ASTM_E384-11e1.pdf

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Designation: E384 − 11

Standard Test Method for

Knoop and Vickers Hardness of Materials 1 This standard is issued under the fixed designation E384; the number immediately following the designation indicates the year of  original origin al adoption or, in the case of revis revision, ion, the year of last revision. revision. A number in paren parenthese thesess indicates the year of last reappr reapproval. oval. A superscript epsilon (´) indicates an editorial change since the last revision or reapproval. This standard has been approved for use by agencies of the U.S. Department of Defense. 1

NOTE—Sections 8.3  8.3  and  A1.1.4  A1.1.4 were  were editorially corrected in March 2012. ε NOTE—Sections

1. Scope*

standard d doe doess not purport purport to add addre ress ss all of the 1.6   This standar safety safe ty co conc ncern erns, s, if an anyy, as asso soci ciat ated ed wit with h its us use. e. It is th thee responsibility of the user of this standard to establish appro priate safety and health practices and determine the applicability of regulatory limitations prior to use.

1.1 This test method covers covers determination determination of the Knoop Knoop and Vickers hardness of materials, the verification of Knoop and Vicke ickers rs har hardne dness ss tes testing ting mach machine ines, s, and the cal calibr ibratio ation n of  standardized Knoop and Vickers test blocks. 1.2 This test metho method d covers Knoop and Vickers Vickers hardn hardness ess tests made utilizing test forces in micro (9.807 × 10 -3 to 9.807 N ) ( 1 to 1000 gf ) and macro (>9.807 to 1176.80 N) ( >1kg to 120 kgf ) ranges.

2. Referenced Documents 2.1   ASTM Standards: 2 C1326 Test Meth Method od for Kno Knoop op Ind Indent entatio ation n Har Hardne dness ss of  Advanced Ceramics C1327 Test Meth Method od for Vick ickers ers Ind Indenta entatio tion n Har Hardne dness ss of  Advanced Ceramics E3 Guide E3  Guide for Preparation of Metallographic Specimens E7 Terminology E7  Terminology Relating to Metallography E29 Pra Practic cticee for Using Sig Signifi nifican cantt Dig Digits its in Test Data to Determine Conformance with Specifications E74 Practice E74  Practice of Calibration of Force-Measuring Instruments for Verifying the Force Indication of Testing Machines E92 Test E92  Test Method for Vickers Hardness of Metallic Materials (Withdrawn 2010) 3 E122 Practice E122  Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or Process E140 Hardness E140  Hardness Conversion Tables for Metals Relationship Among Brinell Hardn Hardness, ess, Vi Vickers ckers Hardn Hardness, ess, Rockw Rockwell ell Hardness, Superficial Hardness, Knoop Hardness, Scleroscope Hardness, and Leeb Hardness E175 Terminology E175  Terminology of Microscopy E177 Practice E177  Practice for Use of the Terms Precision and Bias in ASTM Test Methods E691 Practic Practicee for Condu Conducting cting an Interl Interlabora aboratory tory Study to Determine the Precision of a Test Method E766 Practice E766  Practice for Calibrating the Magnification of a Scanning Electron Microscope

NOTE 1—Previous versions of this standard limited test forces to 9.807 N (1 kgf).

1.3 This tes testt met method hod includes includes all of the req requir uireme ements nts to perform macro Vickers hardness tests as previously defined in Test Method E92 Method  E92,,  Standard Test Method for Vickers Hardness Testing. 1.4 Thi Thiss test method method incl include udess an ana analys lysis is of the possible possible sourcess of err source errors ors tha thatt can occ occur ur dur during ing Kno Knoop op and Vicker Vickerss testing and how these factors affect the accuracy, repeatability, and reproducibility of test results. NOTE 2—While Committee E04 is primarily concerned with metals, the test procedures described are applicable to other materials.

1.5   Units— When When Knoop and Vickers hardness tests were developed, the force levels were specified in units of gramsforce (gf) and kilograms-force kilograms-force (kgf). This stand standard ard specifi specifies es the units of force and length in the International System of  Units (SI); that is, force in Newtons (N) and length in mm or µm. However, because of the historical precedent and continued ue d co comm mmon on us usag age, e, fo forc rcee va valu lues es in gf an and d kg kgff un units its ar aree provided for information and much of the discussion in this standar stan dard d as wel welll as the method method of reportin reporting g the test res result ultss refers to these units. 1

Thiss tes Thi testt met method hod is und under er the jur jurisd isdict iction ion of AS ASTM TM Com Committ mittee ee E04 on Metallography Metallograp hy and is the direct respo responsibil nsibility ity of Subco Subcommitte mmitteee E04.05  E04.05 on  on Microindentation Hardness Testing.With this revision the test method was expanded to include the requirements previously defined in E28.92, Standard Test Method for Vickers Hardness Testing of Metallic Material that was under the jurisdiction of  E28.06 Current Curre nt editio edition n approv approved ed Aug. 1, 2011 2011.. Publi Published shed August 201 2011. 1. Origin Originally ally approved in 1969. Last previous edition approved in 2010 as E384 – 10 2. DOI: 10.1520/E0384-11E01.

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For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [email protected]. For  Annual Book of ASTM  Standards volume information, refer to the standard’s Document Summary page on the ASTM website. 3 The last app approv roved ed ver versio sion n of thi thiss his histor torica icall sta standa ndard rd is refe referen renced ced on www.astm.org.

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*A Summary of Changes section appears at the end of this standard Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States

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E384 − 11 2.2   ISO Standards: 4 ISO 6507 6507-1 -1 Metallic Materia Materials—V ls—Vickers ickers hardn hardness ess Test— Part 1: Test Method ISO/IEC 17011 Conformity 17011  Conformity Assessment—General Requirements for Accreditation Accreditation Bodies Accrediting Accrediting Confo Conformity rmity Assessment Bodies. ISO/IEC 17025  General Requirements for the Competence of Testing and Calibration Laboratories

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recovery after force removal. The test results are normally in the Knoop or Vickers scales. 3.2.5  macroindention hardness test, n— a hardness test using a calibrated machine to force an indenter of specific geometry into the surface of the material being evaluated, in which the test forces are normally higher than 9.807 N (1 kgf). Macroindentation test scales include Vickers, Rockwell and Brinell. NOTE  3—Use of the term microhardness should be avoided because it implies that the hardness, rather than the force or the indentation size, is very low.

3. Terminology 3.1   Definitions— For For the standard definitions of terms used in this test method, see Terminology E7 E7..

3.2.6   verifying, checking g or test testing ing the ins instru trumen mentt to verifying, v— checkin assure conformance with the specification.

3.2  Definitions of Terms Specific to This Standard: 3.2.1   calibrating, v— determining determining the values of the significantt par can paramet ameters ers by com compar pariso ison n wit with h val values ues indicated indicated by a reference instrument or by a set of reference standards.

Vickers har hardness dness numbe numberr, HV HV,, n— an 3.2.7   Vickers an exp expres ressio sion n of  hardness obtained by dividing the force applied to a Vickers indenter by the surface area of the permanent indentation made by the indenter.

3.2.2   Knoop an exp expres ressio sion n of  Knoop har hardne dness ss num number ber,, HK, n— an hardness obtained by dividing the force applied to the Knoop indent ind enter er by the pro project jected ed are areaa of the per perman manent ent ind indent entatio ation n made by the indenter.

3.2.8  Vickers indenter, n— a square-based pyramidal-shaped diamond indenter with face angles of 136° (see  Fig. 1). 1). 3.2.9   scale, n— a specific combination of indenter (Knoop or Vick ickers ers)) and the test force. force. For example, example, HV1 HV10 0 is a sca scale le defined as using a Vickers indenter and a 10 kgf test force and HK 0.1 is a scale defined as using a Knoop indenter and a 100 gf test force. See 5.8 5.8 for  for the proper reporting of the hardness level and scale.

Knoop p ind indente enterr, n— a rho 3.2.3   Knoo rhombic mbic-bas -based ed pyr pyramid amidalalshaped diamond indenter with edge angles of  / A = 172° 30' and / B = 130° 0' (see  Fig. 2) 2 ). microindent indentation ation har hardness dness test, n— a ha 3.2.4   micro hard rdne ness ss tes testt using usi ng a cali calibra brated ted mac machin hinee to for force ce a dia diamon mond d ind indente enterr of  spec sp ecific ific ge geom ometr etry y in into to th thee su surf rfac acee of th thee ma mater terial ial be bein ing g evaluated, in which the test forces are 9.807 × 10 -3 to 9.807 N (1 to 1000 gf) and the indentation diagonal, or diagonals are measured with a light microscope after load removal; for any test, it is assumed that the indentation does not undergo elastic

3.3   Formulae— The The formulae presented in 5.5 and 5.6 for calcula calc ulating ting Kno Knoop op and Vickers Vickers har hardne dness ss are bas based ed upo upon n an ideal ide al test tester er.. The mea measur sured ed val value ue of the Kno Knoop op and Vicker Vickerss hardness of a material is subject to several sources of errors. Based on Eq on  Eq 1-9, 1-9,  variations in the applied force, geometrical variations variati ons between diamond indenters, indenters, and human errors in measuring indentation lengths can affect the calculated material hardness. The influence each of these parameters has on the calcu ca lcula lated ted va valu luee of a Kn Knoo oop p or Vic icke kers rs me meas asur urem emen entt is discussed in Section 10 10..

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Available from International Organization for Standardization (ISO), 1, ch. de la Voie oie-Cr -Creus euse, e, Cas Casee pos postal talee 56, CHCH-121 1211, 1, Gen Geneva eva 20, Sw Switz itzerl erland and,, htt http:/ p://  /  www.iso.org.

FIG. 1 Vickers Indenter

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E384 − 11

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FIG. 2 Knoop Indenter Indenter

4. Significance and Use

elastic recovery. Thus, the Knoop indenter is very useful for evalua eva luating ting har hardne dness ss gra gradien dients ts or thi thin n coa coatin tings gs of sec section tioned ed samples.

4.1 Har Hardne dness ss test testss hav havee bee been n fou found nd to be very use useful ful for material mate rialss eva evalua luation tion,, qua quality lity con contro troll of man manufa ufactu cturin ring g pro pro-cesses cess es and res resear earch ch and dev develo elopme pment nt ef effor forts. ts. Har Hardne dness, ss, although empirical in nature, can be correlated to tensile strength for many metals, and is an indicator of wear resistance and ductility.

5. Principle of Test 5.1 In this test method, a Knoop or Vickers Vickers hardness number is det determ ermine ined d bas based ed on the formation formation of a rela relativ tively ely sma small ll indentation made in the test surface of samples being evaluated.

4.2 Micro Microinden indentation tation hardness hardness tests extend testing to materials th rials that at ar aree to too o th thin in or to too o sm small all fo forr ma macr croi oind nden enta tatio tion n hardne har dness ss tes tests. ts. Mic Microi roinde ndenta ntatio tion n har hardne dness ss test testss als also o allo allow w specific spe cific pha phases ses or con constit stituen uents ts and reg region ionss or gra gradie dients nts too small for macroindentation hardness testing to be evaluated.

5.2 A Kno Knoop op or Vick ickers ers ind indent enter er,, mad madee fro from m dia diamon mond d of  specific geometry, is pressed into the test specimen surface by an accu accurate rately ly con contro trolled lled app applied lied for force ce usi using ng test mac machin hines es specifically designed for such work.

4.3 Bec Becaus ausee the Kno Knoop op and Vicker Vickerss har hardne dness ss will rev reveal eal hardness variations that may exist within a material, a single test value may not be representative of the bulk hardness.

5.3 Knoop Knoop and Vickers Vickers har hardne dness ss test testing ing is div divide ided d int into o micro and macro-test force ranges as defined:

4.4 The Vickers Vickers indenter usually produces produces a geomet geometrically rically similar indentation at all test forces. Except for tests at very low forces that produce indentations indentations with diagonals smaller than about 25 µm, the hardness number will be essentially the same as produced by Vickers machines with test forces greater than 1 kgf, as long as the material being tested is reasonably homogeneous. For isotropic materials, the two diagonals of a Vickers indentation indentation are equal in size. Recommendations Recommendations for low force microindentation testing can be found in  Appendix X5.. X5

Range Micro Macro

Test Force 9.807 × 10-3 to # 9.807 N ( 1 to # 1000 gf) > 9.807 to # 1176.80 N ( > 1 to # 120 kgf)

5.3.1 Knoop 5.3.1 Knoop sca scale le test testing ing is nor normal mally ly per perfor formed med usi using ng micro-range test forces (1kg and less) while the Vickers scale is used over both the micro and macro-ranges. NOTE  4—The user should consult with the manufacturer before applying test forces in the macro-ranges (over 1 kg) with diamond indenters previously used for micro-range testing. The diamond mount may not be strong enough to support the higher test forces and the diamond may not be large enough to produce the larger indentation sizes.

4.5 The Knoop indenter indenter does not prod produce uce a geomet geometrically rically similar indentation as a function of test force. Consequently, thee Kn th Knoo oop p ha hard rdne ness ss wi will ll va vary ry wi with th te test st fo forc rce. e. Du Duee to its rhombic shape, the indentation depth is shallower for a Knoop indentation compared to a Vickers indentation under identical test conditions. The two diagonals of a Knoop indentation are markedly different. Ideally, the long diagonal is 7.114 times longer than the short diagonal, but this ratio is influenced by

5.4 The size of the ind indent entatio ation n is mea measur sured ed usi using ng a lig light ht microscope equipped with a filar type eyepiece, or other type of measur measuring ing device (see Termino erminology logy   E175). E175). Micro Micro-rang -rangee inde in dent ntss ar aree ty typi pica cally lly mea measu sure red d in µm (m (micr icrom omet eter ers) s) an and d macro-range indents are measured in mm. The formulas for both units are given below. 3

E384 − 11 5.5 The Knoop Knoop har hardne dness ss num number ber is bas based ed upo upon n the force divided by the projected area of the indentation 5.5.1 For Knoop hardness hardness testing, testing, test loads are typical typically ly in grams-force gramsforce (gf) and inden indentation tation diagonals are in microm micrometers eters (µm). The Knoop hardness number, in terms of gf and µm, is calculated using the following: 3

 HK 5 1.000 3 10

or

3

~ P /  A  p ! 5 1.000 3 10

3

~ c p 3 d  !

3 P / 

2

 HK 5 14229 3 P / d  d 2 tan

contained in Appendix in Appendix X6. X6. To obtain HV values when other test forces are employed, emplo yed, multiply the HV value from Table from Table X6.2 for X6.2  for the  d  value by the actual test force, gf.

5.6.2 Macro range range Vickers Vickers hardness hardness is typically typically determined determined using kgf and mm and is calculated as follows:  HV 5 1.8544 3 P 1 / d  d 1 2

(1 )

where:

(2 )

force, ce, kgf kgf,, and and P1 = for d 1 = mean diagonal diagonal length length of of the indentatio indentations, ns, mm.

/ B

 Indenter constant 5 c p 5

2 tan

2 / A

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5.6.3 The Vicker 5.6.3 Vickerss har hardne dness ss rep report orted ed wit with h uni units ts of GPa is determined as follows:

(3 )

 HV 5 0.0018544 3 P 2 / d  d 2 2

2

where:

where:

P d   A p / A / B

P2 d 2

= = = = =

force fo rce,, gf, length len gth of lon long g dia diagon gonal, al, µm, projected proje cted area of indent indentation, ation, µm 2 included includ ed longitudi longitudinal nal edge edge angle, angle, 172° 172° 30’ 30’ includ inc luded ed transve transverse rse edge edge angle, angle, 130° 130° 0’ (see   Fig. 2 and, = inden indenter ter const constant ant relatin relating g projecte projected d area area of the indentation to the square of the length of the long diagonal, ideally 0.07028.

c p

(4 )

where:

= force, force, kgf kgf,, and = len length gth of lon long g diago diagonal, nal, mm.

5.5.3 The Knoop hardnes 5.5.3 hardnesss rep report orted ed with units of GPa is determined as follows:  HK 5 0.014229 3 P 2 / d  d 2 2

(5 )

5.9 The reported Knoop Knoop and Vickers Vickers hardness number shall be reported rounded to three significant digits in accordance with Practice E29 E29 (for  (for example, 725 HV 0.1, 99.2 HK 1).

where: P2 d 2

= fo forc rce, e, N, an and d = length of the the long diago diagonal nal of the indentatio indentation, n, mm.

6. Apparatus

5.6 The Vickers Vickers hardness hardness number is based upon the force divided by the surface area of the indentation. 5.6.1 For the micromicro-range range Vickers Vickers hardness hardness test loads are typically in grams-force (gf) and indentation diagonals are in micrometers (µm). The Vickers hardness number, in terms of gf  and µm, is calculated as follows:  HV 5 1.000 3 103 3 P /  A s 5 2.000 3 103 3 Psin~ α / d 2  /2 2 ! / d 

(6 )

 HV 5 1854.4 3 P / d  d 2

(7 )

6.1   Test Machine— The The test machine shall support the test specimen and control the movement of the indenter into the specimen under a preselected test force, and should have a light optical microscope to select the desired test location and to measure the size of the indentation produced by the test. The plane of the surface of the test specimen should be perpendicular to the axis of the indenter and the direction of the force application. Vibration Control— During 6.1.1   Vibration During the entire test cycle, the test machine should be protected from shock or vibration. To minimize vibrations, the operator should avoid contacting the machine in any manner during the entire test cycle.

or

where: P  As d  α

= = = =

force, gf, force, surfac sur facee area of the the indentat indentation ion,, µm2, mean diagon diagonal al length length of the the indentat indentation ion,, µm, and facee angle fac angle of the the indente indenter, r, 136° 136° 0’ 0’ (see (see  Fig. 1) 1). –3

NOTE   6—HV 6—HV nu numb mber erss fo forr a 1 gf (9 (9.8 .807 07 × 10

= fo forc rce, e, N, an and d = mean diagona diagonall length length of the the indentations indentations,, mm.

5.8 Th 5.8 Thee sy symb mbol olss HK fo forr Kn Knoo oop p ha hard rdne ness ss,, an and d HV fo forr Vick ickers ers har hardne dness ss sha shall ll be use used d wit with h the rep report orted ed num numeri erical cal values. 5.8. 5. 8.1 1 Fo Forr th this is st stan anda dard rd,, th thee ha hard rdne ness ss te test st re resu sults lts can be reported in several different ways. For example, if the Knoop hardness was found to be 400, and the test force was 100 gf, the test results may be reported as follows: 5.8.1.1 5.8.1 .1 In the kilogram force system: system: 400 HK 0.1. 5.8.1.2 5.8.1 .2 In the gram force system: system: 400 HK 100 gf. 5.8.1.3 5.8.1 .3 In the SI system: 3.92 GPa. 5.8.1.4 5.8.1 .4 For nonstanda nonstandard rd dwell times, times, other than 10 10 to 15 s, the hardness would be reported as 400 HK 0.1 /22. In this case, 22 would be the actual time of full load dwell time in seconds.

5.5.2 5.5. 2 Th Thee Kn Knoo oop p ha hard rdne ness ss,, in ter terms ms of kg kgff an and d mm mm,, is determined as follows:

P1 d 1

(9 )

5.7 It is assumed that elastic recovery does does not occur when the indenter is removed after the loading cycle. That is, it is assumed that the indentation retains the shape of the indenter after the force is removed. In Knoop testing, it is assumed that thee ra th ratio tio of th thee lo long ng di diag agon onal al to th thee sh shor ortt di diag agon onal al of th thee indentation is the same as for the indenter.

