4 I....... 1,2
05~
,.......
V
1,6 " V~I--
',-
1,0
'I
1,8
02=
1,00
rlI
»:
fl
2,0
0,15~
V
I,
0,05~
0,06 -0,08 0,1,
./
II I /
2,2
I
I
'fT
_f- 025
././
111//
2,4
I .= f-O,O~_ I
Ii
.
rIb == 00~5-
Kt,b
OO~
'''-C::: p Bib == 2,...
2,6
.
v..... l-
1,4 V 1,2
3,0
I
1-:::f-O,015
-'" -
II. II .(/ V
2,0
1,6
.......
'
rIb ==
Kt,b
rib ==
Kt,b
Thickness s
.5.2.24
F/2
Kt,zd 6
5
\
4
3 2
---bThickness s
\
r-, r-, ~ h£:
0,05
I
r
3b I 3b bis 5b
~
.....
i!J.?
0,075 0,1 rl b=
5.2.~5
II
o
0,2
"'(
0,4
0,6
0,8
1,0
(b - r)
Figure 5.2.25 Stress concentration factors for flat bar with shoulder and concentrated compression loads at the specified positions, after Peterson (Ref.: Hetenyi), photoelastic study.
186
5.2 Stress concentration factors
5 Appendices
Stress concentration factors for flat bars with shoulder head and distributed compression loads at the specified line positions after Figure 5.2.26.
Figure 5.2.26 Stress concentration factors for flat bars with shoulder head and distributed compression loads at the specified line positions, after Peterson (Ref.: Hetenyi), photoelastic study. r / b = 0,05; 0,075; 0,1 and 0,2.
5.2.26
Thickness s
Kt,Zd
11 Kt,zd
10
13
I ~~' I I \'Q~ "r., A
12
~
~'''1, II
1/ /
10
VI),b?
/
1/
,/
/ ,/
9 8
7
_.......
I.....
/'
1/ L..-1/
_I'
5
1/
,
""
-
_fo-
r-::~
I
I I I
6
5
0,9°095 ';;;_~ fo- \ ,0F==-
4
--
-
-
\,51I·
V
"......
\)01)
./
./
\)§Y ./
V
......
v"..
".. V
./
./
1\).....,:'0;.. ..,::: 7"
"..
' - .-
-
\)r-~~-;; ".".
::; \),~() ~ :;;.
V
~~- o~~::::::\,1.)
I--
..... ......
"-
3
.
-- \.5
-
3,0
2,5
2,0
3,0
Bib Kt,zd
10
13
I
12
I
rib =0,075 V
~?~
10
\'Q"?
~/
9
./'
fo-
r---.
I'I"--.
4 3
.....
""
".
""
_, '" v
/'
V
V
/
V
7
v,/
6
.....
~;;.-'i:(~",,~ 11)
I)~'> ~
"'~~"" I)'b\)~~
-
",v """v' 9\) 9~
-
- - - .....
.....
--
-1)'7~ ".. \.0. k::;;:-
\;. 1--\,5",,13,0 -
I I 1,5
2,0
2,5
3,0 Bib
rl/~~oI2Jo ,
~\/~ bl) ~ /'
5
4
I
~
8
1/
~./
./
7 1/
r.," ~
I).
v
8
5
j
,/
11
6
9
1/
~
3,0
BIb
Kt,zd
-'
2
I ! I r
2,5
.>
~\)~ "V I),,>" ./ . / ......
-~-
2,0
"
.' \"~ 1-» "" 1/
~
1,2=-
4 I- r I b = 0,050 I I I I
3 1,5
_
~'f,5l::::::1-~
:-'
I-
I
7
o~O ~
1/
I-I-
8
"..-
O~i-"""
V
I'- I--
L..--~
./
I
9 V
,
""'"
v
........11) 0,
~
~
6
""
()~I)
./
11
""
I-~ Ib = 0,100' I
./
,/
./
/./
./
/'./V
/-
e~;...:::::'--
3
I), I)b'>
"\)~\)'" 'b0
./~\)' 0
S__~~ I' __ :c- :-::;"':~~\i'
-.. . ,; ; ~:'S, 3,0
2
I J I I 2,0
I
I 2,5
3,0 Bib
187
5.3 Fatigue notch factors
5.3 Fatigue notch factors
1R53 EN.dog
Content
Page
5.3.0
General
5.3.1
Fatigue notch factors derived from stress concentration factors
5.3.2
Fatigue notch factors for bars with cone- or wedge-shaped portion or with longitudinal hole General Round bars with cone-shaped portion Flat bars with wedge-shaped portion Round bars with longitudinal hole
5.3.2.0 5.3.2.1 5.3.2.2 5.3.2.3 5.3.3 5.3.3.0 5.3.3. 1 5.3.3.2 5.3.3.3 5.3.3.4 5.3.3.5 5.3.3.6
Experimentally determined fatigue notch factors General Round bars with groove for a snap ring Round bars with V-groove Round bars with tranverse hole 191 Shafts with keyway Shafts with press-fitted members Shafts with splines
187
5 Appendices
5.3.1 Fatigue notch factors derived from stress concentration factors For structural details for which stress concentration factors are given in Chapter 5.2 - for example round bars or flat bars - the fatigue notch factors, Kf,zd(d) , ..., are to be computed from the stress concentration factors, Kt,zd , ..., using the Kt-Kf ratios, ncr(r), according to Chapter 2.3.2.1.
Nominal stresses 189
190
193
5.3.4
Fatigue notch factors for components from cast iron materials and from aluminum alloys
5.3.5
Fatigue notch factors determined by the user
The nominal stresses for tension, for bending and for torsion are the same as for the stress concentration factors, Chapter 5.2, Eq. (5.2.1) for round bars or Eq. (5.2.11) for flat bars *2.
5.3.2 Fatigue notch factors for bars with cone- or wedge-shaped portion or with longitudinal hole 5.3.2.0 General
For round bars and for flat bars with cone- or wedgeshaped portion or with longitudinal hole the fatigue notch factors are to be determined as follows.
194 5.3.2.1 Round bars with cone-shaped portion
5.3.0 General The fatigue notch factors are applicable to round bars and to flat bars. Concerning their determination the following cases are to be distinguished: - Round bars and flat bars, for which stress concentration factors are given in Chapter 5.2, - Round bars and flat bars with cone-shaped or wedgeshaped portion as well as round bars with a longitudinal hole, Chapter 5.3.2, - Round bars for which experimentally determined fatigue notch factors are available, Chapter 5.3.3, - Components from cast iron materials and from aluminum alloys, Chapter 5.3.4, Components with fatigue notch factors determined by the user, Chapter 5.3.5.
For round bars with cone-shaped portion, Figure 5.3.1, the fatigue notch factors for tension, for bending and for torsion are to be computed in two steps: 1. Step: Computing the fatigue notch factor for the round bar with shoulder fillet, Kf,zd , ..., from the stress concentration factor, Kt,zd , ..., and the Ki-K, ratio, llcr(r), ..., according to Chapter 2.3.2.1: Kf,zd = Kt,zd / ncr(r), ... ,
(5.3.1)
2. Step: Determining the fatigue notch factor for the round bar with cone-shaped portion, Kf,zd,Ol , ..., from that of the round bar with shoulder fillet, Kf,zd , ..., modified according to the slope angle co, Figure 5.3.2.
Fatigue notch factors are applicable in combination with nominal stresses *1. Figure 5.3.1 Round bar with cone-shaped portion. Slope angle ro and length I of slope. 1 The nominal stress may be defined in a different way, see Eq. (5.3.2) for round bars, Eq. (5.3.5) for round bars with a longitudinal hole or Eq. (5.3.15) for round bars with tranverse hole.
188
5.3 Fatigue notch factors 4,0
Kr,c.o
3,8 3,6 3,4 3,2 3,0 2,8
I
_.- - . 1 m.,----::
r
..... Mb
),<\' Mt
Cll
Nominal stresses
= 90"
~ ~
50'
45'
40'
55'
r
35' 30'
fit'
The nominal stresses for tension (load F), for bending (bending moment M, ) and for torsion (torsion moment M t ) are '2 4 F I 1td2 ,
25'
:-Ii
2,4
I
(5.3.2)
32 Mbl 1td3 , 16 Mtl 1td3 .
20'
2,6 2,2
5 Appendices
The diameter d is shown in the respective figures. 15'
I
2,0
,
1,8
10'
I
1,6
r
5'
1,4
J,2 1,0 0' 1,0 1,2 1,4 1,6 1,8 2,0 2,2 2,42,6 2,8 3,03,2 3,4 3,63,84,0
Kr Figure 5.3.2 Influence of the slope angle co on the fatigue notch factor of a round bar with cone-shaped portion.
Ktto
Kr,w
Fatigue notch factor of the bar with shoulder, Slope angle, Fatigue notch factor of the bar with cone-shaped portion.
The initial diagram - after Peterson (Ref: Leven and Frocht), photoelastic study - applies to the stress concentration factor for bending of flat bars with a notch on one-side. It is applied here as an approximation for the fatigue notch factor of round and flat bars with different shape of the notch and for all types of stress.
Example For a round bar with cone-shaped portion, Figure 5.3.1, the fatigue notch factor is to be determined for bending. Dimensions d = 42 mm, D = 50 mm, t = (D - d) I 2 = 4 mm, r = 1 mm, co = 15 0, 1 = 14,9 mm, Rm = 583 MPa.
1. Step: Computation of the fatigue notch factor for the round bar with shoulder fillet: Kt,b
Figure 5.2.5 Tab. 2.3.3 Eq. (2.3.15) Eq. (2.3.17) Eq. (2.3.13) Eq. (2.3.10)
= 2,47,
G cr (r) = 2,53 mrrr", llcr(r) = 1,24, G cr (d) = 2 I d = 0,048 mnr", ncr(d) = 1,03, Kf,b = Kt,b I (llcr(r) . llcr(d» = 2,47 I (1,24 . 1,03) = 1,9.
2. Step: Determining the fatigue notch factor for the round bar with cone-shaped portion from the value Kf,b = 1,9 and co = 15°: Figure
Kf, b,e = 1,6.
Special case For round bars with shoulder fillet and with two different notch radii ro ;::: t and r ;::: t I 4, Figure 5.3.3 (top), the fatigue notch factors are the same as for round bars with cone-shaped portion where r = 2 t and co = 30 0, Figure 5.3.3 (bottom).
5.3.2
Note: The stress concentration factor for the round bar with cone-shaped portion that follows from Kt,b = 2,47 and co = 15 0, Figure 5.3.2
Kt,b,w = 1,82,
must not be applied because of the following inequality, Figure 5.3.4: Kf,b,w;t: Kt,b,w I ( llcr(r)' llcr(d) ). 1,6;t: 1,82 I (1,24' 1,03) = 1,4.
(5.3.3)
Kt,b o------~Kt,b,C'O I
X' Cll =
Figure 5.3.3 Round bar with shoulder fillet, special case with two notch radii (top) and equivalent round bar with cone-shaped portion (bottom).
90'
I
Kr,b ' « - - - - - - - ) ' Kr,b,c.o
Kf,b,w'
Stress concentration factors for shear are not available. Therefore no formula for the nominal shear stress is contained in Eq. (5.2.1) or (5.3.2).
ICll I
I
Figure 5.3.4 Relationship between
2 In the following tension or compression or tension-compression are mentioned as tension throughout.
I
Kt,b , Kf,b , Kt,b,w
and
189
5.3 Fatigue notch factors 5.3.2.2 Flat bars with wedge-shaped portion
5 Appendices Nominal stress
For flat bars with wedge-shaped portion, Figure 5.3.5, the fatigue notch factors for tension-compression and for bending are to be determined analytically as for the round bar with cone-shaped portion, Chapter 5.3.2.1.
The nominal stress for torsion (torsion moment M, ) is to be calculated according to Eq. (5.3.5): T -
16M t
(5.3.5) 4 4 x-d '(l-d L /d ) The diameters d and d L are shown in Figure 5.3.6. t-
3
5.3.3 Experimentally determined fatigue notch factors 5.3.3.0 General
5.3.$
Figure 5.3.5 Flat bar with wedge-shaped portion. Slope angle ro , length of slope I. , plate thickness s .
The following experimentally determined fatigue notch factors for tension, for bending and for torsion apply to round bars of rolled steel with tensile strength values from Rm = 400 to 1250 MFa *2.
Nominal stress
Concerning the consideration of the surface roughness see Chapter 2.3.3, Eq. (2.3.27).
The nominal stresses for tension (load F) and for bending (bending moment M, ) are to be computed according to Eq. (5.5.4): *2:
Distinctive values of the radius and of the diameter and conversion of the fatigue notch factor
Szd = F / (s .. b), Sb =6Mb/(S. ·b2
(5.5.4) ).
Thickness s and width b are shown in Figure 5.3.5.
5.3.2.3 Round bars with longitudinal hole Longitudinal holes, Figure 5.3.6, are possible for round bars with groove, with shoulder fillet or with coneshaped portion.
~. m_--i_~ __--±_-t --d - ~~\ . ____________ D---
~--
Mt
Figure 5.3.6 Round bar with longitudinal hole. Fatigue notch factors of round bars with longitudinal hole in tension or in bending are not available, nor a reliable way of computation based on fatigue notch factors of round bars without longitudinal hole. In the case of torsion, however, fatigue notch factors of a round bar with a longitudinal hole may approximately be derived from the fatigue notch factors of the round bar without a longitudinal hole in combination with the nominal stress for the round bar with longitudinal hole.
Normally an experimentally determined fatigue notch factor Kf(dp) refers to a notched test bar (with radius I'p, diameter dp ) and not to the component in question (with radius r, diameter d). Therefore the experimentally determined fatigue notch factor is to be converted according to Chapter 2.3.2.2, Eq. (2.3.18) in order to apply to the different radius r and diameter d of the component in question *3. For that the Ki-K, ratios ncr(rp), ncr(r), ncr(d) and nirp), n1;(r), n1;(d) for the distinctive values rp , rand d have to be known. Because of the similarity of bar and component there is r / rp = d / dp,
(5.3.6)
r, rp Notch radii ofthe component and of the test bar, d, dp Diameters of the component and of the test bar. From three known values the missing fourth value may be computed. In the following the distinctive values rp and dp are indicated if they may not be obvious. Example For a shaft with keyway - component diameter d = 100 mm - the fatigue notch factor for torsion is to be determined The experimentally determined fatigue notch factor Kf,t
3 For consideration of the size effect and for particulars of the method of calculation see footnote 12 on page 53.
190
5.3 Fatigue notch factors
5 Appendices
The distinctive values for Figure 5.3.10 are rp = 0,18 mm, dp = 15 mm. With d = 100 mm the radius r is, Eq. (5.3.6),
r = rp . d I dp = 0,18 mm 100 115 = 1,2 mm. (5.3.7) Then the conversion from the fatigue notch factor of the test bar, Kf,t(dp), to the fatigue notch factor of the component in question, Kf,t = Kf,t(d), is possible with the Ki-K, ratios n~(rp), ..., according to Chapter 2.3.2.2, Eq. (2.3.18), as follows: K
f,t
=K
f,t
(d)'
p
n~ (rp) n~(r).n~(d)·
Figure 5.3.7 Round bar with groove for a snap ring.
5.3.3.2 Round bars with V-groove (5.3.8)
In the special case, if the distinctive values of the component and of the test bar are identical, d = dp, r = rp, then
The fatigue notch factors, Kf,zd(dp), ..., for round bars with V-groove for tension-compression and for bending are to be read off Figure 5.3.8 or computed according to the following equations: Kf,zd(dp) = 1,06 + 0,0011 . Rm I MFa, Kf,b(dp) = 0,97 + 0,00095' Rm I MFa.
(5.3.9)
(5.3.12)
For torsion there is
Nominal stresses Normally the nominal stresses for tension (load F), for bending (bending moment Mg) and for torsion (torsion moment Mt ) are to be computed with the diameters dp or d according to the equations (5.3.10); the diameter dp is given with the figures:
Kf,t(dp) = 1 + 0,60' (Kf,b(dp) - 1). Distinctive values: rp dp = 15 mm, d = given.
=
(5.3.13)
0,1 mm, rafter Eq. (5.3.6),
Nominal stresses: See Eq. (5.3.10).
(5.3.10)
Szd Sb T,
= 4 = =
F I nd p 2
32 Mb I nd p 3 16 M, I nd p3
or or or
Szd = 4 F I nd 2 , Sb = 32 Mbl nd 3 , Tt = 16 Mtl 1td3 .
Otherwise the equations for computing the nominal stresses are given with the figures *4. Kr~(df)
2,4 2,2 . K f,b (dp) 20
5.3.3.1 Round bars with groove for a snap ring
, 1,8
The fatigue notch factors Kf,zd(dp), ... of a round bar with groove for a snap ring, Figure 5.3.7, for tensioncompression, for bending and for torsion are "S
=
Distinctive values given by design: rp = r, dp = d. *6.
,,1 r Y'
LA
I
LA"
Bending
,
1,4
1,2 I,D 400
0,9' (1,14 + 1,08 ·J(D-d)/2rf),
Kf,t(dp) = 1,48 + 0,45 ·J(D-d)/2rf , (5.3.11) rf = r + 2,9 p* , p* = 0,3 mm for austenitic steel, p* = 0,1 mm for other kinds of steel, Rm:s; 500 MFa, p* = 0,05 mm for other kind of steel, Rm>500 MFa, p* = 0,4 mm for cast steel and for GGG.
I I
Tension
1,6
Kf,zd(d p) = 0,9' (1,27 + 1,17 ·J(D-d)/2rf), Kf,b(dp)
I
5.3.1
'I
600
r
800 1000 1200 RmiriMPa
Figure 5.3.8 Fatigue notch factors for round bars with V-notch for tension-compression and for bending, after Tauscher. Test bar: notch radius rp = 0,1 mm, diameter dp = 15 mm, t / d = (D - d) / 2d = 0,05 to0,20. For both smaller and larger values t / d the fatigue notch factors are smaller.
Nominal stresses: See Eq. (5.3.10). If values Kf,zd(dp), Kf,b(dp) > 4 or Kf,t(dp) > 2,5 are obtained from Eq. (5.3.11) then the values Kf,zd(dp), Kf,b(dp) = 4 or Kf,t(dp) = 2,5 are to be used instead. 5FollowingDIN 743 (2000). These fatigue notch factors are valid here for the component (rp = r, dp = d). Nevertheless the conversion described by the example in Chapter 5.3.3.0 is necessary.
6
4
See footnote 1.
191
5.3 Fatigue notch factors 5.3.3.3 Round bars with tranverse hole
The fatigue notch factors, Kf,zd(dp), ..., for a round bars with transverse hole for tension-compression, for bending and for torsion are to be read off Figure 5.3.9 or computed according to the following equations: Kf,zd(dp) = Kf,b(dp) = Kf,t(dp) = 1,54 + 0,0004 . Rm 1MFa.
(5.3.14)
Distinctive values: d and r = dq /2 given, dP = 15 mm, rp according to Eq. (5.3.6). Nominal stresses: (5.3.15) Szd
s, Tt
F n·d
4F
2/4-2rd
n.d
Mb n·d 3 132-rd 2 13
2(1-4.d
Q I(nd)) , 32M b
3
n· d (1-16d Q 1(3nd)) ,
Mt
16M t
3
2
n·d 116-rd 13
E)··9:· ~
i ...;-----+--r-- d
M.'.·..l... . Mo.. ....
I...,-..,.....,....,.....,..,-...+-+--~--'
(JQ
Kf;td (dp ) 2 4
Kf,b(d p ) Kr,t (d, )
Teli~i~nm
r
2~
2~O 1,8 1,6 1,4
..
F=
Distinctive values: rp = 0,18 mm, dp = 15 mm, d = given, r according to Eq. (5.3.6). Nominal stresses: See Eq. (5.3.10).
t-'r5-~M~9 f'-{~H~M~9 Kr.b (dp) 2,6 Kf,t (dp )
r 2,4 2,2 Detail B 2,0 1,8 1,6
lA
i/' :
0"
,,\o~<'''I~
?>e~M\1
K
Detail A I I 1
1,2
1,~OO
iOe.,,&~~r t;;;
,.1 'c... . ' / " I ' Y /
600
I
800 1000 1200
'Rm in MPa Figure 5.3.10 Fatigue notch factors of shafts with sledrunner or profiled keyway, structural detail A or B, for bending and for torsion, after Haenchen. Test bar: notch radius rp = 0,18 mm (Radius atthe basis of the keyway), diameter dp= 15 mm..
, J I
,
'-1
I. l
1,2 f
1,200
Bendmg .:
T ' - 'po 'tersion
5 Appendices
5.3.3.5 Shafts with press-fitted members
"
600800 1000· 1200·
Rm ioWa
Figure 5.3.9 Fatigue notch factors for round bars with transverse hole for tension-compression, for bending and for torsion, after Tauscher (Ref.: Hempel). Test bar: notch radius rp = do,p / 2 (dQ,p diameter ofthe transverse hole ofthe test bar), diameter dp = 15 rom, 2 r / d = 0,15 to 0,25. For both smaller and larger values 2 r / d the fatigue notch factors are smaller.
5.3.3.4 Shafts with keyway
The fatigue notch factors, Kf,b(dp), ..., for shafts with keyway for bending and for torsion are to be read off Figure 5.3.10. The values for bending also apply for tension-compression. Structural details A and B (sled-runner or profiled keyway) are to be distinguished. The fatigue notch factors apply to the end of the keyway. If two keyways are arranged in the same section of a shaft, Kf,b(dp) is to be increased by a factor of 1,15.
The fatigue notch factors for shafts with press-fitted (or shrink-fitted) member are to be determined from Table 5.3.1 orfrom Figure 5.3.11.
Fatigue notch factors from Table 5.3.1 The fatigue notch factors for shafts with press-fitted member for bending, Kf,b(dp), are to be determined from Table 5.3.1. The structural details no. 2, no. 3 and no. 4 are to be distinguished. The fatigue notch factor for tension-compression, Kf,zd(dp), is approximately the same as for bending. The fatigue notch factor for torsion is Kf,t(dp) = 1 + 0,45' (Kf,b(dp) - 1).
(5.3.16)
The fatigue notch factors apply to the section of the shaft where the press-fitted member ends. Distinctive values: dp = 40 mm, rp from Eq. (5.3.6), r = 0,06' d, d = given. Nominal stresses: See Eq. (5.3.10).
192
5.3 Fatigue notch factors Table 5.3.1 Fatigue notch factors, Kf,b(dp), of shafts with press-fitted member for bending, after Tauscher (Ref.: Lehr). Test bar: notch radius rp = 0,06 . dp , diameter dp = 40 mm. The bending moment is transmitted via the fitted member. The same fatigue notch factors are valid for fits with closer seat.
5 Appendices Fatigue notch factors after Figure 5.3.11 The fatigue notch factors for shafts with press-fitted member for bending are *6 Kf,b(dp)
=
,
"
Kf,b,O(d)' C;; . C;; ,
(5.3.17)
Kf,b,O(d), C;;' and C;;' , from Figure 5.3.11. 1200
The fatigue notch factor for tension-compression, Kf,zd(d), is approximately the same as for bending. The fatigue notch factor for torsion is Kf,t(dp) = 1 + 0,45' (Kf,b(d) - 1).
3,2 No.2 H8 / u8 interference fit.
For the fatigue notch factor after Figure 5.3.11 it is to be determined in addition, whether the loading is transmitted via the press-fitted member or not. The fatigue notch factors apply to the shaft where the pressfitted member ends. Distinctive values: rp = given, dp = d given. Nominal stresses: See Eq. (5.3.10).
2,9
NO.3 H8 / u8 interference fit.
1,5
(5.3.18)
Comment concerning Figure 5.3.11: The fatigue notch factors are higher than those from Table 5.3.1. The shown dependence on the pressure p and the distinction, whether the bending moment is transmitted via the press-fitted member or not, may be useful; however.
2,3
NO.4 H7 / n6 interference fit. KC,b.1) I--+-.......J.-I-H.
2,6
1-~~~~=+--4b}without 1--.....+--+-+
III
2 I';;~-i-'-""+'. bending moment transmitted by the press-fitted member
30
d In mm
~' ~H
2,0
Note to No.1: The given fatigue notch factors are approximate values dependent on design. For plain rotating bending they may be 1,3 times higher. Note to No.4: The fatigue notch factor is to be calculated for both the press fit and for the shaft with shoulder fillet, Chapter 5.3.1. The less favorable case is relevant. Increasing the difference of the diameters d, and d is of little influence on the fatigue notch factors of the press-fit, but if the diameter d, differs only a little from diameter d an unfavorable interaction may occur (see No.2 for d j = d).
1,8
./v
1,6 1,4 1,2
"
(J,9
V ./ ./
1,00/ 500 700
1,0 0,8
!
Q;7
V
V
v
-\.)
..
/
900 1100 0,60
Bmin MPa
./
..
100 200 300 pressure p in Mfa
Figure 5.3.11 Fatigue notch factors of shafts with pressfitted member for bending, after Kogaev (Ref.: several authors).
193
5.3 Fatigue notch factors 5.3.3.6 Shafts with splines The fatigue notch factors of a splined or serrated shafts for torsion are to be determined for the nominal stress computed with the innermost diameter either from Figure 5.3.12 or according to the following equation: Kf,t
=
expl4,2.10-7
.(R m /MPa)2 j.
(5.3.19)
5 Appendices Comment: In this case the definition of the fatigue notch factor is that ofEq. (5.3.28), and the surface treatment factor, is KV,RSV = 1. (5.3.24) The fatigue notch factors apply to the section at the transition from the splined part into the plain part of the shaft; the shaft diameter must be smaller than (d- 0,5 mm)! Distinctive values: rp = 0,6 mrn (structural detail A and C) and rp = 0,25 mm (detail B), rafter Eq. (5.3.6), dp = 29 mm, d given. Nominal stress: after Eq. (5.3.10) with the innermost diameter d.
A,
~r d
Detail
Kt;t{d p)
5.3.4 Fatigue notch factors for components from cast iron or aluminum materials
2,2
The fore-mentioned experimentally determined fatigue notch factors apply to notched test bars of steel. The fatigue notch factors of components from cast iron or aluminum materials are different because the Kj-K, ratios are material-dependent. For example for components from cast iron materials the fatigue notch factors are less than for steel, since the Kj-K; ratios are higher.
2,0
v
1,8 1,6
'/
1,4
V
1,2
t-- J....1,°400 600
V
V 1000
800
1200
Rm inMPa
5.3.12
Figure 5.3.12 Fatigue notch factors of splined or serrated shafts for torsion, after Meisel, Schuster, Contag, Koch.
If fatigue notch factors are not available for notched test bars from cast iron or aluminum materials, they can approximately be computed according to the following equations for tension-compression, for bending and for torsion: K
Test bar: notch radius rp = 0,6 mm (structural detail A and C) or rp = 0,25 mm (detail B), innermost diameter: dp = 29 mm. The torsion momentum is transmitted via the hub.
The fatigue notch factors for bending are to be computed for splined shafts after Eq. (5.3.20) and for serrated shafts after Eq. (5.3.21): Kf,b(dp) Kf,b(dp)
= I + 0,45 . (Kf,t(dp) - 1), = I + 0,65 . (Kf,t(dp) - 1).
(5.3.20) (5.3.21)
For tension-compression approximately the same values apply as for bending. For serrated shafts with involute profile the lower fatigue notch factors are valid for all types of stress: Kf,Ev (dp)
=
I + 0,75 . (Kf(dp) - 1).
For case-hardened splined or serrated shafts there is Kf,RSV (dp) = 1.
(5.3.23)
(d) f,b,GA P
=
K
(d) f,t,GA p
n't,St (rp) = Kf,t,St (d) P . () ,
Kf,zd,St(dp), ... I1cr,St(rp), ... ncr,GA(rp), ...
rp dp
K
ncr,St (rp ) ( )' ncr,GA Ip
K
Kf,zd,GA(dp),...
(5.3.22)
The value Kt
(d ) - K (d i f,zd,GA P - f,zd,St P
(5.3.25)
(d) ncr,St (rp ) f,b,St P . () , ncr,GA rp
n't,GA rp
Fatigue notch factor of the test bar from cast iron or aluminum material, Fatigue notch factor of the test bar from steel Kt-Kr ratio of the test bar of steel according to rp , KcK r ratio of the test bar from cast iron or aluminum material according to rp , Notch radius of the test bar, Diameter of the test bar.
The Kt-Kf ratios ncr(rp), ... are to be computed according to the type of stress and according to the related stress gradient G cr (rp ), ... , Chapter 2.3.2.1 and Eq. (2.3.13) to (2.3.15).
194
5.3 Fatigue notch factors If values Kf,zd,GA(dp ), ... < 1 are obtained from Eq. (5.3.25) then the values to be used are Kf,zd,GA (dp ), ... = 1.
(5.3.26)
According to Chapter 5.3.3.0 the so-derived experimentally based fatigue notch factors for bars of cast iron or aluminum materials, Kf,zd,GA (dp) ..., are to be converted according to Chapter 2.3.2.2, Eq. (2.3.18), by taking into account the KcK r ratios ncr,GA(rp ), ncr,GA(r), ncr,GA(d) or n"GA(rp), n"GA(r), n"GA(d) '7.
5 Appendices Distinctive values: rp, r, dp, d in accordance with Eq. (5.3.6). According to Chapter 5.3.3.0 the so-defined fatigue notch factors for bars, Kf,RSy(dp) , ..., are to be converted, see Chapter 2.3.2.2 and Eq. (2.3.18), by taking into account the Kt-Kr ratios ncr,GA(rp), ncr,GA(r), ncr,GA(d) or n"GA(rp), n"GA(r), n"GA(d) for the kind of material considered.
5.3.5 Fatigue notch factors determined by the user Generally fatigue notch factors that have been determined by the user for a particular type of stress are valid under the following conditions - here only for test bars from steel : The fatigue notch factor is valid for a nominal stress to be specified '8. It is valid for the test bar with the notch radius rp and the diameter dp, and it is defined as follows '9 (5.3.27) K{(d p) = W. unnotched specimen, no surface treatment W. notched specimen, no surface treatment Nominator and denominator are to be determined for the same diameter dp and for the same type of stress. A surface treatment is not to be considered, as the surface treatment factor KV according to Chapter 2.3.4 is to be applied additionally. The roughness R, is experimentally considered, so that the roughness factor KR according to Chapter 2.3.3 is not to be applied (KR = 1).
Surface treatment Fatigue notch factors in case of an existmg surface treatment are valid under the following conditions: The definition of the fatigue notch factor is *9 (5.3.28) Kf,RSV(dp) = = W. unnotched specimen, no surface treatment W. notched specimen, with surface treatment' Nominator and denominator are to be determined for the same diameter dp and for the same type of stress. The surface treatment factor, Ky , according to Chapter 2.3.4 is not to be applied, that is KY,RSY= 1.
(5.3.29)
7 The conversion according to Eq. (5.3.25) refers to an exchange of the kind of material, while the conversion according to Eq. ( 2.3.18) allows for the size effect and the requirements of the assessment procedure, see footnote 12 on page 53 . 8 In general there are various possibilities of defining the nominal stress - as for instance for a round bar with tranverse hole - so that the corresponding fatigue notch factor may be different, too. 9 W. = alternating fatigue strength.
195 5.4 Component classes for welded components of structural steel and of aluminum alloys
5.4 Fatigue classes (FAT) for welded components of structural steel and of aluminum alloys IR54 EN.dog Contents
Page
5.4.0 General 195 5.4.1 Fatigue classes for an assessment with nominal stresses 195 / 197 5.4.2 Fatigue classes for an assessment with structural stresses 195 /208 5.4.3 Fatigue classes for an assessment with effective notch stresses 196
5.4.0 General This chapter contains the fatigue classes (FAT) of welded components of structural steel and of aluminum alloys. To a major part the classes were derived with reference to the IIW-Recommendations /9/ *1 *2. The fatigue classes of the structural details are different for an assessment using nominal stresses, Chapter 2.3.1.2, and for an assessment using structural stresses or effective notch stresses, respectively, Chapter 4.3.1.2 *3.
5 appendices
5.4.1 Fatigue classes for an assessment with nominal stresses Fatigue classes for an assessment using'nominal stresses are given in Table 5.4.1 (nominal normal stress, page 197) and in Table 5.4.2 (nominal shear stress, page 207) *4.
5.4.2 Fatigue classes for an assessment with structural stresses Fatigue classes for an assessment using structural stresses are given in Table 5.4.3 (structural normal stress, page 208) *5. For the structural details in Table 5.4.3 (all were taken from Table 5.4.1) the following comments apply: - Structural stresses are to be applied for an assessment of the stress at the toe of a weld only, but not of the stress at the root of a weld *6. - There are no details for longitudinally loaded weld seams, as structural stresses do not apply for welded sections *7. - Butt welds loaded transverse, details no. 200, are full penetration butt welds. - Fillet welds, details no. 300, may be load-carrying or non-load-carrying ·8.
1 Kinds of material according to the IIW-Recommendations are ferriticperlitic or quenched and tempered structural steels, or aluminum alloys 5000, 6000, 7000. For other kinds of material (conditionally weldable steel, stainless steel, weldable cast iron materials, or other weldable aluminum alloys) the fatigue classes are provisional and therefore they are to be applied with caution. 2 Fatigue classes different from the IIW-Recommendations: The fatigue classes for the base material and normal stress - FAT 160 (structural steel) or FAT 70 (aluminum alloys 5000, 6000) or FAT 80 (aluminum alloys 7000) - are not contained in Table 5.4.1 since the assessment for the base material is to be carried out as for non-welded components. The fatigue classes for the base material and shear stress - FAT 100 (structural steel) or FAT 36 (aluminum alloys) - are included in Table 5.4.2, as they are valid also for full penetration butt welds. For an assessment of welds in structural steel on the basis of the effective notch stress the fatigue class FAT 225 for normal stress is complemented by the fatigue class FAT 145 for shear stress. Both values were determined experimentally /19,20/. The corresponding fatigue classes for aluminum alloys are FAT 81 and FAT 52. They are derived by a factor 0,36 from the equivalent fatigue classes for structural steel; therefore these fatigue classes are provisional and are to be applied with caution. 3 Concerning the definition of the stresses see Figure 0.0.6 and 0.0.7 on page 15. 4 For structural steel see Table 3.2.1 and 3.2.2 and for aluminum alloys see Table 3.2.3 and 3.2.4 of the IIW-Recommendations. The component classes for nominal stress allow for the influences of the component form, of the shape of the weld seam and of the weld seam itself, see Table 5.5.1 on page 210.
- For cruciform joints or T-joints, details no. 400, a minor misalignment does not need to be considered when determining structural stresses *9.
5 For structural steel the fatigue classes for structural stresses were taken from Tab 3.3.1 of the IIW-Recommendations. The fatigue classes for aluminum alloys were supplementary ones, derived by a factor 0,36 from those for structural steel. Therefore they are provisional and are to be applied with caution. Values for shear stress in weld seams are not necessary, see footnote 7. The fatigue classes for structural stresses allow for the influences of the shape of the weld seam and of the weld seam itself, but not for the influence of the component form, since-this is considered in evaluating the structural stresses, see Table 5.5.1 on page 212. Example: "Transition in thickness and width", detail no. 221 of Table 5.4.1 when using nominal stresses, but detail 211 of Table 5.4.3 when using structural stresses. 6 The stresses at the root of a weld are to be assessed using nominal stresses or effectivenotch stresses. Example: "Cruciform joint", Detail no. 414 of Table 5.4.1.
7 The stress (normal stress or shear stress) along the weld seam is to be regarded as constant here so that the structural stress is equal to the nominal stress and therefore the fatigue classes for nominal stress apply. Examples: - "Longitudinal load carrying butt weld", detail no. 312 of Table 5.4.1 (direct stress). - "Full penetration butt weld", Detail no. 1 of Table 5.4.2 (shear stress).
196
5.4 Component classes for welded components of structural steel and of aluminum alloys
5.4.3 Fatigue classes for an assessment with effective notch stresses Fatigue classes for an assessment using effective notch stresses do not need to be specified by structural details, because for an assessment according to Chapter 4.3.1.2, Eq. (4.3.8) and (4.3.9), structural particularities are accounted for when determining effective notch stresses *10.
8 Examples, for which the fatigue classes of detail no. 300 of Table 5.4.3 are applicable: - "Transverse non-load-carrying attachment", detail no. 511 of Table 5.4.1: externally and internally non-loaded fillet weld. Structural stress and nominal stress are identical. - "Longitudinal flat side gusset welded at the edge of a flange", detail no. 525 of Table 5.4.1: externally non-loaded, but internally loaded fillet weld. The assessment is to be carried out with the structural stress at the end of the gusset welded. Structural and nominal stress are different. - "Cruciform joint", detail no. 411 of Table 5.4.1: externally and internally loaded fillet welds. The assessment is in general to be carried out with the structural stress observing the misalignment. Structural and nominal stress are different if the misalignment is large, but they are about the same if the misalignment is small. Some smaller misalignment is already allowed for by the fatigue class of detail 411. 9 Because some smaller misalignment is already allowed for by the fatigue class. 10 The fatigue classes for effective notch stresses - FAT 225 for normal stress and FAT 145 for shear stress (structural steel) and FAT 81 for normal stress and FAT 52 for shear stress (aluminum alloys) - allow for the influence of the weld seam, but not for the influence of the component form and of the shape of the weld seam, since these are considered in evaluating the effective notch stress, see Table 5.5.1 on page 210.
5 appendices
197 5.4 Fatigue classes (FAT) for welded components of steel and of aluminum alloys
5 Apendices
Table 5.4.1 Fatigue classes (FAT) for structural details in steel and aluminum alloys (nominal normal stress),after Hobbacher /9/ No. 100 121
Strctural detail
Description
FAT Steel
AI
140
-
FAT
Thermally cut edges .?'
/~ 1~1I11111. ,
I /'
Machine gas cut or sheared material with no drag lines, comers removed, no cracks by inspection, no visible imperfections
.?'
122
!,/~ /' 1~1I111/.
Machine thermally cut edges, comers removed, no cracks 125 by inspection
40
Manually thermally cut edges, free from cracks and severe notches
100
-
Manually thermally cut edges, uncontrolled, no notch deeper than .5 mm
80
-
.?'
123
Ll I,/~ /' IUIIlI11
124
.?'
/~ IIIII.! ,
I /'
IU
200
Butt welds, transverse loaded
211
.-~~-
Transverse loaded butt weld (X-groove or V-groove) ground flush to plate, 100% NDT* I.
125
50
212
-~-
Transverse butt weld made in shop in flat position, toe angle ~ 30°, NDT
100
40
213
-~~-
Transverse butt weld not satisfying conditions of 212, NDT
80
32
214
-~~-
Transverse butt weld, welded on ceramic backing, root crack
80
-
215
-~-
Transverse butt weld on permanent backing bar
71
25
71 45
28 18
45
-
216
217
~ --r%%'~~%~~~/1/// {II . .' II"
Transverse butt welds welded from one side without backing bar, full penetration root controlled by NDT noNDT Transverse partial penetration butt weld, analysis based on stress in weld throat sectional area, weld overfill not to be taken into account. The detail is not recommended for fatigue loaded members.It is recommended to verify by fracture mechanics (3.8.5.2)!
1 NDT = Non-destructive testing
198 5 Apendices
5.4 Fatigue classes (FAT) for welded components of steel and of aluminum alloys
Ta bl e 5.4.1 Fatizue classes (FAT) for structural details in steel and aluminum allovs (nominal normal stress), cont'd. No.
Strctural detail
200
Butt welds transverse loaded
221
Description
~
40 32 25
~
Transverse butt weld made in shop, welded in flat position, weld profile controlled, NDT, with transition in thickness and width: *2 slope 1:5 slope 1:3 slope 1:2
100 90 80
32 28 25
80 63
25 22 20
Transverse butt weld, different thicknesses without transition, centres aligned. In cases, where weld profile is equivalent to a moderate slope transition, see no. 222.
71
22
Three plate connection, root crack·
71
22
Transverse butt weld flange splice in built-up section welded prior to the assembly, ground flush, with radius transition, NDT
112
45
Transverse butt weld splice in rolled section or bar besides flats, ground flush, NDT
80
-
71 45
-
~.~.
slope
-.........
~~ 223
-+
.
~,-
J
-ECJ sJope
--l"
C=
-J~ I
224
-~-
225
-~-
226
FAT AI
Transverse butt weld ground flush, NDT, with transition in thickness and width *2 125 slope 1:5 100 slope 1:3 80 slope 1:2
slope
222
FAT Steel
,,~
~
~~, ~b~l
I,,> b)
231
!u$
232
t~l -JO ~
Transverse butt weld, NDT, with transition on thickness and width*2; slope 1:5 slope 1:3 slope 1:2
Transverse butt weld splice in circular hollow section, welded from one side, full penetration, root inspected by NDT noNDT
2 Some smaller misalignement is already allowed for by the fatigue class
71
-
199 5.4 Fatigue classes (FAT) for welded components of steel and of aluminum alloys
5 Apendices
Table 5.4.1 Fatigue classes (F AT) for structural details in steel and aluminum alloys (nominal normal stress), cont'd. No.
Strctural detail
200
Butt welds transverse loaded
233
234
.zo:t:J). l--J---ID ~~=1
241
ground \---.
-
..-
242
-
..-
243
ground
--n
,..,.....,....
\-
~~
~
Description
FAT Steel
FAT AI
Tubular joint with permanent backing.
71
-
Transverse butt weld splice in rectangular hollow section, welded from one side, full penetration, root inspected by NDT noNDT
56 45
-
Transverse butt weld ground flush, weld ends and radius ground, 100% NDT at crossing flanges, radius transition.
125
-
Transverse butt weld made in shop at flat position, weld profile controlled, NDT, at crossing flanges, radius transition.
100
-
Transverse butt weld ground flush, NDT, at crossing flanges with welded triangular transition plates, weld ends ground. Crack starting at butt weld.
80
-
Transverse butt weld, NDT, at crossing flanges, with welded triangular transition plates, weld ends ground. Crack starting at butt weld.
71
-
Transverse butt weld at crossing flanges. Crack starting at butt weld.
50
-
----'-'-
244
ground
,..,--...
\-
-~ ~li...o.o...-
245
ground ,..,.....,....
-~ ~'---
200 5.4 Fatigue classes (FAT) for welded components of steel and of aluminum alloys
5 Apendices
Table 5.4.1 Fatigue classes (FAT) for structural details in steel and aluminum alloys (nominal normal stress), cont'd. No.
Strctural detail
300
Longitudinal load-carrying welds
311
312
313
321
FAT Steel
FAT Al
125 90
50 36
125
50
125 90
45 36
Continuous automatic longitudinal fully penetrated K-butt weld without stop/start positions (based on stress range in flange) NDT.
125
50
Continuous automatic longitudinal double sided fillet weld without stop/start positions (based on stress range in flange).
100
40
Continuous manual longitudinal fillet or butt weld (based on stress range in flange). weld (based on and at weld ends).
90
36
=0 = 0.0 - 0.2 = 0.2 - 0.3 = 0.3 - 0.4 = 0.4 - 0.5 = 0.5 - 0.6 =0.6-0.7 > 0.7
80 71 63 56 50 45 40 36
32 28 25 22 20 18 16 14
Longitudinal butt weld, fillet weld or intermittent weld with cope holes, cope holes not higher than 40% of web. r:/a = =0 normal stress in flange a = 0.0 - 0.2 and = 0.2 - 0.3 shear stress in web r: = 0.3 - 0.4 at weld ends = 0.4 - 0.5 = 0.5 - 0.6 > 0.6
71 63 56 50 45 40 36
28 25 22 20 18 16 14
Description
~~
/~ /~ .s.>:>
:t:;f ---
~-
:-----
Automatic longitudinal seam in hollow sections without stop/start positions with stop/start positions Longitudinal butt weld, both sides ground flush parallel to load direction, 100% NDT.
Longitudinal butt weld, without stop/start positions, NDT with stop/start positions
-~~~
322
323
~ --------~
~ ---=---:::::-~
-~-:-
--- =..----::::?
~;:::::::.------
324
Intermittent longitudinal fillet
~ 325 ~-='~
~ ::::::r:::------......:::::
~-:::.--~
normal stress in flange a and shear stress in web r at weld ends
r:/a
=
201 5.4 Fatigue classes (FAT) for welded components of steel and of aluminum alloys
5 Apendices
Table 5.4.1 Fatigue classes (FAT) for structural details in steel and aluminum alloys (nominal normal stress), cont'd.
No.
FAT Steel
AI
Cruciform joint or T-joint, K-butt welds, full penetration, no lamellar tearing, misalignment e<0.15·t, weld toes ground, toe crack.
80
28
Cruciform joint or T-joint, K-butt welds, full penetration, no lamellar tearing, misalignment e<0.15·t, toe crack.
71
25
413
Cruciform joint or T-joint, fillet welds Of partial penetration K-butt welds, no lamellar tearing, misalignment e < 0.15- t, toe crack.
63
22
414
Cruciform joint or T -joint, fillet welds or partial penetration K-butt welds including toe ground joints, weld root crack. Analysis based on stress in weld throat.
45
16
300 331
Strctural detail
Description
FAT
Longitudinal load-carrying welds Joint at stiffened knuckle of a flange to be assessed according to no. 411 - 414, depending on type of joint.
CI,
Stress in stiffener plate: = 2 sin r Stress in weld throat: w = 2 sin Ar = area of flange ASt = area of stiffener A", = area of weld throat 332
Unstiffened curved flange to web joint, to be assessed according to no. 411 - 414, depending on type of joint. Stress in web plate
= F, / (r
t),
Stress in weld throat:
= F, / (r
a),
F r axial force in flange t thickness of web plate a weld throat 400
Cruciform joints or T -joints
411
-[/////~
412
~v.t///1-
t
~
t.
~ e~
.
~
-v/////
.!/¥///_
~ ~
202 5.4 Fatigue classes (FAT) for welded components of steel and of aluminum alloys
5 Apendices
Table 5.4.1 Fatigue classes (FAT) for structural details in steel and aluminum alloys (nominal normal stress), cont'd. No.
Strctural detail
400
Cruciform joints or T-joints
421
422
JIrj~ -- 0
[-~~~-Il-I .. - - - ..
~
~ 423
---I 0
r~---~~---- ---~
424
t~·~·:I1·----l ---- ._---
C
~ 425
t-~;.- ~ ----
___ I[[] u
----
~ 431
~
h
~ -/
Description
FAT Steel
FAT AI
Splice of rolled section with intermediate plate, fillet welds, weld root crack. Analysis base on stress in weld throat.
45
-
56 50
-
45 40
-
Splice of rectangular hollow section, single-sided butt weld, toe crack wall thickness > 8 mm wall thickness < 8 mm
50 45
-
Splice of rectangular hollow section with intermediate plate, fillet welds, root crack wall thickness > 8 mm wall thickness < 8 mm
40 36
-
Splice of circular hollow section with intermediate plate, singlesided butt weld, toe crack wall thickness > 8 mm wall thickness < 8 mm
Splice of circular hollow section with intermediate plate, fillet weld, root crack. wall thickness > 8 mm wall thickness < 8 mm Analysis based on stress in weld throat.
Weld connecting web and flange, loaded by a concentrated force in web plane perpendicular to weld. Force distributed on width
b
= 2·h + 50mm.
Assessment according to no. 411 - 414. A local bending due to eccentric load should be considered.
-
~-
203 5.4 Fatigue classes (FAT) for welded components of steel and of aluminum alloys
5 Apendices
Table 5.4.1 Fatigue classes (FAT) for structural details in steel and aluminum alloys (nominal normal stress), cont'd. No.
Strctural detail
500
Non-load-carrying attachments
511
Description
Transverse non-load-carrying attachment, not thicker than main plate K-butt weld, toe ground Two-sided fillets, toe ground Fillet weld(s), as welded, also single sided Attachment thicker than main plate
~ ./' ~ /
512
U: I)
(l
---
513
r---
FAT Steel
FAT AI
100 100 80 71
36 36 28 25
Transverse stiffener welded on girder web or flange, not thicker than main plate. 100 K-butt weld, toe ground Two-sided fillets, toe ground 100 Fillet weld(s), as welded, also single sided 80 71 stiffener thicker than main plate For weld ends on web principle stress to be used
36 36 28 25
Non-load-carrying stud, as welded
80
28
Trapezoidal stiffener to deck plate, full penetration butt weld, calculated on basis of stiffener thickness, out of plane bending.
71
25
Trapezoidal stiffener to deck plate, fillet or partial penetration weld, calculated on basis of stiffener thickness and weld throat, whichever is smaller, out of plane bending.
45
16
80 71 63 50
28 25 20 18
90
32
-~~ 514
,
I I
I
t
_.g'UIIPene.:.....n..... ~
515
fillet weld /
i~r 0.5
HI
ray
\
:\.1£ •
/1;
""..
I H.r::
H·I
521
-=-
;=-
-I
---
~
~-
--
522
..,.,~
--~
r
I~-+ t
I
-T
Longitudinal fillet welded gusset at length I 1< 50 mm 1< 150mm 1< 300 mm I> 300 mm gusset near edge: see 525 "flat side gusset". Longitudinal fillet welded gusset with radius transition, end of fillet weld reinforced and ground, gusset not at edge of flange, c < 2' t, max 25 mm, r> 150 mm.
204 5.4 Fatigue classes (FAT) for welded components of steel and of aluminum alloys
5 Apendices
Table 5.4.1 Fatigue classes (FAT) for structural details in steel and aluminum alloys (nominal normal stress), cont'd. No.
Strctural detail
500
Non-load-carrying attachments
523
Description
t~
9-
(tl
-+
.!-~"--
u
--
I -l't 524
r~ t L~- ____
a-
(tv
u
..-
J +
(t )
1
525
526
.II;
j
FAT AI
71 63
25 20
Longitudinal flat side gusset welded on plate edge or beam flange edge, with smooth transition (sniped end or radius). c < 2· t, max 25 mm; r> 0,5· h 50 45 r < 0,5 h or q> < 20 0 • For Ii < 0.7 t., FAT rises 12%.
18 16
~
Longitudinal flat side gusset welded on plate or beam flange edge, gusset length I: 1< 150 mm 1< 300 mm I> 300 mm
50 45 40
18 16 14
~
Longitudinal flat side gusset welded on edge of plate or beam flange, radius transition ground. r> 150 mm or r / w > 1 /3 1/6
90 71 50
36 28 22
tr CfFJ ~
Circular or rectangular hollow section, fillet welded to another section. Section width parallel to stress direction < 100 mm, else like longitudinal attachment
71
-
~
~
r
531
-.
-
Longitudinal fillet welded gusset with smooth transition (sniped end or radius) welded on beam flange or plate, not at edge. C < 2 t, max 25 mm; r > 0,5· h r < 0,5 h or rp < 20 0
FAT Steel
--- ,,..,, --,, ,I ,I
1-:;;' 100
I I
mm
205 5.4 Fatigue classes (FAT) for welded components of steel and of aluminum alloys
5 Apendices
Table 5.4.1 Fatigue classes (FAT) for structural details in steel and aluminum alloys (nominal normal stress), cont'd. No.
Strctural detail
600
Lap joints
611
612
613
_VZ~«~ZI-
1U'~C;> " l'~ L""=~)~: -.
t
-c
f
t \
700
FAT AI
Transverse loaded lap joint with fillet welds Fatigue of parent metal Fatigue of weld throat Stress ratio must be 0< R< 1 !
63 45
22 16
Longitudinally loaded lap joint with side fillet welds Fatigue of parent metal Fatigue of weld (calculation based on max. weld length of 40 times the throat of the weld).
50 50
18 18
63 56 50
22 20 18
56 50 45
20 18 16
71 63 56
28 25 22
50
20
80 71
32 25
Lap joint gusset, fillet welded, non-load-carrying, with smooth transition (sniped end with
Reinforcements
711
tD~
t~
1 712
FAT Steel
Description
~··t"'l
t
~~ ... t .",.", .""~.1 ~.
~
~.
'..
.
.",
L.·
/'
End of long doubling plate on I-beam, welded ends tD ~ 0.8 t 0.8 t < tD ~ 1.5 t tD> 1.5 t Based on stress range in flange at weld toe. End of long doubling plate on beam, reinforced welded ends ground tD ~ 0.8t 0.8 t < tD~1.5t t D> 1.5t Based on stress range in flange at weld toe.
/'
721
~
~~~
End of reinforcement plate on rectangular hollow section. wall thickness: t< 25mm
~EJ 731
ground
~
--[@I-
Reinforcements welded on with fillet welds, toe ground Toe as welded Analysis based on modified (local) nominal stress·
206 5.4 Fatigue classes (FAT) for welded components of steel and of aluminum alloys
5 Apendices
Table 5.4.1 Fatigue classes (FAT) for structural details in steel and aluminum alloys (nominal normal stress), cont'd. No.
Strctural detail
800
Flanges, branches and nozzles
t~·
811
812
•
~
~
821
~~
I
i
•
~ll.
822
~
~~ ,l~ 831
~
-~
I
r-..
I
~~
T ~
""III
841
I ..... ~
Y
'r
I
-~ ~ 842
I
I i
,
3 If the diameter is
FAT Steel
FAT AI
Stiff block flange, full penetration weld.
7I
25
63 45
22 16
Flat flange with almost full penetration butt welds, modified nominal stress in pipe, toe crack.
7I
25
Flat flange with fillet welds, modified nominal stress in pipe, toe crack.
63
22
Tubular branch or pipe penetrating a plate, K-butt welds *3.
80
28
Tubular branch or pipe penetrating a plate, fillet welds *3.
7I
25
Nozzle welded on plate, root pass removed by drilling *3.
71
25
Nozzle welded on pipe, root pass as welded *3.
63
22
Stiff block flange, partial penetration or fillet weld toe crack in plate root crack in weld throat.
"~
i
832
Description
-
.""" ""J~ ~
~~ ~ ~ ....
'"
"\",,:,' \.'\.'\.
> 50 mm, stress concentration of cutout has to be considered
!
207 5.4 Fatigue classes (FAT) for welded components of steel and of aluminum alloys
5 Apendices
Table 5.4.1 Fatigue classes (FAT) for structural details in steel and aluminum alloys (nominal normal stress), cont'd. No.
Strctural detail
900
Tubular joints
911
-CB-
912
t
• mAl
913
¥629?
921
931
E)
E> 932
1-
:::0)
FAT Steel
FAT AI
Circular hollow section butt joint to massive bar, as welded.
63
22
Circular hollow section welded to component with single side butt weld, backing provided . Root crack.
63
22
Circular hollow section welded to component single sided butt weld or double fillet welds. Root crack.
50
18
90 90 71
32 32 25
Tube-plate joint, tubes flattened, butt weld (X-groove) Tube diameter < 200 mm and plate thickness < 20 mm.
71
-
Tube-plate joint, tube slitted and welded to plate tube diameter < 200 mm and plate thickness < 20 mm tube diameter> 200 mm and/or plate thickness > 20 mm
63
-
45
-
-
Circular hollow section with welded on disk K-butt weld, toe ground Fillet weld, toe ground Fillet welds, as welded
1-
I-I SoI
Description
~
Table 5.4.2 Fatigue classes (FAT) for structural details in steel and aluminum alloys (nominal shear stress), after Hobbacher /9/ No. 1
2
Strctural detail
~ ~ ~
Description
FAT Steel
FAT AI
Full penetration butt welds
100
36
Fillet weld, partial penetration
80
28
208 5.4 Fatigue classes (FAT) for welded components of steel and of aluminum alloys
5 Apendices
Table 5.4.3 Fatigue classes (FAT) for structural details in steel and aluminum alloys (structural normal stress), after Hobbacher /9/ No.
Strctural detail
200
Butt welds, transverse loaded
211
.-~-
FAT Steel
FAT AI
Transverse loaded butt weld (X-groove or V-groove) ground flush to plate, 100% NDT *4.
125
50
100
40
Description
212
-~~-
Transverse butt weld made in shop in flat position, toe angle ~ 30°, NDT.
213
-~~-
Transverse butt weld not satisfying conditions of 212, NDT
80
32
Toe ground To as welded
112 100
-
Cruciform joint or T-joint, K-butt welds, full penetration, no lamellar tearing, misalignment e<0.15·t, weld toes ground, toe crack.
80
28
Cruciform joint or T-joint, K-butt welds, full penetration, 71 no lamellar tearing, misalignment e<0.15·t, toe crack.
25
Cruciform joint or T-joint, fillet welds or partial penetration K-butt welds, no lamellar tearing, misalignment e < 0.15' t, toe crack.
22
300
Fillet welds Fillet welds at weld toe
400 411
Cruciform joints or T-joints e
l~ ~ i'-' -v///// I'- ~v t // /1f ~
l
t:::
412
I
~
-v/////.
f
e
t\ ~
~
l
~V.t///I-
~
413
'j~
-VZ/fC ~:«t-
4 NDT = Non-destructive testing.
63
209 5.5 Comments about the fatigue strength of welded components
5.5.1.1 Assessment of the fatigue strength using nominal stresses
5.5 Comments about the fatigue strength of welded components ~c-55=-= ENC":".C":"do-'q
Content
Page
5.5.0
General
5.5.1
Compilation of the relationships for welded components of steel General Assessment of the fatigue strength using nominal stresses Assessment of the fatigue strength using structural stresses Assessment of the fatigue strength using effective notch stresses
5.5.1.0 5.5.1.1 5.5.1.2 5.5.1.3
209
210 211
Explanation of the relationships for welded components 5.5.2.0 General 5.5.2.1 Specific fatigue limit values of welds in steel for completely reversed stress 5.5.2.2 Mean stress factor and residual stress factor Example General Assessment using nominal stresses Assessment using structural stresses Assessment using effective notch stresses
The assessment using nominal stresses is applicable for the toe section and for the throat section of rod-shaped (lD) and of shell-shaped (2D) welded components. Nominal stresses do not account for the stress concentration caused by the form of the component nor by the shape of the weld seam. Therefore the component strength value is depending not only on the fatigue strength value of the weld but also on the form of the component and on the shape of the weld seam, Tab. 5.5.1 *4. Specific fatigue limit values of welds in steel for completely reversed stress Independent of the kind of steel *5 the specific fatigue limit values of welds in steel for completely reversed normal stress and shear stress are, Chapter 2.2.1.2 *6,
5.5.2
5.5.3 5.5.3.0 5.5.3.1 5.5.3.2 5.5.3.3
5 Appendices
92 MFa, 37 MFa.
GW,zd = GW,W = 'tW,s = 'tw,W =
(5.5.1)(2.2.3)
213
Design factors for nominal stress 214
The design factors for normal stress and for shear stress are, Chapter 2.3.1.2 *7, KWK,zd =
215
5.5.0 General The assessment of the fatigue strength of professionally welded components *1 made of structural steel *2 agrees with or closely follows the IIW-Recommendations and Eurocode 3. The assessment is in general to be carried out separately for the toe section (or the toe of the weld) and for the throat section (or the root of the weld), since the crosssection values, the relevant stresses and the fatigue classes FAT will normally be different. The particular relationships that apply to welded components made of steel are compiled in Chapter 5.5.1 and explained in Chapter 5.5.2. Equivalent relationships apply to components made of aluminum alloys.
5.5.1 Compilation ofthe relationships for welded components of steel 5.5.1.0 General The assessment of the fatigue strength can be carried out with nominal stresses, Chapter 2, or with local stresses, Chapter 4, where the local stresses of welded components may be derived as structural stresses *3 or as effective notch stresses.
KWK,s=
225 / FAT, 145/FAT.
(5.5.2)(2.3.4)
Fatigue classes for the assessment with nominal stresses are (FAT:::; 140 for normal stress and FAT:::; 100 for shear stress) are given in Chapter 5.4.1. Fatigue classes are not applicable to the base material, however.
1 Weld imperfections corresponding to normal production standards are allowable. 2 For other kinds of material (relatively weldable steel, stainless steel, weldable cast iron material) these specific fatigue limit values of welds in steel are provisional and are to be applied with caution therefore. 3 Also termed geometrical stresses or hot-spot-stresses. 4 The numbers of the equivalent tables and equations in Chapter 2 are given here as well. 5 The type of structural steel (specified by the yield stress R, and further properties) is important only for an assessment of the static strength, not ofthe fatigue strength. The same applies in the case of aluminum alloys. 6 All the following is valid for structural steel only. For aluminum alloys the values 92 MPa and 37 MPa after Eq. (2.2.3) are to be replaced by 33 MPa and 13 MPa after Eq. (2.2.4) (Factor 0,36). For aluminum alloys the values 225 MPa and 145 MPa after Eq. (2.3.4) are to be replaced by 81 MPa and 52 MPa after Eq. (2.3.6) (Factor 0,36). These values for aluminum alloys are provisional ones and are to be applied with caution. 7 Thickness factor ft , surface treatment factor, KV and constant KNL,E are not considered here, since they are not essential in the present context.
210 5.5 Comments about the fatigue strength of welded components
Table 5.5.1 Differences between the assessments using nominal stresses, structural stresses or effective notch stresses. The stress increasing effects of the form of the component and the notch effects of the shape of the weld seam are allowed for in a complementary way either by the stress value or by the strength value.
Form of the component Shape of the weld Form of the component Shape of the weld Effect of welding
Assessment with nominal structural effective stresses S notch stresses cr stresses ex Allowed for bv the stress value no yes yes no
no
yes
Allowed for by the strength value yes no no yes
yes
no
yes
yes
yes
Component fatigue limit for completely reversed nominal stress The values of the component fatigue limit for completely reversed normal stress and shear stress are, Chapter 2.4.1: SWK,Zd = crw,w/ KWK,zd, TWK,s = "W,W / KWK,s .
(5.5.3)(2.4.1)
5 Appendices
Table 5.5.2 (Table 2.4.1 or 4.4.1) Residual stress factors KE,cr , KE,~ and component mean stress sensitivities Mc;, M~ for welded components. Residual stress high moderate low
KE,cr
M cr
KE;t
M~-¢ol
1,00 1,26 1,54
0 0,15 0,30
1,00 1,15 1,30
0 0,09 0,17
c-I For shear stress there is M~ = fw.~· M cr 2.2.1 or 4.2.1.
,
fw.~
= 0,577 after Table
5.5.1.2 Assessment of the fatigue strength using structural stresses
The assessment using structural stresses is applicable for the toe of the weld of rod-shaped (lD) and of shellshaped (2D) components *9 , but not for the root of the weld. Structural stresses allow for all stress increasing influences of the form of the component, but do not account for influences of the weld shape. Therefore the component strength value is determined by the shape of the weld seam and by the specific fatigue strength value of welds, but not by the form of the component, Table 5.5.1 *10. Specific fatigue limit values of welds in steel for completely reversed stress Independent of the kind of steel the specific fatigue limit values of welds in steel for completely reversed normal stress and shear stress are, Chapter 4.2.1.2, crW,zd = crw,w = 92 MFa, "w,S = "W,W = 37 MFa.
(5.5.6)(4.2.3)
Component fatigue limit for nominal stress The mean stress dependent values of the component fatigue limit *8 for normal stress and for shear stress are, Chapter 2.4.2.0: SAK,zd = KAK,zd . KE,cr' SWK,zd, TAK,s = KAK,s' KE,~' TWK,s.
(5.5.4)(2.4.6)
The mean stress factors KAK,zd and KAK,s after Chapter 2.4.2.1, are to be determined with the component mean stress sensitivity M; and M~ after Chapter 2.4.2.4, Table 5.5.2, the residual stress factors KE,cr and KE,~ after Chapter 2.4.2.3, Tab. 5.5.2. By combining Eq. (5.5.2), (5.5.3) and (5.5.4) the component fatigue limit for normal stress and for shear stress is obtained in the form . FAT SAK,zd = K AK,zd ' KE,cr ' - '
Design factors for structural stress The design factors for normal stress and for shear stress are as above *7, Chapter 4.3.1.2, KWK,zd = 225 / FAT, KWK,s = 145/ FAT.
(5.5.7)(4.3.4)
Fatigue classes for the assessment using structural stresses are given in Chapter 5.4.2.
8 The component variable amplitude fatigue strength is not considered here, since it is not essential in the present context.
(5.5.5) 9 Also applicable for block-shaped (3D) components welded at the surface. laThe numbers of equivalent tables and equations in Chapter 4 are given here as well.
211 5.5 Comments about the fatigue strength of welded components Component fatigue limit for completely reversed structural stress The values of the component fatigue limit for completely reversed normal stress and shear stress are, Chapter 4.4.1: (5.5.8)(4.4.1)
CJWK = CJw,w I KWK,cr, LWK
=
LW,W
I
KWK;t .
Component fatigue limit for structural stress The mean stress dependent values of the component fatigue limit '8 for normal stress and for shear stress are, Chapter 4.4.2.0: (5.5.9)(4.4.6)
CJAK = KAK,cr . KE,cr . CJwK, LAK
=
KAK;t . KE,'t . LWK .