NOTE 5—HK values for a 1gf (9.807 × 10 –3 N) test force are contai contained ned in   Appendix Appendix X6 X6..   To To ob obta tain in HK va valu lues es wh when en ot othe herr te test st fo forc rces es ar aree employed, multiply the HK value from Table from  Table X6.1 for X6.1  for the  d  value by the actual test force, gf.

 HK 5 14.229 3 P 1 / d  d 1 2

(8 )

6.2   Vickers Indenter— The The ideal Vickers indenter (see   Fig. 1)   is a hig highly hly pol polish ished, ed, poi pointe nted, d, squ square are-ba -based sed pyr pyramid amidal al

N) te test st lo load ad ar aree

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E384 − 11 diamond with face angles of 136° 0'. The effect that geometrical variations of these angles have on the measured values of  Vickers hardness are discussed in Section 10 10.. 6.2.1 The four faces of the Vickers Vickers indenter indenter shall be equally inclined to the axis of the indenter and shall meet at a sharp point. The line of junction (offset) between opposite faces shall not exceed the limits defined in A1.3.5.1 in  A1.3.5.1..

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indentation size, the more critical is the surface preparation. Specimen preparation should be performed in accordance with applicable applic able section of Guide E3 E3..   In all test tests, s, the pre prepar paratio ation n should be such that the indentation perimeter and the indentation tips in particular, can be clearly defined when observed by the measuring system. 7.1.1. 7.1 .1.1 1 The test sur surface face shall be fre freee of any def defects ects that could affect affect the indentation or the subsequent subsequent measur measurement ement of  the dia diagon gonals als.. It is wel welll kno known wn tha thatt imp improp roper er gri grindi nding ng and polishing methods can alter test results either due to excessive heating or cold work. Some materials are more sensitive to prepar pre paratio ation-i n-indu nduced ced dam damage age tha than n oth others ers;; the theref refore ore spe specia ciall precautions must be taken during specimen preparation. Specimen preparation must remove any damage introduced during these steps. 7.1.1.2 7.1.1 .2 The specimen surface surface shou should ld not be etched before making an indentation. Etched surfaces can obscure the edge of  the indentation, making an accurate measurement of the size of  the indentation difficult. However, when determining the microindentation hardness of an isolated phase or constituent, a light etch can be used to delineate the object of interest. 7.1.2   Alignment— To obt obtain ain usa usable ble inf inform ormatio ation n fro from m the test, the specimen should be prepared or mounted so that the test surface is perpendicular to the axis of the indenter. This can readily rea dily be acco accompl mplish ished ed by sur surfac facee gri grindi nding ng (or oth otherw erwise ise machining) the opposite side of the specimen parallel with the sidee to be test sid tested. ed. Non-para Non-parallel llel samples samples can be test tested ed usi using ng clamping and leveling fixtures designed to align the test surface properly to the indenter. 7.1.3   Mounted Samples— In In many instances, it is necessary to mount the specimen for convenience in preparation and to maintain a sharp edge when surface gradient tests are to be perfor per formed med on the sam sample ple.. Whe When n mou mountin nting g is req requir uired, ed, the specim spe cimen en mus mustt be ade adequa quately tely sup suppor ported ted by the mou mountin nting g medium med ium so tha thatt the spe specime cimen n doe doess not move dur during ing force appl ap plic icati ation on,, th that at is is,, av avoi oid d th thee us usee of po poly lymer meric ic mo moun untin ting g compounds that creep under the indenter force. 7.1.4   Thickness— the the thickness of the specimen tested shall be such that no bulge or other marking showing the effect of  the test force appears on the side of the piece opposite the indentation. The thickness of the material under test should be at least ten times the depth of the indentation. This is also to be used as a guideline for the minimum depth of a coating on a material. 7.1.5   Radius of Curvature— due due caution should be used in interpreting or accepting the results of tests made on spherical or cylindrical surfaces. Results will be affected even in the case of th thee Kn Knoo oop p tes testt wh wher eree th thee ra radi dius us of cu curv rvatu ature re is in th thee direction of the short diagonal.  Table 1, 1,   Table 2 and  Table 3 provid pro videe cor correc rection tion fac factor torss tha thatt sha shall ll be app applied lied to Vick ickers ers hardness values obtained when tests are made on spherical or cylind cyl indric rical al sur surfac faces. es. The cor correc rectio tion n fac factor torss are tab tabula ulated ted in terms of the ratio of the mean diagonal d of the indentation to the diamete diameterr  D  of the sphere or cylinder. Examples of the use of these tables are given in Example 1 and 2:

6.3   Knoop Indenter— The The ideal Knoop (see  Fig. 2) 2) indenter is a highly polished, pointed, rhombic-based, pyramidal diamond. The included longitudinal edge angles are 172° 30' and 130° 0'. The ideal indenter constant,  c p, is 0.07028. The effect that geometrical variations of these angles have on the measured values of Knoop hardness are discussed in Section 10 10.. 6.3.1 The four faces of the Knoop Knoop indenter shall shall be equally inclined to the axis of the indenter and shall meet at a sharp point. The line of junction (offset) between opposite faces shall not exceed the limits defined in A1.3.5.2 in  A1.3.5.2.. 6.4 Whe When n meas measuri uring ng ind indent entatio ation n dia diagon gonal al len length gthss 40 µm and larger the test machine’s measuring device shall be capable of reporting the diagonal lengths to within 0.5 µm or 0.5% which ever is larg larger er.. When measuring indentation indentation diago diagonal nal lengths less than 40 µm the measuring device shall be able to report the diagonal lengths within 0.25 µm. In all cases, smaller measurement increments may be reported if the equipment is capable of displaying smaller measurement increments. NOTE  7—This is the reported length and may not be the resolution of  the system used for performing the measurements. As an example, if a length of 200 µm corresponds corresponds to 300 filar units or pixels, the corres correspondponding calibration constant would be 200/300 = 0.6667. This value would be used to compute diagonal lengths, but the reported length may only be reported to the nearest 0.5 or 0.25 µm.

6.4.1 6.4 .1 The measurin measuring g dev device ice may be an int integr egral al par partt of the tester or a stand alone instrument. 6.4.2 6.4 .2 The opt optical ical portion portion of the meas measuri uring ng dev device ice sho should uld have Köhler illumination (see  Appendix X1). X1 ). 6.4.3 To obtain maximu maximum m resolution, the measuring microscope should have adjustable illumination intensity, adjustable alignment, aperture, and field diaphragms. 6.4.4 Magnifi Magnification cationss should be provi provided ded so that the diagonal can be enlarged to greater than 25 % but less than 75 % of  the field width. The device may be built with single or multiple magnifying objectives. 6.5   Verifications— All All testers and indenters used to perform Knoop and Vickers hardness tests shall meet the requirements defined in Annex in  Annex A1  prior to performing hardness tests.

7. Test Specimen 7.1 Th 7.1 Ther eree is no sta stand ndar ard d sh shap apee or siz sizee fo forr a Kn Knoo oop p or Vickers test specime specimen. n. The specim specimen en on which the indentation is made should conform to the following: 7.1.1   Preparation— For For optimum accuracy of measurement, the test should be performed on a flat specim specimen en with a polish polished ed or oth otherw erwise ise sui suitabl tably y pre prepar pared ed sur surfac face. e. The qua quality lity of the required surface finish can vary with the forces and magnificatio cat ions ns us used ed.. Th Thee lo lowe werr th thee tes testt fo forc rcee an and d th thee sm smal aller ler th thee

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E384 − 11 TABLE 1 Correction Factors for Use in Vickers Hardness Tests Made on Spher Spherical ical Surfaces Convex Surface

A

TABLE 2 Corre Correction ction Factors for Use in Vicker Vickers s Hardn Hardness ess Tests Made on Cylind Cylindrical rical Surfaces (Diagonals at 45° to the axis)

Concave Surface  

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Convex Surface

Correction Factor

Concave Surface

d  / D  D  A

Correction Factor

d  / D  D  A

0 .0 04 0 .0 09 0 .0 13

0 .9 9 5 0 .9 9 0 0 .9 8 5

0 .0 0 4 0 .0 0 8 0 .0 1 2

1. 00 5 1. 01 0 1. 01 5

0 .0 0 9 0 .0 1 7 0 .0 2 6

0. 99 5 0. 99 0 0. 98 5

0 .0 0 9 0 .0 1 7 0 .0 2 5

1 .0 0 5 1 .0 2 0 1 .0 1 5

0 .0 18 0 .0 23 0 .0 28

0 .9 8 0 0 .9 7 5 0 .9 7 0

0 .0 1 6 0 .0 2 0 0 .0 2 4

1. 02 0 1. 02 5 1. 03 0

0 .0 3 5 0 .0 4 4 0 .0 5 3

0. 98 0 0. 97 5 0. 97 0

0 .0 3 4 0 .0 4 2 0 .0 5 0

1 .0 2 0 1 .0 2 5 1 .0 3 0

0 .0 33 0 .0 38 0 .0 43

0 .9 6 5 0 .9 6 0 0 .9 5 5

0 .0 2 8 0 .0 3 1 0 .0 3 5

1. 03 5 1. 04 0 1. 04 5

0 .0 6 2 0 .0 7 1 0 .0 8 1

0. 96 5 0. 96 0 0. 95 5

0 .0 5 8 0 .0 6 6 0 .0 7 4

1 .0 3 5 1 .0 4 0 1 .0 4 5

0 .0 49 0 .0 55 0 .0 61

0 .9 5 0 0 .9 4 5 0 .9 4 0

0 .0 3 8 0 .0 4 1 0 .0 4 5

1. 05 0 1. 05 5 1. 06 0

0 .0 9 0 0 .1 0 0 0 .1 0 9

0. 95 0 0. 94 5 0. 94 0

0 .0 8 2 0 .0 8 9 0 .0 9 7

1 .0 5 0 1 .0 5 5 1 .0 6 0

0 .0 67 0 .0 73 0 .0 79

0 .9 3 5 0 .9 3 0 0 .9 2 5

0 .0 4 8 0 .0 5 1 0 .0 5 4

1. 06 5 1. 07 0 1. 07 5

0.119 0 .1 2 9 0 .1 3 9

0. 93 5 0. 93 0 0. 92 5

0 .1 0 4 0.112 0.119

1 .0 6 5 1 .0 7 0 1 .0 7 5

0 .0 86 0 .0 93 0 .1 00

0 .9 2 0 0 .9 1 5 0 .9 1 0

0 .0 5 7 0 .0 6 0 0 .0 6 3

1. 08 0 1. 08 5 1. 09 0

0 .1 4 9 0 .1 5 9 0 .1 6 9

0. 92 0 0. 91 5 0. 91 0

0 .1 2 7 0 .1 3 4 0 .1 4 1

1 .0 8 0 1 .0 8 5 1 .0 9 0

0 .1 07 0.114 0 .1 22

0 .9 0 5 0 .9 0 0 0 .8 9 5

0 .0 6 6 0 .0 6 9 0 .0 7 1

1. 09 5 1. 1 0 0 1. 10 5

0 .1 7 9 0 .1 8 9 0 .2 0 0

0. 90 5 0. 90 0 0. 89 5

0 .1 4 8 0 .1 5 5 0 .1 6 2

1 .0 9 5 1 .1 0 0 1 .1 0 5

0 .1 30 0 .1 39 0 .1 47

0 .8 9 0 0 .8 8 5 0 .8 8 0

0 .0 7 4 0 .0 7 7 0 .0 7 9

1.110 1.115 1. 20 0

0.169 0.176 0.183

1.110 1.115 1.120

0 .1 56 0 .1 65 0 .1 75

0 .8 7 5 0 .8 7 0 0 .8 6 5

0 .0 8 2 0 .0 8 4 0 .0 8 7

1. 12 5 1. 13 0 1. 13 5

0.189 0.196 0.203

1.125 1.130 1.135

0 .1 85 0 .1 95 0 .2 06

0 .8 6 0 0 .8 5 5 0 .8 5 0

0 .0 8 9 0 .0 9 1 0 .0 9 4

1. 14 0 1. 14 5 1. 15 0

0.209 0.216 0.222

1.140 1.140 1.150

d  / D  D 

Example 2. Example Concave Cylinder, One Diagonal Parallel to Axis:

Correction Factor

d  / D  D 

A

Correction Factor

A

D  =  = diameter of sphere in millimeters. d  =  = mean diagonal of indentation in millimeters.

Example 1. Example Convex Sphere:

A

D  =   = diameter of cylinder. d  =  = mean diagonal of impression in millimeters.

Diameter of sphere, D = 10 mm, Load = 10 kgf Mean diagonal of impression, d = 0.150 mm d/D = 0.150/10 = 0.015 From Table X6.2, HV = 824 From Table From  Table 1, 1,  by interp interpolatio olation, n, correc correction tion factor = 0.983 Hardness of sphere = 824 X 0.983 = 810 HV 10 Diameter of cylinder, D = 5 mm, Load = 30 kgf Mean diagonal of impression, d = 0.415 mm, d/D = 0.415/5 = 0.083 From Table Table Table  Table X6.2, X6.2,  HV = 323 From Table From  Table 3, 3,  correction factor = 1.075 Hardness of cylinder = 323 X 1.075 = 347 HV 30.

8.2   Indenter— Select Select the desired indenter, either Knoop or Vickers, to suit the desired test scale to be performed. Refer to the manufacturer’s instruction manual for the proper procedure if it is necessary to change indenters. 8.2.1 After each change, change, or removal and replacement, replacement, of the inde in dent nter er it is re reco comm mmen ende ded d th that at a we week ekly ly ve veri rific ficati ation on be perf pe rfor ormed med as de defin fined ed in   A1.5. A1.5.   At le least ast tw two o pr preli elimin minar ary y indenta ind entatio tions ns sho should uld be mad madee to ens ensure ure that the indenter indenter is seated properly. properly. The result resultss of the prelim preliminary inary indentations indentations shall be disregarded. 8.2.2 8.2 .2 Occ Occasio asional nally ly clean the indenter indenter with with a cott cotton on swab and alco alcohol hol.. Avoi void d crea creatin ting g stat static ic cha charg rges es dur during ing clea cleanin ning. g. Inde In dent ntin ing g a pi piec ecee of pa pape perr wi will ll of often ten re remo move ve oi oill fr from om th thee indenter 8.2.3 8.2 .3 Ind Indent enters ers sho should uld be exa examin mined ed per period iodical ically ly and replac pl aced ed if th they ey be beco come me wo worn rn,, du dulle lled, d, ch chip ippe ped, d, cr crack acked ed or separated from the mounting material. Checks of the indenter by th thee us user er ma may y be pe perf rfor ormed med by vi visu sual al in insp spec ectio tion n of th thee resulting indentation; it is sufficient to verify the absence of  defects from the shape of indentations performed on test blocks

NOTE  8—A method for correcting Vickers hardness readings taken on spherical spheric al or cyl cylind indric rical al sur surfac faces es can be fou found nd in the Int Intern ernati ationa onall Organization for Standardization (ISO) Vickers Hardness Standard (ISO 6507-1).

8. Procedure Test temperature— Knoop 8.1   Test Knoop and Vick ickers ers har hardne dness ss test testss should shoul d be carried out at a temper temperature ature within the limits of 10 to 35°C (50 to 95°F). Because variations within this temperature range may affect results, users may choose to control temperature within a tighter range. 6

E384 − 11 TABLE 3 Correction Factors for Use in Vickers Hardness Tests Made on Cylind Cylindrical rical Surfaces (One diagonal parallel to axis) Convex Surface d  / D  D 

A

0 .0 0 9 0 .0 1 9 0 .0 2 9 0 .0 4 1 0 .0 5 4 0 .0 6 8 0 .0 8 5 0 .1 0 4 0 .1 2 6 0 .1 5 3 0 .1 8 9 0 .2 4 3

Correction Factor

d  / D  D 

0 .9 9 5 0 .9 9 0 0 .9 8 5 0 .9 8 0 0 .9 7 5 0 .9 7 0 0 .9 6 5 0 .9 6 0 0 .9 5 5 0 .9 5 0 0 .9 4 5 0 .9 4 0

Concave Surface

A

d  / D  D  A

Correction Factor

0 .0 0 8 0 .0 1 6 0 .0 2 3 0 .0 3 0 0 .0 3 6 0 .0 4 2

1 .0 0 5 1 .0 2 0 1 .0 1 5 1 .0 2 0 1 .0 2 5 1 .0 3 0

8.6.4 Remove the test force without without shock or vibration. 8.7   Test location— After After the force is removed, switch to the measuring mode, and select the proper objective lens. Focus the image, adjust the light intensity if necess necessary ary,, and adjust the diaphragms for maximum resolution and contrast. 8.7.1 Examin Examinee the inden indentation tation for its position relative relative to the desired location and for its symmetry. 8.7.2 If the indentation indentation did not occur occur at the desired spot, the tester is out of alignment. Consult the manufacturer’s instruction manual for the proper procedure procedure to produce alignment. Make another indentation and recheck the indentation location. Readjust and repeat as necessary.

Concave Surface

 

A

0 .0 4 8 0 .0 5 3 0 .0 5 8 0 .0 6 3 0 .0 6 7 0 .0 7 1 0 .0 7 6 0 .0 7 9 0 .0 8 3 0 .0 8 7 0 .0 9 0 0 .0 9 3 0 .0 9 7 0 .1 0 0 0 .1 0 3 0.105 0.108 0.111 0.113 0.116 0.118 0 .1 2 0 0 .1 2 3 0 .1 2 5

´1

Correction Factor 1 .0 3 5 1 .0 4 0 1 .0 4 5 1 .0 5 0 1 .0 5 5 1 .0 6 0 1 .0 6 5 1 .0 7 0 1 .0 7 5 1 .0 8 0 1 .0 8 5 1 .0 9 0 1. 09 5 1 .1 0 0 1. 10 5 1.110 1.115 1. 12 0 1 .1 2 5 1 .1 3 0 1 .1 3 5 1 .1 4 0 1 .1 4 5 1 .1 5 0

8.8   Indentation examination: 8.8. 8. 8.1 1 Fo Forr a Kn Knoo oop p in inde dent ntati ation on,, if on onee ha half lf of th thee lo long ng diagonal is greater than 10 % longer than the other, or if both ends of the indentation are not in sharp focus, the test specimen surface may not be perpendicular to the indenter axis. Check  the spe specim cimen en alig alignme nment nt and mak makee ano anothe therr test test.. Ind Indent entss tha thatt exceed the 10% limit should be noted in the test report. 8.8.2 For a Vickers Vickers indentation, indentation, if one half of either diagodiagonal is more than 5 % longer than the other half of that diagonal, or if the four corners of the indentation are not in sharp focus, the test surface may not be perpendicular to the indenter axis. Check the specimen alignment and make another test. Indents that exceed the 5% limit should be noted in the test report. 8.8.3 If the diagonal legs are unequal as described described in  8.8.1 or 8.8.2 or  8.8.2 rotate  rotate the specimen 90° and make another indentation in an unt untest ested ed reg region ion.. If the non nonsym symmet metrica ricall asp aspect ect of the indentations has rotated 90°, then the specimen surface is not perpen per pendic dicula ularr to the ind indente enterr axi axis. s. If the non nonsym symmetr metrica icall nature of the indentation remains in the same orientation, check  the indenter for misalignment or damage. 8.8.4 8.8 .4 Som Somee mat materia erials ls may hav havee non nonsym symmetr metrical ical ind indent entaations tio ns ev even en if th thee in inde dent nter er an and d th thee sp spec ecime imen n su surf rface ace ar aree perf pe rfect ectly ly ali align gned ed.. Tes ests ts on sin singl glee cr crys ystal talss or on tex textu ture red d materials may produce such results. When this occurs, check  the alignment using a test specimen, such as a standardized test block, known to produce uniformly shaped indentations. Testers that do not perform symmetrical indents on those specimens shall not be used until they meet the requirements of  sections 8.8.1 sections  8.8.1 and and 8.8.2  8.8.2.. 8.8. 8. 8.5 5 Bri Brittl ttlee ma mater teria ials ls such as ce cera ramic micss may crack crack as a result of being indented. Specific details for testing ceramics are contained in Test Methods  C1326 and and C1327  C1327..

D  =   = diameter of cylinder. d  =  = mean diagonal of impression in millimeters.

8.3  Magnitude of Test Force— Select Select the desired test force on the tester by following the manufacturer’s instructions. 8.3.1 After each each change change of a test force, force, it is recommended recommended that the operation of the machine be checked by performing a weekly verification as defined in A1.5 in  A1.5.. 8.4  Mount the specimen to the tester— Mount Mount the specimen on th thee tes teste terr sta stage ge or pl place ace it in th thee to topp-su surf rface ace in inde dexe xed d moun mo unti ting ng fix fixtu ture re on th thee st stag agee so th that at th thee te test st su surf rfac acee is perpendicular to the indenter axis. 8.5  Locate the test point— Focus Focus the measuring microscope with a low power objective objective so that the specimen surface surface can be observed. Adjust the light intensity and adjust the diaphragms for optimum resolution resolution and contra contrast. st. Adjust the position of the sample samp le so that the indentati indentation on will be made in the des desired ired location on the test surface. Before applying the force, make a final fin al fo focu cuss us usin ing g th thee me meas asur urin ing g ob objec jectiv tivee or th thee hi high ghes estt magnification magnifi cation objecti objective ve availab available. le. Application—  ation— Appl 8.6   Force Applic A pply y th thee se sele lecte cted d tes testt fo forc rcee as follows without shock or vibration: 8.6.1 For micro test force range testing, the inden indenter ter shall contact the specimen at a velocity between 15 and 70 µm/s. For macro test force ranges the contact velocity should not exceed 0.2 mm/s. 8.6.2 The time from the initial application application of the force until the full test force is reached shall not be more than 10 s. 8.6.3 The full test force force shall be applied for for 10 to 15 s unless otherwise specified. 8.6.3.1 8.6.3 .1 For some applications applications it may be necessary necessary to apply the test force for longer times. In these instances the tolerance for the time of the applied force shall be 6 2 s. The application application time shall be defined in the report

8.9   indentation Measurement: 8.9.1 Measu Measure re the long diagonal diagonal of a Knoo Knoop p indentation, indentation, or both bot h dia diagon gonals als of a Vicke ickers rs ind indent entatio ation, n, by ope operat rating ing the measuring device in accordance with the manufacturer’s instruction manual. 8.9.2 Determ Determine ine the length of the diagonals diagonals to 0.5 µm or less (see 6.4 (see  6.4). ). The indentation shall be measured using the highest magnification available that allows the full indentation to be seen and measured in the field of view. To stay within the flat field of the objective, the indentation length should not exceed 75% of the field width. The objective selected to measure the indentation should also have an objective resolution (r obj ) that is ≤   2% of the diagonal diagonal len length gth to be mea measur sured. ed. Objective Objective 7

E384 − 11 resolution (robj) is a function of the Numerical Aperture (NA) of the objective objective,, see   Note Note 9.   The minimu minimum m recomm recommended ended diagona diag onall len length gthss to be mea measur sured ed by typ typical ical obj objecti ectives ves are shown in Table in  Table 4. 4.  When availab available, le, the manuf manufacturer’ acturer’ss recommendations should be followed to stay within the 2% limit.

9.1.3 The total force application application time if outside outside the limits of  10 to 15 s as defined in  8.6.3  8.6.3.. 9.1.4 Any unusual conditions conditions encountered encountered during the test, and 9.1.5 9.1 .5 The tes testt temp tempera eratur ture, e, whe when n the out outsid sidee the rec recomommended allowable range of 10°C to 35°C (50°F to 95°F).

NOTE   9—The objective’s resolution (robj) is defined as, r opj 5 λ  / ~ 2  x NA!

 

10. Precision and Bias

(10)

10.1 The precision precision and bias of Knoop and Vickers Vickers hardness hardness measur mea sureme ements nts dep depend end on str strict ict adh adheren erence ce to the stat stated ed tes testt proced pro cedure ure and are infl influen uenced ced by ins instru trumen mental tal and mate materia riall factorss and indent factor indentation ation measur measurement ement error errors. s.

where: λ 

 NA

= the wave wave leng length th of the the light light in µm (app (approx rox.. 0.55 0.55 µm for for green green light) = th thee Nu Nume meri rica call Ap Aper ertu ture re of th thee ob obje ject ctiv ivee as defined defined by th thee manufacturer. (The NA is frequently marked on the side of each objective.) Example: For a 50× objective with a NA of 0.65 using green light. robj  = 0.55 µm / (2 × 0.65) = 0.42 µm

10.2 The consistency consistency of agreement agreement for repeated tests on the same material is dependent on the homogeneity of the material, reproducibility of the hardness tester, and consistent, careful measurement of the indents by a competent operator.

8.9.3 For the Vickers Vickers indentations, average the two diagonal length measurements.

10.3 Instr Instrumenta umentall factors that can af affect fect test results include: accuracy of loading; inertia effects; speed of loading; vibrations tio ns;; th thee an angl glee of in inde dent ntati ation on;; lat later eral al mo move veme ment nt of th thee indenter inden ter or specim specimen; en; inden indentation tation and inden indenter ter shape deviations. 10.3.1 10.3. 1 Vi Vibratio brations ns during inden indenting ting will produ produce ce larg larger er indentations with the influence of vibrations becoming larger as the force decreases  (  (11,  2  2)).5 10.3.2 10. 3.2 The ang angle le bet betwee ween n the ind indent enter er axi axiss and specimen specimen surface should be within 2° of perpendicular. Greater amounts of tilt tilting ing pro produc ducee non nonuni unifor form m ind indent entatio ations ns and inv invalid alid tes testt results.

8.10   Knoop or Vickers hardness calculation: 8.10.1 8.1 0.1 Com Comput putee the Kno Knoop op or Vick ickers ers har hardne dness ss num number ber using the appropriate equation in 5.5 or 5.6 or or Table  Table X6.1 or Table X6.2, X6.2,  respectivel  respectively y.  Table X6.1 and X6.1  and  Table X6.2 show X6.2  show the Knoop Kno op or Vick ickers ers har hardne dness ss for ind indent entatio ations ns wit with h dia diagon gonal al lengths from 1 to 200.9 µm using 1 gf. If the force was not 1 gf, multiply the value from  Table X6.1 or or Table  Table X6.2  by the actual gram-force value to obtain the correct hardness number. Spacing g of Inden Indentation tations—  s— Genera 8.11   Spacin Generally lly mor moree tha than n one indentation is made on a test specimen. It is necessary to ensure that the spacing between indentations is large enough so that adjacent tests do not interfere with each other. 8.11.1 8.1 1.1 For most testing testing purpos purposes, es, the minimum minimum rec recomommended spacing between separate tests, and minimum distance betw be tween een an in inde dent ntati ation on an and d th thee ed edge ge of th thee sp speci ecime men n ar aree illustrated in Fig. in  Fig. 3. 3. 8.11.2 For some applications, closer spacing of indentations than those shown in Fig. in  Fig. 3 may 3  may be desired. If closer indentation spacin spa cing g is use used, d, it sha shall ll be the responsi responsibil bility ity of the testing testing laboratory to verify the accuracy of the testing procedure.

10.4 Mat 10.4 Materi erial al fac factor torss that can af affec fectt tes testt res result ultss inc includ lude: e: specimen homogeneity, orientation or texture effects; improper specimen preparation; low specimen surface reflectivity; transparency of the specimen. 10.4.1 10. 4.1 Residual Residual def deform ormatio ation n fro from m mec mechan hanical ical pol polish ishing ing must be removed, particularly for low-force testing. 10.4.2 10. 4.2 Distort Distortion ion of the ind indent entatio ation n sha shape pe due to eith either er crystallographic or microstructural texture influences diagonal lengths and the validity of the calculated hardness. 10.4.3 10. 4.3 Plas Plastic tic def deform ormatio ation n dur during ing ind indent enting ing can pro produc ducee ridging around the indentation periphery that will affect diagonal measurement accuracy. 10.4.4 10.4. 4 Testing of etched surfa surfaces, ces, depending depending on the extent of etching, can produce results that are different from those obtained on unetched surfaces  (  (11).

9. Report 9.1 Repor Reportt the follow following ing information: information: 9.1.1 The results results (see 5.8 (see  5.8), ), the number of tests, and, where appropriate, the mean and standard deviation of the results, 9.1.2 Test force,

10.5 Measu Measurement rement errors errors that can af affect fect test results include: inaccurate inaccu rate cali calibra bratio tion n of the meas measuri uring ng dev device; ice; ina inadeq dequate uate resolving resolv ing power of the object objective; ive; insuf insuffficient magni magnification fication;; operator bias in sizing the indentations; poor image quality; nonuniform illumination, improper zeroing of the measuring device. 10.5.1 10.5. 1 The accuracy of Knoop and Vickers Vickers hardness hardness testing is strongly influenced by the accuracy to which the indentations can be measured. 10.5.2 10.5. 2 The error in measuring the diagonals diagonals increases increases as the numerical aperture of the measuring objective decreases  (  (33, 4  4)).

TABLE 4 Recommended Indent Diagonal Length for Commonly used Objectives and NA Commonly used Objective MagnificationsA

Typical NA (will vary by objective type)

Objective resolution (robj  ) µm

Recommended Diagonal lengths length s µm

5× 10 × 20 × 40 × 50 × 10 0 ×

0. 10 0. 25 0. 4 0. 55 0. 65 0 .8

2 .7 5 1. 1 0 .6 9 0. 5 0 .4 2 0 .3 4

1 3 7. 5 or l on g er 55 o r l o n ge r 3 4 .5 o r l o n g e r 25 o r l o n ge r 2 1 o r l on g er 1 7 o r l on g er

´1

A

This is the magnification of the objective and may not be the total magnification of the system. system. Man Many y sys system tems s hav have e a 10× eyepiece eyepiece tha thatt inc increa reases ses the tot total al magnification by a factor of 10 at the operator’s eye. This additional magnification does not change the optical resolution (robj) or the recommended diagonal lengths.

5

The boldface numbers in parentheses refer to the list of references at the end of  this standard.

8

E384 − 11

´1

FIG. 3 Minimum Recommended Spacing for Knoop and Vickers Indentations

shown in Table in  Table 5. 5.  Thus a 1 % change in  P  or a 2.836 % error in α   creates creates a 1 % err error or in the Vick ickers ers har hardne dness ss num number ber.. Howe Ho weve verr, on only ly a 0. 0.5 5 % er erro rorr in th thee me meas asur ured ed di diag agon onal al is needed to create a 1 % error in Vickers Vickers hardness. Furthermore, Furthermore, thiss ana thi analys lysis is ind indicat icates es tha thatt the calc calcula ulated ted Vick ickers ers har hardne dness ss number is not strongly influenced by errors in the angle of the indenter. 10.7.2   Knoop— Similarly, Similarly, using Eq 1, it follows that:

10.5.3 Bias is introduced if the operator consistently 10.5.3 consistently underundersizes or oversizes the indentations. 10.6 Som 10.6 Somee of the fac factor torss tha thatt af affec fectt test results results pro produc ducee systema sys tematic tic err errors ors tha thatt infl influen uence ce all test res result ultss whi while le oth others ers primarily influence low-force test results (5). Some of these problems occur continually, others may occur in an undefined, sporadic manner. Low force hardness tests are influenced by these factors to a greater extent than high force tests.

S D ]

dV 5

]

V  P

S D S D ]

dP1

V 

dd 1

] d 

]

V 

]

α

d α

 

dK 5

S D S D S D ]

V 

5

P

]

V 

]

d 

]

]

3

22

3 d 

2 3 10

3

5 2 4 3 10

V  α

5

103

3

23 3 P 3 d 

22 3 P 3 d 

SD SD SD

sin

cos

 

2

sin

SD 2

S D

S D c p

]

dc p

]

K 

]

c p

1

5

dc p

1

S D ]

K 

]

d 

3

P

2 2 3 10

3

c p d 

dd 

 

dd 

]

A

]

c p

] /  A

D

S D S D S  D ]

dA1

(11) 2 5

c p

 

dB

] B

tan

2

4 si sin n

(12)

(15) (16)

 

(17)

/  B

2 / A

 

(18)

2

and

 α

sin  α

2

 

2

 

(13) (14)

TABLE 5 Vicker Vickers s Hardn Hardness ess Analysis—1 % Error 1 % Error

For a material having a hardness of 500 HV when tested with a 500 gf force, d  =   = 43.06 µm, α  = 136°, and  α

dP1

and since the indenter has two different angles, A and B,

S

 α

K 

]P

103 103 P dP dc p 1 c p  d 2 c p2 d 2

and ]

S D ]

10.7 For both the Vicker 10.7 Vickerss and Knoop Knoop har hardne dness ss test tests, s, the calcula calc ulated ted har hardne dness ss is a fun functio ction n of thr three ee var variab iables: les: for force, ce, indenter geometry and diagonal measurement. Total differentials of the equations used to calculate the hardness can be used to evaluate the effect variations in these parameters can cause. 10.7.1   Vickers— using using Eq 6,   the tota totall dif differ ferent ential ial for the Vickers hardness number is:

5 0.927184.

10.7.1.1 Consid 10.7.1.1 Consider er introducing introducing a 1 % error into the hardness hardness of the material through an error in either the applied force, the indenter constant or the measured diagonal length. In this case, the hardness would be HV' = 505 or  dV  = 5. Using  Eq 12-14, 12-14 , the cor corres respon pondin ding g err errors ors in the var variou iouss par parame ameter terss are as

Forc Fo rce, e, gf

Diag Di agon onal al,, µm

10 20 50 10 0 20 0 50 0 10 0 0

6 .0 9 0 8 .6 1 2 1 3 .6 1 7 1 9 .2 5 8 2 7 .2 3 5 4 3 .0 6 2 6 0. 89 9

∆  P ,

gf

0. 10 0 0. 20 0 0. 49 9 0 .9 9 9 1 .9 9 8 4 .9 9 4 9 .9 8 8

∆   Diagonal,

– 0 .0 3 0 – 0 .0 4 3 – 0 .0 6 8 – 0 .0 9 6 – 0 .1 3 6 – 0 .2 1 5 – 0 .3 0 4

µm

∆  Angle,

°

2 .8 3 6 2 .8 3 6 2 .8 3 6 2 .8 3 6 2 .8 3 6 2 .8 3 6 2 .8 3 6 2° 50' 24"

9

E384 − 11

S

]

c p

] /  B

D

S D S D

ranges6. The test forces were 25, 50, 100, 200, 500, and 1000 gf on thr three ee fer ferrou rouss and fou fourr non nonfer ferrou rouss spe specim cimens ens (6, 7  7)). Twelve laboratories laboratories measur measured ed the indentations, indentations, five of each type at each force on each sample. Additional details of this study are given in  Appendix X3. X3 . 10.8.1.1 10.8. 1.1 Tests of the three ferro ferrous us specimens revealed that nine laboratories laboratories prod produced uced similar measur measurements ements while two laboratories consistently undersized the indentations and one laboratory consistently oversized the indentations. These latter result res ultss wer weree mos mostt pro pronou nounce nced d as the for force ce dec decreas reased ed and specim spe cimen en har hardne dness ss inc increa reased sed (th (that at is, as the dia diagon gonal al size decrea dec reased sed)) and wer weree obs observ erved ed for bot both h Vick ickers ers and Kno Knoop op indentations. Results for the lower hardness nonferrous indentations tati ons pro produc duced ed bet better ter agr agreem eement ent.. How Howeve ever, r, non nonee of the laboratories that obtained higher or lower results on the ferrous specimens measured the nonferrous indentations. 10.8.1.2   Repeatability Interval— The The difference due to test error between two test results in the same laboratory on the same material increases with increasing specimen hardness and with decreasing test force (see X3.4.4 (see  X3.4.4). ). 10.8.1.3   Reproducib T he di difffe fere renc ncee in te test st Reproducibility ility Interv Interval—  al— The result res ultss on the sam samee mat materi erial al test tested ed in dif differ ferent ent lab labora orator tories ies increased with increasing specimen hardness and with decreasing test force (see  X3.4.5  X3.4.5). ). 10.8.1.4 The within-laboratory and between-laboratory precision values improved as specimen hardness decreased and test force increased. The repeatability interval and reproducibility ibi lity int interv erval al wer weree gen genera erally lly lar larger ger tha than n the pr preci ecisio sion n estimate esti mate,, par particu ticularl larly y at low test for forces ces and hig high h spe specim cimen en hardnesses. Analysis is Measu Measurem rements—  ents— An 10.8.2   Image Analys An interl interlaborat aboratory ory test program was conducted in accordance with Practice E691 Practice  E691 to develop information regarding the repeatability and reproducibil duc ibility ity of Kno Knoop op and Vicke ickers rs mea measur sureme ements nts mad madee wit with h automated automa ted Image Analysis Analysis system systemss and manual proc procedures edures.. Four ferrous specimens were used in the round robin. The test were conducted at 100 gf and 300 gf. The participants in the testt pr tes prog ogra ram m me meas asur ured ed th thee sa same me in inde dent ntat atio ions ns on th thee fo four ur specim spe cimens ens.. Sev Seven en labs mea measur sured ed the spe specime cimens ns usi using ng bot both h procedures proce dures.. The Knoop indentations indentations on specimen C1 were too long for accurate measurements to be made by one lab; hence, only six sets of measurements were made on this specimen. Near the end of the test program, specimen B1 was lost in shipping; thus only six sets of measurements were made on this specim spe cimen. en. Addition Additional al det details ails of the stu study dy are con contain tained ed in Appendix X4. X4 . 10.8.2.1 10.8. 2.1 Repeatab Repeatability ility concerns the variab variability ility between individual test results obtained within a single laboratory by a single operator with a specific set of test apparatus. For both the man manual ual and aut automa omated ted mea measur suremen ements, ts, the rep repeata eatabil bility ity interval increased with specimen hardness and decreasing test force,   Appendix Appendix X4 X4..   For equ equiva ivalen lentt tes testing ting con condit dition ions, s, the repeatability interval for automated measurements was slightly larger than for manual measurements. 10.8.2.2 10.8. 2.2 Reprod Reproducibili ucibility ty deals with the variab variability ility between single test results obtained by different laboratories applying

/  A

cot 5

2

 

/  B

2

4 co coss

(19)