Values KAK,cr,
...
FAT
225 . CJw,w,
(5.5.10)
FAT
= KAK,'t . KE,'t 'l45 . LW,W
The design factors for normal stress and for shear stress are, Chapter 4.3.1.2, KWK,crK=225/FAT= 1, = 145 I FAT = 1.
.
Fatigue classes FAT = 225 for normal stress and FAT = 145 for shear stress.
Component fatigue limit for completely reversed effective notch stress The values of the component fatigue limit for completely reversed normal stress and shear stress are, Chapter 4.4.1:
Effective notch stresses, computed with the effective notch radius r = 1 mm, see Figure 0.0.7, account both for the influence of the form of the component and for the influence of the shape of the weld seam (that is all stress increasing influences). Therefore the component fatigue limit value is identical with the specific fatigue limit value of welds for completely reversed stress and does not contain any influence of the form of the component nor of the weld seam, Tab. 5.5.1 *10. Specific fatigue limit of welds in steel for completely reversed stress Independent of the kind of steel the specific fatigue limit values of welds in steel for completely reversed normal stress and shear stress are, Chapter 4.2.1.2, CJW,zd = CJw,w LW,S = LW,W
= 92 MPa, = 37 MPa.
(5.5.11)(4.2.3)
(= CJw,w) (5.5.13)(4.4.1) (= LW,W).
The mean stress dependent values of the. component fatigue limit '8 for normal stress and for shear stress are, Chapter 4.4.2.0: CJAK,K
The assessment with effective notch stresses is applicable both to the toe and to the root of the weld of rod-shaped (lD) and of shell-shaped (2D) welded components *9.
= LW,W I KWK,'tK
Component fatigue limit for effective notch stress
LAK,K
5.5.1.3 Assessment of the fatigue strength using effective notch stresses
(5.5.12)(4.3.8)
KWK;tK
LWK,K
By combining Eq. (5.5.7), (5.5.8) and (5.5.9) the component fatigue limit for normal stress and for shear stress is obtained in the form
LAK
Design factors for effective notch stress
CJWK,K = CJw,w I KWK,crK
as above, Chapter 4.4.2.1 ....
CJAK = KAK,cr . KE,cr'
5 Appendices
= KAK,crK . KE,cr = KAK,'tK • KE,'t .
Values KAK,crK,
...
. CJWK,K,
(5.5.14)(4.4.6)
LWK,K·
as above, Chapter 4.4.2.1 ....
By combining Eq. (5.5.12), (5.5.13) and (5.5.14) the component fatigue limit values for normal stress and for shear stress are obtained in the form CJAK,K = KAK,crK . KE,cr . CJw,w, LAK,K
(5.5.15)
= KAK,'tK . KE,'t . LW,W·
5.5.2 Explanation of the relationships for welded components 5.5.2.0 General The relationships between the fatigue limit of welds for completely reversed stress, the mean stress factor and the residual stress factor are illustrated by Figure 5.5.1 and explained in the following.
5.5.2.1 Specific fatigue limit values of welds for completely reversed stress According to the concept of the present guideline the same safety factors are to be applied for non-welded components and for welded components in order to maintain a uniform procedure of assessment. These safety factors are, however, higher than those of the IIW-Recommendations and of the Eurocode 3, Tab. 5.5.3.
212 5.5 Comments about the fatigue strength of welded components
5 Appendices
~aAI\ (aAI\ )
145(73)
225(113)
III
MPa
(2,19)
k
T=5
( 1,36)
66 33
etre bildtlkl
N
sira bild9lkl
ND,a~:~
I
II b
~
/
f
0,17 0,09
°
°
i'~-
Ma
'" -1
aife bhghsk
1
83 MPa
°
aifll bhghtk
0
3
3
Figure 5.5.1 Fatigue limit of welds in structural steel. Top: Component constant amplitude SoN curves for high residual stresses and/or for high stress ratios Rcr ~ 0,5 or R~ ~ 0,5 . Numerically shown are the stress ranges (double amplitudes) and amplitudes (in parenthesis) corresponding to Eq. (5.5.17) . Value L'>crAK = 225 (145) MPa according to the llW-Recommendations. Bottom: Haigh-diagrams presenting the mean stress dependent amplitudes or ~AK at the fatigue limit or at NO c or NO t , respectively. Component mean stress sensitivity for high ;esidual stress (M cr = M~ = 0), for moderate residual stress (M cr = 0,15 , M~ = 0,09), for low residual stress (M cr = 0,3 , M"t = 0,17).
crAK
Left: Normal stress. Right: Shear stress.
The difference of the safety factors is 1,5/ 1,35 = 1,11. Therefore the specific fatigue limit values of welds for completely reversed stresses crw,w and 'Cw,w specified in the guideline,
crw,w = 92 MFa, 'Cw,w = 37 MFa,
(5.5.16)
are higher by a factor of about 1,11 than the original values to be derived from the fatigue classes (FAT) given by the IIW-Recommendations and by Eurocode 3
crw,w = 83 MFa, 'Cw,w = 33 Mpa,
(5.5.17)
Hence in applying the respective safety factors the same allowable stress values will be obtained. Table 5.5.3 Safety factors
The fatigue classes (FAT) and the values ofEq. (5.5.17) derived from these are displayed in Figure 5.5.1.
Safety factors for steel according to the present guideline (Table 2.5.1 or 4.5.1).
jo regular Inspection
Consequence of failure high low
I I
no yes
1,5 1,35
1,3 1,2
Safety factors for structural steel according to Eurocode 3.
jo regular Inspection
I I
no yes
Consequence of failure high low 1,35 1,15 1,25 1,00
The above fatigue limit values crw,w and 'Cw,w and the corresponding values ~crAK and ~'CAK of the fatigue classes FAT = 225 and FAT = 145 are valid in the case of high residual stresses and/or high stress ratios Rcr~ 0,5 or R~~ 0,5 in combination with an exponent of the constant amplitude S-N curve of k cr = 3 or k, = 5 and an average probability of survival of PD = 97,5 %.
Deriving the original fatigue limit values For normal stress the original fatigue limit value of the IIW-Recommendations, Eq. (5.5.17), is
crw,w = 83 MFa
(5.5.18)
213 5.5 Comments about the fatigue strength of welded components This is the stress amplitude of the fatigue limit at a number of cycles ND,a = 5 . 106 . It corresponds to the experimentally established value of the IIWRecommendations: (5,5, (9)
!:ierAK = 225 MPa.
This is the stress range or double-amplitude of the fatigue strength at the reference number of cycles of N c = 2· 106 , The relationship between these values follows from the component constant amplitude S-N curve and the values No,cr, N c and k cr = 3, Figure 5.5,1: erw,w = (Nc / No,cr) I /kcr. !:ierAK / 2 (5.5.20) (2 . 106/5 . 106 ) 1/3 ·225/2 = 83 MPa.
=
For shear stress the original fatigue limit value of the IIW-Recommendations, Eq. (5.5, 17), is T-W,W
=
5 Appendices
The residual stress factor is defined for a stress ratio R; = -I (R, = -I) and is equal to the reciprocal of the mean stress factor for a stress ratio Rcr = 0,5 (R, = 0,5). The product KAK,cr . KE,cr or KAK,"t' KAK,"t describes the increase of the component fatigue limit as a function of the mean stress compared to the basic value for high residual stress which is not dependent on mean stress.
Product KAK,O' . KE,cr for normal stress The mean stress sensitivity in the case of high, moderate or low residual stresses is, Table 5.5.2: M; = 0; 0,15 and 0,30.
(5.5.25)
The residual stress factor in the case of high, moderate or low residual stresses derived from Eq. (2.4.13) or (4.4.13) is
(5,5.21)
33 MPa
= 3.(I+M cr
.,.,..,.....
This is the stress amplitude of the fatigue limit at a number of cycles NO,"t = 108 . It corresponds to the experimentally established value of the IIWRecommendations *11 (5.5.22) This is the stress range or double-amplitude of the fatigue strength at the reference number of cycles of Nc = 2.10 6 . The relationship between these values follows from the component constant amplitude S-N curve and the values NO,"t , Nc and k, = 5, Figure 5,5.1: T-w,w = (Nc / NO,"t) 1 /k"t. !:iT-AK / 2 = (2 . 106 / 10 8 ) 1/5 . 145/2 = 33 MPa.
(5,5.24)
KAK,cr,R=0,5
f
3 + M cr (5.5.26)
I; 1,26 and 1,54.
For Rcr = -00 (zero-compression stress) it follows from Eq. (2.4.9) or (4.4.9), Figure 5.5.1, (5.5.27)
1 KAKcr' KEcr = - - - . KEcr = 1; 1,48 and 2,19. 1-Mcr ' , , For Rcr = -1 (alternating stress) it follows from Eq. (2.4.10) or (4.4.10) (5.5.28) KAK,cr' KE,cr
= 1 . KE,cr =
1; 1,26 and/or 1,54.
For Rcr = 0 (zero-tension stress) it follows from Eq. (2.4.10) or (4.4.10) (5.5.29)
1
KAKcr' KEcr = - - . KEcr = I; 1,10 and 1,18. I+M cr ' , , 5.5.2.2 Mean stress factor and residual stress factor Mean stress factor and residual stress factor are closely related to each other, Chapter 2.4.2 or 4.4.2. The mean stress factor KAK,cr or KAK,"t describes the amplitude of the component fatigue limit as a function of the mean stress. For a stress ratio Rcr = -lor R, = -1 there is KAK,cr = 1 and KAK,"t = 1. For reasons of uniformity it is determined the same way as for nonwelded components, but with different values of the mean stress sensitivity M; and M, assigned to the case of high, moderate or low residual stresses, Table 5.5.2. The residual stress factor KE,cr or KE,"t describes how the amplitude of the component fatigue limit differs in the case of high, moderate or low residual stresses, Table 5.5.2.
For Rcr = 0,5 it follows from Eq. (2.4.13) or (4.4.13) (5.5.30) KAK,u~ . KE,u~ .
=
3( + M cr \2 . KE,~ 3· 1+ Mcrl U
= I;
I and 1.
Product KAK,"t . KE,"t for shear stress The mean stress sensitivity in the case of high, moderate or low residual stresses is, Table 5.5.2: (5.5.31)
M,
= f"t'
M, = 0,58' M cr = 0; 0,09 and 0,17.
The residual stress factor in the case of high, moderate or low residual stresses derived from Eq. (2.4.13) or (4.4.13) is 3.(I+M"t)2
11 Actually a value 6"tAK R= -I = 190 MPa was experimentally establishes for a stress ratio = -1 and low residual stresses, which is about a factor 1,30 higher than in the case of high residual stresses, Figure 5.5.1: (5.5.23)
R"t
6"tAK,R= -1 = 1,30' L'l"tAK = 1,30 . 145 MPa = 190 MPa.
K AK,"t,R=0,5 I; 1,15 and 1,30.
3 + M, (5.5.32)
214 5.5 Comments about the fatigue strength of welded components For Rcr = -I (alternating stress) (2.4.10) or (4.4.10)
it follows from Eq. (5.5.33)
*12
KAK;t' KE;t = 1 . KE,cr = 1; 1,15 and 1,30. For Rcr = 0 (zero-tension stress) it follows from Eq. (2.4.10) or (4.4.10) (5.5.34) 1 KAKt' - ' KEt = 1; 1,06 and 1,11. , K E,t = I+M ' t
For
Rcr = 0,5 it follows from Eq. KAK t . K E t , ,
-
3+M t 3.(I+M
t
)2
(2.4.13) or (4.4.13) (5.5.35) .
KE t = 1; 1 and 1.
'
Although somewhat differing from the IlWRecommendations and from Eurocode 3 the application of the concept presented here appears to be acceptable as different Haigh-diagrams are given in the two references and as the present concept is a more or less intermediate one, Figure 5.5.2.
5 Appendices
5.5.3 Example 5.5.3.0 General The basic way of calculation using nominal stresses, structural stresses or effective notch stresses is explained by the example of a transverse butt weld in a flange with wedge-shaped transition in width (slope 1:2) and with high residual stresses (KE,cr = 1, M cr = 0, Table 5.5.2), Figure 5.5.3. In simplification the task is to examine the 'existing safety factor' jYorh for an alternating constant amplitude loading (tension-compression, R zd = R, = -1, mean stress factor KAK,zd = KAK, cr = KAK, crK = 1). If the three methods of calculation are compatible, the results will agree.
~
~
-+------+f~;__--------\-~
2 , 1 9 - - -..... I r-e l mm
K~'(TK a.;a,i ~.rn~
1,6,~~~'%:-~~
::::::_
1,3,-----\---="'iiiiil;d
aifa b 5 5 8 _
aila b552
-1
o
3
Figure 5.5.2 Standardized Haigh diagrams according to the IlW-Recommendations (IlW), to Eurocode 3 (EC3) and to the present guideline (Ri). I1W-Recommendations: Haigh-diagram for high (1), for moderate (1,3) and for low (1,6) residual stresses. Eurocode 3: Haigh-diagram for high (1) and for low (1,67) residual stresses. The diagram not presented in Eurocode 3 agrees to the given rule, that only 60 % of the compression part ofthe stress cycle isto be considered. Present Guideline: Haigh-diagram for high (1), for moderate (1,48) and for low (2,19) residual stresses.
_
_
....._ _
Figure 5.5.3 Transverse butt weld in a flange with wedge-shaped transition in width (slope 1:2). Stress concentration factor due to the transition in width: Kt,cr = 1,25. Combined stress concentration factor due to the transition in width and due to the transverse butt weld with an assigned effective notch radius r = 1 mm, Figure 0.0.7: Kt,crK = 3,5.
5.5.3.1 Calculation using nominal stresses Nominal stress amplitude Sa= 20 MFa.
(5.5.36)
The component fatigue limit results from Eq. (5.5.5): FAT SAK,zd = 225 . crw,w .
(5.5.37)
Considering the stress concentration due to the transition in width (form of the component) and due to the reinforced weld seam (shape of weld seam) the fatigue class FAT = 63 (no. 223 in Tab. 5.4.1) appears to be appropriate and accordingly 63 SAK,zd = 225 . 92 MFa = 26 MFa. (5.5.38) The available safety factor is The stress ratio R'[ = -CX) is not mentioned because the Haighdiagram for shear stresses tm < 0 issymmetrically totm > O. 12
jvorh = SAK,zd / Sa = 26 / 20 = 1,3.
(5.5.39)
215 5.5 Comments about the fatigue strength of welded components 5.5.3.2 Calculation using structural stresses
Structural stress amplitude including the stress concentration ofthe transition in width, Kt,cr = 1,25, O"a =
1,25' 20 MPa = 25 MPa.
(5.5.40)
The component fatigue limit results from Eq. (5.5.10): O"AK =
FAT 225 . O"w,w
(5.5.41)
.
Considering the stress concentration of the reinforced weld seam (shape of weld seam) the fatigue class FAT = 80 (no. 213 in Tab. 5.4.3) appears to be appropriate and accordingly 80
0" AK
= 225 . 92 MPa = 33 MPa.
(5.5.42)
The available safety factor is as before jYorh = 0"AK / O"a =
33 /25 = 1,3.
(5.5.43)
5.5.3.3 Calculation using effective notch stresses
Effective notch stress amplitude including the stress concentration of the transition in width and of the reinforced weld seam with an assigned effective notch radius r = I mm, Kt,crK = 3,5 , O"a,K
= 3,5 . 20 MPa = 70 MPa.
(5.5.44)
The component fatigue limit results from Eq. (5.5.15): O"AK,K
= O"w,w = 92 MPa.
(5.5.45)
The available safety factor is as before jYorh = 0" AK,K / O"a,K =
92 /70
= 1,314 =
1,3
(5.5.46)
5 Appendices
216 5.6 Adjusting the stress ratio of a stress spectrum and deriving a stepped spectrum
5.6 Adjusting the stress ratio of a stress spectrum to agree with that of the S-N curve and deriving a stepped spectrum IRs6 EN.dog Content
5.6.0 5.6.1
Page General Adjusting the stress ratio of a stress spectrum
Deriving a stepped stress spectrum
In a second step a so derived stress spectrum for R, = R"i = -1 may be converted to any other uniform stress ratio of interest after Chapter 5.6.1.2, Figure 5.6.1 The following equations are written for local normal stress o , but accordingly they are valid for a nominal stress as well. For shear stress the normal stress c is to be replaced by 1:, and the mean stress 1:m ,i, for i = 1 to j is always to be regarded as positive *3.
216
5.6.1.1 Conversion to a stress ratio R., = -1
5.6.1.0 General 5.6.1.1 Conversion to a stress ratio R, = -1 5.6.1.2 Conversion to an other stress ratio R, 5.6.2
5 Appendices
217
5.6.0 General This chapter describes how to convert the stress ratios of the steps of a stress spectrum to agree with the stress ratio of the component constant amplitude S-N curve, and how to derive a stepped stress spectrum, in order to allow a damage calculation.
5.6.1 Adjusting the stress ratio of a stress spectrum *1
This chapter is of relevance mainly for stress spectra the steps of which show different stress ratios. In particular these are mean stress spectra, Figure 2.1.2 (on top) or Figure 4.1.2 (on top), or more general, all other types of (one-parametric) stress spectra where the amplitudes cra,i and mean values crm,i result in different stress ratios Ra,i of the individual steps. Furthermore the described method of conversion is applicable to two-parametric stress spectra, like rain-flow matrices for example, where the matrix elements show different amplitudes, mean values and stress ratios as well. In a first step the amplitudes of all steps i = 1 to j are to be converted to a stress ratio Ra = -1 . This conversion results in the damage equivalent amplitudes cra,i,Rcr=-I. In performing the conversion the four fields of mean stress are to be distinguished, see Chapter 2.4.2 or 4.4.2:
5.6.1.0 General
Field I (fluctuating compression stress)
Usually a component constant amplitude S-N curve is derived for a constant stress ratio over the whole range of stress amplitudes. To perform a damage calculation, Chapter 2.4.3 or 4.4.3, the stress ratios of the individual steps of the stress spectrum, R"i, and the stress ratio R of the component constant amplitude S-N curve must agree. Otherwise the differing stress ratios of all steps, i = 1 to j, are to be converted to a uniform stress ratio R"i = R, = R, as described below.
For crm,i / cra,i < -1 there is cra,i,Rcr=-1 = cra,i . (l - M; )
A conversion to a uniform stress ratio R, = R"i = -1 is normally to be preferred, Chapter 5.6.1.1, as analytically a S-N curve is primarily derived for a stress ratio R = -1, Chapter 4.4.1 *2
(5.6.1)
Field II (alternating stress) For -I s crm,i / cra,i S I there is cra,i,Rcr=- I = cra,i . (l + M, . crm,i / cra,i ) ,
(5.6.2)
Field III (lower range of fluctuating tension stress) For I < crm,i / crsa,i < 3 there is M, crm i 1+-·--' 3 o a,i cra,i,Rcr=- I = cra,i' 1+ M /3
(5.6.3)
cr
I+M cr Field IV (upper range of fluctuating tension stress) for crm,i / cra,i ~ 3 there is
_
cra,i Rcr=-I - cra,i
,
I Also known as the method of 'amplitude transformation'. 2 A conversion to the stress ratio of step i = I with the largest amplitude of the spectrum is common for variable amplitude fatigue tests. Converting to the stress ratio of the most damaging step would be another alternative. For the most damaging step imax the term of Eq. (4.1.10), hi' (a i / sa I )k , reaches a maximum value. (Number of cycles hi a~d ampiitude a.i of step i = imax, amplitude sa, I of the step I with the largest amplitude, exponent of the constant amplitude S-N curve kcr ). In the case of a damage calculation and an analytically derived SNcurve both alternatives would not make any difference, however.
f
.3.(I+M cr 3 +M cr
,
(5.6.4)
cra,i
stress amplitude in step i of the initial spectrum
crm,i
mean amplitude in step i of the initial spectrum
M;
component mean stress sensitivity, Chapter 2.4.2.3 or 4.4.2.3 .
3 See footnote 5 on page II 5.
217 5.6 Adjusting the stress ratio of a stress spectrum and deriving a stepped spectrum
5 Appendices
R c, I
Figure 5.6.1 Converting the amplitudes in the steps of a stress spectrum to a uniform stress ratio R, .
R a =-1
R fJ =0
!!l! lIlY
Initial stress amplitudes O"a,i , mean stresses O"m,i and stress ratios ~,i . Converted stress amplitudes O"a,i,Ra=-1 for the stress ratio ~ = -1 (step 1), and converted stress amplitudes O"a,i,Ro,1 for an other stress ratio ~ = ~,l , for example. Amplitude ofthe component fatigue limit according to mean stress, oAK ,
bS8t
amplitude ofthe component fatigue limit for completely reversed stress
aWK ' component mean stress sensitivity Ma
5.6.1.2 Conversion to an other stress ratio R(J In a second step the amplitudes O"a,i,Ra=-1 of the stress spectrum for a stress ratio ~ = -1 can be further converted to any other uniform stress ratio ~, for example to O"a,i, Ro,l for ~ = ~,l . Again the four fields of mean stress are to be distinguished:
5.6.2 Deriving a stepped stress spectrum If a stress spectrum is presented as a continuous spectrum a corresponding stepped spectrum may be derived sufficiently exact by the graphical method according to Figure 5.6.2.
Field I For
t---a.---...
~,l
> 1 (O"m,l /
< - 1) there is / (1 - M; ),
O"a,l
O"a,i,Rcr,1 =O"a,i,Ro=-1
(5.6.5)
cr••1 1,0 cr.,1
0,8
Field II 0,6
for
-00
:s; ~,l :s; 0 (-I:S; O"m,l /
O"a,i,Rcr,1 = O"a,i,Ro=-l .
1 M
+
O"a,l
:s; 1) there is *4
1 a ·O"m,l
/
O"a,l
'
0;4
(5.6.6)
0,2
O'"---......l...-
L...l
Field III 5.6;2
for 0
<~,l
0"'
a,I,Ra,1
< 0,5 (l < O"m,l /
=0"'
_.
a,I,Rcr--l
O"a,l
< 3) there is
I+M cr /3 l+M 0 M
1+~. O"m,l
3
Figure 5.6.2 Deriving a stepped stress spectrum. Presented example: 8 steps. '
(5.6.8)
O"a,l
Field IV for
~,l;::::
0,5
(O"m,I / O"a,l ;::::
3) there is
3+M o O"a,i,Ro,1 = O"a,i,Ro=-l . - - - = - -
(5.6.9)
3.(1 +Maf
4 O"m "1 fO"a I =(1 +Ra , 1 )f(1-Rcr, l)'
(5.6.7)
The expression using the ratio of mean stress to stress amplitude avoids numerical problems when Ro,l = - 00.
218
5.7 Assessment using classes of utilization
5.7 Assessment using classes of utilization 1R57
EN.dog
Content
Page
5.7.0 General 5.7.1 Non-welded components 5.7.2 Welded components
5 Appendices Table 5.7.1 Variable amplitude fatigue strength factors for non-welded and for welded components, for normal stress, KBK,cr, and for shear stress, KBK,~, according to the classes of utilization B ~ 1 ~2
5.7.0 General This chapter applies to components made of steel and of cast iron materials without surface treatment. According to this chapter the variable amplitude fatigue strength factors KBK,a , KBK,t *1 for a given class of utilization *2 can be determined, Tab. 5,7.1 *3, The appropriate class of utilization is to be determined by the user according to existing experience and outside of this guideline, The classes of utilization allow the assessment of the variable amplitude fatigue strength to be carried out in a simplified manner, Chapter 2.1.4.2 and 2.4.3,1 or 4.1.4.2 and 4.4,3.1. A class of utilization is an approximately damage~uivalent combination of the required number of cycles N with the shapes of particular standard stress spectra, the frequency distribution of which is of binomial or exponential type modified by a spectrum parameter p. Concerning the relationship between the classes of utilization, the required total number of cycles Nand the spectrum parameter p for binomially or exponentially distributed standard stress spectra see Table 5.7.2 to 5,7.5. Because of different slopes of the component constant amplitude S-N curves non-welded and welded components as well as normal stress and shear stress are to be distinguished.
Welded components
Non-welded
218
components KBK,cr B-7 B-6 B-5 B-4 B-3 B-2 B-1 BO Bl B2 B3 B4 B5
B6 B7 B8 B9 B10
-
12,59 10,00 7,94 6,31 5,01 3,98 3,16 2,51 2,00 1,58 1,26 1,00
-
-
KBK,~
6,49 5,62 4,87 4,22 3,65 3,16 2,74 2,37 2,05 1,78 1,54 1,33 1,15 1,00
-
KBK,cr
42,9 29,2 19,9 13,6 9,24 6,30 4,29 2,92 2,00 1,36 1,00
-
-
KBK,~
27,5 21,9 17,4 13,8 11,0 8,71 6,91 5,49 4,38 3,46 2,76 2,19 1,74 1,38 1,10 1,00
-c- 1The table applies to binomially and exponentially distributed standard stress spectra. ~2 For an intermediate value of the class of utilization (for example B1/2) the geometrical mean ofthe neighboring values applies.
5.7.1 Non-welded components
spectrum parameter p = 1 the class of utilization B6 applies. The class B6 corresponds to the component fatigue limit and serves as a reference value. High values of the variable amplitude fatigue strength factor, although formally correct, may be irrelevant and excluded by an assessment of the static strength.
Variable amplitude fatigue strength factors are given by Figure 5.7.1 (left columns), For a required number of
5.7.2 Welded components
cycles at the knee point, N
= ND,a = ND,t = 106 , and a
1KBK,cr, ...for local stresses; KBK,zd, .... for nominal stresses. 2 Following DIN 15018 Table 5.7.1 to 5.7.5 and Figure 5.7.1 correspond to a damage calculation with the elementary version of Miner's rule with a critical damage sum DM = 1, Eq. (4.4.51) and with Va after Eq. (4.1.10) orTable
3
4.1.1. It is supposed, that the recommended damage sum ~ < 1 isconsidered by the user according to the his experience in selecting the appropriate class ofutilization.
Variable amplitude fatigue strength factors are given by Figure 5.7.1 (right columns). For a reference number of cycles Nc = 2 . 106 and a spectrum parameter p = 1 the class of utilization B6 applies. In this case the B6-class, however, does not correspond to the component fatigue limit but serves as a reference value only. The class of utilization corresponding to the component fatigue limit is B7 for normal stress and B10 for shear stress. High values of the variable amplitude fatigue strength factor, although formally correct, may be irrelevant and excluded by an assessment of the static strength.
219
5.7 Assessment using classes of utilization Table 5.7.2 Non-welded components, binomially distributed standard stress spectra, classes of utilization according to the spectrum parameters Nand p. Normal stress
~1 ~2.
Required total number of cycles N ... 104 3,2 . 3,2 . 104 ... 105 ... 3,2 . 3,2' 105 ... 106 ... 3,2 . 3,2 . 106 ... 107 ... 3,2 . 3,2 . 107 ... 108 ... 3,2 . 3,2' 108 ... 109 ... 104 ...
Shear stress
104 105 105 106 106 107 107 108 108 109
... 104 104 ... 3,2 . 3;2 . 104 ... 105 ... 3,2 . 3,2 . 105 ... 106 ... 3,2 . 3,2 . 106 ... 107 ... 3,2 . 3,2 . 107 ... 108 ... 3,2 . 3,2 . 108 ... 109 ...
104 105 105 106 106 107 107 108 108 109
Spectrum parameter p
0
1/3
2/3
I
B-3 B-2 B-1 BO B1 B2 B3 B4 B5 B6 B6 B6
B-1 BO BI B2 B3 B4 B5 B6 B6 B6 B6 B6
BOil B1/2 B2/3 B3/4 B4/5 B5/6 B6 B6 B6 B6 B6 B6
B2 B3 B4 B5 B6 B6 B6 B6 B6 B6 B6 B6
Spectrum parameter p
0
1/3
B-5/-4 B-3/-2 B-4/-3 B-2/-1 B-3/-2 B-1/0 B-2/-1 BOil B-1/0 B1/2 BOil B2/3 BI/2 B3/4 B2/3 B4/5 B3/4 B5/6 B4/5 B6 B5/6 B6 B6 B6
2/3
I
BO BI B2 B3 B4 B5 B6 B6 B6 B6 B6 B6
B2 B3 B4 B5 B6 B6 B6 B6 B6 B6 B6 B6
-c- 1 For example BO/1 means the geometrical mean value of the classes
106 and p = 1 corresponds to the component fatigue limit and to the class of utilization B6 .
N = ND,o = ND," =
~1 ~2.
Required total number of cycles N ... 104 3,2 . 3,2 . 104 ... 105 ... 3,2 . 3,2 . 105 ... 106 ... 3,2 . 3,2 . 106 ... 107 ... 3,2 . 3,2 . 107 ... 108 ... 3,2 . 3,2' 108 ... 109 ... 104 ...
Shear stress
BO and to B1.
~2
Table 5.7.3 Non-welded components, exponentially distributed standard stress spectra, classes of utilization according to the spectrum parameters Nand p. Normal stress
~1 ~2.
Required total number of cycles N
5 Appendices
104 105 105 106 106 107 107 108 108 109
Spectrum parameter p
0
1/3
2/3
1
B-5 B-4 B-3 'B-2 B-1 BO BI B2 B3 B4 B5 B6
B-2/-1 B-1/0 BOil B1/2 B2/3 B3/4 B4/5 B5/6 B6 B6 B6 B6
BOil B1/2 B2/3 B3/4 B4/5 B5/6 B6 B6 B6 B6 B6 B6
B2 B3 B4 B5 B6 B6 B6 B6 B6 B6 B6 B6
~1 ~2.
Spectrum parameter p
Required total number of cycles N
0
1/3
2/3
1
... 104 104 ... 3,2 . 104 3,2 . 104 ... 105 105 ... 3,2 . 105 3,2 . 105 ... 106 106 ... 3,2 . 106 3,2 . 106 ... 107 107 ... 3,2 . 107 3,2 . 107 ... 108 108 ... 3,2' 108 3,2' 108 ... 109 109 ... 3,2 . 109 3,2 . 109 ... 10 10 1010 ...
B-7 B-6 B-5 B-4 B-3 B-2 B-1 BO B1 B2 B3 B4 B5 B6
B-4 B-3 B-2 B-1 BO B1 B2 B3 B4 B5 B6 B6 B6 B6
B-1/0 BOil B1/2 B2/3 B3/4 B4/5 B5/6 B6 B6 B6 B6 B6 B6 B6
B2 B3 B4 B5 B6 B6 B6 B6 B6 B6 B6 B6 B6 B6
220
5.7 Assessment using classes of utilization
5 Appendices
Table 5.7.4 Welded components, binomially distributed standard stress spectra, classes of utilization according to the spectrum parameters Nand p.
Table 5.7.5 Welded components, exponentially distributed standard stress spectra, classes of utilization according to the spectrum parameters Nand p.
Normal stress
Normal stress
-¢>1 -¢>2.
Required total number of cycles
Spectrum parameter p
0
113
2/3
1
... 2' 104 2 . 104 ... 6,3 . 104 6,3 . 104 ... 2 . 105 2 . 105 ... 6,3 . 105 6,3 . 105 ... 2 . 106 2 . 106 ... 6,3 . 106 6,3 . 106 ... 2 . 107 2 . 107 ... 6,3 . 107 6,3 . 107 ... 2 . 108 2 . 108 ... 6,3 . 108 6,3 . 108 ...
B-2/-1 B-I10 BOil BII2 B2/3 B3/4 B4/5 B5/6 B6/7 B7 B7
Bl Bl B2 B3 B4 B5 B6 B7 B7 B7 B7
Bl B2 B3 B4 B5 B6 B7 B7 B7 B7 B7
B2 B3 B4 B5 B6 B7 B7 B7 B7 B7 B7
N ... 2' 104 2 . 104 ... 6,3 . 6,3 . 104 ... 2 . 2 . 105 ... 6,3 . 6,3 . 105 ... 2 . 2 . 106 ... 6,3 . 6,3 . 106 ... 2 . 2 . 107 ... 6,3 . 6,3 . 107 ... 2 . 2 . 108 ... 6,3 . 6,3' 108 ... Shear stress
-¢>1 -¢>3.
Required total number of cycles N 104
... 2' 2 . 104 ... 6,3 . 104 6,3 ",104 ... 2 . 105 2 . 105 ... 6,3 . 105 6,3 . 105 ... 2 . 106 2' 106 ... 6,3 . 106 6,3 . 106 ... 2 . 107 2 . 107 ... 6,3 . 107 6,3 . 107 ... 2 . 10 8 2 . 108 ... 6,3 . 10 8 6,3 . 108 ... 2 . 109 2 . 109 ... 6,3 . 109 6,3 . 109 ... 2 . 10 10 2' 1010 ...