2

10.7.2.1 10.7.2 .1 Using the dif differ ferenti entials als cite cited d in   10.7.2, 10.7.2, for the Knoop test at various forces, forces, for a 1 % error in hardness hardness that is, HK = 505 or d K = 5, the corresponding errors in the force, diagona diag onall meas measure uremen mentt and ind indent enter er ang angle le are as sho shown wn in Table 6. 6. From this analysis it follows that 1 % error in  P  creates a 1 % error in HK, 0.5 % error in the measured diagonal creates a 1 % error in HK, and 1 % error in c  creates a 1 % error in HK. 10.7.2.2 10.7. 2.2 Since the indenter constant constant is compo composed sed of terms from two different angles, either a 4' 3" error in /A, or a 26' 20"" er 20 erro rorr in /B pr prod oduc uces es a 1 % er erro rorr in HK HK.. Un Unlik likee th thee Vicke ickers rs ind indent enter er,, the calc calcula ulated ted Kno Knoop op har hardne dness ss num number ber is very strongly influenced by small errors in the two angles of  the indenter. indenter. The The A angle, 172° 172° 30' 00", is the most sensitive of  these parameters. The actual value of  c p  for each indenter can be calculated using using the certified A and B angles provided provided by the indenter manufacturer. This will enhance the accuracy of the test measurements. 10.8 Over a period of several years, four separate separate interlabointerlaboratory studies have been conducted in accordance with Practice E691  to determine the precision, repeatability, and reproducibility ibil ity of thi thiss test method. method. The fou fourr stu studie diess are defined defined as follows: a) Knoop and Vickers tests, six test forces in the micro range, twelve labora laboratories tories,, manua manuall measur measurements, ements, seven dif differen ferentt hardness level samples. See 10.8.1 See  10.8.1 and and Appendix  Appendix X3. X3 . b) Knoop and Vickers tests, two test forces in the micro range, seven laboratories, Image Analysis and manual measurements, four different hardness level samples. See 10.8.2 See  10.8.2 and  and Appendix  Appendix X4.. X4 c) Knoop and Vickers tests, six test forces in the micro range, twenty-five twenty -five labor laboratories atories,, manual measur measurements ements,, six dif differen ferentt hardness level samples. See 10.8.3 See  10.8.3.. d) Vickers Vickers tests, four test forces forces in the macro ran range, ge, seven laboratories labora tories,, manual measur measurements ements,, three dif different ferent hardn hardness ess level samples. See 10.8.4 See  10.8.4.. 10.8.1 10. 8.1 An int interla erlabor borato atory ry test pro progra gram m was con conduc ducted ted in accordance with Practice E691 Practice  E691 to  to develop information regarding the pre precisi cision, on, rep repeata eatabil bility ity,, and rep reprod roduci ucibili bility ty of the measurement of Knoop and Vickers indentations in the micro

TABLE 6 Knoop Hardness Analysis—1 % Error 1 % Error Force, gm Diagon Diagonal, al, µm µm 10 20 50 1 00 2 00 5 00 1 0 00

16 . 8 7 23 . 8 6 37 . 7 2 53. 35 75. 45 119.29 1 6 8 .7 1

∆  P   P  gf  gf

0 .1 0 0 .2 0 0 .5 0 1 .0 0 2 .0 0 5 .0 0 1 0. 00

∆  diagonal,

µm – 0. 08 – 0. 12 – 0. 19 – 0. 27 – 0. 38 – 0 .6 0 – 0 .8 4

∆  A,

°

∆  B,

°

0 .0 7 5 0 .0 7 5 0 .0 7 5 0 .0 7 5 0 .0 7 5 0. 07 5 0 .0 7 5

0 .4 3 9 0 .4 3 9 0 .4 3 9 0 .4 3 9 0 .4 3 9 0 .4 3 9 0 .4 3 9

4' 30"

26 ' 2 0 "

´1

6

Supporting data have been filed at ASTM International Headquarters and may be obtained by requesting Research Report RR:E04-1004.

10

E384 − 11 the same test methods to the same or similar test specimens. For both the manual and automated measurements, the reproducibility interval increased with specimen hardness and decreasin crea sing g test for force, ce,   Append Appendix ix X4 X4..   For equ equiva ivalen lentt tes testing ting conditions, the reproducibility interval for automated measurements was slightly larger than for manual measurements.

´1

was followed for the design and analysis of the data; the details are given in ASTM Research Report No. E04-1006. 7 Repeatability limit (r)— Two test results obtain 10.8.3.1   Repeatability obtained ed within one laboratory shall be judged not equivalent if they differ by more than the “r” value for that material; “r” is the interval representing the critical difference between two test results for the same material, obtained by the same operator usin us ing g th thee sa same me eq equi uipm pmen entt on th thee sa same me da day y in th thee sa same me laboratory. 10.8.3.2 10.8. 3.2 Repeatab Repeatability ility limits in diago diagonal nal lengths (µm) are listed Table listed  Table 7 a 7  and nd Table  Table 8 and 8  and in hardness units (HK, HV) in Table 9 and and Table  Table 10. 10. 10.8.3.3   Reproducibility limit (R)— Two Two test results shall be  judged not equivalent if they differ by more than the “R” value for that material; “R” is the interval representing the critical differ dif ferenc encee bet betwee ween n two tes testt res result ultss for the sam samee mate materia rial, l, obtained obtain ed by dif differen ferentt opera operators tors using different different equip equipment ment in different laboratories.

10.8.2.3 Practic 10.8.2.3 Practicee  E691  E691 nor  nor any other ASTM standard deals with comparing test results of a single property made by two different test methods. Hence it is not possible to statistically and accurately compare the hardness measurements made by the manual and automated procedures. However, this information is graphically represented for comparative purposes,  X4.6  X4.6.. 10.8.3 10.8 .3 Th Thee pr preci ecisio sion n of th this is tes testt me meth thod od is ba base sed d on an interlaborato interla boratory ry study of E384E384-07, 07, Standard Test Method for Microindenta Microi ndentation tion Hardness of Materi Materials, als, condu conducted cted in 2007 2007.. Twenty-five laboratories tested a total of six ferrous materials for Vicke ickers rs Har Hardne dness ss and thir thirteen teen lab labora orator tories ies sub submitt mitted ed Knoop Hardness results. Every “test result” was recorded, and the laboratory means represent an average of five individual determination determi nationss (for Knoop) or five separate measur measurements ements,, each the average of two readings (for Vickers). Practice  E691

7 Supporting data have been filed at ASTM International Headquarters and may be obtained by requesting Research Report RR:E04-1006.

TABLE 7 Precisi Precision on Statistics for an Interl Interlaborat aboratory ory Study of the Knoop Microindentat Microindentation ion Hardness Test for Ferrou Ferrous s Specime Specimens ns in Diagonal Units (µm) S pe c i m e n

A

B

C

D

E

T

Test Force (gf)

25 50 1 00 3 00 5 00 10 0 0 25 50 1 00 3 00 5 00 10 0 0 25 50 1 00 3 00 5 00 10 0 0 25 50 1 00 3 00 5 00 10 0 0 25 50 1 00 3 00 5 00 10 0 0 25 50 1 00 3 00 5 00 10 0 0

Average Diagonal (µm)

Standard Deviation (µm)

Reproducibility Standard Deviation (µm) SR

Repeatability Limit (µm)

Reproducibility Limit (µm)

Sx

Repeatability Standard Deviation (µm) Sr

¯  d 

r

R

3 5 .6 1 5 1 .7 7 7 4. 84 13 2. 28 17 1. 51 243.11 2 3 .6 6 3 4 .3 3 4 9. 61 8 8. 64 115.48 1 6 4. 38 2 7 .6 2 3 9 .4 7 5 6. 66 10 0. 14 13 0. 19 1 8 4. 84 3 1 .0 4 4 4 .6 4 6 4. 22 113.94 14 8. 16 2 1 0. 10 2 0 .0 2 2 9 .0 3 4 2. 21 7 6. 03 9 9. 25 1 4 1. 67 1 7. 14 2 5 .5 9 3 7. 20 6 7. 43 8 8. 27 1 2 6. 96

1 .4 0 1 .3 3 1. 65 2 .6 3 2 .0 7 1 .7 2 0 .9 5 0 .9 4 1. 12 1. 39 1 .6 8 1 .6 5 1 .3 3 1 .1 4 1. 05 1 .2 5 1 .5 0 1 .7 9 1 .0 4 0 .8 5 1. 08 0 .9 4 1 .1 6 2 .0 3 0 .7 2 1 .0 0 1. 15 1. 00 1. 06 1 .2 7 0. 88 1 .0 3 1. 45 1. 39 1.11 1 .4 7

0 .7 2 1.11 1. 77 2. 57 2. 46 2 .9 6 0 .4 8 0 .5 6 0. 65 0. 88 1.11 1 .5 2 0 .4 9 0 .5 0 0. 64 0. 81 0. 83 1 .1 9 0 .4 6 0 .4 6 0. 67 0. 82 0. 74 1 .6 4 0 .4 8 0 .4 8 0. 52 0. 53 0. 49 0 .8 5 0. 48 0 .4 7 0. 52 0. 65 0. 66 0 .7 5

1 .5 4 1 .6 6 2. 28 3 .5 0 3 .0 2 3 .1 6 1 .0 4 1 .0 7 1. 26 1. 59 1 .9 5 2 .1 4 1 .4 1 1 .2 2 1. 20 1 .4 4 1 .6 8 2 .0 8 1.11 0 .9 5 1. 24 1 .1 9 1 .3 3 2 .5 0 0 .8 4 1 .0 9 1. 24 1.11 1. 15 1 .4 8 0 .9 8 1 .1 2 1. 52 1. 51 1. 26 1 .6 1

2 .0 0 3 .1 2 4. 95 7 .2 0 6 .8 9 8 .2 9 1 .3 4 1 .5 7 1. 82 2. 45 3.11 4 .2 5 1 .3 8 1 .3 9 1. 79 2 .2 6 2 .3 3 3 .3 3 1 .2 8 1 .3 0 1. 89 2 .2 9 2 .0 6 4 .5 8 1 .3 6 1 .3 4 1. 46 1. 48 1. 37 2 .3 9 1. 35 1 .3 2 1. 46 1. 82 1. 85 2 .0 9

4 .3 1 4 .6 6 6 .4 0 9 .7 9 8 .4 5 8 .8 4 2 .9 1 2 .9 9 3 .5 4 4 .4 6 5 .4 6 5 .9 8 3 .9 3 3 .4 3 3 .3 5 4 .0 3 4 .6 9 5 .8 2 3 .1 2 2 .6 5 3 .4 7 3 .3 3 3 .7 3 7 .0 0 2 .3 4 3 .0 5 3 .4 6 3 .1 0 3 .2 1 4 .1 5 2. 76 3 .1 2 4 .2 6 4 .2 2 3 .5 3 4 .5 2

11

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´1

TABLE TA BLE 8 Precisi Precision on statistics for an Interl Interlaborat aboratory ory Study of the Vicker Vickers s Microin Microindentat dentation ion Hardness Test for Ferrou Ferrous s Specime Specimens ns in Diagonal Units (µm) S pe c i m e n

A

B

C

D

E

T

Test Force (gf)

25 50 1 00 3 00 5 00 10 0 0 25 50 1 00 3 00 5 00 10 0 0 25 50 1 00 3 00 5 00 10 0 0 100 3 00 5 00 10 0 0 100 3 00 5 00 10 0 0 30 0 5 00 10 0 0

Average Diagonal (µm)

Standard Deviation (µm)

Reproducibility Standard Deviation (µm) SR

Repeatability Limit (µm)

Reproducibility Limit (µm)

Sx

Repeatability Standard Deviation (µm) Sr

¯  d 

r

R

1 3 .8 9 1 9 .8 1 2 8. 10 4 9. 19 6 3. 65 9 0 .4 8 9 .3 5 1 3 .0 6 1 8. 51 32.11 4 1. 68 5 9 .2 1 1 0 .8 1 1 5 .1 3 2 1. 34 3 6. 85 4 7. 68 6 7 .6 0 2 4 .5 0 4 2. 52 5 5. 02 7 8 .1 4 1 5 .6 1 2 7. 25 3 5. 26 5 0 .0 6 2 3 .9 4 3 1. 00 4 4 .1 2

0 .7 5 0 .6 1 0. 57 0. 75 0. 81 0 .9 8 0 .4 0 0 .3 7 0. 39 0. 43 0. 51 0 .5 5 0 .5 3 0 .4 2 0. 40 0. 38 0. 55 0 .5 8 0 .4 3 0. 41 0. 50 0 .7 0 0 .4 0 0. 41 0. 43 0 .4 1 0 .4 7 0. 51 0 .5 0

0 .3 0 0 .3 4 0. 45 0. 72 0. 88 1. 31 0. 25 0 .2 3 0. 39 0. 30 0. 36 0. 52 0 .1 9 0 .2 0 0. 22 0. 21 0. 24 0. 33 0 .2 9 0. 28 0. 25 0. 34 0 .1 8 0. 25 0. 20 0. 24 0. 17 0. 21 0. 25

0 .8 0 0 .6 8 0. 70 0. 99 3. 16 1 .5 3 0. 46 0 .4 2 0. 52 0. 50 0. 60 0 .7 2 0 .5 6 0 .4 6 0. 45 0. 43 0. 59 0 .6 5 0. 50 0. 48 0. 55 0 .7 7 0. 43 0. 46 0. 46 0 .4 6 0 .4 9 0. 55 0 .5 5

0 .8 5 0 .9 5 1. 26 2. 02 2. 47 3 .6 6 0 .6 9 0 .6 3 1. 09 0. 84 1. 00 1 .4 6 0 .5 4 0 .5 7 0. 62 0. 59 0. 67 0 .9 3 0 .8 2 0. 80 0. 70 0 .9 7 0 .5 2 0. 70 0. 55 0 .6 7 0 .4 9 0. 59 0 .6 9

2 .2 4 1 .9 1 1 .9 6 2 .7 7 1 .1 3 4 .2 8 1. 28 1 .1 8 1 .4 7 1 .4 1 1 .6 9 2 .0 3 1 .5 6 1 .2 9 1 .2 5 1 .2 0 1 .6 4 1 .8 3 1. 40 1 .3 5 1 .5 4 2 .1 5 1. 20 1 .3 0 1 .3 0 1 .2 9 1. 38 1 .5 3 1 .5 3

10.8.3.4 Repro 10.8.3.4 Reproducib ducibility ility limits in diago diagonal nal lengths (µm) are listed in   Table 7 and   Table 8 and   Fig. 4 and   Fig. 5   and in hardness units (HK, HV) in   Table 9 and and Table  Table 10 and and Fig.  Fig. 6 and Fig. and  Fig. 7. 7. 10.8.3.5 10.8. 3.5 The above terms (repeatability (repeatability limit and repro reproducducibility limit) are used as specified in Practice  E177  E177.. 10.8. 10 .8.3.6 3.6 Any jud judgme gment nt in acc accor ordan dance ce wit with h sta statem tement entss 10.8.3.1 and  10.8.3.3  would have an approximate 95% probability of being correct. 10.8.3.7 10.8. 3.7 The precision statement was determi determined ned through statistical examination of results from twenty-five laboratories, on six fer ferrou rouss mate material rials. s. The These se six fer ferrou rouss mate material rialss wer weree described describ ed as: Specimen A: H13, mill annealed, hardness less than 20 HRC Specimen B: H13, austenitized, quenched, and tempered ~ 50 HRC Specimen C: H13, austenitized, quenched, and tempered ~ 40 HRC Specimen D: H13, austenitized, quenched, and tempered ~ 30 HRC Specime Spe cimen n E: O1, aus austen tenitiz itized, ed, que quench nched ed and temp tempere ered d O1 steel, ~ 60 HRC Specimen Specime n T: T15 P/M, austenitized, austenitized, quenched and tempere tempered d~ 67 HRC To judge the equivalency of two test results, it is recommended to cho choose ose the mate material rial closest closest in cha charac racter teristi istics cs to the test material. 10.8.4 The macro Vickers Vickers precision statement is based on an interlaboratory study of  E92,  E92, Standard Test Method for Vickers

Hardness of Metallic Materials, conducted in 2001. (With this revisio rev ision n Test Meth Method od E92   is no now w pa part rt of E3 E384 84)) Se Seve ven n laboratories tested three different standard hardness test blocks using macro range test forces of 1kg, 5kg, 10kg, and 20kg. Only four laboratories were also able to provide results at 50kg test force. Every “test result” represents represents an individual determination of the Vickers hardness of the material. Each laboratory was asked to report triplicate test results in order to permit the estimation estimati on of Intra Intralabora laboratory tory precis precision. ion. Practi Practice ce   E691 was followed for the design and analysis of the data; the details are given in ASTM Research Report No. RR:E04-1007. 8 Repeatability limit (r)— Two test results obtain 10.8.4.1   Repeatability obtained ed within one laboratory shall be judged not equivalent if they differ by more than the “r” value for that material; “r” is the interval representing the critical difference between two test results for the same material, obtained by the same operator usin us ing g th thee sa same me eq equi uipm pmen entt on th thee sa same me da day y in th thee sa same me labora lab orator tory y. Rep Repeata eatabil bility ity lim limits its are list listed ed in   Tables Tables 11 11-15 -15 below. 10.8.4.2   Reproducibility limit (R)— Two Two test results shall be  judged not equivalent if they differ by more than the t he “R” “R ” value for that material; “R” is the interval representing the critical differ dif ferenc encee bet betwee ween n two tes testt res result ultss for the sam samee mate materia rial, l, obtained obtain ed by dif differen ferentt opera operators tors using different different equip equipment ment in different laboratories. Reproducibility limits are listed  listed   Tables 11-15 in 11-15  in below. 8

Supporting data have been filed at ASTM International Headquarters and may be obtained by requesting Research Report RR: RR:E04-1007.