Spectrum parameter p
Required total number of cycles
N
Shear stress
-¢>1 -¢>2.
Spectrum parameter p
104 105 105 106 106 107 107 108 108
0
113
2/3
1
B-3 B-2 B-1 BO Bl B2 B3 B4 B5 B6 B7
Bl Bl B2 B3 B4 B5 B6 B7 B7 B7 B7
Bl B2 B3 B4 B5 B6 B7 B7 B7 B7 B7
B2 B3 B4 B5 B6 B7 B7 B7 B7 B7 B7
-¢>1 -¢>3.
Required total number of cycles
0
113
2/3
1
B-3 B-2 B-1 BO Bl B2 B3 B4 B5 B6 B7 B8 B9 BlO
B-1 BO Bl B2 B3 B4 B5 B6 B7 B8 B9 BlO BlO BI0
BOil BII2 B2/3 B3/4 B4/5 B5/6 B6/7 B7/8 B8/9 BlO BlO BlO BI0 BlO
B2 B3 B4 B5 B6 B7 B8 B9 BlO BlO BlO BlO BlO BlO
-c- 1 For example 80/1 means the geometrical mean value of the classes 80 and to 81.
-¢>2 N = NC = 2 . 106 and p = 1 corresponds to the class of utilization 86. The class of utilization 87 corresponds to the component fatigue limit at ND.cr = 5 . 106 . -¢>3 N = NC = 2 . 10 6 and p = 1 corresponds to the class of utilization 86. The class of utilization 810 corresponds to the component fatigue limit at ND.t = 10 8
Spectrum parameter p
N
0
113
2/3
1
... 2' 104 2 . 104 ... 6,3 . 104 6,3 . 104 ... 2 . 105 2 . 105 ... 6,3 . 105 6,3 . 105 ... 2 . 106 2 . 106 ... 6,3 . 106 6,3 . 106 ... 2 . 107 2 . 107 ... 6,3 . 107 6,3 . 107 ... 2 . 108 2 . 108 ... 6,3 . 10 8 6,3 . 108 ... 2 . 109 2 . 109 ... 6,3 . 109 6,3 . 109 ... 2 . 10 10 2 . 10 10 ...6,3 . 10 10 6,3 . 10 10 ...2 . 1011 2' 1011 ...
B-5 B-4 B-3 B-2 B-1 BO Bl B2 B3 B4 B5 B6 B7 B8 B9 BlO
B-2/-1 B-I10 BOil BII2 B2/3 B3/4 B4/5 B5/6 B6/7 B7/8 B8/9 BlO BlO BI0 BI0 BI0
BOil BII2 B2/3 B3/4 B4/5 B5/6 B6/7 B7/8 B8/9 BI0 BlO BlO BlO BlO BI0 BI0
B2 B3 B4 B5 B6 B7 B8 B9 BlO BlO BlO BlO BlO BlO BlO BlO
221
5.7 Assessment using classes of utilization
5 Appendices
Non-welded components,
Welded components,
Normal stress
Normal stress KBK,
19,9,r-"'Ir--,---,--.--r-----:r-----.---,---B_l
'N . B-4 O,a= 106 7,94 t---t---'t<---+--1--+--+--r"':'-t--+B-3 6,31,
- - _.- -._-
--~. -~.
:&-:2
5,01
B-1
3,98'
no
3,16
ni
2,51 I'-<--+--"":
82
B3
~1--~...-+~t--*-+-t--_1_-_+_-Bl
~--+--+--+--B2
4,29
2,92
84 B5
2,00
-,
D6
106
1,36
N
~-+"""'-+--B6
6,32
1,00
2-10 4
'---'"'-"'--c-:-"-"-------l~B 7
2-10 8
2-10S
Shear stress KBK,1' 6,49 5,62
Shear stress
r-,
4,87 1--. 4,22 <, <,
3,65 3,1.6 2,74 2,37
1'-.'-... <,
~
2,05
1,78
os::
F/J
-
1"'-,
"
.-
---
~=lL_
,.
D-7'
.B'-6
... - N n,1' = 106 B-5
,
'" i'-'," ..."--l/J""'"0 <, I " ,
B-4 B~3
R;.2
B-1
no
P""l/.j............. ''-... B1 ~ r--<' . '-.... .B2 P"" /.] I " '-..." B3
1,54 ~ O ~ I~ <, 1,33 ,"e"t~l N n 1' I::: 1,15 3,16 I -I\i('I( . . . ' ~ 1,00 104
lOS
""e f'06
I"- "
<,
10'
'-..."
108
84 85, B6
KBK,t
27,5
"'-
21;9 17,4
.K.
13,8
n,o
r-,
8,71
,~
6,91 5,49
3,46
Solid straight lines: binomially distributed standard stress spectra, dashed straight lines: exponentially distributed standard stress spectra.
* Marked point in CD as an example: when combining
N
= 10 7 and p =
class of utilization B3 applies
a
in the case of a binomially
distributed standard spectrum and results in KBI(,cr '" 2.
2,76
""
<, ~. ._~.-
<,
~
<.
"'"
~P""
- - - ' - ' - - - JB-3
B-2 8-1
'"
r-,
~p~~,
80
<,
<.
-. i~ r-. .. '" <: ,
2,19 1,74 1,38 1,10 !-- r-6,3'" 1,00. 4 HO 2'105
~
<'11"0 1 ~ ~ -~,
Nc "
....
Bl 82
<,
~~ <; <, '~t'ljl" ~
B-4
No,;"" 108
...._.
~ ". ~r~o <,
~~ -.
..
-
r<,
1"'( K
4,38 --
Figure 5.7.1 Relationship between the variable amplitude fatigue strength factors KBK,cr and KBK, 't, the class of utilization B, the required total number of cycles N and spectrum parameter p.
.-.
B-5
~=5
~
i~ ~.~
<,
B3
84
<,
"'-: <, B7 <,
B8
"'-I ~~t )?s B9BI0
2-10'
N
HOll
222 5.8 Particular strength characteristics of components with surface treatment
5.8 Particular strength characteristics of surface hardened components
~--~
5 Appendices
(less favorable) than for components not surface hardened, since the tensile strength Rm *4 of the hardened surface layer is higher.
1R58 EN.dog
In this chapter particular strength characteristics of surface hardened components are compiled, which are contained at the mentioned positions of Chapter 1.3 (component static strength) and of Chapter 2.3 and 2.4 (component fatigue strength) * 1. Surface hardening is caused by an application of chemothermical procedures of surface treatment (nitriding, case hardening, carbonitiding) or thermal procedures of surface treatment (inductive hardening, flamehardening), Table 2.3.5. Mechanical procedures of surface treatment (cold-rolling, shot-peening) are not referred to in the present context, however.
In the case of surface hardened components the surface treatment factor is dependent on whether the origin of a crack is expected at the surface or in the core. Essential are the ratio of the fatigue limit values of the surface layer and that of the core material as well as the ratio of the load induced local stresses at the surface and in the core just below the hardened layer (depth of case or hardened layer).
Chapter 2.4.2.4, following Eq. (2.4.34), Component mean stress sensitivity Ma, ....
Chapter 1.3.2, Eq. (1.3.6), Section factors npl,b .... In the case of surface hardened components (components with chemo-thermical or with thermal surface treatment), see Table 2.3.5, the section factors npl,b ... > 1 are not to be applied *2: npl,b, ... = 1 .
Chapter 2.3.4, following Eq. (2.3.28), Surface treatment factor, Kv .
(1.3.6)
Chapter 2.3.2.1, following Eq. (2.3.15),
Kt:Kf ratios ncr .., . In the case of surface hardened components (components with chemo-thermical or with thermal surface treatment) the Kt-Kf ratios are lower than in the case of components not surface hardened *3 *4.
Chapter 2.3.3, preceding Eq. (2.3.27), Roughness factor KR,cr '" . In the case of surface hardened components and a crack originating at the surface the roughness factor is lower
1 OrChapter 3.3, 4.3 and 4.4: In the following the mentioned chapters, tables, and equations always refer tothe corresponding ones ofChapter 3 and4aswell.
In the case of surface hardened components the component mean stress sensitivity is greater than for components not surface hardened, because of the higher tensile strength Rm of the hardened surface layer.
Chapter 2.4.3.2, 4th paragraph, Slope of the component constant amplitude S-N curves, k cr , .... In the case of surface hardened components the slope of the component constant amplitude S-N curves are less steep than in the case of components not surface hardened. Values kcr = 15 and k, = 25 apply for surface hardened, non-welded components of steel and cast iron materials instead of the values kcr = 5 and k, = 8 that apply to components not surface hardened, Tab. 2.4.4. The number of cycles at the knee points ND,cr and ND,~ remain unchanged, however.
Chapter 2.6, following Eq. (2.6.6) and (2.6.14), strength hypothesis for combined stress. For surface hardened components there is q = 1 *5.
2 Section factors npl,zd , ... > 1 require a reasonable local plasticty to occur at notches. The limited plasticity of a hardened surface layer, however, does not allow that but may give rise tocracks instead. Possibly Eq. (1.3.6) is a demand too far on the safe side, as according to DIN 743 a value npl = 1,1 isallowed for case-hardened shafts. 3 For cracks originating atthe surface the Kj-Kj ratios are lower because ofthe higher tensile strength Rm ofthe hardened surface layer compared to the lower tensile strength of the tender core (according to material standard). For cracks originating in the core the Kt-Kf ratios are lower since the related stress gradients Gcr and G~ are lower in the core of the component than the related stress gradients atthe surface notch.
4The tensile strength ofthe hardened surface layer approximately follows from its Vickers hardness number HV: Rm = (3,3 . HV) Mpa. This equation, however, was not especially established for hardened surface layers and therefore it is to be applied with caution . In particular the fatigue limit for completely reversed stress of a hardened surface layer must not be computed from the tensile strength (crw,zd :F fW,cr . Rm ! ). 5 That means that the normal stress criterion istobe applied.
223 5.9 An improved method for synchronous multiaxial stresses
5.9 An improved method for computing the component fatigue limit in the case of synchronous multiaxial stresses 1R59 EN.docl Page
Content
5.9.0
General
5.9.1 5.9.1.1 5.9.1.2 5.9.1.3
Equivalent stress amplitude and equivalent mean stress Rod-shaped (ID) components Shell-shaped (2D) components Block-shaped (3D) components
5.9.2
Mean stress factor
223
224 225
According to this chapter the component fatigue limit may be computed by an improved method and with higher reliability than according to Chapter 2.4.2 or 4.4.2, Figure 5.9.1. The computation applies for nonwelded components of steel subject to synchronous multiaxial stresses *1, where
/.J3
= 0,58
5.9.1 Equivalent stress amplitude and equivalent mean stress *2 Equivalent stress amplitude in related form:
~ sa,v =Vsa +t a ' where *3 Sa,zd Sa,b +--sa SWK,zd SWK,b'
D
ISm,y
r
Sa,y
t mt = (liE) . {AI 'S~ +A 4 Sm,zd Sm,b Sm = +--SWK,zd SWK,b' Tm,s
tm = - - -
TWK,s
According to Chapter 2.4.2 or 4.4.2 an individual mean stress factor KAK,zd, ... is to be computed for every single stress amplitude Sa,zd, , either from a single acting mean stress Sm,zd , or from an equivalent mean stress Sm,v or Tm,v , respectively. Using these mean stress factors the amplitude values of the component fatigue limit, SAK,zd, ... are to be computed. After the method described in this chapter an equivalent stress amplitude Sa,v (in terms of a related value sa,v ) is
TWK,t
(5.9.5)
where *4 sms = (3 /7) . (Bl . Sm + B3 . 1m),
~LJ~
Figure 5.9.1 Example for the significance of the improved method: Mean stress in the direction or perpendicular to the stress amplitude (Nominal stresses). The improved method distinguishes these cases whereas the method after Chapter 2.4.2 or 4.4.2 does not.
Sa,zd, ... SWK,zd ...
Sm,zd ...
(5.9.6)
.t~ +A 5 ,sm .t m } 1I 2
Tm,t
+-TWK,t
stress amplitude, Chapter 2.1.1.1 (or 4.1.1.1), component fatigue limit for completely reversed stress, Chapter 2.4.1 (or 4.4.1), constant, Table 5.9.1, with sa,x = Sa , Sa,y = 0, mean stress, Chapter 2.1.1.1 (or 4.1.1.1).
2 The equations in Chapter 5.9.1.1 and 5.9.1.2 are written for nominal stresses. They apply to local stresses as well, if S andT arereplaced bya and "to The equations in Chapter 5.9.1.3, however, apply for local stresses only.
3 For local stresses there is sa = aa I <:5WK '
ta 4
I seeChapter 0.3.5.
+--.
sm,v = 0,87 . (sms + t mt ),
S m . x I I Sm.,x
alta bUdlq
(5.9.3)
Equivalent mean stress in related form:
!Sa,y
rSa,y
(5.9.2)
Ta,t
-
TWK,s
Sa,y
!Sm,y
Ta,s
ta = -
(5.9.1)
(Shear fatigue limit for completely reversed stress ""Cw,s, axial fatigue limit for completely reversed stress crW,zd)'
!
computed from all single stress amplitudes Sa,zd , ... , and an equivalent mean stress Sm,v (in terms of a related value sm,v ) is computed from all single mean stresses Sm,zd, ... , and/or T rn.s- ... , and finally from these a common mean stress factor KAK,v . Using this common mean stress factor the amplitude values of the component fatigue limit, SAK,zd , ... , are to be determined as before.
5.9.1.1 Rod-shaped (ID) components
5.9.0 General
fw,"t = ""Cw,s / crW,zd = 1
5 Appendices
=
(5.9.4)
"t a I"tWK·
For local stresses there is sm = am I aWK , t m = "t m I "tWK .
(5.9.7)
224
5.9 An improved method for synchronous multiaxial stresses Table 5.9.1 Coefficients Al to A6 and BI to B3 .
Al
2 2 2 4s ax +3s a,y -4s a, 'Say x' , +(7/3)·t a 2 2 2 Sa.x +S a.y -Sa,x'Sa,y+t a
A2
2 2 2 3s a,x +4s a,y -4s a"x 'Say +(7/3)·t a 2 2 2 Sa,x +S a,y -Sa,x 'Sa,y +t a
A3
_4s 2 -4s 2 +6sa,x,say-2t 2 a,x 'a a,y 222 Sa,x +S a.y -Sa,x'Say+t , a
A4
2 2 2 7s a,x +7sa,y -6sa,x 'Sa,y +12t a 2 2 2 Sa,x +S a,y -Sa,x 'Sa,y +t a
1 AS
13' 1
sm,x = Sm,x 1 SWK,x , Sm,y = Sm,y 1 SWK,y , t m = Tm/T WK , Sa,x ...
stress amplitude, Chapter 2.1.1.2 (or 4.1.1.2), SWK,x, ... component fatigue limit for completely reversed stress, Chapter 2.4.1 (or 4.4.1), BI,... constant, Table 5.9.1, Sm,x ... mean stress, Chapter 2.1.1.2 (or 4.1.1.2).
5.9.1.3 Block-shaped (3D) components Equivalent stress amplitude in related form: sa,v =
±.
lOsa,x . t a - 6s a,y . t a 2 2 2 Sa,x +S a,y -Sa,x 'Sa,y +t a
13
BI
2 2 2 5s a,x +S +2s a"x 'Say +(4/3)·t a a,y 2 2 2 3s a.x +3s a,y +2s a,x 'Sa,y +(4/3).t a
13
B3
(5.9.16) (5.9.17)
where
Sms = (3/7) . (D! . sm,! + D2 . sm,2 + D3 . Sm,3), t mt
= (1 1J2l) .
2 2 2 . (C! .Sm, + C2 .Sm, 2 + C3 .Sm 3 + + C4 . sm,! . sm,2 + Cs . Sm,2 . sm,3 + C6' Sm,3 . sm! ) 1/ 2 ,
+
Sm,1 = CY m,! 1 CYWK,l , sm,2 = CYm,2 1 CYWK,2 , sm,3 = CY m,3 1 CYWK,3 ,
5.9.1.2 Shell-shaped (2D) components Equivalent stress amplitude in related form:
stress amplitude, Chapter 4.1.1.3, component fatigue limit for completely reversed stress, Chapter 4.4.1, constant, Table 5.9.2, mean stress, Chapter 4.1. 1. 3 .
CYa , ! . CYWK,! .. (5.9.8) DI, CY m , !
where "5 sa,x = Sa,x 1 SWK,x , Sa,y = Sa,y 1 SWK,y , ta = 1 TWK.
(5.9.15)
sm,v = 0,87 . (sms + t mt),
8,(sa,x +Sa,y )·t a 2 2 2 3s a,x +3s a,y +2s a"x 'Say +(4/3)·t a
~ S2 +s 2 -Sa,x'Sa,y+t 2 , Sav= , a,x a,y a
~ + (Sa,3 - Sa,IP ),
Equivalent mean stress in related form:
2 2 Sa.x +5s a,y +2s a"x 'Say +(4/3)·t a 2 2 2 3s a,x +3s a,y +2s a"x 'Say +(4/3)·t a
I
((Sa,1 -Sa,2)2 +(Sa,2 -sa,3
sa,! = CYa,1 1 CYWK,I , Sa,2 = CY a,2 1 CYWK,2 , sa,3 = CY a,3 1 CYWK,3 .
2
B2
(5.9.14)
where
-6s a,x . t a + lOSa,y . t a 222 Sa,x +S a.y -Sa,x 'Sa,y +t a
A6
5 Appendices
. .
(5.9.9)
r,
Equivalent mean stress in related form: sm,v = 0,87 . (sms + t mt ), where "6
5
(5.9.11) (5.9.12)
Sms = (3 17) . (BI . sm,x + B2 . Sm,y + B3 . t m), t mt
= (1 IJ21)
.
2 2 - (A! .s m,x + A2 .Sm,y + A3 . sm,x . Sm,y 2 ) 1/2 +~·tm +AS·sm,x.tm+A6·Sm,y·tm ,
For local stresses there is sa,x = O"a,x / O"WK,x , Sa,y = O"a,y / O"WK,y , t a = "ta /
(S.9.!0)
"tWK .
6 For local stresses there is
sm,x = O"m,x / O"WK,x , Sm,y = O"m,y / O"WK,y , t m = "tm /
"tWK .
(5.9.13)
225
5.9 An improved method for synchronous multiaxial stresses Table 5.9.2 Coefficients
5.9.2 Mean stress factor The mean stress factor KAK,v common for all types of stress is to be calculated according to the expected type of overloading. It is Smin,v
=
sm,v - sa,v ,
5 Appendices
2 4s a.1
CI
to C6 and Dl to D3.
2 +3s a.3 -4S a,I Sa.2 -2S a,2 Sa,3 -4S a,3 Sa,1
2 2 2 Sa,1 +Sa,2 +Sa,3 -Sa,1 Sa,2 -Sa,2 Sa,3 -Sa,3 Sa,1
(5.9.18)
smax,v = sm,v + sa,v , Rcr,v = smin,v 1 smax,v ,
2 + 3Sa,2
c,
.
.
+ 4s;, 2 + 3s; 3 - 4s a" I Sa 2 - 4s a. 2 Sa ,3 - 2s a"3S a I 2 2 2 Sa,1 +Sa,2 +Sa,3 -Sa,I Sa,2 -Sa,2 Sa,3 -Sa,3 Sa,1
3s; I
Cz
sm,v, sa,v after Chapter 5.9.1.1 to 5.9.1.3.
3S;,1
+3S';,2 +4S';,3 -2S a,I Sa,2 -4S a,2 Sa,3 -4S a,3 Sa,1 2 2 2 Sa,1 +Sa,2 +Sa,3 -Sa,lSa,2 -Sa,2 Sa,3 -Sa,3 Sa,1
C3
Type of overloading F2 KAK,v is to be calculated according to Chapter 2.4.2.1 or 4.4.2.1, type of overloading F2, after having replaced Sm,zd 1 Sa,zd or am 1 aa by sm,v 1 sa,v (and Rzd or R cr by Rcr,v ).
2Sa,1 2 2 + 2 Sa,2 C4
Type of overloading Fl KAK,v is to be calculated according to Chapter 2.4.2.1 or 4.4.2.1, type of overloading Fl, after having replaced sm,zd or Sm by sm,v .
C6
Type of overloading F3
Type of overloading F4 KAK,v is to be calculated according to Chapter 2.4.2.1 or 4.4.2.1, type of overloading F4, after having replaced Smax,zd or Smax by smax,v .
2
2 2 Sa,2 +2S a,3 -Sa,1 Sa,2 -3S a,2 Sa,3 -Sa,3 Sa,1 2 2 2 Sa,! +Sa,2 +Sa,3 -Sa,lSa,2 -Sa,2 Sa,3 -Sa,3 Sa,l
+
2 2 2S a,l +Sa,2
DI
KAK,v is to be calculated according to Chapter 2.4.2.1 or 4.4.2.1, type of overloading F3, after having replaced smin,zd or Smin by smin,v .
2 2 2 Sa,1 +Sa,2 +Sa,3 -Sa,lSa,2 -Sa,2 Sa,3 -Sa,3 Sa,l 2 Sa,!
Cs
2 +Sa,3 -3S a,lSa,2 -Sa,2 Sa,3 -Sa,3 Sa,1
2
+ 2S a,3
- Sa,1 Sa,2 - Sa,2 Sa,3 - 3S a,3 Sa,l
2 2 2 Sa,l +Sa,2 +Sa,3 -Sa,lSa,2 -Sa,2 Sa,3 -Sa,3 Sa,l
2 2 2 5s a,1 +Sa2 , +Sa3 , +2S a,lSa,2
+(2/3)sa,2 Sa,3
+2S a,3 Sa,1
2 2 2 3s a,1 + 3s a,2 + 3s a,3 + 2S a,1 Sa,2 + 2Sa,2S8,3 + 2Sa,3 Sa,1
Dz
2 2 2 Sa,2 +2S a,2Sa,3 +(2/3)sa,3 Sa,1 Sal, +5s a,2 +Sa3 , +2S a,l 2 2 2 3s a,1 +3s a,2 +3s a,3 +2S a,lSa,2 +2S a,2Sa,3 +2S a,3 Sa,1
D3
2 2 2 Sa,l + Sa,2 + 5s a,3 + (2/3) Sa,lSa,2 + 2s a,2Sa,3 + 2s 8,3 Sa,l 2 2 2 3s a,1 +3s a,2 +3s a,3 +2S a,lSa,2 +2S a,2Sa,3 +2S a,3 Sa,1
226
5.10 Approximate assessment for non-proportional multiaxial stresses
5 Appendices
5.10 Approximate assessment of the fatigue strength in the case of nonproportional multiaxial stresses
while the directions of the principle stresses remain constant. Moreover the histories and the spectra of all stress components are identical with those of the respective loading, and they differ by particular scaling factors only.
Content
Hence for each of the particular loadings there is no doubt that the assessment procedure described in Chapter 2 or 4 is applicable on the basis of the resulting types of stress (tension-compression stress, ... , normal stress ... , principle stresses) in order to derive the corresponding degree of utilization for the combined types of stress according to Chapter 2.6 or
~~-51-0-EN"""."""do-'q
5.10.0 5.10.1 5.10.2
Page General Background information Procedure
226
5.10.0 General The procedure described in this chapter is a rough approximation to assess the fatigue strength *1 in the most general case of non-proportional multiaxial stresses *2. It may be supposed that it provides a result that is always on the safe side, but possiblyfar on the safe side *3. The approximate procedure is applicable for rodshaped (10), shell-shaped (2D) and block-shaped (3D) components. The assessment can be carried out with nominal stresses or with local stresses. A background information and a description of the procedure are presented in the following.
4.6.
Each of the particular loadings is to be considered in this manner. Finally the degrees of utilization derived for the particular loadings are to be added linearly to obtain the overall degree of utilization due to the combined action of all loadings. In principle the most detrimental kind of interaction of the particular loadings is assumed with the linear summation of the particular degrees of utilization.
5.10.2 Procedure
5.10.1 Background information
The particular loadings that act non-proportionally on the component, are to be determined as Loading I, (5.10.1) Loading II,
Non-proportional multiaxial stresses result if a component observes at least two different loadings that vary with time independently. In general different histories and spectra apply to the these loadings.
For everyone of these particular loadings I, II ... the resulting stresses are to be determined according to Chapter 2.1 or 4.1 and thereafter the assessment is to be carried out according to Chapter 2 or 4.
Under the combined action of the different loadings a multiaxial state of stress occurs at the reference point *4, where both the magnitude and the direction of the principle stresses vary with time and where the stress spectra of the principle stresses (as well as the spectra of any other stress components) are different.
From the particular assessments the degrees of utilization for the combined types of stress according to Chapter 2.6 or 4.6 are obtained for everyone of these particular loadings I, II ... aSK,Sv,I or aSK,crv,I, (5.10.2) aSK,Sv,I1 or aSK,sv,I1,
On the other hand a separate action of each of the particular loadings produces a state of stress at the reference point that varies proportionally with time
These particular degrees of utilization are to be added linearly to obtain the overall degree of utilization due to the combined loadings.
1 The procedure is applicable both for an assessment of the variable amplitude fatigue strength and of the fatigue limit. 2 Also in the special case of non-proportional uniaxial stresses. 3 Mechanically reasonable methods of calculating the fatigue strength under non-proportional multiaxial stresses require a high computing effort and the application of a suitable computer program. 4 Under the action of more than one loading the very reference point may be different from the respective reference points that would result for each of the particular loadings. This is because the maximum damage from the combined loadings may occur at a location different from the locations where the particular loadings produce maximum stresses.
aSK,Sv,ges
= aSK,Sv,I + aSK,Sv,I1 + ...
(5.10.3)
aSK,sv,ges
= aSK,crv,I + aSK,O'V,I1 + ...
(5.10.4)
or A necessary reservation against this procedure is, that in every case of application both the loading situation and the final result has to be carefully and critically analyzed. In cases of doubt a suitable computer program is to be applied, or an experimental assessment is to be carried out.
227 5 Appendices
5.11 Experimental determination of component strength values
5.11 Experimental determination of 1R511 EN.docl component strength values Page
Content 5.11.0 5.11.1 5.11.2
General Experimental determination of a mean value Standard deviation and statistical confidence
227
229 b5Jlle
19(5x)
19(5i,~
19(5x,50%)
Component strength (logarithmic scale)
5.11.0 General According to this chapter component static strength values and/or component fatigue strength values can be determined experimentally. The given recommendations are aimed at obtaining component strength values that are sufficiently reliable, although the number of tests will be limited in most cases *1. The loading conditions for these tests may be specified in terms of loads, moments or stresses observing the proper load or stress ratio. The obtained test results may be presented in terms of loads, nominal stresses or local stresses (structural stresses or effective notch stresses for welded structures) *2. Practically a component may be subject to several kinds of service loadings according to its operating conditions. The testing procedure described below is restricted to a single kind of loading the component strength value for which is of particular interest. Nevertheless this single kind of loading may cause multiaxial stresses of the component, which are proportional stresses, however *3. As test results will normally show a reasonable scatter several identical repetitions of the same test are necessary in order to allow a statistical evaluation of the results. It is common to assume a logarithmic Gaussian scatter distribution to exist, Figure 5.11.1.
Figure 5.11.1 Sufficiently reliable component strength value Sx to be derived from a number of experimentally determined component strength values Si,X . LSD
= logarithmic standard deviation = standard deviation of 19( SiX) .
From a larger sample it would be possible to determine the logarithmic standard deviation, LSD, too. If the sample is small, however, this result would not be reliable. Therefore with small samples an experienced estimate of the logarithmic standard deviation, LSD, has to be used instead. Then, from the experimentally obtained geometric mean and the experienced logarithmic standard deviation it is possible to derive the wanted component strength value for a probability of survival of Po = 97,5 %. It is obtained by dividing the geometric mean, SX,50% , by a statistical conversion factor, jn,s after Table 5.11.1, which is dependent on the logarithmic standard deviation, LSD, and on the number of tests, n, Figure 5.11.1 *5.
From an experimental examination of the component strength, which is usually restricted to a small sample because of testing time and cost, only the (geometric) mean of the component strength value, SX,50% , can be determined sufficiently exact. It is associated with a probability of survival of Po = 50 % *4.
4 The geometric mean is the antilog of the logarithmic mean computed I The same procedure also applies to material strength values. 2 The description bellow is given in terms of nominal stresses, but it
from Eq. (5.11.1) 5.11.4) or (5.11.7), respectively.
also is valid for loads or local stresses.
between the (geometric) mean
3 Multriaxial testing by applying more than one different kind ofloading
strength value for PO = 97,5 %, and moreover for the statistical
simutaneously, which will result in non-proportional stresses of the
uncertainty of an experimentally determined (geometric) mean as a
component, is not considered here.
function of the sample size.
5
The statistical conversion factor Jn ,s allows for the difference
(PO
=
50
%)
and the component
228
5 Appendices
5.11 Experimental determination of component strength values 5.11.1 Experimental determination of the geometric mean value Component static strength The logarithmic mean value of the experimentally obtained component static strength values Si,SK (yield stress or rupture stress, sample size n) is 1
19 (SSK ,50%)
n
= -n . "lg (S,,SK ) ~
(5.11.1)
i=!
SSK,50% = antilog [lg ( SSK,50% )]
(5.11.2)
where the number of cycles at the knee point, ND, and the slope of the S-N curve, k, are those from Table 2.4.4 or 4.4.4.
Component variable amplitude fatigue strength To determine the component variable amplitude fatigue strength for a given stress spectrum and a required total number of cycles N the experimental examination can be carried out at some stress amplitude exceeding the expected fatigue limit *7 , The experimental examination of n test pieces on that stress level, SL = Sa,1 results in the numbers of cycles N i,L , (i= 1 ... n), the logarithmic mean value of which is
Component fatigue limit For an experimental examination of the component fatigue limit several possibilities exist.
(5.11.7)
Stair case tests and other test methods Having available a sufficiently large sample of test pieces (n ;::: 15 as a minimum) the component fatigue limit can be experimentally determined in a direct approach (without extrapolation) by the stair case test method, or by other test methods proposed in the literature. Result of the evaluation procedure of the respective test method is the mean value of the component fatigue limit,
N L,50% = antilog [lg (N L,50% )]
The mean value of the component variable amplitude fatigue strength for the required number of cycles N follows from an extrapolation of the variable amplitude fatigue life curve: SBK,50%
SAK,50%
= resultofevaluationprocedure (5,11.3)
Tests on a stress level above the fatigue limit In order to reduce the required testing time and if the number of possible tests is less than 15 (1 ::; n < 15), the experimental examination can be carried out at some stress amplitude exceeding the expected fatigue limit *6. The experimental examination of n test pieces on that stress level, SL, results in the numbers of cycles N, L , (i = 1 ... n), the logarithmic mean value of which is ' 19 (NL,50%)
1
= -n . "lg(NiL) ~ .
NL,50% = antilog [lg (NL,50%)]
(5.11.4) (5.11.5)
The geometric mean value of the component fatigue limit follows from an extrapolation along the constant amplitude S-N curve down to its knee point: SAK,50% = S L . (NL,50% / ND ) 1 / k
(5.11.8)
=
{-
SL . ,N L•50%
/
-)lIk N
(5.11.9)
In a first approach the slope k of the variable fatigue
life curve may approximately be taken equal to the slope k of the component constant amplitude S-N curve after Table 2.4.4 or 4.4.4. Taking k = k means a fatigue life curve after the elementary version of Miner's rule being valid, see Figure 2.1.5 or 4.1.5. The actual slope of the variable amplitude fatigue life curve k may, however, be somewhatlarger than that of the constant amplitude S-N curve, (k ;::: k), see Eigure 2.1.5 or 4.1.5. To observe the actual slope k the extrapolation has to be based on a fatigue life curve derived by the consistent version of Miner's rule for a rough estimate of the fatigue limit, the values k and ND after Table 2.4.4 or 4.4.4, and the spectrum of concern, Chapter 2.3,L or 4,3,1 *8. The stress amplitudes S*a,1,50% for N L,50% and S*a,l for N may be read off that fatigue life curve for an extrapolation as follows:
SBK,50%
SL"
[S*a 1 for N ]
(5.11.10)
[S*a,I,50% for N L,50%]
(5.11.6)
7 Provided that there is a sufficient distance to the yield strength. 6 Provided that there is a sufficient distance to the yield strength and that the critical location and the type of failure does not change when increasing the stress.