12

E384 − 11

´1

TABLE 9 Precisio Precision n statist statistics ics for an Inter Interlabora laboratory tory Study of the Knoop Microindentation Microindentation Hardness Hardness Test for Ferro Ferrous us Specim Specimens ens in Hardness units (HK) S pe c i m e n

A

B

C

D

E

T

Test Force

Average Diagonal (µm)

(gf)

d 

25 50 1 00 3 00 5 00 10 0 0 25 50 1 00 3 00 5 00 10 0 0 25 50 1 00 3 00 5 00 10 0 0 25 50 1 00 3 00 5 00 10 0 0 25 50 1 00 3 00 5 00 10 0 0 25 50 1 00 3 00 5 00 10 0 0

3 5 .6 1 5 1 .7 7 7 4. 84 13 2. 28 17 1. 51 243.11 2 3 .6 6 3 4 .3 3 4 9. 61 8 8. 64 115.48 1 6 4. 38 2 7 .6 2 3 9 .4 7 5 6. 66 10 0. 14 13 0. 19 1 8 4. 84 3 1 .0 4 4 4 .6 4 6 4. 22 113.94 14 8. 16 2 1 0. 10 2 0 .0 2 2 9 .0 3 4 2. 21 7 6. 03 9 9. 25 1 4 1. 67 1 7. 14 2 5 .5 9 3 7. 20 6 7. 43 8 8. 27 1 2 6. 96

Standard Deviation (HK) Sx

Repeatability Standard Deviation (HK) Sr

Reproducibility Standard Deviation (HK) SR

2 2 .0 7 1 3 .6 4 11.20 9 .7 0 5 .8 4 3 .4 1 5 1 .0 7 3 3 .0 7 26.11 1 7. 04 1 5. 52 1 0 .5 7 4 4 .9 6 2 6 .3 9 1 6. 43 1 0. 63 9 .6 7 8 .0 7 2 4 .7 5 1 3 .6 0 11.61 5 .4 3 5 .0 8 6 .2 3 6 3 .8 8 5 8 .2 0 4 3. 53 1 9. 43 1 5. 43 1 2 .7 1 1 2 4 .5 0 8 7 .5 3 8 0. 22 3 8. 71 2 2. 97 2 0 .4 4

11.35 11.39 1 2. 02 9. 48 6. 94 5 .8 6 2 5 .7 9 1 9 .7 0 1 5. 15 1 0. 79 1 0 .2 6 9 .7 4 1 6 .5 5 11.57 1 0. 01 6 .8 9 5. 35 5 .3 6 1 0 .9 4 7. 36 7. 20 4. 73 3. 24 5 .0 3 4 2 .5 7 2 7 .9 2 1 9. 68 1 0. 30 7. 13 8 .5 1 6 7 .8 5 3 9 .9 1 2 8. 75 1 8. 10 1 3. 65 1 0 .4 3

2 4. 29 1 7. 03 1 5 .4 9 1 2. 91 8 .5 2 6 .2 6 5 5. 92 3 7. 65 2 9 .3 8 1 9 .4 9 1 8 .0 2 1 3 .7 1 4 7. 67 2 8. 24 1 8 .7 8 1 2 .2 4 1 0. 83 9 .3 7 2 6. 42 1 5 .2 0 1 3. 33 6 .8 7 5 .8 2 7 .6 7 7 4. 54 6 3. 44 4 6 .9 4 2 1 .5 6 1 6. 74 1 4 .8 1 1 3 8 .6 9 9 5. 19 8 4 .1 0 4 2 .0 6 2 6 .0 7 2 2 .3 9

Repeatability Limit (HK)

Reproducibility Limit (HK)

r

R

3 1. 56 3 2 .0 5 3 3 .6 8 2 6 .6 0 1 9. 45 1 6 .4 3 7 2. 09 5 5 .2 7 4 2 .4 5 3 0 .0 4 2 8. 75 2 7. 24 4 6. 65 3 2 .1 9 2 8 .0 2 1 9 .2 2 1 5 .0 3 1 5 .0 1 3 0. 48 2 0. 80 2 0 .3 2 1 3. 22 9 .0 1 1 4 .0 6 12 0. 86 7 8 .0 2 5 5 .2 8 2 8 .7 6 1 9 .9 4 2 3. 92 1 9 1 .3 3 112.23 8 0 .7 7 5 0 .7 0 3 8 .2 8 2 9 .0 7

6 8 .4 1 4 7 .9 8 4 3. 61 3 6 .2 1 2 3 .8 6 1 7 .5 2 1 5 7 .5 0 1 0 5 .5 5 8 2. 72 5 4. 74 5 0 .5 0 3 8 .3 4 1 3 4 .0 5 7 9 .6 7 5 2. 50 3 4. 29 3 0 .2 6 2 6 .2 4 7 4 .6 0 4 2 .4 6 3 7 .3 4 1 9 .2 3 1 6 .3 2 2 1 .4 9 2 0 8 .9 0 1 7 8 .3 7 13 1. 37 6 0. 27 4 6 .7 4 4 1 .5 5 3 9 5 .0 7 26 6. 90 23 7. 05 117.74 7 3. 09 6 2 .9 0

10.8.4.3 10.8. 4.3 The above terms (repeatability (repeatability limit and repro reproducducibility limit) are used as specified in Practice  E177  E177..

11. Conversion Conversion to Other Hardness Scales or Tensile Strength Values

10.8.4.4 10.8. 4.4 Any jud judgme gment nt in acc accor ordan dance ce wit with h statem statement entss 10.8.4.1 and  10.8.4.2  would have an approximate 95% probability of being correct.

11.1 The 11.1 There re is no gen genera erally lly acce accepted pted method method for accurate accurate conversion conve rsion of Knoop or Vickers Vickers hardn hardness ess numbers to other hardness scales or tensile strength values. Such conversions are limited in scope and should be used with caution, except for special cases where a reliable basis for the conversion has been obtained by comparison tests. For loads ≥ 100 gf microi microindenndentation Vickers hardness numbers are in reasonable agreement with macroi macroindenti ndention on Vickers hardness numbers. Refer to Test Method E140 Method  E140 for  for hardness conversion tables for metals.

10.8.4.5   Bias— There There is no recognized recognized standard by which to estimate the bias of this test method. 10.8.4.6 10.8. 4.6 The precision statement was determi determined ned through statistical examin statistical examination ation of 288 results, from seven laboratories, laboratories, on th thre reee tes testt bl bloc ocks ks.. Th Thee mat mater erial ialss we were re de desc scri ribe bed d as th thee following: Material 1: 200 HV Material 2: 400 HV Material 3: 800 HV

12. Keywords 12.1 hardn hardness; ess; inden indentation; tation; Knoop; microindentation microindentation;; macroindentation; Vickers

13

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´1

TABLE 10 Precisi Precision on statistics for an Interlaboratory Interlaboratory Study of the Vickers Microindentation Microindentation Hardness Hardness Test for Ferrou Ferrous s Specim Specimens ens in Hardness units (HV) Spec i men

A

B

C

D

E

T

Test Force

Average Diagonal (µm)

(gf)

d 

25 50 10 0 30 0 50 0 1 0 00 25 50 10 0 30 0 50 0 1 0 00 25 50 10 0 30 0 50 0 1 0 00 1 00 30 0 50 0 1 0 00 1 00 30 0 50 0 1 0 00 3 00 50 0 1 0 00

1 3 .8 9 1 9 .8 1 2 8 .1 0 4 9 .1 9 6 3 .6 5 9 0 .4 8 9. 35 1 3 .0 6 1 8 .5 1 32.11 4 1 .6 8 5 9 .2 1 1 0 .8 1 1 5 .1 3 2 1 .3 4 3 6 .8 5 4 7 .6 8 6 7 .6 0 2 4. 50 4 2 .5 2 5 5 .0 2 7 8 .1 4 1 5. 61 2 7 .2 5 3 5 .2 6 5 0 .0 6 2 3 .9 4 3 1 .0 0 4 4 .1 2

Standard Deviation (HV) Sx

Repeatability Standard Deviation (HV) Sr

Reproducibility Standard Deviation (HV) SR

2 5. 99 1 4 .5 6 9. 53 7. 01 5. 83 4. 91 4 5 .4 1 3 0 .8 1 2 2 .8 1 1 4 .4 5 1 3 .0 6 9. 83 3 8. 95 2 2 .5 0 1 5 .2 7 8. 45 9. 41 6. 96 1 0 .8 5 5. 93 5. 57 5. 44 3 9 .0 1 2 2 .5 5 1 8 .1 9 1 2. 12 3 8. 12 3 1 .7 5 2 1. 59

1 0 .3 8 8.11 7. 52 6. 73 6. 33 6. 56 2 8. 37 1 9 .1 5 2 2. 81 1 0. 08 9. 22 9. 29 1 3 .9 5 1 0 .7 1 8. 40 4. 67 4.11 3. 96 7 .3 1 4. 05 2. 78 2. 64 1 7 .5 5 1 3. 75 8. 46 7. 10 1 3 .7 9 1 3. 07 1 0 .8 0

2 7 .7 3 1 6 .2 3 11.70 9 .2 6 2 2 .7 5 7 .6 6 5 2 .2 4 3 4 .9 8 3 0 .4 2 1 6 .8 1 1 5 .3 7 1 2 .8 7 4 1 .1 6 2 4 .6 4 1 7 .1 8 9 .5 6 1 0 .0 9 7 .8 0 1 2 .6 1 6 .9 5 6 .1 2 5 .9 9 4 1 .9 4 2 5 .3 0 1 9 .4 6 1 3 .6 0 3 9 .7 4 3 4 .2 4 2 3 .7 5

Repeatability Limit (HV)

Reproducibility Limit (HV)

r

R

2 9 .4 6 2 2 .6 9 2 1 .0 8 1 8 .9 0 1 7 .7 8 1 8 .3 4 7 8 .4 8 5 2 .5 1 6 3. 85 2 8. 24 2 5 .6 2 2 6 .0 9 3 9 .6 9 3 0 .5 4 2 3 .6 7 1 3 .1 2 11.46 11.17 2 0 .6 9 11.58 7 .7 9 7 .5 4 5 0 .7 3 3 8. 50 2 3 .2 7 1 9. 81 3 9 .7 4 3 6. 73 2 9 .8 0

7 8 .5 2 4 5. 77 3 2. 84 2 5 .9 4 8. 13 2 1. 45 1 4 6 .5 6 9 8. 63 8 6 .2 4 4 7 .4 3 4 3. 32 3 6. 29 115.71 6 9. 32 4 7. 79 2 6 .7 0 2 8. 07 2 1. 98 3 5 .3 6 1 9 .5 5 1 7 .1 5 1 6 .7 2 117.35 7 1 .5 6 5 5. 03 3 8 .1 5 112.09 9 5 .3 5 66.11

FIG. 4 The Relationship Relationship betwe between en Repro Reproducibi ducibility lity (R) and Diagonal length ( d ) from  Table 7  in µm units, for the Knoop Hardness Tests for Specimens B, C, D, E and T

14

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FIG. 5 The Relationship Relationship between Reproducibility Reproducibility and Diago Diagonal nal length ( d ) from  Table 8  in µm units, for the Vickers Hardness Tests for Specimens B, C, D, E and T

FIG. 6 The Relationship between Reproducibility (R) and Diagonal length ( d ) from  Table 9  in HK units, for the Knoop Hardness Tests for Specimens B, C, D, E and T

15

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FIG. 7 The Relationship Relationship betwee between n Repro Reproducibi ducibility lity (R) and Diagonal length ( d ) from  Table 10  in HV units, for the Vickers Hardness Tests for Specimens B, C, D, E and T TABLE 11 Vickers hardness at 1 kgf Test Force (HV) Test Block Nominal Hardness (HV)

200 400 800

Bias

Repeatability Standard Deviation (HV)

¯  X 

%

sr

2 0 9. 2 4 1 3. 8 8 1 2. 9

N/A N/A N/A

4 .1 8 .1 2 1 .8

Average (HV)

 

Reproducibility Standard Deviation (HV)

Repeatability Limit (HV)

Reproducibility Limit (HV)

sR

r

R

7 .1 1 5 .6 2 1 .8

11.5 2 2. 8 6 1 .1

1 9 .9 4 3. 7 6 1 .1

Repeatability Limit (HV)

Reproducibility Limit (HV)

TABLE 12 Vickers hardness at 5 kgf Test Force (HV) Test Block Nominal Hardness (HV)

200 400 800

Bias

Repeatability Standard Deviation (HV)

¯  X 

%

sr

sR

r

R

1 9 9. 0 4 2 1. 8 8 2 8. 0

N/A N/A N/A

1 .7 4 .8 8 .9

5 .2 7 .3 1 9 .5

4. 7 1 3. 3 2 5. 0

1 4 .5 2 0 .5 5 4. 6

Repeatability Limit (HV)

Reproducibility Limit (HV)

Average (HV)

 

Reproducibility Standard Deviation (HV)

TABLE 13 Vickers hardness at 10 kgf Test Force (HV) Test Block Nominal Hardness (HV)

200 400 800

Bias

Repeatability Standard Deviation (HV)

¯  X 

%

sr

sR

r

R

1 9 8. 1 3 9 8. 5 8 0 0. 2

N/A N/A N/A

2 .1 2 .9 2 .3

3 .0 9 .1 11.7

6. 0 8. 2 6 .6

8 .5 2 5 .4 3 2 .7

Average (HV)

 

16

Reproducibility Standard Deviation (HV)

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´1

TABLE 14 Vickers hardness at 20 kgf Test Force (HV) Test Block Nominal Hardness (HV)

200 400 800

Bias

Repeatability Standard Deviation (HV)

¯  X 

%

sr

1 9 7 .2 4 1 5 .7 811.5

N/A N/A N/A

1 .8 2 .5 8 .3

Average (HV)

 

Reproducibility Standard Deviation (HV)

Repeatability Limit (HV)

Reproducibility Limit (HV)

sR

r

R

3. 5 5. 1 1 6. 6

4 .9 7 .0 2 3 .3

9 .9 1 4 .2 4 6. 6

Repeatability Limit (HV)

Reproducibility Limit (HV)

TABLE 15 Vickers hardness at 50 kgf Test Force (HV) Test Block Nominal Hardness (HV)

200 400 800

Bias

Repeatability Standard Deviation (HV)

¯  X 

%

sr

sR

r

R

1 9 1 .2 3 9 9 .9 8 1 4 .4

N/A N/A N/A

0 .5 1 .1 2 .8

1. 5 2. 0 1 2. 0

1 .4 3 .1 7 .7

4 .3 5 .7 3 3 .6

Average (HV)

 

Reproducibility Standard Deviation (HV)

ANNEXES (Mandatory Information) A1. VERIFICA VERIFICATION TION OF KNOOP AND VICKERS HARDNESS HARDNESS TESTING MACHINES AND AND INDENTERS

A1.1 Scope

TABLE A1.1 Verification Schedule for a Knoop and Vickers Hardness Testing Machine

A1.1.1   Annex A1   specifies specifies thr three ee typ types es of pro proced cedure uress for verifying Knoop and Vickers hardness testing machines: direct verification, indirect verification, and weekly verification. This annex also contains geometric specifications for the indenter.

Verification Procedure

A1.1.2 Dir A1.1.2 Direct ect ver verifica ificatio tion n is a pro proces cesss for ver verify ifying ing tha thatt critical components components of the hardness testing machine are within allowab allo wable le tole toleran rances ces by dir directl ectly y mea measur suring ing the test for forces ces,, indentation measuring system, and testing cycle. A1.1.3 A1. 1.3 Indirect Indirect ver verific ificatio ation n is a pro proces cesss for per period iodical ically ly verifying the performance of the testing machine by means of  standardized standa rdized test blocks blocks.. A1.1.4 The weekly verification A1.1.4 verification is a process for monitoring monitoring thee pe th perf rfor orma manc ncee of th thee te testi sting ng ma mach chin inee be betw twee een n in indi dire rect ct verifications by means of standardized test blocks.

 

Schedule

Direct Dir ect Ve Verifi rificat cation ion

When Whe n a tes testin ting g machi machine ne is is new, new, or whe when n adjus adjustme tments nts,, modifications or repairs are made that could affect the application of the test forces or the measuring system. When a testin testing g machin machine e fails an indir indirect ect verification. verification.

Indirect Indire ct Verifica Verification tion

Shall be preform preformed ed followi following ng a direct verifi verification cation before placing the tester in servic placing service. e. Shall be no longer than every 18 months. Recommended every 12 months. Recommended when a test machine is installed or moved.

Weekly Wee kly Veri Verifica ficatio tion n

Requir Req uired ed each each week week that that the the machin machine e is used used.. Required whenever the machine is moved. Recommended Recomm ended whenever the indenter or test force is changed.

A1.2 General Requirements A1.2.4 Direct verification verification of newly manufactured manufactured or rebuilt test te stin ing g ma mach chin ines es ma may y be pe perf rfor orme med d at th thee pl plac acee of  manufacture, rebuild or the location of use.

A1.2.1 The test A1.2.1 testing ing mach machine ine sha shall ll be ver verified ified at spe specifi cificc instances and at periodic intervals as specified in  Table A1.1, A1.1, and when circumstances occur that may affect the performance of the testing machine.

NOTE A1.1—It is recommended that the calibration agency that is used to con conduc ductt the ver verific ificatio ations ns of Kno Knoop op or Vick ickers ers,, har hardne dness ss tes testin ting g machines machi nes and inden indenters ters be accred accredited ited to the requirements requirements of ISO/ ISO/IEC IEC 17025 (or an equivalent) by an accrediting an body recognized by the International Intern ational Labora Laboratory tory Accreditation Accreditation Coope Cooperation ration (ILAC (ILAC)) as operat operating ing to the requirements of ISO/IEC 17011.

A1.2.2 All ins A1.2.2 instru trumen ments ts use used d to mak makee mea measur sureme ements nts required by this Annex shall be calibrated traceable to national standards when a system of traceability exists, except as noted otherwise.

A1.3 Direct Verification Verification

A1.2.3 Indir A1.2.3 Indirect ect verification verification of the testing machine shall be performed at the location where it will be used.

A1.3.1 A direct direct verification of the testing machine shall be performed perfo rmed at specific instances instances in accord accordance ance with Table with  Table A1.1. A1.1. 17

E384 − 11 The test forces, indentation measuring system, testing cycle, and indenters shall be verified as follows.

´1

shall be 148° 6’ 36” 6  45’. The edge angles shall be equally inclined to the axis of the indenter within 6 30’. (2) The offset shall not exceed 1 µm when testing with test forces of 1 kgf and greater. When testing with forces less than 1 kgf the offset shall not exceed 0.5 µm.

NOTE   A1.2—D A1.2—Direct irect verification verification is a usefu usefull tool for determ determining ining the sources of error in a Knoop or Vickers hardness testing machine. It is recommended that testing machines undergo direct verification periodically to make certain that errors in one component of the machine are not being offset by errors in another component.

NOTE A1.4—It is permissible to verify the offset by using a microscope with at least 500× magnification to view an indentation created by the indenter and compare the offset length to a known dimension.

A1.3.2  Verification of the Test Forces— For For each Knoop and Vickers hardness scale, or both, that will be used, the corresponding test force shall be measured. The test forces shall be measu mea sure red d by mea means ns of a Cla Class ss A ela elasti sticc fo forc rcee me measu asuri ring ng instrument having an accuracy of at least 0.25 %, as described in Practice E74 E74.. A1.3 A1 .3.2 .2.1 .1 Make Make th thre reee me meas asur urem emen ents ts of ea each ch fo forc rce. e. Th Thee forces shall be measured as they are applied during testing; however, longer dwell times are allowed when necessary to enable the measur measuring ing device to obtain accurate measurements. measurements. A1.3.2 A1. 3.2.2 .2 Eac Each h tes testt for force ce P   shall shall mee meett the req requir uireme ements nts specified in Table in  Table A1.2. A1.2.

(3)  The four faces of the diamond shall be equally inclined to the axis of the indenter to within 6 30' A1.3.5.2   Knoop Indenter: (1)  T  The he Kno Knoop op dia diamon mond d ind indent enters ers (se (seee   Fig. 2, 2,   used for standard testing and indirect verifications shall have included longitudinal edge angle A of 172° 30' 60.10° (6’) (2)  The corresponding angle B = 130° must be contained within the dimensions listed in  Table A1.3 and A1.3  and graphically as described descri bed by by Fig.  Fig. A1.1. A1.1. (3)  The indenter constant (cp  ) shall be 0.07028 within 6 1 % ( 0.06958 ≤  c p ≤  0.07098). (4)   The offset shall not be more than 1 µm in length for indentations greater than 15 µm in length, as shown in  Fig. 2. 2. For shorter inden indentations tations the of offset fset shoul should d be prop proportion ortionally ally less. (See Note (See  Note A1.4.) A1.4.) (5)  The four faces of the diamond shall be equally inclined to the axis of the indenter to within 6 30'.

A1.3.3  Verification of the Indentation Measuring System—  Each magnification of the measuring device used to determine the diagonal of the indentation shall be verified at five evenly spaced intervals over the working range by comparison with an accurate scale such as a stage micrometer. The accuracy of the certified line interval of the stage micrometer shall be 0.1 µm or 0.05 % of any interval, which ever is greater. Throughout the range covered, the difference between the reading of the device and of the stage shall not exceed 0.4 µm or 0.5 % , which ever is greater.

Direct Verifica erification tion Failur Failure—  e— If A1.3.6   Direct I f an any y of th thee di dire rect ct verifications verific ations fail the specified requirements, requirements, the testing machine shall not be used until it is adjust adjusted ed or repair repaired. ed. If the test forces, indentation measuring system or testing cycle may have been affected by an adjustment or repair, the affected components shall be verified again by a direct verification.

Verification tion of the Testing Cycle— The A1.3.4   Verifica The testing machine shall be verified to be capable of meeting the testing cycle cyc le tol tolera erance ncess spe specifie cified d in 8.6 8.6..   Direct Direct ver verifica ificatio tion n of the testing cycle is to be verified by the testing machine manufacturer at the time of manufacture, or when the testing machine is returned to the manufacturer for repair, or when a problem with the testing cycle is suspected. Verification of the testing cycle is recommended but not required as part of the direct verification at other times.

A1.3.7   Indirect Verification— Following Following a successful direct verification, verific ation, an indir indirect ect verifi verification cation according to A1.4 to  A1.4 shall  shall be performed.

A1.4 Indirect Verification Verification A1.4.1 An indirect verification A1.4.1 verification of the testing machine shall be performed in accordance with the schedule given in  Table A1.1.. Indirect verifications may be required more frequently A1.1 than stated in Table in  Table A1.1 and A1.1  and should be based on the usage of  the testing machine.

NOTE   A1.3—Ins A1.3—Instrume truments nts that have timing contro controlled lled by softw software are or other nonadjustable components do not have to be verified providing that the design has been proven to produce the correct time cycles.

A1.3.5   Verifica T he ge geom ometr etry y of ea each ch Verification tion of Inden Indenters—  ters— The indenter shall be directly verified when new before placing into service ser vice.. The dev device ice use used d to ver verify ify the ind indente enterr ang angles les sha shall ll havee a max hav maximu imum m unc uncerta ertaint inty y of  6   40 mi min. n. Th Thee in inde dent nter er geometry tolerances are specified as follows: A1.3.5.1   Vickers Indenter: ickers ers dia diamon mond d ind indent enter er,, see   Fig. Fig. 1,   used used for (1)   The Vick standar stan dard d tes testing ting and ind indire irect ct ver verifica ificatio tions ns sha shall ll hav havee fac facee angles of 136° 0’ 6 30’. As an alternate, the 136° face angles may be verified by measuring the angles between the opposite edges rather than the faces. When measured, the edge angles

A1.4.2 A1. 4.2 The testing testing mac machin hinee sha shall ll be ver verifie ified d for each test force and for each indenter that will be used prior to the next indirec ind irectt ver verifica ification tion.. Har Hardne dness ss test testss mad madee usi using ng Kno Knoop op or Vickers hardness scales that have not been verified within the schedule given in Table in  Table A1.1 do A1.1  do not meet this standard. A1.4.3 Stand A1.4.3 Standardized ardized test blocks used for the indir indirect ect verification shall meet the requirements of  Annex   Annex A2. A2 . NOTE A1.5—It is recognized that appropriate standardized test blocks are not available for all geometric shapes, materials, or hardness ranges.

TABLE A1.3 Angular Tolerances for Knoop Indenters TABLE A1.2 Accuracy of Applied Forces Applied Force, gf P < 20 0 P $ 20 0

A Angle, °

Accuracy, % 1 .5 1 .0

1 7 2 .4 1 7 2 .6

18

B Angle, ° M i ni m um

M a x i mu m

12 8. 97 13 0. 15

1 2 9 .8 5 1 3 1 .0 2

E384 − 11

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A1.4.7  Indirect Verification Procedure— The The indirect verification procedure is designed to verify that for all of the Knoop and Vickers Vickers hardness hardness scales to be used, each test force is being accurately applied, each indenter is correct, and the measuring device is calibrated correctly for the range of indentation sizes thatt the tha these se scal scales es pro produc duce. e. Thi Thiss is acco accompl mplish ished ed by mak making ing hardness measurements on test blocks that have been calibrated for appropriate Knoop and Vickers hardness scales that employ each of the corresponding test forces. A1.4.7.1 A1.4.7 .1 The test testing ing machine machine sha shall ll be ver verified ified with the user’s indenter(s) normally used for testing. A1.4.7.2 A minimum of two standardized test blocks shall A1.4.7.2 be us used ed fo forr th thee ve veri rific ficati ation on of th thee te testi sting ng ma mach chin ine. e. Th Thee hardness values and hardness scales of the test blocks shall be chosen such that the following criteria are met:

FIG. A1.1 Schematic Representing Representing the Accept Acceptable able Regions of Knoop Indenter Angles

A1.4.7.3 A1.4.7 .3 Each test force will be used.

A1.4.4 The indenter(s) A1.4.4 indenter(s) to be used for the indirect verification shall meet the requirements of  A1.3.5.   A1.3.5.

A1.4.7.4 A1.4.7 .4 At least one hardness test block calibrated calibrated according to Annex to  Annex A2, A2 ,  shall be used for each scale to be verified.

A1.4.5   As-found I t is re reco comm mmen ende ded d th that at th thee As-found Condi Condition—  tion— It as-found condition of the testing machine be assessed as part of  an indirect verification. This is important for documenting the historical performance of the machine. This procedure should be conducted by the verification agency prior to any cleaning, maintenance, mainten ance, adjust adjustments, ments, or repair repairs. s. A1.4.5 A1. 4.5.1 .1 The asas-fou found nd con condit dition ion of the tes testing ting mach machine ine shall be determined with the user’s indenter that is normally used with the testing machine. One or more standardized test blocks in the range of normal testing should be used for each Knoop Kno op or Vicke ickers rs har hardne dness ss scal scalee tha thatt will und underg ergo o ind indirec irectt verification. A1.4.5 A1. 4.5.2 .2 On eac each h stan standar dardiz dized ed tes testt blo block, ck, mak makee at leas leastt three measurements distributed uniformly over the test surface. Let d 1, d 2, ..., d n   be the inden indentation tation diagonal measur measurement ement ¯  values, and  d  be the average of the measurements.

A1.4.7.5 At least two of the blocks shall be from different A1.4.7.5 different hardne har dness ss ran ranges ges,, low low,, mid or hig high h har hardne dness ss as spe specifi cified ed in Table A1.4. A1.4.   The hardness difference between the two blocks used for verification shall be a minimum of 100 points. For example, if only one scale is to be verified, and one block  having a hardness of 220 is used to verify the low range, then a block having a minimum hardness of 320 shall be used to verify the mid hardness range. See more examples below of the test blocks needed when performing multi-scale verifications. A1.4.7.6 The highest test force shall be verified on a block  A1.4.7.6 from the lower of the chosen hardness ranges to produce the largest indentation size, and the lowest test force shall be used on the block from the higher of the chosen hardness ranges to produc pro ducee the sma smalles llestt ind indent entatio ation n siz size. e. The two ext extrem remes es of  indenta ind entatio tion n siz sizee will ver verify ify the cap capabi ability lity of the mea measur suring ing device.

NOTE A1.6—When testing at low forces it may be necessary to increase the number of tests in order to obtain more consistent results.

 Example 1— A testing machine is to be verified for the HV 0.5 an 0.5 and d HK 1 sc scale ales. s. Two tes testt bl bloc ocks ks ar aree ch chos osen en fo forr th thee verifica ver ification tion:: 450 HV 0.5 (mid-ran (mid-range) ge) and 200 HK 1 (lo (lowwrange). range ). In this case, both of the test force forcess are verifie verified d by using only two blocks. The highest test force (1000 gf) is used on a low-range hardness block, and the lowest test force (500 gf) is used on a mid-range test block, which is the higher of the two hardness ranges.

A1.4.5.3 Determ A1.4.5.3 Determine ine the repeatability repeatability R ind  and the error  E  in the performance of the testing machine for each standardized test block that is meas measure ured d usi using ng   Eq A1.1 and   Eq A1.3 in section A1.7 section  A1.7.. A1.4.5.4 A1.4. 5.4 The repeatability Rind   and the error E   should be within the tolerances of  Table   Table A1.5 or A1.5  or  Table A1.6. A1.6. A1.4.5.5 A1.4. 5.5 If the calculated values values of the repeat repeatability ability R ind  or the err error or E   fall fall out outsid sidee the spe specifie cified d tol tolera erance nces, s, thi thiss is an indication that the hardness tests made since the last indirect verification may be suspect.

 Example 2— A testing machine is to be verified for the HK 0.1, HV 0.3 and HV 1 scales. Three test blocks are chosen for the verification: 720 HK 0.1 (high-range), 480 HV 0.3 (midrange) and 180 HV 1 (low-range). In this case, there are three test forces that must be verified. The highest test force (1000 gf) is used on a low-range hardness block, and the lowest test force (100 gf) scale is used on the high-range test block. The midd mi ddle le tes testt fo forc rcee (3 (300 00 gf gf)) sc scale ale could could be us used ed on eit eithe herr a low-range or mid-range test block.

Maintenance nance—  — Perform A1.4.6   Cleaning and Mainte Perform cleaning and routine maintenance of the testing machine when required in accordance with the manufacturer’s specifications and instructions.

TABLE A1.4 Hardness Ranges Used for Indirect Verification Range Low Mi d High

K no o p

Vickers

< 25 0 25 0– 6 50 > 65 0

< 24 0 24 0 – 60 0 > 600

 Example 3–  A   A testing machine is to be verified for the HV 0.5 an 0.5 and d HV 1 sc scale ales. s. Two test bl bloc ocks ks ar aree ch chos osen en fo forr th thee verification: 150 HV (low-range) and 450 HV (mid-range). In this case, both of the test forces are verified by using only two blocks. The highest test force (1000 gf) is used on a low-range 19

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´1

TABLE A1.5 Repeatability and Error of Test Machines—Indirect Verification by Standardized Test Blocks Based on Measured Diagonal Lengths Using Test Forces 1000 gf and Less A Force, gf

R ind  Maximum Repeatability (%)

E  Maximum Error (%)B 

1 # P <100 1 00 # P # 1 0 00

13 13

3 3

13 5 4

2 2 2

8 4 3

2 2 2

Hardness Range of Standardized Test Blocks

A

K n oo p

Vickers

HK > 0 HK < 100

HV > 0 HV < 100

100 # HK # 250 250 < HK # 650 HK > 650

100 # HV # 240 240 < HV # 600 HV > 600

100 # HK # 250 250 < HK # 650 HK > 650

100 # HV # 240 240 < HV # 600 HV > 600

10 0

5 00

#

#

P < 5 00

P

#

1 0 00

In all cases, the repeatability is satisfactory if (d  (d max –d min ) is equal to 1 µm or less. In all cases, the error is satisfactory if E  if E  from  from Eq  Eq A1.2) A1.2)  is equal to 0.5µm or less.

B 

TABLE A1.6 Repeatability and Error of Test Machines—Indirect Verification by Standardized Test Blocks Based on Measured Diagonal Lengths Using Test Forces greater than 1000 gf A Hardness Range of Standardized Test Blocks

Force, gf

R ind  Maximum Repeatability (%)

E  Maximum Error (%)B 

100 to # 240 > 240 to # 600 >600

> 10 0 0 > 10 0 0 > 1 00 0

4 3 2

2 2 2

#

A

In all cases, the repeatability is satisfactory if (d  (d max –d min ) is equal to 1 µm or less. In all cases, the error is satisfactory if E  if E  from  from Eq  Eq A1.2) A1.2)  is equal to 0.5µm or less.

B 

hardness block, and the lowest test force (500 gf) is used on a mid-range test block, which is the higher of the two hardness ranges  Example 4–  A   A testing machine is to be verified for the HV 1000 gf, HV 3000 gf and HV 5000 gf scales. Three test blocks are chosen for the verification: 180 HV (low-range), 480 HV (mid-range) and 720 HV (high-range). In this case, there are three test forces that must be verified. The highest test force (5000 gf) is used on a low-range hardness block, and the lowest test force (1000 gf) scale is used on the high-range test block. The middle test force (3000 gf) scale could be used on either a low-range or mid-range test block. A1.4.7.7 A1.4. 7.7 On each standardized standardized test block, make five measurements distributed uniformly over the test surface. Let d 1, d 2, ...,  d 5  be the five indentation diagonal measurement values, and d¯ be the average of the five measurements. Determine the repeatability Rind   and the error E   in the performance of the testing machine using Eq using Eq A1 A1.1 .1 and  and Eq  Eq A1 A1.3 .3 in  in section A1.7 section A1.7,, for each hardness level of each Knoop and Vickers hardness scale to be verified. The repeatability Rin ind  d   and the error E  shall be within the tolerances of  Table   Table A1.5 or A1.5  or  Table A1.6. A1.6. A1.4.7.8 A1.4. 7.8 If the measurements measurements of error error  E  or   or repeatability R ind  using the user’s indenter fall outside of the specified tolerances, the indirect verification measurements may be repeated using a different indenter.

A1.4.7 A1. 4.7.9 .9 The ind indire irect ct ver verific ificatio ation n sha shall ll be app approv roved ed onl only y when the testing machine measurements of repeatability and error meet the specified tolerances with the user’s indenter. A1.4.8 In cases where where it is necess necessary ary to replace the indenter indenter during dur ing the per period iod bet betwee ween n ind indirec irectt ver verific ificatio ations, ns, the new inde in dent nter er mu must st be ve verifi rified ed fo forr us usee wi with th th thee sp spec ecifi ificc tes testin ting g machine. The user shall perform the verification by following the as-found procedures given in  A1.4.5  A1.4.5..  If the repeatability,  Rind , and error, E , values fall within the tolerances in   Table A1.5 or or Table  Table A1.6 the A1.6  the indenter can be used. A1.4.9 A1. 4.9 Whe When n the com combin binatio ation n of blo block ck har hardne dness ss and test force produces indentations with diagonals less than 20 µm long, indirect verification using standardized test blocks is not recommended recomm ended.. In these situatio situations, ns, the inden indentation tation measurement error represents a significant proportion of the diagonal length. This can lead to substantial deviations in hardness from the stat stated ed val value. ue. Exa Exampl mples es of the these se err errors ors are con contain tained ed in Section 10 and   Tab Table less 5 an and d 6.   Also Also se seee   Appendi Appendix x X5 X5,, Recommendations for Light Force Microindentation Hardness Testing.

A1.5 Weekly Verification Verification A1.5.1 The weekly verification A1.5.1 verification is intended intended as a tool for the user us er to mo moni nito torr th thee pe perf rfor orma manc ncee of th thee te testi sting ng ma mach chin inee

20

E384 − 11 between ind between indire irect ct ver verific ificatio ations. ns. At a min minimu imum, m, the wee weekly kly verification shall be performed in accordance with the schedule given in T in Table able A1.1 A1.1 for  for each Knoop and Vickers hardness scale that will be used. The weekly procedure shall be preformed whenever the testing machine is moved.

´1

A1.6.2.3 Identi A1.6.2.3 Identification fication of the hardn hardness ess testing machine and the indenters used. A1.6.2.4 A1.6.2 .4 Means of verification (test blocks, elastic proving devices,etc.) device s,etc.) with statemen statements ts definin defining g traceab traceability ility to a nation national al standard. A1.6.2.5 The Knoop and Vickers hardness hardness scale(s) verified. A1.6.2.6 A1.6.2 .6 The individual individual or calculat calculated ed results used to deter deter-mine whether the testing machine meets the requirements of  the verification performed. Measurements made to determine the as-found condition of the testing machine shall be included whenever they are made. A1.6.2.7 Description of adjustments or maintenance done to the testing machine. A1.6.2.8 A1.6.2 .8 Date of verification and reference reference to the verify verifying ing agency or department. A1.6.2.9 A1.6.2 .9 Signat Signature ure of the person performing performing the verific verificaation.

A1.5.2 A1.5 .2 It is re reco comm mmen ende ded d th that at th thee we week ekly ly ve veri rific ficati ation on procedures be performed whenever the indenter or test force is changed. A1.5.3   Weekly Verification Procedures— The The procedures to use when performing a weekly verification are as follows. A1.5.3.1 A1.5. 3.1 At least one standardized standardized test block that meets the requirements requir ements of  of    Annex A2   shall shall be use used d for each har hardne dness ss scale to be used. When test blocks are commercially available, thee ha th hard rdne ness ss le leve vell of th thee te test st bl bloc ocks ks sh shal alll be ch chos osen en at approximately the same hardness value as the material to be measured. A1.5.3.2 A1.5. 3.2 The indenter indenter to be used for the weekly verificatio verification n shall be the indenter that is normally used for testing. A1.5.3.3 A1.5. 3.3 Befor Beforee perfo performing rming the weekly verification verification tests, ensure that the testing machine is working freely, the stage and test block are clea clean, n, and the meas measuri uring ng dev device ice is pro proper perly ly adjusted and zeroed. A1.5.3 A1. 5.3.4 .4 Mak Makee at leas leastt thr three ee har hardne dness ss mea measur suremen ements ts on each of the verification test blocks. The tests shall be distributed uniformly over the surface of the test blocks. ¯  be the average of the measurements. DeterA1.5.3.5 A1.5. 3.5 Let d  mine the error E  in the performance of the testing machine using   Eq A1.3   for each standardized test block that is measured. A1.5.3 A1. 5.3.6 .6 If the err error or E   calcula calculated ted for each test block is within the tolerances given in  Table A1.5 or  Table A1.6, A1.6, the testing machine with the indenter may be regarded as performing satisfactorily. A1.5.3.7 A1.5. 3.7 If the error error  E  calculated for any of the test blocks is out outsid sidee the tole toleran rances, ces, fol follow low the man manufa ufactu cturer rerss tro troubl ublee shooting recommendations and repeat the test. If the average of  the hardness measurements again falls outside of tolerances for any of the test blocks, an indirect verification shall be performed. A1.5 A1 .5.3 .3.8 .8 Whene Wheneve verr a te testi sting ng mac machi hine ne fa fail ilss a we week ekly ly verification, the hardness tests made since the last valid weekly verification may be suspect.

A1.7 Exam Example ple Calculations Calculations of Repeat Repeatability ability and Error A1.7.1   Repeatability of Knoop and Vickers Hardness Testers: A1.7.1.1 Repeatability, Rind , of the tester (%) is calculated by the following equation:  R ind  5 100

S

 d max 2 d min

H d 

D

 

(A1.1)

where d max  d min Hd 

= is th thee lo long nges estt of th thee fiv fivee di diag agon onal alss (o (orr me mean an diagonals), = is the shor shortes testt of the five five diagon diagonals, als, and and =   is the mean diagonal length.