8 An experimental determination of the slope k from (a small number of tests an two stress levels would yield an unreliable result and cannot be recommended.
229 5.11 Experimental determination of component strength values 5.11.2.2 Logarithmic standard deviation and statistical conversion factor An estimate of the logarithmic standard deviation LSD is to be applied, Table 5.11.1, as a reliable determination of the standard deviation is not possible because of usual test samples being too small.
The "reliable" value of the component strength Sx for Po = 97,5 % is, with SX,50%= Figure 5.11.1, Sx = SX,50% / jn,s,
(5.11.11)
where .
=
In,s
1O(2+IIFn"j.LsD
(5.11.12)
SX,50% Geometric mean value SSK,50%, SAK,50% or SBK,50% of the experimentally determined stress values S, x , Statistical con~ersion factor, Table 5.11.1 *5, In,s Sample size, n Logarithmic standard deviation applicable to LSD the experimentally determined stress values Si,X , Table 5.11.1.
Tab 5.11.1 Statistical conversion factor jn,s as a function of the logarithmic standard deviation LSD and of the sample size n ~ 1. LSD 0,02 0,04 0,06 -c- 1
~2 ~3 ~4
1
2
4
n 6
10
100
oc
1,15 1,32 1,51
1,13 1,28 1,45
1,12 1,26 1,41
1,12 1,25 1,39
1,11 1,24 1,38
1,10 1,21 1,34
1,10 1,20 1,32
Statistical conversion factor according to IIW Recommendations,
~ 2 Experienced logarithmic standard deviation ofthe static strength of non-welded or welded components, ~3 Experienced logarithmic standard deviation ofthe fatigue strength of non-welded components, ~4 Experienced logarithmic standard deviation ofthe fatigue strength of welded components.
5 Appendices
230
5 Appendices
5.12 Stress concentration factor for a substitute structure
5.12 Stress concentration factor for a substitute structure IRS12 EN.dog To compute the design factors after Chapter 4.3.1.1, Eq. (4.3.1) to (4.3.3), stress concentration factors Kt,cr and Kt;t must be known, if the effect of surface roughness is to be considered in relation to the notch severity. The stress concentration factor, however, may not be known, as in the case of a finite element calculation for instance. Then it is to be derived for a substitute structure from the following approximation formula. This formula provides a general estimate of the stress concentration factors for normal stress, Kt,cr , and for shear stress, Kt, ~ , as a function of the notch radius r and the "wall thickness" b *1"1:
Notch radius The notch radius r is given by the drawing, or an apparent notch radius r is approximately to be derived from the related stress gradient G cr or G~, see Table 2.3.3: r=2/G cr
'
(5.12.2)
r = 1 (G~ .
Wall thickness The wall thickness b is given by the drawing, or it is to be determined from the equivalent diameter deff . Concerning deff two cases are to be distinguished according to kind of material, see Table 3.2.3.
Kt,cr = Kt,~ =
= K, = MAX (10 O,066-0,36·lg(r/s) ; 1)
(5.12.1)
Case 1 The notch radius r and the wall thickness b are to be determined from the available design data. The approximation formula for the substitute structure, Eq. (5.12.1), is exactly valid for a flat specimen with a deep single-sided notch in bending, Figure 5.12.1 *2. .. ..
"-nnnTM -;:;-r I b ~O,04
r--
1I
! r
,
3,4
_.
3,2 3,0
- -
-.
0,08
~I
-
2,8 2,6 2,4
".'""
i
OJ2 I
0,2
,
],6 1,4 I
1,2 1,0
I
:
.
0;4 0,6 I
I
.,
-\
"'"7J ;
;
i.o 1;21,41,61,8 2,02,22,42,62,K 3,() -.
(5.12.3)
Case 2 For components (also forged coniponents) of nonalloyed structural steel, of fine grain structural steel, of normalized quenched and tempered steel, of cast steel and of aluminium alloys there is s = deff.
I
2,2
1,8
s = deff/ 2.
I I
2,0
For components (also forged components) of quenched and tempered steel, of case-hardened steel, of quentched and tempered and nitrided nitriding steel, of heat treatable steel casting, GGG, GT and GG there is
.
- 1Ilb
Figure 5.12.1 Stress concentration factor for the substitute structure, with reference to Chapter 5.2, Figure 5.2.15.
1 MAX means, that the larger term one the right side of the equation applies. 2 The approximation formula is a provisional one and is to be applied with caution.
(5.12.4)
231
6.1 Shaft with shoulder
6 Examples
2 MATERIAL PROPERTIES
6 Examples 1R61 EN.docl
6.1 Shaft with shoulder *1
Tensile strength and yield strength for the standard dimension Rm,N = 1000 MPa, Rp,N = 800 MPa.
Key words: Shaft with shoulder, milled steel, assessment of static strength, assessment of fatigue limit, fatigue notch factor by calculation, type of overloading F2, multiaxial stresses, rotating bending and torsion. Supplemented: improved calculation of the fatigue limit, calculation using a class of utilization. Given:
Tab. 5.1.4
Technological size factor ad,m = 0,30, ad,p = 0,44 , deff,N = 16 mm, deff = d = 42 mm, ~,m = 0,895, Kd,p = 0,841 .
Tab. 1.2.1 Tab. 1.2.3 (1.2.9)
Anisotropy factor
Stresses: constant amplitude loading in bending and torsion, where the nominal stresses are, Figure 6.1.1,
(1.2.17) Tensile strength and yield strength of the component R m = 0,895 . 1 . 1000 MPa = 895 MPa, R, = 0,841 . 1 . 800 MPa = 672 MPa .
Sb = ±Sa,b = ±150 MPa, Tm,t ± Ta,t = 50 MPa ± 100 MPa.
r, =
(1.2.1)
3 DESIGN PARAMETERS The calculation is carried out by applying the section factor np1, although a satisfactory assessment could be obtained without considering the section factor, that is np1 = 1 (results given in parenthesis).
Figure 6.1.1 Shaft with shoulder.
Material: 41 Cr 4 after DIN EN 10 083.
Design factor for bending
Dimensions: D = 50 mm, d = 42 mm, r = 5 mm, t = 4 mm, d / D = 0,84, r / d = 0,119, r / t = 1,25.
Section factor
Surface: average roughness Rz = 10 urn. Type of overloading: When overloaded in service the stress ratios remain constant (Type of overloading F2). Safety requirement: according to the statements "with moderate consequences of failure; regular inspections".
Rp,max = 1050 MPa, Tab. 1.3.1 Rp = 685 MPa, Kp,b = 1,70, Tab. 1.3.2 Ilpl,b = MIN (J1050/685; 1,70) = 1,250 (1,000). (1.3.9) Design factor KSK b =
,
I
1,250 (1)
0,800 (1,000).
=
(1.3.1)
Task: Assessment of the component static strength and of the component fatigue limit.
Design factor for torsion
Method of calculation: Rod-shaped (ID) component. Assessment with nominal stresses, Chapter 1 and 2.
Section factor Rp,max = 1050 MPa, = 685 MPa, Kp,t = 1,33 ,
Tab. 1.3.1
R,
ASSESSMENT
npl,t = MIN ( .J1050 / 685 ; 1,33) = 1,250 (1,000). (1.3.9)
OF THE COMPONENT STATIC STRENGTH
1 CHARACTERISTIC STRESSES Maximum stresses Smax,ex,b = + Sa,b = 150 MPa, Tmax,ex,t = Tm,t + Ta,t = 150 MPa.
1 Results
ofcomputation obtained by the PC-program
Tab. 1.3.2
Design factor (1.1.1) *2
"WELLE".
2 Numbering of equations, tables and figures according to the main chapters of the guideline.
KSK t =
,
1
1,250 (1)
=
0,800 (1,000).
(1.3.1)
232
6.1 Shaft with shoulder
4 COMPONENT STATIC STRENGTH
Combined types of stress
Component static strength for bending and torsion Component static strength for bending resulting from the tensile strength and the design factor: fa = 1, 1·895:MPa SSK b = = 1119 , 0,800 (1)
6 Examples
Tab. 1.2.5 (895) MPa.
(1.4.1)
Component static strength for torsion resulting from the shear strength factor f,; , the tensile strength and the design factor: f,; = 0,58, Tab. 1.2.5 T _ 0,58· 895:MPa SK,t 0,800 (1) = 646 (519) MPa. (1.4.1)
f,; = 1 /..[3, q = 0, s = aSK,b = 0,235 (0,294), t = aSK,t = 0,406 (0,506), aGH =
Tab. 1.2.5 (1.6.7) (1.6.6)
~0,235 (0,294)2 +0,406 (0,506)2
(1.6.5)
= 0,469 (0,585), aSK,Sv = 0,469 (0,585).
(1.6.4)
The degree of utilization of the component static strength is 47 % (or without section factor 59 %). The assessment of the static strength is achieved.
ASSESSMENT OF THE FATIGUE STRENGTH
5 SAFETY FACTORS
1 CHARACTERISTIC STRESSES
In general there is
Constant amplitude stresses
jm = 2,0, jp = 1,5.
Tab. 1.5.1
For moderate consequences of failure and high probability of occurrence of the characteristic stress, however, there is jm = 1,75 , jp = 1,3.
Tab. 1.5.1
For normal temperature there is KT,m = KT,p = 1,
(1.2.26)
and in Eq. (1.5.4) the terms 3 and 4 have no relevance: Rp = 685 MPa, Rm = 895 MPa,
jges =MAX(I,75;1,3. 895) 685
Sb = ± Sa,b = ±150 MPa, r, = Tm,t ± Ta,t = 50 MPa ± 100 MPa.
(2.1.1)
2 MATERIAL PROPERTIES Material fatigue limits for completely reversed normal stress, crW,zd , and shear stress, 'tw,s : R m = 895 Mpa, Tab. 2.2.1 fw,e = 0,45 , crW,zd = 0,45 . 895 MPa = 403 Mpa , (2.2.1) fw,,; = 0,58, Tab. 2.2.1 'tw,s = 0,58 . 403 MPa = 233 Mpa . (2.2.1)
(1.5.4) .
3 DESIGN PARAMETERS
= MAX (1,75; 1,70) = 1,75. The tensile strength R m (term 1) is determining.
Design (actor for bending Fatigue notch factor
6 ASSESSMENT
Analytically derived from the stress concentration factor
Maximum stresses for bending and for torsion, see above,
Stress concentration factor
Smax,ex,b = 150 MPa, T max.ex.t
0=
150 MPa.
Component static strength for bending and for torsion, see above, SSK,b = 1108 (895) MPa, TSK,t, = 642 (519) MPa. Degrees of utilization Individual types of stress, bending and torsion 150 aSK,b = 1119 (895)/1,75 = 0,235 (0,294), (1.6.1) 150 aSK,t = 646 (519)/1,75 = 0,406 (0,506).
r / d = 0,119, r / t = 1,25, d / D = 0,84, Kt,b = 1,557 . (5.2.7) KcKfratio d / D = 0,84, t / r = 0,8 ,
Tab 2.3.3
Tab. 2.3.2 (2.3.14)
233
6.1 Shaft with shoulder d = 42mm, Gcr(d) = 2 I d = 0,0476 mm" , ncr (d) = 1,022
For no surface treatment is Ky = 1. Therefore: (2.3.17) (2.3.13)
Design factor KWKt , = 1,134
Fatigue notch factor 1,557 Kfb = - - - - , 1, 109 ·1, 022
6 Examples
1,374.
(2.3.10)
Tab. 2.3.4 (2.3.26)
For no surface treatment is Ky= 1. For steel and cast iron materials is Ks = 1. For materials except GG is KNL,E = 1. Therefore: Design factor KWK,b = 1,374 + 1 10,857 - 1 = 1,541
(2.3.1)
Fatigue strength reduction factor Analytically derived from the stress concentration factor. Stress concentration factor
rid = 0,119, r/t = 1,25, diD = 0,84, Kt,t = 1,283 . (5.2.8) Kt- Kf ratio
Tab. 2.3.3 Tab. 2.3.2
Component fatigue limit for completely reversed torsional stress resulting from the material fatigue limit for shear stress and the design factor for torsion: TWK,t = 233 MPa 11,224 = 190 MPa .
(2.4.1)
Rm = 895 MPa, aM = 0,00035, bM = -0,1 , Mcr = 0,213 , fw,'t = 0,577 , M't = 0,577 . 0,213 = 0,123 .
Tab. 2.4.2 (2.4.34) Tab. 2.2.1 (2.4.34)
Equivalent mean stress Sm = Sm,b = 0, T m = Tm,t =.50 MPa, fw,'t = 0,577 , q = Smv , = Smv , ,GH =
(2.4.31) Tab. 2.2.1 (2.4.29)
J3 . 50 MPa =
86,6 MPa , (2.4.29) (2.4.28) Tm,v = 0,577 . 86,6 MPa = 50 MPa . (2.4.30) Calculation for the type of overloading F2.
Tab. 2.2.1
(2.3.14) (2.3.17) (2.3.13)
Fatigue notch factor
Mean stress factor for bending Smin b v = 86,6 MPa- 150 MPa =- 63,4 MPa , Sma:,~,v = 86,6 MPa + 150 MPa = 236 MPa, Rb,v =- 0,267 , (2.4.27) Because of -
00
< -0,267
~
0 field II applies:
M cr = 0,213 , 1 KAK,b = 1+0,213.86,61150 =
°' 890 .
(2.4.10)
(2.3.10) Mean stress factor for torsion
. Roughness factor Rm = 895 MPa, Rz = 10 urn , fw,'t = 0,58 , aR,cr = 0,22, Rm,N,min = 400 MPa , KR,'t = 0,917 .
(2.4.1)
SWK,b = 403 MPa I 1,541 = 261 MPa .
°,
Rm is to be replaced by fw,.. Rm.
1,283 Kf,t = 1,097.1,031 = 1,134 .
Component fatigue limit for completely reversed bending stress resulting from the material fatigue limit for normal stress and the design factor for bending:
Mean stress sensitivity
The calculation is as for bending.
fw,'t = 0,577 , Rm = 895 MPa, fw,'t' R m = 517 MPa, n't (r) = 1,098 . d = 42 mm, G't(d) = 2 I d = 0,0476 mml, n't(d) = 1,031.
4 COMPONENT FATIGUE STRENGTH
Amplitude of the component fatigue limit for the given mean stress for bending and torsion
Design factor for torsion
diD = 0,84, t I r = 0,8 , r = 5mm G't (r) = 0,230 mm-I , aa = 0,5, bG = 2700 ,
(2.3.1)
Component fatigue limit for completely reversed bending and torsional stress
Roughness factor R m = 895 MPa , Rz = 10 urn , aR,cr = 0,22, Rm,N,min = 400 MPa, KR,cr = 0,857 .
+ 1 10,917 -1 = .1,224
Tab. 2.2.1 Tab. 2.3.4 (2.3.26)
T mm, . t,v = 50 MPa- 100 MPa =- 50 MPa, Tmax,t,v = 50 MPa + 100 MPa = 150 MPa , (2.4.27) Rt,v =- 0,333 ,
234
6.1 Shaft with shoulder Because of -1 < -0,333
s
°
Amplitude of the component variable amplitude fatigue strength for bending and for torsion, see above,
field II applies:
M, = 0,123 , 1
KAK,I
= 1+0,123.50/100 = 0,942 .
(2.4.10)
Residual stress factor for normal stress and for shear stress KE,cr = KE,'t = 1.
= 0,890 . 1 . 261 MPa = 233 MPa, (2.4.6) = 0,942 . 1 . 190 MPa = 179 MPa .
Component variable amplitude fatigue strength for bending and torsion Considering the component constant amplitude fatigue limit, N > No,cr and N > No,'t , and the S-N curve model I (horizontal for N > No,cr and N > No,'t) the variable amplitude fatigue strength factors for bending and for torsion is
(2.4.48)
The amplitude of the component variable amplitude fatigue strength results from the variable amplitude fatigue strength factor and from the amplitude of the component fatigue limit for bending and for torsion, SBKb = 1· 233 MPa = 233 MPa, TB~,t = 1 . 179 MPa = 179 MPa .
(2.4.41)
5 SAFETY FACTORS In general there is
In =
(2.5.1)
1,5 .
For moderate consequence of failure and regular inspection, however, there is jo = 1,2.
Tab. 2.5.1
For normal temperature there is KT,o
=
1,
(2.2.4)
and therefore jges
= 1,2.
Degrees of utilization Individual types of stress, bending and torsion,
150 = 0 773 a BK,b = 233/1,2 ' ,
The amplitude of the component fatigue limit results from the mean stress factor, the residual stress factor and the component fatigue limit for completely reversed bending and torsional stress:
. KBK,b = KBK,I = 1.
TSBK,b = 233 MPa, TBK,I = 179 MPa.
(2.4.5)
Amplitude of the component fatigue limit
SAK,b TAK,I
6 Examples
(2.5.4)
6 ASSESSMENT Largest stress amplitudes for bending and for torsion, see above, Sa,b,1 = Sa,b = 150 MPa , T a.t, I = Ta.t = 100 MPa.
a
BK,t
= 100
179/1 ,2
(2 6 1) ..
= 0 670 . '
Combined types of stress fw,'t = 1//3, q = 0, Sa = aBK,b = 0,773 , ta = aBK,t = 0,670 , aGH
= ~0,7732 +0,670 2
aBK,Sv = 1,023 .
Tab. 2.2.1 (2.6.7) (2.6.6)
1,023 ,
(2.6.5) (2.6.4)
The degree of utilization of the component fatigue limit is 102 %• The assessment of the fatigue limit is approximately achieved.
235
6.1 Shaft with shoulder
6 Examples
Complementary assessment 1:
Degrees of utilization
Amplitude of the component fatigue limit for the given mean stress - improved method of calculation according to Chapter 5.9
Individual types of stress, bending and torsion,
Related equivalent stress amplitude for bending and torsion Sa,b = 150 MPa, SWK,b = 262 MPa , Sa = 150 / 262 = 0,573 , Ta,l = 100 MPa, TWK,1 = 190 MPa, t a = 100 / 190 = 0,526 , 2
sa,v =JO,573 +0,526
2
(5.9.3)
= 0,778 .
(5.9.2)
J3
7.0,573 2 +12.0,526 2 2
0,573 +0,526
2
= 7,224
a
BK,1
Tab. 5.9.1
(2.6.1)
°
= 168/1,2 100 = 715 . '
Combined types of stress
/.J3,
Related equivalent mean stress for bending and torsion 1 8·0,573·0,526 B3 = - ' = 1028 ' 3.0,573 2 +(4/3).0,526 2 A4
aBK b = 150 = 0,732 , , 246/1,2
Tab. 2.2.1 (2.6.7) (2.6.6)
fw,'t = 1 q = 0, sa = aBK,b = 0,732 , ta = aBK,1 = 0,715 , 2
=JO,732 +0,715 aBK,Sv = 1,023 . aGH
2
= 1,023 ,
(2.6.5) (2.6.4)
Complementary assessment 2: Assessment applying a class of utilization
The constants B I , Al and AS are not needed as Sm =0.
= 50 MPa, TWK,1 = 190 MPa, t m = 50/190 = 0,263 , Sm = 0, Sms = (3/7) . 1,028' 0,263 = 0,116 ,
Tm,l
t ml
= (1
/E) .J7,224.0,263
sm,v = 0,87 . (0,116
+ 0,154)
2
=
(5.9.6)
= 0,154, 0,235 .
Common mean stress factor smin,v = 0,235 - 0,778 = - 0,543 , smax,v = 0,235 + 0,778 = 1,013 , Rcr,v - 0,543 / 1,013
(5.9.5) (5.9.18)
- 0,536
Differing from the constant amplitude loading conditions and the assessment of the fatigue limit considered above an assessment of a variable amplitude loading according to the class of utilization B5 is carried out here. In this case the class of utilization B5 may, for example, stand for binominally distributed amplitudes of the stress spectrum, a spectrum parameter p = 1/3 and a required total number of cyclesN = 107 , Table 5.7.2. The variable amplitude fatigue strength factor for the class of utilization B5 for bending and for torsion is KBK,b
Because of - 00 < -0,267 ~ 0 field II applies: Mcr = 0,213 , 1 KAK,v = 1+0,213.0,235/0,778 = 0,940. (2.4.13) Residual stress factor for normal stress and for shear stress KE,cr
= KE;t = 1.
(2.4.5)
The amplitude of the component fatigue limit results from the mean stress factor, the residual stress factor and the component fatigue limit for completely reversed bending and torsional stress: SAK,b = KAK,v . KE,cr . SWK,b = (2.4.6) = 0,940' I . 262 MPa = 246 MPa, TAK,1 = KAK,v . KE,'t . SWK,b = = 0,940 . 1 . 190 MPa = 168 MPa. Using these values instead of the values 233 MPa and 179 MPa somewhat different degrees of utilization are obtained.
= 1,26, KBK,1 = 1,15 .
Tab 5.7.1
The amplitudes of the component variable amplitude fatigue strength for bending and for torsion for bending and for torsion are (2.4.41) SBK,b = KBK,b . SAK,b = 1,26' 246 MPa = = 310 MPa, TBK,1 = KBK,I' TAK,1 = 1,15' 168 MPa = = 193 MPa. With these values instead of the values 246 MPa and 168 MPa the degrees of utilization are lower than those from above.
236
6.2 Shaft with V-belt drive
6.2 Shaft with V-belt drive
6 Examples
Surface: average roughness of the shaft: Rz = 25 J..Lm.
*1 lR62 EN .docl
Key words: Shaft, V-belt drive, rolled steel, assessment of the static strength, assessment of the fatigue limit, type of overloading F 1, combined types of stress.
Given
Loading: Maximum torque (rated torque), idealized as a fluctuating loading (load ratio RM = 0), figure 6.2.1:
M, = M max = 1 kNm.
(6.2.1)
Type of overloading: when overloaded in service the tension of the belt remains constant and with that the mean stress remains approximately constant as well (Type of overloading Fl). Safety requirements: according to the statements "severe consequences of failure; no regular inspections" .
Task: Assessment of the component static strength and assessment of the component fatigue limit. Method of calculation: Rod-shaped (ID) componerit. Assessment using nominal stresses, Chapter 1 and 2.
Material: St 60 after DIN EN 10 025. Dimensions: Length of shaft 1 = 400 mm, diameter of shaft d = 56 mm.
ASSESSMENT OF THE COMPONENT STATIC STRENGTH
Pulley in center position, bearing on the left horizontally fixed, torque input at the right end.
1 LOADINGS Specifying the loadings is not subject of the guideline. Therefore the loadings are outlined here in brief *2.
M, is the torque input to the shaft. The torque input results in a maximum of six loads F x , ... , M, at the pulley. The initial tension of the belt results in a maximum of two lateral forces F y , Fz . The sense of rotation and direction of input and output are not important for the loads.
ZCA.l--~-+-HlI.-----~Mf---t
The torque is transmitted by the initial tension and frictional contact of the belt. Therefore the loadings "torque" and "initial tension" are to be distinguished. The axial load of the shaft and the lateral moments at the pulley are zero: Z
(6.2.2)
Data ofthe drive Diameter of pulley No.1: d 1W = 200 mm, Diameter of pulley No 2: d2W = 100 mm, Center distance: e = 200 mm, Wedge angle: Ys = 35°, Friction coefficient between belt and pulley: J..L= 0,1.
Figure 6.2.1 Shaft and loads due to the torque M n at the V-belt drive. F I
-
F 2 = F,
*2
Calculation equations Loading "torque" Circumferential force transmitting the torque
Ft=Mn ' 2/d 1w , = 1000 kNmm . 2 I 200 mm
= 10 kN.
(6.2.3)
Inclination of the belt 1 Results of computation obtained by the PC-program "Welle" 2 Full presentation of the example s given in the manual of the PC-program "Welle".
sin a,
a,
= (d 1w - d2w) 12e, (6.2.4) = (200 - 100) mm I (2 . 200 mm) = 0,25 ,
= 14,48°.
237
6.2 Shaft with V-belt drive
6 Examples Mz - 2,349kNm A ..----'''--'---------~i1___7z
Resulting loads
r, = Fy = 0,
y~
(6.2.5)
..;.,::
o
Fz = + F, . sin a. = 10 kN . 0,25 = 2,5 kN , M, = M; = I kNm , My=Mz= O.
lI:l C>J
B«<::...-----------.J o
II
-:t.
ails b622
Load "initial tension"
Figure 6.2.2 Resulting moments at mid shaft.
Value of the groove angle
Ys = 35
0.
Effective coefficient of friction
(6.2.6)
ASSESSMENT OF THE COMPONENT STATIC STRENGTH
J.lth = ~ / sin(ys / 2) = 0,1 / sin(35012) = 0,3326 . _3
Arc of belt contact at the smaller pulley (No.2) (6.2.7)
~ = 180° - 2 ·1a.1 = 180° - 2· 14,48 = 151,0°. For the smaller pulley there is a. < 0 and ~ < 180 0. For the larger Pulley there is a. > 0 and ~ < 180°.
1 CHARACTERISTIC STRESSES The reference point for the assessment of the static strength is in the middle of the shaft (to the right of the pulley). Maximum bending moment (point B in Figure 6.2.2) Mb= M yz
Auxiliary variable
=~M~ +M;
=~0,250kNm2+ 2, 349kNm 2
m = exp (~th . ~ . n / 180°), . (6.2.8) = exp (0,3326 . 151,0°. n /180°) = 2,403.
(6.2.12) = 2,362 kNm.
Maximum torsion moment Necessary minimum initial tension for transmitting the maximum torque *4 2 m+l Fs p = M, ·-·--·cosa.
I Id
1w
m->I
Extreme maximum stresses *5
(6.2.9)
Smax ex b = 32 Mb / pd 3 (1.1.1) = '32' 2,362 kNm / (n . (56 mm)3 ) = 137 MPa , T max ex t = 16 M t / pd 3 = 't6'· 1 kNm / (rt . (56 mm)3 ) = 29,0 MPa.
2 2,403+1 = 1000 kNmm' 200mm 2,403-1 . cosine 14,47° = 23,49 kN. Resulting loads
F x = 0, Fy = + F sp = 23,49 kN, Fz = 0, M x= M y= M z= O.
(6.2.10)
2 RESULTING MOMENTS AT MID SHAFT
2 MATERIAL PROPERTIES Tensile strength and yield strength for the standard dimension Rm,N = 590 MPa, Rp,N = 335 MPa. Tab. 5.1.1 Technological size factor ad,m = 0,15 , ad,p = 0,3 , deff,N = 40 mm , deff = d = 56 mm , ~,m = 0,982, Kd,p = 0,960 .
From the loadings "maximum torque" (M; = 1 kNm and F z = 2,5 kN) and from the loading "initial tension" (Fy = 23,486 kN) the moments in the middle of the shaft (to the right of the pulley) are
M, = - 1 kNm, (6.2.11) My = + F, . I / 4 = 2,5 kN . 400 mm / 4 = + 0,250 kNm, . M z = - F y . I /4 = 23,49 kN . 400 mm / 4 = - 2,349 kNm . The bending moments My and M, are presented in Figure 6.2.2. The loading without torque (only initial tension) corresponds to the point A. The loading under maximum M, torque (including initial tension) corresponds to the point B.
Tab. 1.2.1 Tab. 1.2.3 (1.2.9)
Anisotropy factor K A = 1.
(1.2.17)
Tensile strength and yield strength of the component R m = 0,982 . 1 ·590 MPa = 579 MPa, Rp = 0,960 . 1 . 335 MPa = 321 MPa .
4
(1.2.1)
Practically anincreased initial tension value needs tobeconsidered.
5 From here on the numbers of equations, tables and figures are those of the guideline. 3
Torque and the pre-tension aretobedetermined for the smaller pulley
238
6.2 Shaft with V-belt drive
6 Examples
3 DESIGN PARAMETERS
6 ASSESSMENT
Design factor for bending
Maximum stresses for bending and for torsion, see above,
Section factor Rp,max = 1050 MPa , Tab. 1.3.1 Rp = 321 MPa, Kp,b = 1,70, Tab. 1.3.2 npl,b = MIN (J1050/321 ; 1,70)= 1,70, 1.3.9)
Smax,ex,b = 137,0 MPa, Tmax,ex,t'= 29,0 MPa. Component static strength for bending and for torsion, see above, SSK,b = 985 MPa, TSK,t = 447 MPa .
Design factor KSK,b = 1 / 1,70 = 0,588.
(1.3.1)
Degrees of utilization Individual types of stress, bending and torsion,
Design factor for torsion 137 = 0376 aSK,b = 985 I 2,70 ' ,
Section factor Rp,max = 1050 MPa , Tab. 1.3.1 Rp = 321 MPa, Kp,t = 1,33 , Tab. 1.3.2 npI,t = MIN (J1050/321 ; 1,33) = 1,33. 1.3.9) Design factor KSK,t = 1 / 1,33 = 0,752.
(1.3.1)
a = 29,0 = 0176. SK,t 447 I 2,70 ' Combined types of stress f't = 0,577 , q = 0, s = aSK,b = 0,376 , t = aSK t = 0,176,
~0,3762 +0,176 2
4 COMPONENT STATIC STRENGTH
aGH =
Component static strength for bending and torsion
aSK,Sv = 0,415 .
Component static strength for bending resulting from the tensile strength and design factor:
(1.6.1)
Tab. 1.2.5 (1.6.7) (1.6.6) = 0,415 ,
(1.6.5) (1.6.4)
The degree of utilization of the component static strength is 42 %. The assessment of the static strength is achieved.
fa = 1 , Tab. 1.2.5 (1.4.1) SSK,b = 579 MPa / 0,588 = 985 MPa . Component static strength for torsion resulting from the shear strength factor f't , the tensile strength and the design factor: f't = 0,577 , Tab. 1.2.5 TSK,t = 0,577 . 579 MPa / 0,752 = 445 MPa . (1.4.1)
For severe consequences of failure and high probability of the occurrence of the characteristic stress there is Tab. 1.5.1
For normal temperature there is KT,m = KT,p = 1,
1 CHARACTERISTIC STRESSES Again the reference point for the assessment of the fatigue strength is in the middle of the shaft (to the right of the pulley).
The mean value and amplitude of the maximum cyclic bending moment is to be determined. The mean value of the bending moment for the rotating shaft is Mm,b =
(1.2.26)
and in Eq. (1.5.4) the terms 3 and 4 have no relevance: Rp = 321 MPa, R m = 579 MPa, jges = MAX (2,0; 1,5. 579) 321 = MAX (2,0; 2,70) = 2,70.
OF THE COMPONENT FATIGUE STRENGTH
Cyclic bending moment
5 SAFETY FACTORS
jm = 2,0 , jp = 1,5.
ASSESSMENT
°
The maximum amplitude of the bending moment for the rotating shaft is, as for the assessment of the static strength, Ma,b = 2,362 kNm.
(1.5.4)
The yield strength Rp (the second term) is determining.
239
6.2 Shaft with V-belt drive The amplitude of the bending moment is varying within the limits defined by no torque input or maximum torque input, points A and B in Figure 6.2.2. The assumption of a continuous action of the maximum bending moment is an approach on the safe side.
6 Examples For no surface treatment is Ky = 1. For steel and cast iron materials is Ks = 1. For materials except GG is KNL,E = 1. Therefore: Design factor
+ 1/0,858 - 1
KWK,b = 0,979
Fluctuating torsion moment The mean value and amplitude of the torsion moment fluctuating between zero and maximum is
= 1,144
(2.3.1)
Design factor for torsion Fatigue notch factor
Mm,t = Ma,t =IMxl /2 = 0,5 kNm.
Stress concentration factor for the cylindrical shaft *6
It is valid for the non-rotating shaft too.
Kt,t = 1.
Characteristic stresses The cyclic stresses resulting from the bending moment and the torsion moment are
(2.1.1) Sm b = 0, , 3 Sa,b = 32 Ma,b / pd = 32 . 2,362 kNm / (n . (56 mmr' ) = 137 MPa Tm,t = 16 Mt,m / pd 3 = 16 . 0,5 kNm / (n . (56 mm)3 ) = 14,5 MPa , Ta,t = Tm,t == 14,5 MPa.
2 MATERIAL PARAMETERS
K,-K r ratios, no notchradius,
G, (r) = 0, n, (r) = 1 , = 56 mm, G, (d) = 2/ d = 0,0357 mm -1 , n, (d) = 1,027 .
d
(2.3.17) (2.3.13)
Fatigue notch factor Kf,t
= 1 / (1 . 1,027) = 0,974.