The repeatability is acceptable if it meets the requirements given in Table in  Table A1.5 or or Table  Table A1.6. A1.6. A1.7.1 A1. 7.1.2 .2 The fol follow lowing ing is an exa exampl mplee of a rep repeata eatabil bility ity calculation. Assume that five Knoop indentations were made on a test block with a nominal hardness of 420 HK at the certified block test force of 300 gf and that the five readings are d 1  = 103.9,  d 2  = 104.8,  d 3  = 102.3,  d  4  = 102.8 and  d 5  = 100.2 µm, respectively. Therefore,  d max –  d min = 104.8 – 100.2 = 4.6 µm and Rind  = 100(4.6)/102.8 = 4.47 %. According to  Table A1.5,, the repeatability for a test block with a hardness >250 to A1.5 650 HK should be ≤5 %. In this example, the tester met the repeatability requirement for this hardness test block and force. Howeve How everr, if the these se diag diagona onals ls had been obt obtaine ained d usi using ng a test block with a nominal hardness of 700 HK and a certified test force of 300 gf, then the repeatability would be inadequate as Table A1.5 requires A1.5  requires Rind ≤  4 % for a hardness >650 HK.

NOTE  A1.7—It is highly recommended that the results obtained from the weekly verifi verification cation testing be recor recorded ded using accept accepted ed Statis Statistical tical Process Control techniques, such as, but not limited to, X -bar -bar (measurement averages) and  R -charts (measurement ranges), and histograms.

A1.6 Verification Report

A1.7.2   Error of Knoop and Vickers Hardness Testers: A1.7.2.1 A1.7. 2.1 The error, error, E , of the machine is:

A1.6.1 A1.6 .1 A ve veri rific ficati ation on re repo port rt is re requ quir ired ed fo forr di dire rect ct an and d indirect indire ct verific verifications. ations. A verification verification report is not required for a weekly verification.

 E  5 H d  2 d s

A1.6.2 A1. 6.2 The ver verific ificatio ation n rep report ort sha shall ll be pro produc duced ed by the person performing the verification and include the following info in form rmati ation on wh when en av avai ailab lable le as a re resu sult lt of th thee ve veri rific ficati ation on performed. A1.6.2.1 A1.6. 2.1 Refere Reference nce to this ASTM ASTM test method method.. A1.6.2.2 A1.6. 2.2 Metho Method d of verific verification. ation.

 

(A1.2)

The pe The perc rcen entt er erro rorr, % E , is cal calcu culat lated ed by th thee fo follo llowi wing ng equation: % E  5 100

Where: 21

S

H 2 d   d  s d s

D

 

(A1.3)

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H 5 102.8 µ m , ( d  H 2 d  ) = 102.8 – 100.8 = 2.0 µm. 300gf). Since d  s Thus, E   = 1.98 %. In this case, the percent error meets the maximum of  6 2 %, which is greater than 6 0.5 µm. For this H 2 d   must be > 6 2.016 µm for the error to be above example,  d  s the limit of  6 2 %.

H d 

= is the meas measure ured d mean diagon diagonal al length length in µm, and reported certified mean mean diagonal diagonal length, µm. µm. d s = is the reported A1.7.2.2 A1.7. 2.2 The error between the certified certified mean diagonal and the measured mean diagonal shall not exceed the tolerances in Table A1.5, A1.5, or 6 0.5 µm, whichever is greater. A1.7.2.3 A1.7. 2.3 The following following is an example of an error calculacalculation based on the data given in  A1.7.1.2  A1.7.1.2,,  and a certified mean diagonal length for the test block, d s, of 100.8 µm (420 HK

A2. REQUIREME REQUIREMENTS NTS FOR ST STANDARDIZ ANDARDIZED ED HARDNESS TEST BLOCKS USED TO VERIFY KNOOP AND VICKERS HARDNESS TEST MACHINES

A2.1 Scope

A2.3.5 The test block test surface shall be polished accordaccording in g to th thee pr proc oced edur ures es in Me Meth thod odss E3   to yi yiel eld d th thee tr true ue microstructure, free from scratches that would interfere with production of the indentation or measurement of the indentation diagonal(s). The mean, centerline average, surface roughness height measurement of the test surface shall not exceed 0.1 µm (4 µin.).

A2.1.1 This annex describes the manuf A2.1.1 manufacture, acture, standardizastandardization procedure, uniformity, marking and certification of standardized hardness test blocks used to verify Knoop and Vickers scale hardness test machines. Requirements for the standardizing izi ng lab labor orat ator ory y an and d th thee sta stand ndar ardi dizi zing ng ma mach chin ines es ar aree als also o defined.

A2.3.6 Repolish A2.3.6 Repolishing ing of the tes testt blo block ck wil willl inv invalid alidate ate the standar stan dardiz dizatio ation n and is not rec recomm ommend ended. ed. Clea Cleanin ning g of the polished test block surface is often required in normal usage but must not alter the hardness or quality of the polished test surface.

NOTE A2.1—Test blocks that were standardized prior to the release of  this edition of E384 may be used to satisfy the requirements of this edition provid pro vided ed tha thatt the they y mee meett all of the req requir uireme ements nts of E92 E92.82 .82 (2003) (2003) or E384–09.

A2.2 Accreditation

A2.4 Standardizing Tester Tester Requirements

A2.2.1 The agency conducting A2.2.1 conducting the standardizations standardizations of test blocks blo cks sha shall ll be acc accred redited ited to the req requir uireme ements nts of ISO ISO/IE /IEC C 17025 (or an equivalent) by an accrediting body recognized by the Int Intern ernatio ational nal Lab Labora orator tory y Accr Accredit editatio ation n Coo Cooper peratio ation n (ILAC) as operating to the requirements of ISO/IEC 17011. The stan standar dardiz dizing ing age agency ncy sha shall ll hav havee a cert certifica ificate/s te/scop copee of  accreditation accredi tation stating the Knoo Knoop p and Vickers Vickers hardn hardness ess scales that are cov covere ered d by the accreditat accreditation ion,, and the stan standar dards ds to which the test block standardizations are traceable.

A2.4.1 The stand standardizin ardizing g tester shall comply with   Annex A1 with A1  with the following additional requirements: A2.4.2 Direct A2.4.2 Direct ver verific ificatio ations ns acco accordi rding ng to   A1.3, A1.3,   shall shall be performed every 12 months. A2.4.3 Indir A2.4.3 Indirect ect verifications verifications should be perfo performed rmed using test blocks blo cks trac traceab eable le to nat nation ional al sta standa ndards rds whe whenev never er the they y are available. NOTE A2.3—Primary standardized test blocks are available as Standard Reference Material from NIST, Gaithersburg, MD 20899.

NOTE   A2.2—A A2.2—Accr ccredi editati tation on is a new req requir uireme ement nt sta starti rting ng wit with h thi thiss edition of the standard.

A2.4.4 The Vickers Vickers indenter shall have the following following angles and tolerances: A2.4 A2 .4.4 .4.1 .1 Th Thee fa face ce an angl gles es sh shall all be 13 136° 6° 0’ 6   6’. 6’. As an alternate, the 136° face angles may be verified by measuring the angles between the opposite edges rather than the faces. When measured, the edge angles shall be 148° 6’ 36” 6 9’. A2.4.4 A2. 4.4.2 .2 The face ang angles les shall be equ equally ally inclined inclined to the axis of the indenter within 6   15’. As an alternate, when the edge angles are measured, they shall be equally inclined to the axis of the indenter within 6 30’. A2.4.4 A2. 4.4.3 .3 The of offse fsett sho should uld not exc exceed eed 0.3 µm, see   Note A1.4.. A1.4

A2.3 Test Block Manufacture A2.3.1 A2.3. 1 The test block thickness thickness shall be greater than twenty times the depth of the indentation made with the certified test force. A2.3.2 The test block material and manufacturing A2.3.2 manufacturing processes processes shall be chosen to produce the required degree of homogeneity, structural stability and uniformity of hardness at the prepared surface. A2.3.3 Ferro A2.3.3 Ferromagnet magnetic ic test blocks shall be demagnetized demagnetized by the manufacturer and shall be maintained in that condition by the user.

A2.4.5 The Knoop indenter indenter shall have an indenter constant constant of 0.07028 6 0.5 %. The offset should not exceed 0.5 µm, see Note A1.4. A1.4.

A2.3.4 The test blo A2.3.4 block ck sup suppor portt sur surfac facee sha shall ll hav havee a fine finely ly ground surface finish. The maximum deviation from flatness of  thee tes th testt an and d su supp ppor ortt su surf rfac aces es sh shall all no nott ex excee ceed d 5 µm µm.. Th Thee maximum error in parallelism shall not exceed 15 µm in 30 mm.

A2.4.6 The test for A2.4.6 force ce app applica licatio tion n time shall be bet between ween 5 and 7 seconds. The test force dwell time shall be between 13 and 15 seconds. 22

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TABLE A2.1 Repeatability of Diagonal Measurements for Standardized Standardize d Test Blocks calibra calibrated ted in the micro force ranges (1000g and less)A

A2.4.7 The indentation A2.4.7 indentation measuring system system shall be verified according to A1.3.3 to  A1.3.3.. The difference between the reading device and the stage micrometer shall not exceed 0.2 µm or 0.25 %, which ever is greater.

Hardne Har dness ss Ran Range ge of Sta Standa ndardi rdized zed Test Blo Blocks cks

Force, For ce, gf

R , %, Less Than

A2.5 Test Block Standardization Procedure

K n oo p

Vickers

A2.5.1 The standardization A2.5.1 standardization of the hardness test blocks shall be performed with a Knoop or Vickers hardness test machine that meets all of the requirements of  A2.4 of  A2.4..

HK > 0

HV > 0

1 # P < 100

12

HK < 100

HV < 100

1 00 < P # 1 00 0

12

100 # HK # 250 250 < HK # 650 HK > 650

100 # HV # 240 240 < HV # 600 HV > 600

10 0

12 4 3

100 # HK # 250 250 < HK # 650 HK > 650

100 # HV # 240 240 < HV # 600 HV > 600

50 0

A2.5.2 Mak A2.5.2 Makee a min minimu imum m of five har hardne dness ss meas measure uremen ments ts arra ar rang nged ed as fo foll llow owss on th thee su surf rfac acee of th thee tes testt bl bloc ockk- on onee indentation near the center of each of the four quadrants of the block and the fifth near the center of the test block. When more than five indents are done, they shall be arranged around the test surface in a similar manner.

#

P < 5 00

P

#

#

1 0 00

7 3 2

A

In all cases, the repeatability limit is the greater of the percentage given or 0.001mm (1 µm).

A2.5.3 A2.5. 3 Adjus Adjustt the illumin illumination ation for the measuring measuring system to produce uniform intensity over the field of view and optimum cont co ntra rast st be betwe tween en th thee in inde dent ntss an and d th thee bl bloc ock k su surf rface ace (s (see ee Appendix X1). X1).

TABLE A2.2 Repeatability of Diagonal Measurements for Standardized Test Standardized Test Block Blocks s Calibr Calibrated ated in the Macro Force Ranges (over 1000g)A

A2.5.4 A2. 5.4 Measure Measure the Kno Knoop op dia diagon gonal al len length gth,, or ave averag ragee Vickers diagonal length of each indentation. Record the data by location and by block.

A2.6 Repeatability of the Standardized Test Block A2.6.1 Calculate A2.6.1 Calculate the mea mean n of the dia diagon gonals, als, or ave averag ragee diagonals, for all of the indentations.

Hardness Range of Standardized Test Blocks

Forc Fo rce, e, kg kgff

Maxi Ma ximu mum m R%

10 0 t o 2 40 i n c l u s i v e Over 240 to 600 inclusive Over 600

>1 >1 >1

3 2 1 .5

A

In all cases, the repeatability limit is the greater of the percentage given or 0.001mm (1 µm).

A2.6.2 A2.6. 2 The repeat repeatability ability,, R, of th thee in inde dent ntat atio ion n si size ze an and, d, therefore, of the hardness, is calculated in the manner described in   A1.4.5.3   by Eq A1 A1.1 .1.. Ca Calcu lcula late te th thee me mean an of all of th thee measured measur ed diago diagonals, nals, or averag averagee diago diagonals, nals, d, and determine dmax  and d min, the longest and shortest of the measurements, respectively. R is a measure of the hardness homogeneity of the test block, although R is influenced by all of the variables that affect the repeatability of test results.

A2.7.3 Each of the calibration measurements measurements shall be identified so that they can be located by the user.

A2.8 Certification of Standardized Test Test Block A2.8.1 At a min A2.8.1 minimu imum m the cert certific ificate ate acco accompa mpanyi nying ng eac each h standardized standa rdized hardness hardness test block shall include the follow following ing information: (See Note (See  Note A2.1. A2.1.) A2.8 A2 .8.1 .1.1 .1 Th Thee si size ze an and d lo loca catio tion n of al alll th thee sta stand ndar ardi dizin zing g indents. A2.8. A2 .8.1.2 1.2 The The ari arithm thmeti eticc mea mean n of all the ind indent entati ation on diagonals, and the corresponding hardness value. A2.8.1.3 A2.8. 1.3 The test force, force, A2.8.1.4 A2.8. 1.4 The serial number number of the test block, A2.8.1.5 A2.8. 1.5 The name of the manufacturer manufacturer and standardizing standardizing organization, A2.8.1.6 A2.8. 1.6 The magnification magnification used to measur measuree the standardstandardizing inden indents, ts, A2.8.1.7 A2.8. 1.7 The date of standa standardizat rdization, ion, A2.8.1.8 A2.8. 1.8 Referen Reference ce to this ASTM test method, A2.8.1.9 A2.8. 1.9 Value of the uncertainty uncertainty in the standardized standardized value with an explanation of how the uncertainty was calculated, A2.8.1.10 A2.8. 1.10 Accred Accreditation itation agency certific certification ation numbe numberr.

A2.6.3   Table A2.1 and   Table A2.2   list the required maximum  R  values for test blocks by indenter type, test force range and hardness range. The measured R   value must be less than these limits for it to be considered sufficiently uniform enough in hardness to function as a standardized test block.

A2.7 Marking A2.7.1 A2. 7.1 Each block shall be per perman manentl ently y mar marked ked wit with h an appropriate identifying serial number and on the test surface either the supplier’s name/mark or thickness or identification mark. A2.7.2 A2.7. 2 When the test blocks are encapsulated encapsulated in a mounting medium, the information contained in A2.7.1 in  A2.7.1 shall  shall be permanently placed on the surface of the medium that contains the test surface. surface. The reported reported test block thic thickne kness ss sha shall ll be the thickness of the mounting medium, not the thickness of the encapsulated block.

23

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APPENDIXES (Nonmandatory Information) X1. ADJUSTMEN ADJUSTMENT T OF KÖHLER ILLUMINATION ILLUMINATION SYSTEMS X1.1 While some optical systems are permanently permanently aligned, others have means for minor adjustments. To gain the utmost in resolu res olutio tion, n, the ope operat rator or sho should uld mak makee the fol follow lowing ing adj adjust ust-ments:

X1.1.5 Rem X1.1.5 Remove ove the eye eyepie piece ce and examine examine the rea rearr foc focal al plane of the objective. If all the components are in their proper places, the source of illumination and the aperture diaphragm will appear in sharp focus. X1.1.6 Full-a Full-apertu perture re diaph diaphragm ragm is prefe preferred rred for maximu maximum m resolving power. If glare is excessive, reduce the aperture, but never use less than the 3 ⁄ 4  opening since resolution would be decrea dec reased sed and dif diffra fractio ction n phe phenom nomena ena cou could ld lead to fals falsee measurements.

X1.1.1 X1.1 .1 Fo Focu cuss th thee su surf rface ace of a fla flatt po polis lishe hed d sp spec ecime imen n to critical sharpness. X1.1.2 X1.1. 2 Center the illumination illumination source. X1.1.3 X1.1. 3 Central Centrally ly align field and aperture diaphragms. diaphragms.

X1.1.7 If the light is too strong for eye comfort, reduce reduce the intensity by the use of an appropriate neutral density filter or rheostat control.

X1.1.4 Open the field diaphragm X1.1.4 diaphragm so that it just disapp disappears ears from the field of view.

X2. CORRELATION OF MICROINDENTA MICROINDENTATION TION HARDNESS TEST DATA DATA BETWEEN LABORATORIES

X2.1 Scope

X2.2.7 A minimum minimum number of indentations indentations shall be established. This shall conform to acceptable statistical methods of  analysis, in accordance with Practice E122 Practice  E122..

X2.1.1 This procedure provides provides guidance in the comparison comparison of mic micro roin inde dent ntati ation on ha hard rdne ness ss te test st da data ta fr from om two or mo more re laboratories.

X2.2.8 Each test specimen shall be indented indented and measured by the laboratory having prepared it, then sent with the data for testing in the other laboratory or laboratories. X2.2.8 X2. 2.8.1 .1 Aft After er the spe specime cimens ns hav havee bee been n exc exchan hanged ged,, eac each h laboratory shall measure and record the indentations applied by the originating laboratory in a manner identical to the initial measurements. X2.2.8.2 X2.2.8 .2 Each laboratory laboratory shall then repeat the inden indentation tation and measuring procedures, as performed in  X2.2.5  X2.2.5 and  and X2.2.6  X2.2.6,, before sending the data and specimen to the remaining laboratory or labor laboratories atories.. X2.2.8.3 X2.2. 8.3 Each laboratory laboratory shall determine a set of microindentation hardness values from the specimen they prepared, as well as sets of values they obtained by indenting and measuring specimens prepared by the other laboratory or laboratories.

X2.2 Correlation Procedure X2.2.1 X2. 2.1 All lab labora orator tories ies sha shall ll firs firstt esta establis blish h that the their ir test equipment conforms to the requirements in Test Method E384. X2.2.2 The specimens X2.2.2 specimens shall be taken from adjoining adjoining areas of the larger specimen prior to being sent to the cooperating laboratories for specimen preparation and testing. X2.2.3 The specimens shall be prepa X2.2.3 prepared red for microindentamicroindentation hardness by two or more labora laboratories tories using essentially essentially the samee pr sam proc oced edur ures es.. If th thee sp spec ecime imens ns ar aree ca capa pabl blee of be bein ing g prepar pre pared ed as met metallo allogra graphi phicc spe specim cimens ens,, esta establi blishe shed d AST ASTM M procedures shall be maintained uniformly among the laboratories as follows: X2.2.3.1 X2.2. 3.1 The same surfaces shall shall be expo exposed sed for the microindentation indent ation hardness hardness test. This is to ensure that grain direction, direction, if a characteristic, is taken into consideration. X2.2.3.2 X2.2. 3.2 The surface preparation preparation of the specim specimens ens shall be in accordance with Methods E3 E3..

X2.2.9 All data shall then be analyzed by the same acceptX2.2.9 able statistical methods to establish the limits of agreement that are attainable attainable between the two labor laboratories atories.. As a minimu minimum, m, the following statistical data shall be evolved: X2.2.9.1 X2.2. 9.1 Mean, X , X2.2.9.2 X2.2. 9.2 Standa Standard rd deviation, σ, and X2.2.9.3 X2.2. 9.3 Standa Standard rd error of the mean, σ /  X .

X2.2.4 X2.2. 4 All laboratories laboratories shall calibrate calibrate the optics of their test apparatus using a stage micrometer in accordance with A1.3.3 with  A1.3.3.. X2.2.5 The ind X2.2.5 indenta entatio tions ns sha shall ll be oriente oriented d the same way relativ rela tivee to gra grain in dir directi ection on in ord order er to avoid avoid dif differ ferenc ences es in results arising from this factor.

X2.3 Referee X2.3.1 If the lab X2.3.1 labora orator tories ies can cannot not esta establis blish h an acce acceptab ptable le correla cor relatio tion n thr throug ough h thi thiss pro proced cedure ure,, it wil willl be nec necessa essary ry to introduce an independent laboratory to act as the referee.