(2.3.10)
Roughness factor
Material fatigue limits for completely reversed normal stress, crW,zd , and shearstress, 'tw,s, : R m = 579 MPa, fw,cr = 0,45 , Tab. 2.2.1 crW,zd = 0,45 . 579 MPa = 261 MPa , (2.2.1) Tab. 2.2.1 f w " = 0,577 , 'tw,s = 0,577 . 261 MPa = 151 MPa . (2.2.1)
R m = 579 MPa , R z = 25 um , fw" = 0,58, aR,cr = 0,22, Rm,N,min = 400 MPa , KR" = 0,918 .
Tab. 2.2.1 Tab. 2.3.4 (2.3.26)
For no surface treatment is Ky = 1. For steel and cast iron materials is Ks = 1. For materials except GG is KNL,E = 1. Therefore: Design factor KWK,t = 0,974
3 DESIGN PARAMETERS
+
1/0,918 - 1 = 1,063
(2.3.1)
Design factor for bending Fatigue notch factor
4 COMPONENT FATIGUE STRENGTH
Stress concentration factor for the cylindrical shaft *6
Component fatigue limit for completely reversed bending and torsional stress
Kt,b = 1.
Component fatigue limit for completely reversed bending stress resulting from the material fatigue limit for normal stress and the design factor for bending,
K,-K r ratios, no notch radius,
G cr (r) = 0, ncr (r) = 1 , d = 56 mm, Gcr(d) = 2/ d = 0,0357 mm -1 , ncr (d) = 1,022 .
SWK,b = 261 MPa /1,144 = 228 MPa.
(2.3.17) (2.3.13)
Fatigue strength reduction factor Kf,b
= 1 / (1 . 1,022) = 0,979 .
(2.3.10)
(2.4.1)
Component fatigue limit for completely reversed torsional stress resulting from the material fatigue limit for shear stress and the design factor for torsion, TWK,t = 151 MPa / 1,063 = 142 MPa .
(2.4.1)
Roughness factor R m = 579 MPa, R z = 25 um , aR,cr = 0,22, Rm,N,min = 400 MPa, KR,cr = 0,858 .
Tab. 2.3.4 (2.3.26)
6 Assuming an unnotched cylindrical shaft is an unrealistic simplification for the present example. Actually a keyway or a press-fit between pulley andshaft, Chapter 5.3.3.4, would have to beconsidered.
240
6.2 Shaft with V-belt drive Amplitude of the component fatigue limit for the given mean stress for bending and torsion Mean stress sensitivity Rm = 579 MPa, aM = 0,00035 , bM = - 0,1 , Me; = 0,103 , fW;t = 0,577 , M't = 0,577 . 0,103 = 0,059 .
model I (horizontal for N > ND,e; and N > ND,'t ) the variable amplitude fatigue strength factors for bending and for torsion is KBK,b = KBK,t = 1.
Tab. 2.4.2 (2.4.34) Tab. 2.2.1 (2.4.34)
Equivalent mean stress
°,
Sm = Sm,b = (2.4.31) T m = Tm,t = 14,5 MPa , fw,'t = 0,577 , Tab. 2.2.1 q = (2.4.29) Sm,v = Sm,v,GH 14,5 MPa = 25,1 MPa, (2.4.29) (2.4.28) Tm,v = 0,577 ·25,1 MPa = 14,5 MPa . (2.4.30)
°,
6 Examples
=J3 .
Mean stress factor for bending
SBK b = 1 . 225 MPa = 225 MPa, TB~,t = 1 . 141 MPa = 141 MPa.
Because of - 1,115:::;; 0,110:::;; 0,907 field II applies:
(2.4.15)
Mean stress factor for torsion
5 SAFETY FACTORS For severe consequence of failure and no regular inspections there is
.io
(2.5.1), Tab. 2.5.1
1,5.
=
Jges
(2.2.5) (2.5.4)
1,5 .
=
6 ASSESSMENT Largest stress amplitudes for bending and for torsion, see above, Sa b l = Sa b = 137 MPa , Ta',t:! = T a:t = 14,5 MPa . Amplitude of the component variable amplitude fatigue strength for bending and for torsion, see above,
tm,t,v = Tm,v / TWK,t = 14,5/142 = 0,102 M, = 0,059, 1 / (1 + M't) = 1 / (1 + 0,059) = 0,944 .
SBK,b = 225 MPa, TBK,t = 141 MPa .
Because of 0:::;; 0,102:::;; 0,944 field II applies:
Degrees of utilization (2.4.15)
Residual stress factor
Individual types of stress, bending and torsion,
aBK,b
=
For normal stress and for shear stress there is KE,e; = KE,'t = 1.
(2.4.41)
KT,D =1,
Sm,b,v = Sm,v / SWK,b = 25,1 /228 = 0,110, Me; = 0,103 , - 1 / (1 - Me;) = - 1 / (1 - 0,103) = - 1,115 , 1 / (1 + Me;) = 1 / (1 + 0,103) = 0,907 .
KAK,'t = 1 - 0,059' 0,102 = 0,994.
The amplitude of the component variable amplitude fatigue strength results from the variable amplitude fatigue strength factor and from the amplitude of the component fatigue limit for bending and for torsion,
For normal temperature there is
Calculation for the type of overloading F1.
KAK,e; = 1 - 0,103 . 0,110 = 0,989 .
(2.4.48)
(2.4.5)
Amplitude of the component fatigue limit The amplitude of the component fatigue limit results from the mean stress factor, the residual stress factor and the component fatigue limit for completely reversed bending stress and torsional stress, SAK,b = 0,989 . 1 . 228 MPa = 225 MPa, (2.4.6) TAK,t = 0,994 . 1 . 142 MPa = 141 MPa .
a
t =
BK,
137 = 225/15 ,
°9~
(2 • 6 • 1)
' ~.J,
14,5 = 0,155 . 141/ 1,5
Combined types of stress Tab. 2.2.1 (2.6.7) (2.6.6)
fw,'t = 0,577 , q = 0, Sa = aBK,b = 0,913 , ta = aBK,t = 0,155 . aGH =
~0,9132 +0,155 2
=
0,926 ,
aBK,Sv = 0,926. Component variable amplitude fatigue strength for bending and torsion Variable amplitude fatigue strength factor
(2.6.5) (2.6.4)
The degree of utilization of the component fatigue limit is 93 %. The assessment of the fatigue limit is achieved. *7
Considering the component constant amplitude fatigue limit, N > ND,e; and N > ND,'t , and the S-N curve 7 See the objections in footnote 4 and 6, however.
241
6 Examples
6.3 Compressor flange made of grey cast iron
6.3 Compressor flange made of grey cast iron "'I 1R63 EN.docl
ASSESSMENT OF THE COMPONENT STATIC STRENGTH
1 CHARACTERISTIC STRESSES Key words: Grey cast iron GG-30, assessment of the static strength, assessment of the fatigue limit, local elastic stresses, type of overloading F2, elevated temperature, combined types of stresses GI and G2 .
*2 (3.1.6)
Maximum stresses
GI ,max ,ex = 33,6 MPa, G2,max ,ex = 11,2 MPa .
2 MATERIAL PROPERIES
Given
Stresses: Proportional, constant amplitude loading, locally elastic stresses in the directions 1 (longitudinal) and 2 (circumferential) at the reference point (node 99) of a block-shaped (3D) component, Figure 6.3.1, GI = GI,m ± GI,a = 15,0 MPa ± 18,6 MPa , G2 = G2,m ± G2,a = 5,0 MPa ± 6,2 MPa , G3 = 0. Stress amplitudes at the neighbouring point (node 98) in a distance s = 7,7 mm below the surface GI,a = ± 10,0 MPa, G2,a = ± 5,3 MPa.
Tensile strength for the standard dimension Rm,N
=
300 MPa .
Tab. 5.1.14
Technological size factor deff = 2s = 2 . 32 mm = 64 mm , Kd,m = 0,800 .
Tab. 3.2.3 (3.2.5)
Anisotropy factor
KA
=
(3.2.18)
1.
Tensile strength of the component Rm = 0,800' 1 . 300 MPa = 240 MPa:
(3.2.1)
Temperature factors
Flange
aT,m = 1,6 , Tab. 3.2.6 KT m = 0,769 , (3.2.31) Crr: = 25 , Tab. 3.2.7 aTt,m = - 1,46, bn,m = 2,36, CTt,m = - 0,90 , Pm = 10 - 4. (380 + 273) . (25 + 19 100.000) = = 1,959, (3.2.35)
111 91.
_ (-1,46+2,36.1,959-0,90.1,959 2 ) KTt,m -10 = 0,511 . 92
3 DESIGN PARAMETERS
87
6.~.1
Section factor for GG
Figure 6.3.1 Compressor flange made of grey cast iron.
Material: GG-30 according to DIN 1691 or DIN EN i,:,61.
Temperature and time: T
npl,O'I = n pl,O'2 = 1.
Constant KNL for the consideration of the non-linear elastic strain characteristic of GG for tension KNL = 1,05.
=
380°C, t
=
100.000 h.
Dimensions: Effective wall thickness at the reference point (node 99) s ;::: 32 mm.
Surface: Skin Type of overloading: : When overloaded in service the stress ratios remain constant (Type of overloading F2).
Safety requirement: according to the statements: "severe consequences of failure; no regular inspection", casting tested non-destructively.
(3.3.7)
Tab. 3.3.4
Design factor for directions 1 and 2 KSK,O'I = KSK,O'2 = 1/ (1'1,05) = 0,952.
(3.3.3)
4 COMPONENT STRENGTH Component strength resulting from the tensile strength and the design factor. For directions 1 and 2 there is fO' = 1 , Tab. 3.2. GI,SK = G2,SK = 240 MFa / 0,952 = 252 MPa . (3.4.3)
Task: Assessment of the static strength and assessment of the fatigue limit. Method of calculation: Block-shaped (3D) component. Assessment using local elastic stresses, Chapter 3 and 4
I Results of computation obtained by the PC-program "RIFESTPLUS" 2 Numbers of Equations, tables and figures arethose of the guideline.
242 6 Examples
6.3 Compressor flange made of grey cast iron
5 SAFETY FACTORS For severe consequences of failure and high probability of the occurrence of the maximum stress and for nondestructively tested castings there is
Jm = 2,5 , jmt = 1,9 .
Tab. 3.5.2
Because of the low elongation of GG the safety factor is to be increased by ~j : ~j =
0,5 , jm = 3,0 , jmt = 2,4 .
(3.5.2)
Jges
=
°.
(3.5.4)
= MAX (3,90; 4,70) = 4,70.
Material fatigue limit for completely reversed normal stress, CfW,zd , R m = 240 MPa, fw,cr = 0,30 , crW,zd = 0,30 . 240 MPa
The creep strength Rm,Tt is is determining, Figure 3.2.2.
= 72,0 MPa .
= 33,6 MPa, cr2,max,ex
Tab. 4.2.2 (4.2.8)
aT,D = 1,0, KT,D = 0,856 .
Maximum stresses, see above, =
11,2 MPa .
3 DESIGN PARAMETERS
Component strength values, see above,
(4.3.16)
Kt-Kf ratios
crl,SK = cr2,SK, = 252 MPa.
Gal Individual types of stress, directions 1 and 2
Go ?:
33,6
I_.(I_IO,OJ 18,6
__ 7,7mm
Degrees of utilizaion
I (I - 6,2 5.3J
-
- 7,7mm'
=
0,0600 0,0189 mm- l ,
aa
= - 0,05, bG = 3200 , nal = 1,179, n cr2 = 1,056.
= 0,209 .
aG H
0,85 , 0,759 , aSK,crl = 0,627 , aSK.cr2 = 0,209 ,
=
~. ((0,627 -0,209)2 +0,209
Tab. 4.3.2 (4.3.10)
Roughness factor
Combined types of stress f, = q = 81 = S2 =
Tab. 4.2.1 (4.2.1 )
Temperature factor
6 ASSESSMENT
aSK,cr2 = 252/4,70
(4.1.1 )
2 MATERIAL PROPERTIES
MAX(~._2LJ 0,769'0,511
crLmax.ex
1 CHARACTERISTIC STRESSES
crl.a = 18,6 MPa, 01,m = 15,0 MPa . cr2,a = 6,2 MPa, 02.m = 5,0 MPa , cr3,a = 0 , 03.m =
KTt,m = 0,511 .
For GG the terms 2 and 4 of Eq. (3.5.4) are not relevant. Therefore .
ASSESSMENT OF THE FATIGUE STRENGTH
Constant amplitude cyclic stresses
Temperature factors, see above, KT,m = 0,769,
Note: For the assessment of the component static strength the presented computation for the combined types of stress applies to both proportional stresses and non-proportio-nal stresses o l and cr2, see footnote 1 in Chapter 3.6.
Tab. 3.2.5 (3.6.23) (3.6.22)
R m = 240 MPa, Rz = 200 um , aR,cr = 0,06, Rm,N.min = 100 MPa, KR,cr = 0,906 , Surface treatment factor,
K v = 1. 2
+0,627
2
)
(4.3.28)
Coating factor
= 0,553 , (3.6.21) a NH = MAX (0,627; 0,209) = 0,627 , aSK.sY = 0,759 . 0,626 + (I - 0,759) . 0,553 = = 0,608 . (3.6.20)
The degree of utilization of the component static strength is 61 %. The assessment of the static strength is achieved.
Ch.4.3.3 Tab. 4.3.4 (4.3.26)
*3
(4.3.29)
KKS = 1. Constant KNL.E KNL,E
=
1,025 .
Tah. 4.3 (
3 Even though the present assessment ofthe creep strength may he the safe side, see Chapter 3.1.0 on.Elevated temperature'
tar on
243 6.3 Compressor flange made of grey cast iron Design factors Kf = 1,
6 Examples
Tab. 4.3.1 1
KWK,al = 1,1\9 -(1+i-( 0,:06 -1))
1·1·1,025
= 0,913,
(4.3.3) 1
KWK,a2
= 1,;56 -( 1+ i -( 0,:06 -1)) 1·1·1,025
= 1,019.
crl,AK = 0,713 . 1 . 79 MPa = 56 MPa , cr2,AK = 0,713 . 1 ·71 MPa = 50 MPa .
Component variable amplitude fatigue strength for bending and torsion Considering the component constant amplitude fatigue limit, N > No,a and N > NO;t , and the S-N curve model I (horizontal for N > NO,a and N > No,'t) the variable amplitude fatigue strength factors for normal stress is KBK,al = KBK,a2 = 1.
4 COMPONENT FATIGUE STRENGTH Component fatigue limit for completely reversed normal stresses Component fatigue limit for completely reversed normal stress resulting from the material fatigue limit for normal stress and the design factors: crl,WK = 72,0 MPa / 0,913 = 79 MPa, (4.4.3) cr2,WK = 72,0 MPa / 1,019 = 71 MPa. Amplitude of the component fatigue limit for the given mean stress Mean stress sensitivity Tab. 4.4.2 (4.4.34)
According to Chapter 4.4.2.2 the individual mean stresses are to be applied instead of an equivalent mean stress. Calculation for the type of overloading F2. Mean stress factor for direction 1
(4.4.26)
crl,min = 15 MPa - 18,6 MPa = - 3,6 MPa , crl,max = 15 MPa MPa + 18,6 = 33,6 MPa, Ral = - 3,6 / 33,6 = - 0,107 . Because of Ma
CX)
< -0,107
~
° field II applies:
= 0,5 ,
KAK,al =
1 1+0,5.15/18,6
(4.4.47)
The amplitude of the component variable amplitude fatigue strength results from the variable amplitude fatigue strength factor and from the amplitude of the component fatigue limit for normal stress crl,BK = 1·56 MPa = 56 MPa, cr2,BK = 1 . 50 MPa = 50 MPa.
(4.4.45)
5 SAFETY FACTORS For severe consequence of failure, for no regular inspection and for castings tested non-destructively
.io =
aM = 0, b M = 0,5 , M a = 0,5 .
(4.4.8)
Tab. 4.5.2
1,9 .
Because of the low elongation of GG the safety factor is to be increased by ~j : ~j
= 0,5
,
(4.5.2)
.in = 2,4. Temperature factor, see above, KT,O = 0,856 . Total safety factor jges =
2,4/0,856 = 2,80 .
(4.5.4)
6 ASSESSMENT
= 0,713 .
(4.4.10)
Stress amplitudes, see above cra,l = 18,6 MPa , cra,2 = 6,2 MPa .
Mean stress factor for direction 2 The stress ratios of both directions agree:
R a 2 = Ral = - 0,107 , KAK,a2 = 0,713 .
Amplitudes of the component variable amplitude fatigue strength, see above, crl,BK = 56 MPa, cr2,BK = 50 MPa .
Residual stress factor Degrees of utilization
For normal stress there is KE,a = 1.
(4.4.5)
Individual types of stress, direction 1 and 2
5:~;680 ,
Amplitude of the component fatigue limit
aBK,al =
The amplitude of the component fatigue limit results from the mean stress factor, the residual stress factor and the component fatigue limit for completely reversed normal stress:
aBK,a2 = 50
~':,80
= 0,929 , =
0,346 .
(4.6.17)
244 6.3 Compressor flange made of grey cast iron
6 Examples
Combined types of stress fw,'t = 0,85 , q = 0,759 , Sl,a = aBK,crl S2,a = a BK,cr2
a GH
= 0,929, = 0,346 ,
. Tab. 4.2.1 (4.6.23) (4.6.22)
= ±.((0,929-0,346)2 +0,346 2 +0,929 2)
= 0,813, (4.6.21) a NH = MAX (0,929; 0,346) = 0,929 , aBK,sv = 0,759 . 0,929 + (1 - 0,759) . 0,813 = = 0,901. (4.6.20)
The degree of utilization of the component fatigue strength is 90 %. The assessment of the fatigue limit is achieved.
Note: Different from an assessment of the static strength the presented calculation for combined types of stress applies in the case of proportional stresses only. For non-proportional stresses o l and cr2 the rules of superposition in Chapter 4.6 are not applicable and the procedure proposed in Chapter 5.10 is to be applied instead.
........
245 6 Examples
6.4 Welded notched component
6.4 Welded notched component
Safety requirement: According to the statements "with moderate consequences of failure; regular inspections".
Key words: Milled steel, welded notched component, assessment of the static strength, assessment of the variable amplitude fatigue strength, type of overloading F2, class of utilization, nominal stress, structural stress, effective notch stress.
Task: Assessment of the static strength and assessment
'--~-64---EN""'.""'do--'q
Given:
Stresses: Cyclic variable amplitude axial stresses, Figure 6.4.1. Characteristic nominal stresses, determined elementary: Szd = Sm,zd ± Sa,zd = 150 MPa ± 75 MPa . Characteristic structural stresses at the edge of the weld seam, determined by finite element analysis without observing the weld seam, (stress concentration factor Kt,cr = O'max / Szd = 2,5), 0'
= O'm ± O'a = 375 MPa ± 187,5 MPa.
Characteristic effective notch stresses at the edge of the weld determined by finite element analysis in considering the weld seam with an effective notch radius r = 1 mm, (stress concentration factor Kt,crK = O'K,max / Szd = 5,6), O'K = O'K,m ± O'K,a = 840 MPa ± 420 MPa . The respective characteristic stress amplitudes refer to the largest amplitude of the stress spectrum which co-responds to the class of utilization B2. S1:d
F
of the variable amplitude fatigue strength. Method of calculation: Rod-shaped (ID) component. The assessment of the static strength is to be carried out using nominal stresses and structural stresses (an assessment of the static strength using effective notch stresses is not possible). The assessment of the variable amplitude fatigue strength is to be carried out using nominal stresses, structural stresses and effective notch stresses. The degrees of utilization obtained with nominal stresses, with structural stresses and with effective notch stresses should agree .
ASSESSMENT OF THE COMPONENT STATIC STRENGTH For welded components the assessment of the component static strength is in general to be carried out separately for the toe section (toe of the weld) and for the throat section (root of the weld). In the present case the assessment of the throat section (root of the weld) is sufficient. An equivalent stress is to be computed for the throat section.
Calculation using nominal stresses 1 CHARACTERISTIC STRESSES
F
~ -t--+-t-~!l--t---~-f-,-........-
*1 (1.1.1)
Maximum nominal stress Smax ,ex,zd = 150 MPa
+ 75
MPa = 225 MPa . (1.1.2)
Maximum equivalent nominal stress Smax,ex,wv,zd
=
Sl.,zd
= Smax,ex,zd = 225 MPa .
2 MATERIAL PROPERTIES
6.4..1
Figure 6.4.1 Welded notched component
Tensile strength and yield strength of the plate material R m = 610 MPa, R p = 500 MPa. Tab. 5.1.2 The values apply to the component. The technological size factor is not relevant, Eq. (1.2.15).
Material: StE 500, DIN 17 102. Dimensions: Width of plate B = 375 mm Thickness of plate s = 20 mm, Radius of cut-out r = 100 mm. Weld seam: Full penetration butt weld, as welded, toe angle S; 30 0, tested non-destructively, low residual stresses. Type of overloading: When overloaded in service the stress ratios remain constant (type of overloading F2).
3 DESIGN PARAMETERS Section factor npl,zd = 1 .
(1.3.9)
Weld factor Ow
Ow
=
1,0 .
Tab. 1.3.3
1 Numbers of equations, tables and figures arethose of the guideline.
246
6 Examples
6.4 Welded notched component Design factor
(3.1.2)
Maximum equivalent structural stress
KSK,zd = 1 / (1 . 1 ) = 1 .
(1.3.4)
O'max,ex,wv = O'-L = 562,5 MPa .
2 MATERIAL PROPERTIES
4 COMPONENT STATIC STRENGTH
Tensile strength and yield stress of the plate material
Nominal value of the component static strength resulting from the tensile strength and the design factor: fer = 1 , Tab. 1.2.5 SSK,zd = 1 ·610 MPa / I = 610 MPa . (1.4.1)
Rm = 610 MPa, R,
=
500 MPa .
Tab. 5.1.2
The values apply to the component. The technological size factor is not relevant, Eq. (3.2.15).
3 DESIGN PARAMETERS
5 SAFETY FACTORS
Plastic notch factor Tab. 1.5.1
For moderate consequences of failure, however, there is Jm = 1,75 , jp = 1,3 .
Tab. 1.5.1
For normal temperature there is KT,m = KT,p = I ,
(1.2.26)
Rm = 610 MPa, Rp = 500 MPa
= MAX (1,75; 1,3· :~~)
(3.3.13)
Section factor E = 2,1 . 105 MPa, Tab. 3.3.1 5 % = 0,05 , Rp = 500 MPa, 5 npl." = MIN 2-, 1-.1-0-.-0-,0-5-/5-0-0; 2,5) = 2,5 . 8 ertr =
and in Eq. (1.5.4) the terms 3 and 4 have no relevance:
. jges
Kp,er = Kt,a = 2,5 .
(1.5.4)
(Jr-
(3.3.9) The section factor is limited by the plastic notch factor . Constant KNL (3.3.16)
KNL = I.
= MAX (1,75; 1,59) = 1,75. Due to a high yield stress, Rp / R m > 0,75 , the tensile strength is deciding.
Weld factor Ow Ow = 1,0.
Tab. 3.3.3
Design factor KSK,er = 1 / (2,5 . 1 . 1,0) = 0,400 .
6 ASSESSMENT
(3.3.4)
Maximum nominal stress, see above, Smax,ex,wv,zd = 225 MPa .
4 COMPONENT STATIC STRENGTH
Component static strength, nominal value, see above, SSK,zd
= 610 MPa
.
Local value of the component static strength resulting from the tensile strength and the design factor: fa = 1 , Tab. 3.2.5 O'SK = 1 ·610 MPa / 0,400 = 1525 MPa. (3.4.4)
Degree of utilization aSK d = .z
225 = 0,646 . 610/1,75
(1.6.1)
The degree of utilization of the component static strength is 65 %. The assessment of the static strength is achieved.
5 SAFETY FACTORS Safety factors according to Chapter 3, as before: jges
= 1,75.
6 ASSESSMENT
.Calculation using structural stresses
1 CHARACTERISTIC STRESSES Maximum structural stress at the inside edge of the weld (3.1.1) O'max,ex = 375 MPa + 187,5 MPa = 562,5 MPa .
Maximum structural stress, see above, O'max,ex,wv = 562,5 MPa . Component structural static strength, see above, O'SK = 1525 MPa .
(3.5.4)
247
6 Examples
6.4 Welded notched component Fatigue class
Degree of utilization 562,5 aSK,cr = 1525/1,75 = 0,646 .
(3.6.1)
FAT 40. Thickness factor
The degree of utilization of the component static strength is 65 % (as with nominal stresses). The assessment of the static strength is achieved.
(2.3.33) Surface treatment factor (2.3.28)
Kv = 1. Constant KNL,E ASSESSMENT
KNL,E
OF THE COMPONENT FATIGUE STRENGTH
For welded components the assessment of the fatigue strength is in general to be carried out separately for the toe section (toe of the weld) and for the throat section (root of the weld). Furthermore the assessment of the fatigue strength for welded components is in general to be carried out separately for the base material (with rolling skin) and for the weld. *2. The less favorable case is deciding. Because of the comparatively low fatigue properties of welded components the weld is normally deciding. In this present case an assessment of the fatigue strength for the root of the weld is sufficient.
For the weld section the (largest) amplitude and the mean value of the characteristic nominal stress is
75 MPa, Sm,zd
=
150 MPa .
(2.1.1)
Independent of the type of steel the weld specific fatigue limit for completely reversed nominal stress is
= 92 MPa .
(2.2.3)
3 DESIGN PARAMETERS The fatigue class (FAT) is required to derive the design factor after Eq. (2.3.4). However the welded notched component considered is not contained in Table 5.4.1 and therefore an assessment using nominal stresses is not possible, on principle. Nevertheless in order to demonstrate the respective way of calculation, a (re-calculated) fatigue class is supposed to be approximately valid for the calculation below:
Because ofdifferent slopes the SoN curves ofnon-welded and ofwelded components may overlap for amplitudes exceeding the fatigue limits
2
(2.3.4)
4 COMPONENT FATIGUE STRENGTH Component fatigue limit for completely reversed stress Component fatigue limit for completely reversed nominal stress resulting from the weld specific fatigue limit for normal stress and the design factor: (2.4.1)
SWK,zd = 92 MPa / 5,63 = 16,3 MPa.
M cr
= 0,3 .
Tab. 2.4.1
Calculation for the type of overloading F2. '.
Stress ratio Smin,zd = 150 MPa - 75 MPa = 75 MPa , (2.4.26) Smax,zd = 150 MPa + 75 MPa = 225 MPa , Rzd = 75 /225 = + 0,333 .
2 MATERIAL PROPERTIES
crW,W
KWK,zd = 225 / (40 . 1 . 1 . 1) = 5,63 .
Mean stress sensitivity, low residual stresses,
1 CHARACTERISTIC STRESSES
=
Design factor
Amplitude of the component fatigue limit for the given mean stress
Calculation using nominal stresses
Sa,zd, I
(2.3.32)
1.
=
Because of 0 < Rzd < 0,5 field III applies: Mean stress factor 1+0,3/3 1+0,3 KAK,zd = 0 3 150 = 0,705 . 1+-'-·3 75
(2.4.12)
Residual stress factor, low residual stresses, KE,cr
=
1,54 .
Tab. 2.4.1
Amplitude of the component fatigue limit The nominal stress amplitude of the component fatigue limit results from the mean stress factor, the residual stress factor and the component fatigue limit for completely reversed nominal stress: (2.4.6) SAK,zd = 0,705 . 1,54' 16,3 MPa = 17,7 MPa.
248
6.4 Welded notched component
6 Examples
Component variable amplitude fatigue strength
Calculation using structural stresses
Variable amplitude fatigue strength factor
1 CHARACTERISTIC STRESSES
For the class of utilization B2 fatigue strength factor is
At the inside edge of the weld the (largest) amplitude and the mean value of the characteristic stress is
*3
the variable amplitude
KBK,zd = 6,30 .
Tab. (5.7.1)
The nominal stress amplitude of the component variable amplitude fatigue strength results from the variable amplitude fatigue strength factor and the amplitude of the component fatigue limit: SBK,zd = 6,30' 17,7 MPa= 112 MPa.
(2.4.41)
cra,l = 187,5 MPa, crm = 375 MPa .
(4.1.2)
2 MATERIAL PROPERTIES Independent of the type of steel the weld specific fatigue limit for completely reversed normal stress is (4.2.3)
crw,w = 92 MPa.
5 SAFETY FACTOR
.in
=
1,5 .
(2.5.1)
For moderate consequences of failure and regular inspection there is, however,
.io
=
1,2.
Tab. 2.5.1
For normal temperature there is KT,D = 1,
(2.2.5)
Therefore jges
= 1,2.
(2.5.4)
3 DESIGN PARAMETERS Fatigue class (FAT) The fatigue class (FAT) for structural stresses of a butt weld with a toe angle s 30 0 is required to derive the design factor after Eq. (2.3.4) for the welded notched component. It is FAT 100.
Tab. 5.4.3, Nr.212
Further factors of influence according to Chapter 4 1 as before, ft = 1 , Kv = 1 , KNL,E = 1 , Design factor
6 ASSESSMENT Characteristic (largest) nominal stress amplitude, see above, Sa,zd,l = 75 MPa .
SBK,zd = 112 MPa. Degree of utilization
,
(4.3.4)
4 COMPONENT FATIGUE STRENGTH
Nominal value of the amplitude of the component variable amplitude fatigue strength, see above,
75 aBK,zd = 112 / I 2 = 0,804 .
KWK,cr = 225 / (100 . 1 . 1 . 1) = 2,25 .
Component fatigue limit for completely reversed stress Component fatigue limit for completely reversed structural stress resulting from the weld specific fatigue limit for normal stress and the design factor: crWK = 92 MPa /2,25 = 40,9 MPa .
(2.6.1)
The degree of utilization of the component variable amplitude fatigue strength is 80 %. The assessment of the fatigue strength is achieved.
(4.4.1)
Amplitude of the component fatigue limit for the given mean stress Mean stress factor according to Chapter 4, as before, KAK,cr = 0,705 ,
(4.4.12)
Residual stress factor according to Chapter 4, as before, KE,cr = 1,54 ,
Tab. 4.4.1
Amplitude of the component fatigue limit The structural stress amplitude of the component fatigue limit results from the mean stress factor, the residual stress factor and the component fatigue limit for completely reversed structural stress: (4.4.6) 3 See Chapter 5.7, Footnote 3.
crAK = 0,705 . 1,54' 40,9 MPa = 44,4 MPa .
249
6 Examples
6.4 Welded notched component Component variable amplitude fatigue strength
4 COMPONENT FATIGUE STRENGTH
Variable amplitude fatigue strength factor according to Chapter 4, as before,
Component fatigue limit for completely reversed stress
KBK,zd = 6,30 .
Tab. (5.7.1)
The structural stress amplitude of the component variable amplitude fatigue strength results from the variable amplitude fatigue strength factor and the amplitude of the component fatigue limit: crBK = 6,30 . 44,4 MPa = 280 MPa .
(4.4.41)
5 SAFETY FACTOR
crK,WK = 92 MPa /1 = 92 MPa .
= 1,2 .
(4.5.4)
(4.4.1)
Amplitude of the component fatigue limit for the given mean stress Mean stress factor according to Chapter 4, as before, KAK,cr = 0,705 ,
Safety factor according to Chapter 4, as before, jges
Component fatigue limit for completely reversed effective notch stress resulting from the weld specific fatigue limit for normal stress and the design factor:
(4.4.12)
c(
Residual stress factor according to Chapter 4, as before, KE,cr = 1,54 , Tab. 4.4.1 Amplitude of the component fatigue limit
6 ASSESSMENT Characteristic (largest) structural stress amplitude, see above, cra,l = 187,5 MPa . Structural stress amplitude of the component variable amplitude fatigue strength, see above,
Degree of utilization
=
187,5 280[1,2
Component variable amplitude fatigue strength Variable amplitude fatigue strength factor according to Chapter 4, as before, KBK,cr = 6,30 , Tab. (5.7.1) '7
crBK = 280 MPa .
aBK cr ,
The effective notch stress amplitude of the component fatigue limit results from the mean stress factor, the residual stress factor and the component fatigue limit for completely reversed effective notch stress: (4.4.6) crK,AK = 0,705 . 1,54' 92 MPa = 99,9 MPa .
= 0,804 .
(4.6.1)
The degree of utilization of the component variable amplitude fatigue strength is 80 % (as with nominal stresses). The assessment of the fatigue strength is achieved.
The effective notch stress amplitude of the component variable amplitude fatigue strength results from the variable amplitude fatigue strength factor and the amplitude of the component fatigue limit: crK,BK = 6,30 . 99,9 MPa = 629 MPa.
(4.4.41)
5 SAFETY FACTOR Safety factor according to Chapter 4, as before,
Ca.lcu.lation using effective notch stresses
jges
= 1,2 .
(4.5.4)
1 CHARACTERISTIC STRESSES At the inside edge of the weld the (largest) amplitude and the mean value of the characteristic stress is crK,a,l = 420 MPa, crK,m = 840 MPa .
(4.1.3)
6 ASSESSMENT Characteristic (largest) effective notch stress amplitude, see above, crK,a,l = 420 MPa .
2 MATERIAL PROPERTIES Independently of the type of steel the weld specific fatigue limit for completely reversed normal stress is crw,w
= 92 MPa .
(4.2.3)
crK,BK = 629 MPa . Degree of utilization 420 aBK,crK = 629/12 , = 0,802 .
3 DESIGN PARAMETERS Factors of influence according to Chapter 4, as before, Kv = 1, KNL,E = 1 . Design factor KWK,crK = 1 / (1 . 1) = 1 .
Effective notch stress amplitude of the component variable amplitude fatigue strength, see above,
(4.3.8)
(4.6.1)
The degree of utilization of the component variable amplitude fatigue strength is 80 % (as with structural stresses. The assessment of the fatigue strength is achieved.
250
6.5 Shaft subject to two independent loads
6.5 Cantilever subject to two independent loads
1R65 EN.dog
6 Examples Safety requirements: According to the statements: "with severe consequences of failure; no regular inspections".
Key words: Cantilever, two independent random loads, assessment of the static strength, assessment of the variable amplitude fatigue strength, combined stresses.
Task: Assessment of the static strength and assessment of the variable amplitude fatigue strength for cross section x = O.
Given
Method of calculation: Rod-shaped (lD) component. Assessment to be carried out using nominal stresses.
Stresses: In cross-section x = 0 due to two independent random loads with binomially distributed amplitudes, figure 6.5.1. In load case G1 the load Fy,Gl acts with a total number of cycles N Gl = 105 which are binominally distributed with a spectrum parameter PGl = O. The characteristic mean value and amplitude are: Fm,y,Gl = 1 kN, Fa,y,GI =
± 23,5 kN.
In load case G2 the the load Fy,G2 acts with a total number of cycles NGl = 107 which are binominally distributed with a spectrum parameter PGl = 0,5. The characteristic mean value and amplitude are: Fm,y,G2
ANALYSIS OF THE STATIC LOADING Load case GI Mm,z,GI = 0,10 kNm, Ma,z,GI = ± 2,35 kNm, Mm,x,Gl = 0,10 kNm, Ma,x,GI = ± 2,35 kNm. Load case G2 M m,z,G2 =- 0,15 kNm, Ma,z,GI = ± 2,50 kNm, M m,x,G2 = 0,15 kNm, Ma,x,GI = ± 2,50 kNm. Superimposed loads, case UI
= - 1,5 kN, Fa,y,G2 = ± 25 kN.
The loads Fy,Gl and Fy,G2 vary non-proportionally (as they observe different load spectra!) and they may act both simultaneously or separately. At the cross-section at x = 0 bending moments Mz,Gl , M z,G2 and torsion moments Mx,Gl, M x,G2 with their mean values (index m) and amplitudes (index a) result from Fy,Gl , Fy,G2 and the lever arms I = 0,1 m.
The highest bending moment (absolute value) results if the amplitudes Fa,y,Gl and Fa,y,G2 act unidirectionally (in direction of the resulting mean value Fm,y,OI = Fm,y,Gl + Fm,y,G2, that is downwards in Figure 5.6.1): Mm,z,OI = (0,1- 0,15) kNm =- 0,05 kNm, Ma,z,OI = (- 2,35- 2,5) kNm =- 4,85 kNm, Mmin,z,OI = (- 0,05- 4,85) kNm =- 4,90 kNm. The related torsion moment is: Mm,x,OI = (0,1 + 0,15) kNm = 0,25 kNm, Ma,x,OI = (- 2,35 + 2,5) kNm = 0,15 kNm, Mmax,x,OI = (0,25 + 0,15) kNm = 0,40 kNm.
y z
Superimposed loads, case U2 The highest torsion moment results if the amplitudes Fa,y,Gl, and Fa,y,G2 act opposingly (in direction of the resulting mean value Mm,y,02 = Mm,y,GI + Mm,y,G2 as shown in Figure 6.5.1): Bile b65
Figure 6.5.1 Cantilever subject to two independent loads.
Mm,x,02 = (0,1 + 0,15) kNm = 0,25 kNm, Ma,x,02 = (+ 2,35 + 2,5) kNm = 4,85 kNm, M max,x,02 = (0,25 + 4,85) kNm = 5,10 kNm. The related bending moment is:
Material: St 60, DIN EN 10 025. Dimensions: Diameter of cantilever at x = 0: d = 57,5 mm, Length oflever arms: 1= 0,1 m. Surface: Average roughness R, = 25 um. Type of overloading: When overloaded in the service the stress ratios remain constant (type of overloading F2).
Mm,z,02 = (0,1- 0,15) kNm =- 0,05 kNm, Ma,z,02 = (2,35- 2,5) kNm =- 0,15 kNm, Mmin,z,02 = (- 0,05- 0,15) kNm =- 0,20 kNm.
251
6.5 Shaft subject to two independent loads ASSESSMENT OF THE STATIC STRENGTH
6 Examples Kp,b = 1,70, Tab. 1.3.2 npl,b = MIN (J1050/321 ; 1,70) = 1,70. 1.3.9)
The assessment of the static strength is to be carried out for each of the superimposed loads, cases VI and V2. The highest degree of utilization is determining.
Design factor
1 CHARACTERISTIC STRESSES
Design factor for torsion
Superimposed loads, case VI
Section factor
The maximum bending stress and the related torsional stress at the reference section with d = 57,5 mm is: Smax,b,-ol
=
32
IMmin,Z,OII I pd3
= 32 . 4,90 kNm I [TC . (57,5 mm)3] = 263 MPa, T max t -01 = 16 M max x -01 I pd3 = 16 : 0,40 kNm I (57,5 mm)3 ] = 10,7 MPa.
[n' .'
KSK,b = 1 I 1,70 = 0,588.
(1.3.1)
Rp,max = 1050 MPa, Tab. 1.3.1 Rp = 321 MPa, Kp,t = 1,33, Tab. 1.3.2 npl,t = MIN (J1050/321 ; 1,33 =1,33. (1.3.9) Design factor KSK,t
= 1 11,33 =
0,752.
(1.3.1)
4 COMPONENT STATIC STRENGTH Superimposed loads, case V2 The maximum torsional stress and the related bending stress at the reference section with d = 57,5 mm is: Smax,b,-02 = 32
IM min,z,0 2I I pd3
= 32· 0,20 kNm I [TC . (57,5 mmj-'] = 10,7 MPa. Tmax t -02 = 16 Mmax x -02 I pd 3 = 16: 5,10 kNm I .'(57,5 mm)3] = 137 MPa,
[n'
2 MATERIAL PROPERTIES
Tab. 5.1.1
Technological size factor ad,m = 0,15, ad,p = 0,3, deff,N = 40 mm, deff = d = 57,5 mm, Kd,m = 0,980, Kd,p = 0,956.
1, Tab. 1.2.5 SSK,b = 1 . 579 MPa I 0,588 = 985 MPa. (1.4.1)
Nominal value of the component static torsional strength resulting from the tensile strength and the design factor f't = 0,577, Tab. 1.2.5, (1.4.1) TSK,t = 0,577 ·579 MPa I 0,752 = 445 MPa.
For severe consequences of failure and a low probability for the simultaneous occurrence of the peak values of the stress spectra there is
jm = 1,8, jp = 1,35. Tab. 1.2.1 Tab. 1.2.3 (1.2.9)
Anisotropy factor K A = 1.
r, =
5 SAFETY FACTORS
Tensile strength and yield strength according to standard Rm,N = 590 MPa, Rp,N = 335 MPa.
Nominal value of the component static bending strength resulting from the tensile strength and the design factor
For normal temperature there is KT,m = KT,p = 1.
Tensile strength and yield strength of the component R m = 0,980 . 1 ·590 MPa = 579 MPa, (1.2.1)
R, = 0,956 . 1 . 335 MPa = 321 MPa.
(1.2.26)
and in Eq. (1.5.4) the terms 3 and 4 have no relevance: Rm = 579 MPa,
(1.2.17)
Tab. 1.5.1
Re = 321 MPa,
= MAX (1,8;1,35. 579) 321 = MAX (1,8; 2,44) = 2,44.
jges
(1.5.4)
The second term, the yield strength R, , is determining.
3 DESIGN PARAMETERS
6 ASSESSMENT
Design factor for bending
Superimposed loads, case VI
Section factor
Maximum stress in bending and related stress torsion, see above,
Rp,max = 1050 MPa, Rp = 321 MPa,
Tab. 1.3.1
Smax,b,-ol = 263 MPa, Tmax,t,-ol = 10,7 MPa.
ill
252
6.5 Shaft subject to two independent loads Component static strength, in bending and in torsion, see above, SSK,b = 985 MPa, TSK,I = 445 MPa. Degrees of utilization
6 Examples ASSESSMENT OF THE FATIGUE STRENGTH
The assessment of the fatigue strength is to be carried out according to Chapter 5.10: For the two nonproportional load cases Gl and G2 the individual degrees of utilization are to be determined and added.
Individual types of stress, bending or torsion, 263 a b= = 0651 SK, 985/ 2,44 ' , 10,7 a K = = 0059. S ,I 445/2 ,44 '
(1.6.1)
Load case Gl Bending and torsion moments (step 1 of the spectrum):
Combined types of stress f't = 0,577, q = 0, s = aSK,b = 0,651, t = aSK,1 = 0,059, aGH =
Tab. 1.2.5 (1.6.7) (1.6.6)
~0,6512 +0,059 2 =
0,654,
(1.6.5) (1.6.4)
aSK,sv = aSK,OI = 0,654.
Superimposed loads, case
Nominal stresses: Sm,b,1 = Sm,b,GI,1 = 32 Mm,z,Gl / pd 3 (2.1.1) = 32· 0,10 kNm/[n . (57,5 mm)3 ] = 5,4 MPa, Sa,b,1 = Sa,b,GI,1 = 32 Ma,z, GI / pd3 = 32 . 2,35 kNm / [n . (57,5 mm)3 ] = 126 MPa,
i6 .
ih
Smax,b,02 = 10,7 MPa, T max,I,U2 = 137 MPa. Component static strength in bending and in torsion, see above,
Ta,I,1 = Ta,I,GI,1 = 16 Ma,x, GI / pd 3 = 16 . 2,35 kNm / [n . (57,5 mm)3 ] = 63 MPa.
Load case G2 Bending and torsion moments: (step 1 of the spectrum): M m,z,G2 =- 0,15 kNm, Ma,z,Gl = ± 2,50 kNm, M m,x,G2 = 0,15 kNm, Ma,x,Gl = ± 2,50 kNm.
SSK,b = 985 MPa, TSK,I = 445 MPa. Degrees of utilization
Nominal stresses:
Individual types of stress, bending or torsion, = 0027 10,7 aSK,b = 985/2,44 ' ,
Sm,b,1 = Sm,b,G2,1 = 32IMm,z,Gl/ / pd3 (1.6.1)
=
(2.1.1)
32· 0,15 kNrn/[n . (57,5 mm)3 ] = 8,0 MPa,
Sa,b,1 = Sa,b,G2,1 = 32 Ma,z, GI / pd3 = 32· 2,50 kNm / [n . (57,5 mm)3 ] = 134 MPa,
137 aSK,1 = 445/2,44 = 0,751.
Tm,I,1 = T m,I,G2,1 = 16 Mm,x, GI / pd 3 = 16· 0,15 kNm / [n . (57,5 mm)3 ] = 4,0 MPa,
Combined stress
~0,0272 +0,751 2 =
Mm,z,GI = 0,10 kNm, Ma,z,GI = ± 2,35 kNm, Mm,x,Gl = 0,10 kNm, Ma,x,GI = ± 2,35 kNm.
T m I I = T m I GI I = 16 M m x GI / pd 3 = 0,10 kN~ / [n . (57,5 ~)3 ] = 2,7 MPa,
Maximum stress in torsion and related bending stress, see above,
aGH =
1 CHARACTERISTIC STRESSES
0,751,
aSK,sv = aSK,02 = 0,751.
(1.6.5) (1.6.4)
Tm,I,1 = Ta,I,G2,1 = 16 Ma,x, Gl / pd 3 = 16· 2,50 kNm / [n . (57,5 mm)3 ] = 67 MPa. The negative sign of the mean stress for bending is not important here.
Definite degree of utilization aSK = MAX (aSK,0 I, aSK,02 )
2 MATERIAL PROPERTIES
= MAX (0,654; 0,751) = 0,751.
Material fatigue limits for fully reversed normal stress, crW,zd, and shear stress, LW,S :
The degree of utilization of the component static strength is 75 %. The assessment of the static strength is achieved.
Rm = 579 MPa, fw,« = 0,45, crW,zd = 0,45 . 579 MPa = 261 MPa, fw,'t = 0,577, LW,S = 0,577 . 261 MPa = 151 MPa.
Tab. 2.2.1 (2.2.1) Tab. 2.2.1 (2.2.1)
253
6.5 Shaft subject to two independent loads
6 Examples
3 DESIGN PARAMETERS
4 COMPONENT FATIGUE STRENGTH
Design factor for bendin..g
Component fatigue limit for completely reversed bending and torsional stress:
Fatigue notch factor
Component fatigue limit for completely reversed bending stress resulting from the material fatigue limit for normal stress and the design factor for bending:
Stress concentration factor of a plain shaft *1, Kt,b = 1.
SWK,b = 260 MPa /1,145 = 228 MPa.
KcKf ratios, no notch radius, Gcr(r) = 0, ncr (r) = 1, d = 57,5 mm, Gcr(d) = 2/ d = 0,0357 mm -I , ncr (d) = 1,021.
(2.3.17) (2.3.13)
Fatigue notch factor
Component fatigue limit for completely reversed torsional stress resulting from the material fatigue limit for shear stress and the design factor for torsion: TWK,t = 150 MPa /1,064 = 141 MPa.
(2.4.1)
Load case Gl
Kf,b = 1 / (1 . 1,021) = 0,979.
(2.3.10)
Roughness factor Rill = 579 MPa, Rz = 25 urn, aR,cr = 0,22, Rm,N,min = 400 MPa, KR,cr = 0,858.
(2.4.1)
Component fatigue limit for the given mean stress for bending and torsion The calculation for type of overloading F2.
Tab. 2.3.4 (2.3.26)
For no surface treatment is KV = 1. For materials except GG KNL,E = 1. Therefore: Design factor KWK,b = 0,979 + 1/0,858 - 1 = 1,145
(2.3.1)
Mean stress sensitivity R m = 579 MPa, aM = 0,00035, bM = - 0,1, M, = 0,103, fw,~ = 0,577 M~ = 0,577 . 0,103 = 0,059.
Tab. 2.4.2 (2.4.34) Tab. 2.2.1 (2.4.34)
Equivalent mean stress Sm = Sm,b,GI = 5,4 MPa, Tm,t,GI = 2,7 MPa, fw,~ = 0,577, q = 0,
Design factor for torsion Fatigue notch factor Stress concentration factor of a plain shaft *1,
KcKf ratios, no notch radius, G~ (r) = 0, v~(r) = 1, d = 56 mm, G~ (d) = 2/ d = 0,0357 mm -I , n, (d) = 1,026.
Tab. 2.2.1 (2.4.29)
Sm,v,l= Sm,v,GH =~5,42+3.2,72 MPa = = 7,1 MPa, (2.24.29) (2.4.28) Tm,v,1 = 0,577 . 7,1 MPa = 4,1 MPa. (2.4.30)
Kt,t = 1.
Stress ratio for bending (2.3.17) (2.3.13)
Fatigue notch factor Kf,t = 1 / (1 . 1,026) = 0,975.
(2.3.10)
Roughness factor R m = 579 MPa, R z = 25 urn, fw,~ = 0,577 aR,cr = 0,22, Rm,N,min = 400 MPa, KR,~ = 0,918.
(2.4.31)
r., =
Rs,v = (Sm,v,1 - Sa,b,Gl,I) / (Sm,v,1 + Sa,b,Gl,l) =(7,1 126) / (7,1 + 126) = - 0,89. Mean stress factor for bending; because of - 00 :;;; Rs,v :;;; field II applies:
°
KAK,b = 1/(1 + Sm,v,1 / Sa,b,GI,I) = 1/(1 + 7,1 / 126) = 0,947. Tab. 2.2.1 Tab. 2.3.4 (2.3.26)
(2.4.10)
Stress ratio for torsion RT,v = (Tm,v,1 - Ta,t,Gl,I) /(Tm,v,1 + Ta,t,GI,I) =(4,1 63) / (4,1 + 63) = 0,88.
For no surface treatment is KV = 1. Therefore Mean stress factor for torsion; field II applies: because of -1:;;; RT,v :;;;
°
Design factor KWK,t = 0,974 + 1 /0,918 - 1 = 1,064
(2.3.1)
I This isa simplifying assumption made for the present example that would not bevalid for a real component, however!
KAK,t = 1 / (1 + Tm,v,1 / Ta,t,Gl,1 ) = 1/(1 + 4,1 /63) = 0,939.
(2.4.10)
Residual stress factor for normal stress and for shear stress KE,cr = KE,~ = 1. (2.4.5)
254
6.5 Shaft subject to two independent loads Amplitude of the component fatigue limit The amplitude of the component fatigue limit results from the mean stress factor, residual stress factor and the component fatigue limit for completely reversed bending or torsional stress: SAK,b = 0,947 . 1 . 228 MPa = 216 MPa, (2.4.6) TAK,t = 0,939 . 1 . 141 MPa = 132 MPa. Component variable amplitude fatigue strength for bending and torsion Variable amplitude fatigue strength factors for bending and torsion KBK,b = 3,84, KBK,t = 2,88.
(2.4.51)
The variable amplitude fatigue strength factors follows from the elementary version of Miner's rule and a critical damage sum D M = 0,3 , Chapter 2.4.3.1. The component variable amplitude fatigue strength results from the variable amplitude fatigue strength factor and from the mean stress dependent amplitude of the component fatigue limit for bending or for torsion: SBK b = 3,84' 216 MPa = 829 MPa, (2.4.41) TB~,t = 2,88' 132 MPa = 380 MPa.
SBK,b ::;; 0,75 . R, . ~,b = 0,75' 321 MPa '1,70 = 409 MPa, (2.4.42) TBK,t ::;; 0,75' ft . R, . ~,t = 0,75' 0,577 . 321 MPa '1,33 = 185 MPa. Relevant component variable amplitude fatigue strength SBK b Gl = MIN (829,409) MPa = 409 MPa, TB~,b',Gl = MIN (380, 185) MPa = 185 MPa.
Load case G2
SBK b = 1,00' 211 MPa = 211 MPa, TB~,t = 1,04' 129 MPa = 134 MPa.
(2.4.41)
5 SAFETY FACTOR For severe consequences of failure and no regular inspections
.io = 1,5.
(2.5.1)
For normal temperature is KT,D = 1,
(2.2.4)
= 1,5.
(2.5.4)
jges
6 ASSESSMENT Load case Gl Characteristic stress amplitudes for bending and for torsion, see above, Sa,b,l = Sa,b,Gl,l = 126 MPa, Ta,t,l = Ta,t,Gl,l = 63 MPa.
SBK,b,Gl = 409 MPa, TBK,t,Gl = 185 MPa. Degrees of utilization Individual types of stress, bending or torsion, 126 409/1,5 = 0462 ' , 63 = 0511. a K = B,t 185/15 ' ,
aBK,b
(2.6.1)
=
Combined types of stress
Component fatigue limit for the given mean stress for bending and torsion An analog calculation results in
(2.4.6)
Component variable amplitude fatigue strength for bending and torsion Variable amplitude fatigue strength factors for bending and torsion KBK,b = 1,00, KBK,t = 1,04.
factor and from the mean stress dependent amplitude of the component fatigue limit for bending or for torsion:
Amplitude of the component variable amplitude fatigue strength for bending and for torsion, see above,
Limitation of the amplitudes
SAK,b = 211 MPa, TAK,t = 129 MPa.
6 Examples
(2.4.51)
The variable amplitude fatigue strength factor follows from the elementary version of Miner's rule and a critical damage sum DM = 0,3 , Chapter 2.4.3.1. The component variable amplitude fatigue strength results from the variable amplitude fatigue strength
fw,"t = 0,577, q = 0, Sa = aBK,b = 0,462, ta = aBK,t = 0,511,
Tab. 2.2.1 (2.6.7) (2.6.6)
aGH = ~0,4622 +0,511 2 = 0,689, aBK,Sv = aBK,Gl = 0,689.
(2.6.5) (2.6.4)
Load case G2 Characteristic stress amplitudes for bending and for torsion, see above, Sa,b,l = Sa,b,G2,l = 134 MPa, Ta,t,l = Ta,t,G2,l = 67 MPa. Amplitude of the component variable amplitude fatigue strength for bending and for torsion, see above, SBK,b,G2 = 211 MPa, TBK,t,G2 = 134 MPa.
255
6.5 Shaft subject to two independent loads Degrees of utilization Individual types of stress, bending or torsion, 134
aBK,b
= 211/1,5
a
=
BK,t
= 0953
'
67
=
134/1,5
,
(2.6.1)
0750. '
Combined types of stress
fw,'t = 0,577, q
Tab. 2.2.1
= 0,
Sa
= aBK,b = 0,953,
ta
= aBK,t = 0,750,
= ~0,9532 +0,750 2 = 1,213, aBK,Sv = aBK,G2 = 1,213.
a GH
(2.6.7) (2.6.6) (2.6.5) (2.6.4)
Total degree of utilization from the combined effect of load case G1 and G2 aBK
=
aBK,GI
= 0,689 +
+
aBK,G2
1,213
= 1,902
(5.10.3)
The cyclical degree of utilization of the component is 190 %. The assessment of the variable amplitude fatigue strength is not achieved.
6 Examples
6.6 Component made of a wrought aluminium alloy
256
6 Examples
6.6 Component made of a wrought aluminium alloy *1 lRi66.docl
ASSESSMENT
Key words: Wrought aluminium alloy, assessment of the static strength, assessment of the fatigue strength for finite life, local elastic stresses, type of overloading F2, combined types of stress, (JI and (J2 .
1 CHARACTERISTIC STRESSES Maximum stresses (3 . 1.6) (JI ,max,ex = 238 MPa, (J2, max ,ex = 58,4 MPa .
Given:
2 MATERIAL PROPERTIES
Stresses: Proportional, constant amplitude, local elastic stresses in the directions 1 (longitudinal direction) and 2 (circumferential direction) at the reference point of a block-shaped (3D) component, Figure 6.6.1,
AlZn4,5Mgl T651, Tab. 5.1.22, pp. 151. R, = 350 MPa, R, = 280 MPa, As = 9 %.
(JI = (JI,m± (JI,a = 119 MPa ± 119 MPa, (J2 = (J2,m ± (J2,a = 29,2 MPa ± 29,2 MPa , (J3 = O. Stress amplitudes at the neighbouring point in a distance s = 1,254 mm below the surface (JI,a = ± 54,1 MPa,
(J2,a = ± 22,5 MPa . 4
Number of cycles: N = 5 . 10 (R, = 0).
OF THE COMPONENT STATIC STRENGTH
*2
Tensile strength and yield strength for the standard dimension Rm,N = 350 MPa , Tab. 5.1.14 Rp,N = 280 MPa . No technological size factor Kd,m = 1.
(3.2.5)
Anisotropy factor KA = 1.
(3.2.18)
Tensile strength and yield strength for the component (3.2.1) R m = 1 . 1 . 300 MPa = 350 MPa, Rp = 1 . 1 . 280 MPa = 280 MPa .
3 DESIGN PARAMETERS Section factor E = 0,70 'lOs MPa ,
Tab. 3.3.1
£crtr=2%, = 280 MPa, ~,cr = 1,7, ~
Figure 6.6.1 Aluminum component with pivot.
0,70.10 5.0,02 npl,crl = MIN ( 280 ; 1,7)
Material: AIZn4,5Mgl , T651, aging wrought aluminium alloy Temperature: T = 50°C (normal temperature). Dimensions: Effective diameter at the reference point: defT = 18 mm. Surface: average roughness
R..
= 10 urn,
Type of overloading: When overloaded in service the stress ratios remain constant (Type of overloading F2). Safety requirements: according to the statements: "with moderate consequences of failure; no regular inspection" .
= MIN (2,24; 1,7) = 1,7 .
(3.3.9)
For n pl,cr2 the same value is assumed: n pl,cr2 = 1,7 . Design factor for directions 1 and 2 KSK,crl = KSK,a2 = 1 / 1,7 = 0,588
(3.3.3)
4 COMPONENT STATIC STRENGTH The component strength results from the tensile strength and the design factor. For directions 1 and 2: fa = 1, Tab. 3.2.5, (3.4.3) (JI,SK = (J2,SK = 1 . 350 MPa / 0,588 = 595 MPa .
Task: Assessment of the static strength and of the constant amplitude fatigue strength for finite life (N = 5 . 104 cycles).
5 SAFETY FACTORS
Method of calculation: Block-shaped (3D) component. Assessment using local elastic stresses, Chapter 3 and 4. For T = 50°C temperature factors do not need to be considered (KT,m ~ ... = 1).
For moderate consequences of failure and a high probability of occurrence of the maximum (constant amplitude) stress there is jm = 1,75, jp = 1,30. Tab. 3.5.1
I
Results of computation obtained by the pc- program "RIFESTPLUS".
2
The numbers of equations, tables and figures are those of the
guideline.
6.6 Component made of a wrought aluminium alloy For an elongation As < 12,5 % (here A s = 9 %) the safety factors are to be increased by ~j:
~j = 0,5 --h/50 = 0,08, jm = 1,83, jp = 1,38 .
(3.5.2) Tab. 3.5.2
For normal temperature the terms 3 and 4 of Eq. (3.5.4) are not relevant.
jg~s =
MAX (1,83: 1,38. 350) 280
6 Examples ASSESSMENT OF THE COMPONENT FATIGUE STRENGTH
1 CHARACTERISTIC STRESSES Proportional constant amplitude stresses O"I,a,1 = 119 MPa, 0"1,01,1 = 119 MPa, (4.1.1) 0"2,a,1 = 29,2 MPa, 0"2,01,1 = 29,2 MPa .
(3.5.4)
2 MATERIAL PROPERTIES
= MAX (1,83, 1,73) = 1,83.
Material fatigue limit for completely reversed normal stress, O"W,zd, for N = 106
The tensile strength R m is deciding.
Rm = 350 MPa, Tab. 4.2.1 fw,a = 0,30 , (4.2.1) O"W,zd = 0,30 . 350 MPa = 105 MPa .
6 ASSESSMENT Maximum stresses, see above, O"I,max,ex = 238 MPa,
257
0"2,max,ex = 58,4 MPa .
Component strength values, see above,
3 DESIGN PARAMETERS K,-Krratios
O"I,SK = 0"2,SK = 595 MPa.
=
1 .(1- 54,1) = 0,435 mm -I, 1,254mm 119
Ga 2 =
1 .(1- 22,5) = 0,183 mm -I, 1,254mm 29,2
Gal
Degrees of utilization Individual types of stress, direction 1 and 2 aSK I =
238 = 0,732, 595/1,83
aSK,a2 =
59~~':'83
.o
(3.6.17)
As = 9 % , q = 0,5, before (3.6.23), Tab. 3.6.1 (3.6.22) Sl = aSK c l = 0,732, S2 = aSK:a2 = 0,179 ,
L((0,732-0,179)2 +0,179 2 +0,732 2 )
2 = 0,660, aNH = MAX (0,732, 0,179) = 0,732,
aSK,sv = 0,5 . 0,732
aa
Tab. 4.3.2 (4.3.14)
= 0,05, b G = 850 , nal = 1,228, na2 = 1,148.
Roughness factor R z = 10 um, aR,a = 0,22, Rm,N,min = 133 MPa, KR,a = 0,841 .
= 0,179 .
Combined types of stress
aGH =
(4.3.16)
(3.6.21) (3.6.20)
+ (1 - 0,5) . 0,660 = 0,696.
The degree of utilization of the component static strength is 70 %. The assessment of the static strength is achieved. This result of the assessment is only exact, however, if the stresses 0"1 and 0"2 are proportional, even if, on principle, it is supposed for the assessment of the component static strength that different types of stress observe their extreme value simultaneously, that is, as if they were proportional. But with non-proportional stresses 0"1 and 0"2 it would be of importance that the individual degree of utilization aSK o l = 0,732 is higher than the degree of utilization 'of the combined types of stress aSK,sv = 0,696 derived.
Surface treatment factor Kv = 1, Ks = 1 .
and
Tab. 4.3.4 (4.3.26)
coating factor (4.3.28) (4.3.30)
A universal value forKf after table 4.3.1 would be: Kf = 2. Tab. 4.3.1 Instead a value forKf derived from the stress concentration factor of a substitute structure after Chapter 5.12 shall be applied here: G a I = 0,435 mm -I , r=2/G a l =4,6mm, derr = b = 18 mm, K = 1OO,066-0,36.1g(rlb) = 1 904 t
"
(5.12.2) (5 12 1)
.
•
nal = 1,228 , I(f,1 = 1,904 I 1,228= 1,550". Accordingly K f ,2 = 1,214. Design factors KWK,al
= 1,;28 {1+
(4.3.3)
1,5~0 {0,~41 -1)) = 0,913 ,
KWK a2 = _1_.(1+!.(_1__ 1)) = 1,007. , 1,056 1 0,906
6.6 Component made of a wrought aluminium alloy
258
6 Examples
.io
4 COMPONENT FATIGUE STRENGTH Component fatigue limit for completely reversed stress The component fatigue limit for completely reversed normal stress results from the material fatigue limit for completely reversed normal stress and the design factors: (4.4.3)
O"I.WK = 105 MPa / 0,913 = 115 MPa , O"2.',VK = 105 MPa / 1,007 = 104 MPa .
Amplitude of the component fatigue limit for the given ""- .
mean stress
Mean stress sensitivity
Tab. 4.5.2
1,3.
=
For an elongation As < 12,5 % (here As safety factors are to be increased by ~j:
~j = 0,5 -.Jg/50 = 0,08;
.io
9 %) the
.
(4.5.2)
1,38.
=
Therefore the total safety factor is
= 1,38.
jges
(4.5.4)
6 ASSESSMENT Characteristic stress amplitudes, see above O"I,a,1 = 119 MPa, 0"2,a,1 = 29,2 MPa.
aM = 1,0, bM = - 0,04, M cr = 0,31 .
Tab. 4.4.2 (4.4.34)
Amplitudes of the component variable amplitude fatigue strength, see above,
According to Chapter 4.4.2.2 no equivalent mean stress is to be applied; the individual mean stresses are to be applied instead. The type of overloading is F2.
Degrees of utilization
Mean stress factor for the direction 1 and 2.
Individual types of stress, direction 1 and 2
Stress ratios Rcrl = R cr 2 = O.
O"I,BK = 160 MPa, 0"2,BK = 145 MPa .
aBK
.c
KAK,crl = KAK,cr2 = 1+ 0,31 = 0,763 . Residual stress factor KE,cr = KE;t = 1 .
(4.4.10)
(4.4.5)
Amplitude of the component fatigue limit The amplitude of the component fatigue limit results from the mean stress factor, the residual stress factor and the component fatigue limit for completely reversed stress, O"I,AK = 0,763 . 1 . 115 MPa = 88 MPa , 0"2,AK = 0,763 . 1 . 104 MPa = 80 MPa .
(4.4.8)
a
I
=
119 160 11,38
= 1,027 ,
(4.6.17)
229,2 = 0,277 . BK.o - 145/1,38
Combined types of stress As = 9 % , q = 0,5, SI,a = aBK,crl = 1,027 , S2,a = aBK cr2 = 0,277 ,
aGH
Tab. 4.6.1 (4.6.22)
= L((1,027-0,277)Z +0,277 2 +1,027 2 )
2 = 0,921 , (4.6.21) aNH = MAX (1,027, 0,277) = 1,027 , (4.6.20) aBK,crv = 0,5 . 1,027 + (1 - 0,5) . 0,921 = 0,974
Component variable amplitude fatigue strength Variable amplitude fatigue strength factor For the constant amplitude stresses of concern with a required number of cycles N = N = 5 . 104, where N < No,cr= 106 , and a component constant amplitude S-N curve model I or model II the variable amplitude fatigue strength factor is (4.4.48) KBK,crl = KBK,cr2 = (10 6 / 5 ' 104 )
(I/S)
= 1,821.
The amplitude of the component variable amplitude fatigue strength results from the variable amplitude fatigue strength factor and the amplitude of the component fatigue limit: O"I,BK = 1,82' 88 MPa = 160 MPa , 0"2,BK = 1,82' 80 MPa = 145 MPa .
(4.4.45)
5 SAFETY FACTORS For moderate consequences of failure and no regular inspection there is
The degree of utilization of the component variable amplitude fatigue strength is 97 %. The assessment of the fatigue strength is achieved. This result of the assessment of the fatigue strength is valid only because the stresses 0"1 and 0"2 are proportional and definitely occur in parallel. Obviously the degree of utilization of the individual type of stress 0"1 is higher than the degree of utilization of the combined types of stress 0"1 and 0"2: aBK,crl = 1,027 is higher than aBK,sv = 0,974.
In the case that - different from the present example 0"1 and 0"2 could occur independent of each other, the higher individual degree of utilization aBK o l of 103 % would be deciding, a result that supports the demand of always considering the degrees of the individual types of stress as well.
259
7 Symbols and basic formulas lRi7 EN.dog
7.1 Abbreviations B
F FAT GS
GG GGG GT GTS GTW
class of utilization (B-7, ... , B 10) type of overloading (FI, F2, F3, F4) fatigue class (for welded components) cast steel and heat treatable cast steel, for general purposes cast iron with lamellar graphite (grey cast iron) nodular cast iron malleable cast iron GT, black heart (non-decarburized) GT, white heart (decarburized)
7 Symbols and basic formulas
7.2 Indices a b eff ex ges i j
amplitude bending effective extreme total number of a step of a stepped stress spectrum number of the last step of a stepped stress spectrum (smallest amplitude), number of all steps mean value maximum value minimum value shear torsion equivalent value equivalent value (assessment of the static strength of welded components) axial direction of rod-shaped (ID) components first direction of shell-shaped (2D) components first lateral direction of rod-shaped' (ID) components second direction of shell-shaped (2D) components second lateral direction of rod-shaped (ID) components tension, compression, or tension-compression component fatigue limit component variable amplitude fatigue strength local stress (effective notch stress) component static strength welded component fatigue limit for completely reversed stress number of the first step of a stepped stress spectrum (largest amplitude) index of the first principle stress index of the second principle stress index of the third principle stress, normal to the surface (pointing into the interior of the component) normal stress shear stress
m max
mm s v
wv
x
x I Applies to Rm . For Rp the m index is to be replaced by p.
y
2 Applies to normal stress. For shear stress c is to be replaced by "to
y
3 Applies to nominal stress. For local stress (also structural stress or effective notch stress) S is to be replaced by cr.
z
4 These symbols apply to nominal stress (tension-compression). Szd , Sa,zd , Sm,zd , Smax,zd , Smin,zd , SAK,zd , SBK,zd ' SSK,zd , SWK,zd , KAK,zd , KBK,zd , KSK,zd , KWK,zd , Rzd , Yzd . ... to other kinds of nominal stress Sb ' T s , T t ' Sx , Sy , T, .... ... to local stress 0',
(!a , ... , oAK ,... , KAK,cr ,... , Rcr , Vcr ,
t , ax ,
cry , 0'1 ,0'2,0'3
zd
AK BK K SK W WK
5 Swv,zd applies to nominal stress (tension-compression). Also Swv,b ' Twv,s, Twv,t, Swv.x . Swv,y, T wv . For local stress crwv , "tw v , crwv,x ' crwv,y . 6 Kt,zd is applies to nominal stress (tension-compression). Also Kt,b ' Kt,s , Kt,t .
I 2 3
Similarly for Kf . 7 aBK,zd applies to nominal stress (tension-compression). Also aBl(,b , aBK,s , aBK.,t , aBK,x , aBK.,y·
cr 1:
For local stress aBK,cr , aBK.,"t , aBK,crx , aBK.,cry , aBK,crl ' aBK,cr2 , aBK.,cr3 . Similarly for aSK and asK.,wv.
7.3 Lower case characters
8 npl,b applies to nominal stress in bending, npl,t in torsion. For local stress npl,cr and npl,"t . 9 Kp,b applies to nominal stress in bending, Kp,t in torsion. For local stress Kp,cr and Kpl,"t. 10 Fatigue strength value. II Type of loading tension or compression zd, also types of loading, b, s, t, X, y.
aBK,Sv
au, . aM,
aR,cr
.
Constant for ~ *1 degree of utilization (for the assessment of the fatigue strength) aBK for combined stresses *3 Constants for ncr '" Constants for M cr Constant for KR,cr
*7
260 aSK.wv.zd aSK for welded components (equivalent stress for a particular type of loading) *7 degree of utilization aSK.zd (for the assessment of the static strength) *7 aSK for combined stresses *3 aSK.Sv aSK,Swv aSK for welded components (for the combined types of loading) *3 constant for KT,m *1 aT,m constant for KT,D aT,D aTt.m ... constants for KTt,m *1 width b diameter d effective diameter of the semi-finished deff product or the raw casting deff for R m *' deff,m deff m for R m N *1 deff,N,m dia~eter of a' longitudinal hole dL diameter of the reference component dp (the test specimen) diameter of a transverse hole diameter of the material test specimen, do = 7,5 rom thickness factor (for welded components) fatigue limit factor for completely reversed stress shear fatigue strength factor compression strength factor shear strength factor number of cycles in step i of the stress spectrum safety factor J total safety factor Jges j for R m and R m,T jm j for Rm,Tt jmt j for ~ and ~,T ~p j for ~,Tt ~pt j for fJw and/or T:w JD partial safety factor for allowable defects in JF castings slope of the constant amplitude S-N curve for kD,cr N > ND,cr *2 slope of the constant amplitude S-N curve for N::; ND,cr *2 n,1 number of cycles in step i of the stress spectrum section factor for static bending *8 KcKf ratio for the fatigue strength *2 ncr due to the related stress gradient from bending or torsion of the cross section *2 ncr (r) ncr due to the related stress gradient caused by a notch of the component in question *2 ncr due to the related stress gradient caused ncr (r p ) by a notch of the reference component (the test specimen) *2 spectrum parameter p q constant for aSK,Sv .. , notch radius of the component in question r rp notch radius of the reference component (the test specimen)
7 Symbols and basic formulas
s
wall thickness of the component time of operation at temperature T depth of a notch damage potential of the stress spectrum *4
Vzd
7.4 Upper case characters A, A 3 , As B Cm
D
DM F
,
<
elongation elongation width Larsen-Miller-constants for KTt,m ... diameter critical damage sum axial load (tension, compression, or tension-compression) related stress gradient *2
total number of cycles in a stress spectrum, H=Hj=L:hi technological size factor Kd Kd for R m and/or fJw Kd,m Kd for Rp ~d,p constant, estimate for Kf Kr fatigue notch factor *6, applying to the Kf,zd component in question, dimensions deff and r Kf,zd (d p ) Kf of the reference component (the test specimen), dimensions d p and r p *6 Kp,b plastic notch factor *9 ~,Zd stress concentration factor *6 KA anisotropy factor KAK zd mean stress factor *4 KBK'Zd variable amplitude fatigue strength factor *4 , *2 KE,cr residual stress factor (welded components) KNL constant allowing for the non-linear stress-strain behavior of GG in the case of static loading constant allowing for the non-linear stress-strain behavior of GG in the case of fatigue loading Roughness factor *2 design factor (static strength) *4 temperature factor KT for Rm,T KT for ~,T KT for fJw KT for Rm,Tt KT for ~,Tt surface treatment factor, . design factor (fatigue strength) *4 bending moment torsion moment mean stress sensitivity *2 number of cycles after the component constant amplitude S-N curve N total number of cycles after the component variable~mplitude S-N curve (fatigue life curve), N = L: ni Reference number of cycles Nc (for the S-N curve of welded components)
261 Number of cycles at knee point of the component constant amplitude S-N curve type I or type II *2 N D,cr,II number of cycles at second knee point of the component constant amplitude S-N curve type II *2 a surface (area) of the considered section of a component Larsen-Miller-parameter for the creep Pm,Pp strength probability of survival compression strength yield strength in compression yield strength tensile strength, "component property according standard" for deff "component actual value" of R m Rm ,1 property according standard of R m for ~,N deff,N,m constant for Kp,cr strength at elevated temperature T creep strength at temperature T and time t "component specified value according to drawing" ofRm yield stress, a generalization of R, or ~O,2 ' "component property according standard" for deff' constant for npl,b (bending) and Rp,max npl,t (torsion) "component actual value" of Rp property according standard of Rp for deff,N,p yield strength at elevated temperature T 1 %-creep stress at temperature T and time t 0.2 % proof stress shear strength yield stress in shear average roughness of the surface stress ratio *4 Rzd of step 1 of the stress spectrum *4 stress amplitude *4 equivalent stress amplitude for a number of cycles ND,cr *4 Sa zd of step i of the stress spectrum *4 Sa,zd,i Sa'zd of step 1 (largest amplitude) of the Sa,zd,1 st;ess spectrum *4 Sm zd mean stress *4 Sm.z ' d', 1Sm zd of step i of*4the stress spectrum *4 , Sm,zd,1 Sm,zd for Sa,zd,1 Smax,zd maximum stress of the stress spectrum *4 . Smax,ex,zd ex treme maximum stress *4 Smax ex wv zd extreme maximum stress of Swv zd *5 *11 Smin ~d ' ~nimum stress of the stress spectru~ *4 Smin:ex,zd extreme minimum stress *4 . Smin,ex,wv,zd ex treme reme mi nummum stress 0 f Swv,zd *5*11 Sm v equivalent mean stress *3 Sw~,Zd equivalent stress (welded component) *5 *11 SAK zd amplitude of the component fatigue limit , for Sm.z d or for Sm.v *4 *10
7 Symbols and basic formulas SAK,II,zd amplitude of the component endurance limit for Sm.z d or for Sm.v *4 *10 amplitude (largest amplitude of the spectrum) of the component variable amplitude fatigue strength for Sm zd or for Sm v *4 *10 component static strength *4'*10 SSK,zd SWK,zd component fatigue limit for completely reversed stress *4 *10 normal stress parallel to the weld seam *3 *11 SII,zd normal stress normal to the weld seam? *11 S.l,zd temperature T shear stress parallel to the weld seam *3 *ll TII,zd shear stress normal to the weld seam *3 *11 T.l,zd V Volume of the considered section of a component
7.5 Greek alphabetic characters weld factor limit value of total strain local stress (non-welded component) or 0' structural stress (welded component) O'K effective notch stress (welded component) *2 O'Sch,zd fatigue limit for zero-tension stress O'Sch,zd,N property according standard of O'Sch,zd for deff,N,m material fatigue limit for completely reversed normal stress "component property according standard" for deff,m O'w for bending b O'W,b O'W,b,N property according standard of O'wb for deff,N,m ' weld specific fatigue limit (normal stress) O'W,W O'w for tension-compression zd O'W,zd O'W,zd,N property according standard of O'w zd for deff,N,m ' O'W,zd,T O'w zd for elevated temperature 0'1 first principle stress *4 stress amplitude at the surface *2 O'I,a 'C material fatigue limit for completely reversed w shear stress "component property according standard" for deff,m 'Cw for shear s property according standard of 'Cw s for deffN ' , ,m 'Cw,s for elevated temperature 'CW,s,T 'Cw for t torsion 'Cw,t property according standard of 'Cw t 'CW,t,N ' for deff,N,m weld specific fatigue limit (shear stress) slope angle of a changing cross section increase of j for non-ductile materials Sertr
262
7 Symbolsand basic formulas
7.6 Basic formulas Assessment of the component static strength The characteristic service stress values are or
Smax,ex
or
Tmax,ex
O"max,ex
or
'tmax,ex
The component static strength values are SSK = f, .R, .npl .(KNL ) or
TTJ< = f t '.Rn npl' (KNL ) O"SK = f, ..Rn . ~l . (KNL ) 'tTJ< = ft '.Rn ~]. (KNL)
The denotations S and T apply when using nominal stresses, the denotations 0" and 't when using local stresses.
Different values ofthe section factor ~I apply to the individual types ofstress. Moreover the sectionfactors used with nominal or local stresses are to be determined in a different way.
The degrees of utilization are derived as:
or
aSK = I Smax,ex / ( SSK . jerf) I ~ 1 aSK = I Tmax,ex/(TsK . jere> I ~1 aSK = I Smax,ex / ( SSK . jerf) I s 1 aSK = I Tmax,ex/(TSK'jerf)1 ~1
Assessment of the component fatigue strength The characteristic service stress values are s., or Ta,J or or
Sa,1 , SBK, Ta,] , TBK or O"BK, O"BK, 'ta,] , 'tBK, respectively, refer to the largest amplitude ofthe stress spectrum ofconcern.
The component fatitgue strength values are for notched components
or
SBK = {fwo' n, 'K AK . KE,a 'KBK'K y '(KNL) } / TBK= {fwt . fwo' .Rn 'K AK ' KE,t 'KBK'K y '(KNL)
{x, / ( no(r) . no(d) ) + 1 / KR,o(RJ -1 } } / {x, / [llr(r) 'llr(d) ] + 1 / KRiRJ -1 } O"BK = {fwo' n, 'K AK . KE,a 'KBK 'K y '(KNL) } / {I + [ 1/ Kf ] . [1 / KR,iRJ -1] . [1/ (llcr(r,d)] } 'tBK = {fwt . fwo·.Rn 'K AK ' KE,t 'KBK'K y '(KNL) } / {I + [ 1 / Kf ] . [1/ KR,lRJ -1] . [1/ (llr(r,d)] }
for welded components: SBK = (JW,zd' KAK ' KE,a' KBK' (Ky ) ' (KNL) (FAT / FATO,O") ':4 TBK = 'tw,s . KAK . KE,t . KBK' (Ky ) . (KNL) . (FAT / FATO,'t) . :4 or (for structural stresses or effective notch stresses) O"BK = (Jw,w' KAK . KE,a . KBK. (Ko) . (KNL) . (FAT / FATO,O") . :4 'tBK = 'tw,w . KAK ' KE,t . KBK' (Ky ) . (KNL) . (FAT / FATO,'t) . :4 The degrees of utilization are derived as:
or
aBK = 1 s., / (SBK' jere> I ~1 aBK = I T a,1 / (TBK' jerf)1 ~1 aBK = I O"a, I / ( O"BK . jerf) 1 ~ 1 aBK = 1'ta,1 / ( 'tBK . jerf ) I ~ 1
In the case ofmultiaxial stresses a total degree ofutilization is computedfrom the individual degrees ofutilization ofnormal or shear stress by means ofan interactionformula.
263
9 Subject index
8 Subject index
component static strength 19, 33, 73, 89 - local failure 19,73 - global failure 19,73
aluminium alloy 2·m. 48f. 78ff. 103f. 13If. 142ff. 193 - aging - 27f. 81. 83 - ductil - 90 - non-aging - 27f. 81. 83. - non-ductil - 91
component fatigue strength 57, 113
anisotropy facto.' 26. 80 assessment - assessment of the fatigue strength -- using local stresses 13,97, 127 -- using nominal stresses 12,41,70 - assessment of the static strength - - using local stresses 12, 19. 73, 93 - - using nominal stresses II, 19, 36 - method of assessment 11 - procedure of calculation 10 binomial frequency distribution 44, 100 - see standard stress spectrum calculation of stress see types of stress case hardening steel 25,79,136, 193 cast aluminium alloys 172ff, 193 - for general application 175 - for high pressure die casting 174, 177 - for investment casting 174, 176, 177 - for permanent mold casting 173, 175, 177 - for sand casting 172, 175, 176, 177 cast iron materials 25ff, 79ff, 140ff, 193 - ductil cast iron 90 - non-ductil cast iron 91 - properties (material tables) 140ff cast iron with lamellar graphite 25, 79, 140 cast steel 25, 79, 139 castings - non-destructively tested 68, 125 - not non-destructively tested 68, 125 characteristic service stress - assessment of the fatigue strength 41,97 - assessment of the static strength 19, 73 - probability of occurrence 34f, 90f class of utilization 43,45,66, 100, 102, 122, 218ff, 235 coating factor 55f, llOf coefficient of variation (static strength) 23, 77 compoment variable amplitude fatigue strength 63ff, 119ff
component, kinds of - 13 - block-shaped (3D) 15, 75, 96 - block-shaped (3D), welded 16, 75 - rod-shaped (lD) 13,20, 36, 73, 93 - rod-shaped (lD), welded 14,20,37, 74, 94 - shell-shaped (2D) 14, 20, 38, 73, 94 .. shell-shaped (2D), welded 15, 20, 38, 74, 95 component fatigue limit 57ff, 113ff - according to mean stress 58ff, 114ff, 223ff - see fatigue limit - see material fatigue limit component constant amplitude S-N curve - see constant amplitude S-N curve compression strength 27,81 compresion strength factor 26, 80 compression yield strength 27, 81 consequence offailure 34,68, 90, 125,212 constant amplitude S-N curve 63,66 F, 119, 123f, 212 - for non-welded components 66f, 123f - for welded components (model I) 66f. 123f - lower boundary of the number of cycles 66, 123 - model I and model II 64ff, 66f, 120ff, 123f - non-welded aluminum alloys (model II) 66f, 123f - non-welded steel and cast iron materials (model II) 66f, 123f - parameters 42,67, 99, 124,212 - see endurance limit - see fatigue limit constant amplitude stress 42, 63f, 99, 120f constant K NL 88 constant K NL E 56, III constant q 37ff, 7lf, 94ff, 128ff - aluminium alloy 7lf, 128ff - component, welded 7lf, 128ff - component, surface treated 7lf, 128ff conversion factor, statistical- 229 corrosion 9 1% creep limit 11, 19, 27ff, 35, 73, 81ff, 92 creep strength 11, 19, 27ff, 35, 73, 81ff, 92 damage potential 42,44,46, 99, 101, 102 damage sum, critical 63,65, 119, 121
264
damage-equivalent stress amplitude 45,66, 102, 122 degree of utilization - assessment of the fatigue strength 12, 13,70,127, 226 - assessment of the static strength 11, 13,36,93 design factor 30, 50f, 85, 106f design parameters - assessment of the fatigue strength 5Off, 106ff - assessment of the static strength 30ff, 85ff diameter, effective - 22, 24, 26, 76, 78, 80 direction of 0'3 99, 106, 109 ductility 12, 37, 71, 94, 128, see elongation effective notch stress 73, 97f, 210, 245ff effective diameter 22, 24, 26, 76, 78, 80 elastic limit load 78 elongation 68f, 125f, 140f, 143ff endurance limit 58,63,64, 66f, 114, 119, 120, 123f, 131, equivalent maximum stress 61f, 117f equivalent mean stress 61f, 117f, 223f equivalent minimum stress 61f, 117f equivalent stress amplitude 44f, 71[, 100, 102, 128f, 223 equivalent stress ratio 61f, 117f examples 231ff - cantilever subject to two independent loads (nominal stress) 250ff - component made of a wrought aluminium alloy (local stress) 256ff - compressor flange made of grey cast iron (local stress) 241 ff - shaft with shoulder (nominal stress) 231ff - shaft with V-belt drive (nominal stress) 236ff - welded notched component (nominal, structural and local stresses) 245ff experimentally determined strength value 227 - mean value 227f - sample size 227f - standard deviation 227ff - statistical conversion factor 228
9 Subject index
fatigue classes (of welded components) 56, II If, 195ff - effective notch stress 112, 196 - nominal stress 56, 195, 197ff - nominal shear stress 207 - structural stress 112, 195, 208ff - structural shear stress 195 fatigue life - computed - 63, 119 - required - 42,63, 99, 119 fatigue life curve 45,63, 102, 119 fatigue limit - according to mean stress 58ff, 114ff - component - 57, 113 - material- 47f, 103f - model I and model II 64ff, 67, 120ff, 124 - number of cycles at knee point 42, 67, 99, 124, 212 - specific values for welds 47, 103 fatigue notch factor 51ff, 187ff - cast iron and aluminum material 193f - derived from stress concentration factor 51, 187 - determined by the user 194 - definition 53 - experimentally determined 52, 189ff - of superimposed notches 54 - round and flat structural details 187ff fatigue strength - see constant amplitude S-N curve - see variable amplitude S-N curve fatigue strength factor - for normal stress 48, 104 - for shear stress 48, 62, 71, 104, 118, 128 fine grain structural steel 25, 79, 133 fluctuating stress spectrum 42 f, 99 f frequency, influence of - 47, 103 Gassnerlinie see fatigue life curve GG see cast iron with lamellar graphite GGG see nodular cast iron GS see cast steel GT see malleable cast iron guideline, field of application 9 Haigh diagram 59,63, 115, 119,212,214,217
exponential frequency distribution 44, 100,219ff - see standard stress spectrum
high quality castings 34, 68, 90, 125
FAT see fatigue classes
individual mean stress 6lf, 117f
hot-spot stress see structural stress
inspection 68, 125,212 kind of material 9,24, 78, 131ff
265
~-Kf
-
ratio 5lf, 108f for normal stress 51, 108 for shear stress 52, 109 for superimposed notches 109 for components being surface treated 52, 108 in the direction of (J 3 106
largest amplitude in stress spectrum 42, 99 Larsen-Miller parameter 29, 83 Larsen-Miller constant 29, 83 malleable cast iron 25, 79, 141 material - ductil 34, 68f, 90, 125f - non-ductil 34, 69, 90f, 126 - brittle 9 material fatigue limit 47f,67, 103f, 124, 131ff - aluminum 67, 124, 131f, 142 - bending 131ff - shear 131ff - steel 47f,67, 103f, 124, 131ff - tension-compression 47, 103, 131ff - torsion 131ff material properties - according to standards 22, 76 - assessment of the fatigue strength 47, 103 - assessment of the static strength 22, 76 material tables 131ff - cast aluminium alloys 172ff - cast iron materials 139ff - steel 132ff - wrought aluminium alloys 143ff material test specimen 22, 76, 131
9 Subject index
modulus of elasticity 86 neighbouring point 14, 15, 109 multiaxial stress 16, 37ff, 41, 7lf, 94ff, 97, 128ff, 222ff, 226, 250ff Neuber's formula 86 nitriding steel 25, 79, 136 nodular cast iron 25, 79, 140 nominal stress 10,11,12,178,181,190,210, 245ff non-destructive testing - of castings 128 - of welds 197 non-proportional stress 17,41,97,226,250 normal stress criterion 37ff, 7lf, 94ff, 128ff notch radius, effective
~
15,211, 214f, 245
number of cycles - at knee point of S-N curve 42,67, 99, 124, 212 - at lower boundary of S-N curve 9,41, 64f, 97, 123f - see constant amplitude S-N curve - see fatigue life - see total number of cycles - see variable amplitude S-N curve parameters of the stress spectrum 41ff, 97ff plastc limit load 87 plastic notch factor 31, 86f principle stress 15, 75, 96, 99, 113, 129 probability of occurrence - of the characteristic stress 34f, 90f
maximum stress 20f, 61, 74f, 117
probability of survival 22f, 34, 47, 68, 76f, 90,103, 125, 131, 227
mean stress 41ff, 58, 59f, 6lf, 97ff, 99, 114ff, 223ff - fields of mean stress 58ff, 114ff
procedure of calculation 10
mean stress factor 58, 59ff, 114ff, 210, 213f, 225
proportional stress 16,41, 97
mean stress sensitivity 59ff, 62, 115ff, 118, 213f
0.2 % proof stress see yield strength
mean stress spectrum 42f, 99
quenched and tempered steel 25, 79, 134, 135
mean value from experiments 227ff
radius, effective notch
method of calculation - variable amplitude fatigue strength 53, 104 - class of utilization 43, 45, 66, 100, 102, 122, 218ff, 235 -constant amplitude stress 63f, 119f - Haibach version of Miner's rule 65, 121 - Miner's rule, elementary version 45,64, IOlf, 120 - Miner's rule, consistent version 45,65, 101, 121 - Miner'rule, modified version 65, 121
raintlow matrix 216
Mises (v.Mises) criterion 37ff, 71f, 94ff, 128ff
~
15,211,214
raintlow cycle counting procedure 43, 100 reference point 10, 13, 14, 15, 36, 93 required total number of cycles 44, 45f, 64ff, 100, 102f, 119ff, 218ff residual stress factor 58,62, 114, 118,210, 213f residual stress 12, 13, 62, 118
266
RIFESTPLUS (PC program) 241,254,271 root of weld 74,85,89, 98, 107,209 roughness, average - 54f, 109f roughness factor 50, 54f, 106, 109f round specimen see material test specimen rule of sign see superposition S-N curve - see constant amplitude S-N curve - see variable amplitude S-N curve safety factor 4ff, 68ff, 90ff, 125ff, 212 - assessment of the fatigue strength 68, 125 - assessment of the static strength 34, 90 - cast aluminium alloy 34, 69, 91, 126 - cast iron material 34, 68f, 90f, 125f - consequence offailure 34,68, 90, 125,212 - creep limit 34f, 90f - creep strength 34f, 90f - inspection 68, 125,212 - non-destructive testing 68, 125 - non-ductile materials 69,91,126 - steel 34, 68, 90, 125 - tensile strength 34f, 90f - total safety factor 35, 69, 92, 126 - wrought aluminium alloy 34,69,91, 126 - yield strength 34f, 90f sample size 227ff section factor 30ff, 85ff semi-finished product 23, 77, 131ff sequence of assessment l lff service life see fatigue life service stress 10 - see characteristic service stress - see parameters of the stress spectrum
9 Subject index
standard stress spectrum 44f, 100f - binomial frequency distribution 44, 100 -exponential frequency distribution 44, 100 static strength see component static strength steel 24ff, 78ff, 131ff - austenitic 31,58,66,67,86,114,123,124,137 - ferritic or martensitic 137 - normalized 25, 79, 138 - quenched and tempered 25, 79 - stainless 25, 79 straight line distribution see exponential frequency distribution strength at elevated temperature 11, 19, 27, 48, 62, 73, 81, 104, 118 strength hypothesis 37, 71f, 94, 128ff stress - allowable - l lf, 36, 70, 93, 127 - characteristic service - 19,41,73,97 - extreme 11, 12, 36, 93 - geometrical - see structural stress - local, elastic - 12, 97 - multiaxial>- 16, 36, 93, 223ff, 226, 235 - non-proportional- 17,41, 97, 226 - proportional- 16; 41, 97 - synchronous - 17,41,97, 223ff, 236 - uniaxial - 16 - see type of stress stress amplitude 41ff, 97ff, 223ff - damage-equivalent stress amplitude 45, 66, 102, 122 - equivalent stress amplitude 44f, 7lf, 100, 102, 128f, 223 - largest amplitude in stress spectrum 42, 99 stress cycle 41, 97
shape of stress spectrum 42, 99
stress gradient - related 52f, 109 - in direction of stress 15, 85, 108f - normal to direction of stress 15,85,106, 108f
shear strength 27, 81
stress history 42, 99
shear strength factor 27, 37, 81, 94
stress ratio 41, 97 - adjusting the stress ratio ofa spectrum 43,100,216
size factor, technological -
24, 78
spectrum see stress spectrum
stress ratio spectrum 42f, 99
spectrum parameter p 44, 101, 219ff
stress spectrum - adjusting the stress ratio 43, 100, 216 - damage potential 42,44, 99, 101 - deriving a stepped spectrum 43, 100,217 - determination of the parameters 43ff, 100ff - parameters of a spectrum 42, 99 - spectrum parameter p 44, 101, 219ff - stress ratio spectrum 42f, 99 - total number of cycles of the spectrum 42,64ff - see standard stress spectrum
stair case tests 229 standard deviation 227ff standard stress spectrum 44, 100 - binomial distribution 44, 101, 219ff - exponential distribution 44,101, 219ff - spectrum parameter p 44,.101, 219ff
267
stress concentration factor 51, 178ff, 187 - for a substitute structure 87, 106,230 - for flat specimen 181ff - for round specimen 178ff structural steel, non-alloyed 25, 79, 132 structural stress 10, 73, 97f, 210, 245ff superposition 19, 36ff, 41, 70ff, 73, 93, 95f, 97, 127, 129f
9 Subject index
type of stress - block-shaped (3D) component 15f - combined ~ 12,37,39,71,72,94,95,96,128,129 - individual ~ l3ff, 36, 38, 71, 93, 94, 96, 128, 129 - rod-shaped (lD) component 13f - shell-shaped (2D) component 14f type of material 24, 78, 131ff ultimate strength see tensile strength uniaxial stress 16
surface hardening 31, 52, 55, 62, 66, 71, 72, 86, 108, 110, 11~ 123, 128, 129,222
variable amplitude fatigue strength 63ff, 119ff
surface roughness see roughness, average ~
variable amplitude S-N curve 45, 63ff, 102, 119ff
surface treatment factor 55f, 11Of, 194
variable amplitude fatigue strength factor 63ff, 119ff, 218, 221
symbols 5, 257ff synchronous stress 17,41,97, 223ff, 236
weld factor Uw 31,87
technological size factor 24, 78
weld imperfections 47, 103
temperature - elevated ~ 19,27,48,62, 73, 81, 104, 118 -Iow~ 27,48,81,104 - normal~ 27,48,81,104
weld seam 210
temperature factor - fatigue strength 48, 104 - static strength 27,81 - short-term strength value 27f, 82f - long-term strength value 28f, 83f
WELLE (pC programm) 231,236,250,271
temperature range 9,27,48,81, 104 tensile strength 22ff, 35, 47, 76ff, 92, 13lff - value according to standard 23f, 77f - component value according to the drawing 23, 77 - actual componentr value 24, 77 test piece (of castings) 23, 77, 131
welded components - comments about the fatigue strength 209ff - specific values of the fatigue strength 47, 103
wrought aluminium alloys 143ff - for extruded section 158ff, 168 - for forgings 169,170,171 - for plates 143ff - for rods / bars 154ff, 157ff - for sheets 143ff, 151ff - for strips 143ff, 151ff - for tubes 154ff yield stress see yield strength
throat section 20f, 42, 209
yield strength 22ff, 35, 76ff, 92, 131ff - value according to standard 23f, 77f - component value according to the drawing 23, 77 - actual componentr value 24, 77
toe of weld 74, 85, 89, 98, 107,209
zfP see non-destructive testing
thickness factor 50f, 56, 107, 112
toe section 20, 42, 209 total safety factor 35, 69, 92, 126 total number of cycles 9, 4lf, 97, 99 - computed fatigue life 63, 119 - of a stress spectrum 42, 64ff - required ~ 42,63, 99, 119 type of overloading 58, - type of overloading Fl - type of overloading F2 - type of overloading F3 - typeofoverioadingF4
115,225 60, 116 59f, 115f 60, 116f 61,117
IiZII IMA Materialforschung und
Geschattsfuhrer: Prof. Dr.-Ing. Wilhelm Hanel· Tel.: +49 351 8837-322' Fax: +49351 8804313 Address: Wilhelmine-Reichard-Ring 4 . Postfachadresse: Postfach 80 01 44 . 01101 Dresden
Anwendungstechnik GmbH
PC-programs RIFESTPLUS and WELLE for the strength assessment of components in mechanical engineering.
Assessment of the static strength and of the fatigue strength (fatigue limit and variable amplitude fatigue strength) of non-welded components made of steel or cast iron materials or of wrought or cast aluminum alloys.
RIFESTPLUS
is intended for shell-shaped (20) and for block-shaped (3D) components
made of steel or cast iron materials or of wrought or cast aluminum alloys the local elastic stresses of which have been determined by a finite element analysis or by a strain gauge analysis, for example. (A German and an English version of RIFESTPLUS is available.)
Shell-shaped (2D) component (on the left), block-shaped (30) component (on the right), local elastic stress amplitudes o, . WELLE
is intendedfor axles and shafts F
made of steel or cast iron materials,
F
F
subject to forces and moments, including those from gears. The calculation is based on nominal stresses. (A German version of WELLE is available only.)
Shaft with bearings and forces F
The two programs are based on the
FKM-Guideline "Analytical Strength Assessment of Components in Mechanical Engineering", Frankfurt: VDMA-Verlag, 4 th edition, 2002 (in German).
Personal contacts:
Dr.-Ing. B. Hanel
Tel. +49 351 8837 324 E-Mail: [email protected]
Dipl.-Ing. G.-R. Bitterlich
Tel. +49351 8837 383 E-Mail: [email protected]
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ISBN 3-8163-0425-7