X2.2.6 The method of measuring the indentations X2.2.6 indentations shall be estab est ablis lishe hed d pr prio iorr to ma maki king ng th thee tes tests ts.. It sh shal alll be th thee mo most st accurate method as described by the equipment manufacturer.

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X3. RESUL RESULTS TS OF INTERLAB INTERLABORA ORATOR TORY Y TEST OF THE MEASUREME MEASUREMENT NT OF MICROINDENTA MICROINDENTATIONS

X3.1 Introduction

hardness. hardne ss. For spe specim cimens ens bel below ow abo about ut 300 HV HV,, ther theree was relatively little difference in HV over the test force range.

X3.1.1 This interlaboratory X3.1.1 interlaboratory test program program was condu conducted cted to develop precision and bias estimates for the measurement of  both bot h Kno Knoop op and Vicker Vickerss ind indent entatio ations ns usi using ng for forces ces of 25 to 1000 gf for ferrous and nonferrous specimens covering a wide range of hardness.

X3.4.3 For the Kno X3.4.3 Knoop op test data, most of the lab labora orator tories ies agreed that the hardness decreased continually with increasing test force and then became reasonably constant. However, the two lab labora orator tories ies tha thatt exh exhibi ibited ted out outlier lier dat dataa for the fer ferrou rouss specimens did show the opposite trend; this is quite unusual. The differ differenc encee in HK val values ues between between low forces forces and high forces increased with increasing specimen hardness. For specimens with hardnesses below about 300 HK, the difference in hardness was quite small over the test force range.

X3.2 Scope X3.2.1 This interlaboratory X3.2.1 interlaboratory test prog program ram provides information on the measurement of the same indentations by different laboratories according to the procedures of Practice  E691  E691..

X3.3 Procedure

X3.4.4   Repeatability The dif differ ferenc encee due to tes testt Repeatability Interv Interval—  al— The error between two test results in the laboratory on the same mater ma teria iall wa wass cal calcu cula lated ted us usin ing g th thee (S r ) j   values, values, the poo pooled led within-laboratory standard deviation. (S r ) j   increased with diagonal size and the relationship varied for each material and test type.  type.   Table X3.1 lists X3.1  lists regression equations that show the relationship relatio nship between (S r ) j   and the diagonal length, µm. The repeatability repeat ability interv interval al I (r ) j, was calculated based on the relationships in Table in  Table X3.1. X3.1. Because the repeatability intervals intervals are also a function of diagonal length, regression equations were also calcula calculated, ted,   Table Table X3.2 X3.2..   The rep repeata eatabili bility ty int interv ervals als,, in terms of Knoop and Vickers values for ferrous and nonferrous specimens, are shown in  Figs. X3.1-X3.4. X3.1-X3.4 .

X3.3.1 X3.3. 1 Five indentations indentations were made under controlled controlled conditions at each force (25, 50, 100, 200, 500, and 1000 gf), with both Knoop and Vickers indenters using three ferrous and four nonferrous specimens. X3.3.2 X3.3. 2 Twelve laboratories laboratories measur measured ed the inden indentations tations on the fer ferrou rouss spe specime cimens ns and the non nonfer ferrou rouss spe specime cimens. ns. Two laboratories measured the hardnesses of both groups. X3.3.3 Each laboratory X3.3.3 laboratory used the same stage microm micrometer eter to calibrate their measuring device. X3.3.4 X3.3. 4 Results were tabulated and analyzed in accor accordance dance with Practice E691 Practice  E691..

X3.4.1 For the three ferro X3.4.1 ferrous us specimens, results results from nine laboratories showed general agreement as to the diagonal sizes. Two other laboratories consistently undersized the indentations (higher hardness) and one laboratory consistently oversized the indent ind entatio ations ns (lo (lower wer har hardne dness) ss).. Thi Thiss bia biass was obs observ erved ed with both Vickers and Knoop indentations sized by these laboratories with the degree of bias increasing as the indentation size decreased and the specimen hardness increased. Test on the four nonferrous nonferrous specim specimens ens produ produced ced gener general al agreem agreement, ent, but none of the three laboratories that produced biased results for the ferrous specimens measured the nonferrous specimens.

X3.4.5   Reproducibility Interval— The The difference in test results on the same material in different laboratories was calculated using the (S  R) j  values, the between-laboratory estimate of  precision. (S  R) j  increased with diagonal size and the relationship varied for each material and test type. Table type.  Table X3.3 lists X3.3  lists the regression equations that show the relationship between ( S  R) j and the diagonal length, µm. The reproducibility intervals ( I  R) j, weree calc wer calculat ulated ed bas based ed on the rel relatio ationsh nships ips sho shown wn in   Table X3.3.. Because the reproducibility intervals are also a function X3.3 of diagonal length, regression equations were also calculated, Table X3.4. X3.4. The reproducibility intervals, in terms of Knoop and Vickers values for the ferrous and nonferrous specimens, are shown in  Figs. X3.1-X3.4. X3.1-X3.4 .

X3.4.2 For the Vick X3.4.2 ickers ers test dat data, a, the calc calcula ulated ted har hardne dness ss increased with increasing force and then became reasonably constant. This trend was apparent in the data from the nine consistent consis tent labor laboratorie atoriess (ferr (ferrous ous specimens) and for the labor laboraatory that oversized the indentations. The two laboratories that consis con sisten tently tly und unders ersized ized the Vick ickers ers ind indenta entatio tions ns exh exhibi ibited ted substantial data scatter for the tests with forces of less than 100 gf. However for higher forces, their indentation measurements weree rel wer relativ atively ely con constan stant. t. The for force ce at whi which ch the har hardne dness ss became relatively constant increased with increasing specimen

X3.4.6 The within within-labor -laboratory atory and betwee between-lab n-laborator oratory y precision cisi on val values ues wer weree cal calcula culated ted fro from m (V r   (%)) j   and ( V  L   (%)) j which are the coefficients of variation for within-laboratory and between-laboratory tests. Both are a function of the length of  the diago diagonal. nal. The withinwithin-labora laboratory tory and between between-labor -laboratory atory precision values were relatively similar for both Vickers and Knoop test data, either ferrous or nonferrous. In general, the repeatability intervals and reproducibility intervals were larger than the precision estimates, particularly at low test forces and high specimen hardnesses.

X3.4 Results

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TABLE X3.1 Relationship Between Diagonal Length and ( S r ) j , the Pooled Within–Laboratory Standard Deviation  

Material

Test

Regression Equation

Ferrous Ferrous Nonferrous Nonferrous

Vickers K no op Vickers Kn o op

¯ 1 (S r ) j  =   = 0.231 + 0.00284 d  0.00284  d  ¯ 1 (S r ) j  =   = 0.216 + 0.006 d  0.006  d  ¯ 1   = 0.373 + 0.008 d  0.008  d  (S r ) j  = ¯ 1 (S r ) j  =   = 0.057 + 0.0177 d  0.0177  d 

Correlation Coefficient        

0.535 0.823 0.862 0.8196

TABLE X3.2 Relat Relationshi ionship p Betwee Between n the Diagonal Length and ( I r ) j , the Repeatability Interval Material

Test

Ferrous Ferrous Nonferrous Nonferrous

Vickers K no o p Vickers K n o op

Regression Equation ¯ 1 (I r ) j  =   = 0.653 + 0.008 d  0.008  d  ¯ 1 (I r ) j  =   = 0.614 + 0.017 d  0.017  d  ¯ 1 (I r ) j  =   = 1.0556 + 0.0226 d  0.0226  d  ¯ 1 (I r ) j  =   = 0.161 + 0.05 d  0.05  d 

TABLE X3.3 Relationship Between Diagonal Length and ( S R ) j , the Between-Laboratory Estimate of Precision Material

Test

Regression Equation

Ferrous Ferrous Nonferrous Nonferrous

Vickers K no o p Vickers K n oo p

¯ 1 (S R ) j  =   = 0.31 + 0.004 d  0.004  d  ¯ 1 (S R ) j  =   = 0.333 + 0.007 d  0.007  d  ¯ 1 (S R ) j  =   = 0.357 + 0.0156 d  0.0156  d  ¯ 1 (S R ) j  =   = 0.378 + 0.0177 d  0.0177  d 

 

Correlation Coefficient        

0.747 0.899 0.8906 0.8616

TABLE X3.4 Relati Relationshi onship p Betwee Between n the Diagonal Length and ( I R ) j , the Repeatability Interval Material

Test

Regression Equation

Ferrous Ferrous Nonferrous Nonferrous

Vickers Kn o op Vickers Kn o op

¯ 1 (I R ) j  =   = 0.877 + 0.0113 d  0.0113  d  ¯ 1 (I R ) j  =   = 0.946 + 0.0198 d  0.0198  d  ¯ 1 (I R ) j  =   = 1.0103 + 0.0441 d  0.0441  d  ¯ 1 (I R ) j  =   = 1.07 + 0.05 d  0.05  d 

FIG. X3.1 Repeat Repeatabilit ability y and Repro Reproducibi ducibility lity Intervals Intervals in Terms of Vickers Hardness (6) for the Ferrous Samples as a Function of Test Load and Specimen Hardness

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FIG. X3.2 Repeat Repeatabilit ability y and Repro Reproducib ducibility ility Intervals Intervals in Terms of Knoop Hardness ( 6) for the Ferrous Samples as a Function of Test Load and Specimen Hardness

FIG. X3.3 Repeat Repeatabilit ability y and Repro Reproducib ducibility ility Intervals Intervals in Terms of Vickers Hardness (6) for the Nonferrous Samples as a Function of Test Load and Specimen Hardness

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FIG. X3.4 Repeatability Repeatability and Repro Reproducibi ducibility lity Intervals in Terms of Knoo Knoop p Hardne Hardness ss ( 6) for the Nonferrous Samples as a Function of Test Load and Specimen Hardness

X4. RESULTS OF AN INTERLABORATORY TEST COMPARING COMPARING MICROINDENTA MICROI NDENTATION TION HARDNESS TESTING USING MANUAL AND AUTOMATED MEASURING SYSTEMS

X4.1 Introduction

X4.4 Repea Repeatabili tability ty

X4.1.1 An interlaboratory X4.1.1 interlaboratory test program was cond conducted ucted to develop information comparing Knoop and Vickers microindentation hardness tests made with Automated Image Analysis systems and manual procedures. Four ferrous specimens were used in the test program.

X4.4.1 Repeata Repeatability bility concerns concerns the variability between between individual vid ual tes testt res result ultss obt obtain ained ed with within in a sin single gle lab labora orator tory y by a single operator with a specific set of test apparatus. For both the man manual ual and aut automa omated ted mea measur suremen ements, ts, the rep repeata eatabil bility ity interval increased with specimen hardness and decreasing test force, Tables force,  Tables X4.1-X4.4, X4.1-X4.4, and and Figs.  Figs. X4.1-X4.4. X4.1-X4.4.  For equivalent testing test ing con condit dition ions, s, the rep repeata eatabili bility ty inte interva rvall for aut automa omated ted measurements measur ements was slightl slightly y large largerr than for manual measurements.

X4.2 Scope X4.2.1 This interlaboratory X4.2.1 interlaboratory test prog program ram provides information tio n on me measu asure reme ment ntss of th thee sa same me in inde dent ntati ation onss mad madee by different laboratories using two different measuring methods according to the procedures of Practice  E691  E691..

X4.5 Repr Reproducib oducibility ility X4.5.1 Repro X4.5.1 Reproducib ducibility ility deals with the variab variability ility between single test results obtained by different laboratories applying the same test methods to the same or similar test specimens. For both the manual and automated measurements, the reproducibility interval increased with specimen hardness and decreasing creasin g test force,   Tables Tables X4.1-X4.4 X4.1-X4.4,, and   Figs. X4.1X4.1-X4.4 X4.4.. For equivalent testing conditions, the reproducibility interval forr au fo auto toma mated ted me meas asur ureme ement ntss wa wass sli sligh ghtly tly lar large gerr th than an fo forr manual measurements.

X4.3 Procedure X4.3.1 The test were condu X4.3.1 conducted cted under controlled controlled conditions conditions using loads of 100 gf and 300 gf. Ten Knoop and ten Vickers indentations were made for each load, a total of 40 indentations. The participants in the test program measured the same indentations on the four specimens. Seven laboratories measured the specimens using both procedures. The results of these seven sets of measurements were used for the analysis. The Knoop indentations on specimen C1 were too long for accurate measurements to be made by one lab; hence, only six sets of  measurements were made on this specimen. Near the end of the test program, specimen B1 was lost in shipping; thus only six sets of measurements were made on this specimen.

X4.6 Comp Comparison arisonss X4.6.1 Practi X4.6.1 Practice ce  E691   nor any other ASTM standard deals with comparing test results of a single property made by two different test methods. Hence it is not possible to statistically 28

E384 − 11 and accurately compare the hardness measurements made by the manual and automated procedures. However, this informa-

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tion is graphically represented for comparative purposes,  Figs. X4.5-X4.8.. X4.5-X4.8

TABLE X4.1 Precision Statistics for Manual and Automated Knoop Tests at 100 gf Load Manual S pec . C1 D1 A2 B1

La bs 7 7 7 6

Me M ea n 2 2 8 .6 2 3 4 4 .8 0 4 9 1 .4 8 9 0 1 .6 7

Sx 6 .8 8 1 0 .5 4 2 8 .6 7 6 2 .4 0

S pec . C1 D1 A2 B1

La bs 7 7 7 6

Mean Me 2 3 2 .0 7 3 4 8 .9 7 5 1 0 .1 3 9 1 4 .7 2

Sx 7 .2 9 1 0 .7 4 3 0 .3 5 5 7 .8 2

Sr 9 .3 0 9. 80 1 4 .8 7 2 1 .1 7 Automated Sr 9 .5 4 9. 54 1 9 .5 3 2 9 .2 2

SR 11.18 1 4 .0 6 3 1. 95 6 5. 55

r 2 6 .0 3 2 7 .4 4 4 1 .6 3 5 9 .2 8

R 3 1 .3 2 3 9 .3 6 8 9 .4 5 1 8 3 .5 5

SR 11.62 1 4 .0 4 3 5. 56 6 4. 13

r 2 6 .7 2 2 6 .7 0 5 4 .6 9 8 1 .8 3

R 3 2 .5 5 3 9 .3 2 9 9 .5 6 1 7 9 .5 6

TABLE X4.2 Precision Statistics for Manual and Automated Knoop Tests at 300 gf Load Manual S pec . C1 D1 A2 B1

La bs 6 7 7 6

Me M ea n 2 1 5 .8 1 3 3 0 .6 4 4 6 6 .9 5 8 2 7 .4 7

Sx 5 .4 9 6 .9 9 1 7 .9 9 2 0 .4 1

S pec . C1 D1 A2 B1

La bs 6 7 7 6

Mean Me 2 1 7 .8 2 3 3 5 .7 6 4 7 6 .9 7 8 2 1 .0 0

Sx 5 .7 3 1 2 .2 3 2 3 .4 6 2 4 .6 2

Sr 7 .6 6 7 .4 9 11.45 1 6 .1 3 Automated Sr 6 .8 7 8. 22 1 0 .5 6 1 0 .8 9

SR 9 .1 0 9 .9 7 2 1. 02 2 5. 51

r 2 1 .4 4 2 0 .9 8 3 2 .0 6 4 5 .1 6

R 2 5 .4 9 2 7 .9 2 5 8 .8 5 7 1 .4 3

SR 8 .6 8 1 4 .5 0 2 5. 51 2 6. 70

r 1 9 .2 4 2 3 .0 3 2 9 .5 8 3 0 .5 0

R 2 4 .3 1 4 0 .6 1 7 1 .4 4 7 4 .7 6

TABLE X4.3 Precisio Precision n Stati Statistics stics for Manual and Automated Automated Vicker Vickers s Tests at 100 gf Load Manual S pec . C1 D1 A2 B1

La bs 7 7 7 6

Me M ea n 2 0 5 .3 1 2 9 9 .5 2 4 8 2 .7 6 8 2 1 .5 6

Sx 6 .3 6 6 .0 7 2 1 .5 8 4 6 .0 1

S pec . C1 D1 A2 B1

La bs 7 7 7 6

Mean Me 2 0 3 .3 0 2 9 9 .7 8 4 8 2 .8 6 8 0 8 .1 7

Sx 6 .9 4 1 4 .3 6 3 2 .0 7 4 7 .7 2

Sr 6 .8 2 7 .6 5 1 2 .2 9 2 4 .0 2 Automated Sr 6 .4 7 5. 23 1 6 .5 0 2 1 .3 0

SR 9 .0 7 9 .4 6 2 4. 53 5 1. 35

r 1 9 .1 0 2 1 .4 3 3 4 .4 2 6 7 .2 5

R 2 5 .4 0 2 6 .5 0 6 8 .6 9 1 4 3 .7 7

SR 9 .2 7 1 5 .1 9 3 5. 69 5 1. 82

r 1 8 .1 2 1 4 .6 3 4 6 .1 9 5 9 .6 3

R 2 5 .9 5 4 2 .5 4 9 9 .9 3 1 4 5 .0 9

TABLE X4.4 Precisio Precision n Stati Statistics stics for Manual and Automated Automated Vicker Vickers s Tests at 300 gf Load Manual S pec . C1 D1 A2 B1

La bs 7 7 7 6

Me M ea n 1 9 7 .0 7 2 9 8 .9 1 4 7 4 .5 8 8 1 0 .6 0

Sx 3 .4 0 5 .4 7 1 8 .0 0 2 9 .6 7

S pec . C1 D1 A2 B1

La bs 7 7 7 6

Mean Me 1 9 6 .3 7 2 9 7 .8 8 4 8 3 .7 2 8 0 9 .5 5

Sx 6 .4 4 1 0 .4 2 1 8 .9 6 2 0 .5 5

Sr 5 .3 2 7 .3 8 1 2 .4 5 1 6 .5 0 Automated Sr 5 .5 7 6. 69 1 2 .3 0 11.60

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SR 6 .0 9 8 .8 9 2 1. 53 3 3. 55

r 1 4 .9 1 2 0 .6 8 3 4 .8 6 4 6 .2 1

R 1 7 .0 6 2 4 .8 9 6 0 .2 8 9 3 .9 4

SR 8 .3 3 1 2 .2 0 2 2. 26 2 3. 31

r 1 5 .6 0 1 8 .7 2 3 4 .4 4 3 2 .4 9

R 2 3 .3 2 3 4 .1 5 6 2 .3 4 6 5 .2 7

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FIG. X4.1 Repro Reproducibi ducibility lity of the Knoop 100 gf Manual and Auto Automated mated Microindentatio Microindentation n Hardn Hardness ess Te Tests sts

FIG. X4.2 Repro Reproducibi ducibility lity of the Knoop 300 gf Manual and Auto Automated mated Microindentatio Microindentation n Hardn Hardness ess Te Tests sts

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FIG. X4.3 Repro Reproducib ducibility ility of the Vickers 100 gf Manual and Auto Automated mated Microindentatio Microindentation n Hardne Hardness ss Tests

FIG. X4.4 Repro Reproducib ducibility ility of the Vickers 300 gf Manual and Auto Automated mated Microindentatio Microindentation n Hardne Hardness ss Tests

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FIG. X4.5 Comparison between Knoop 100 gf Manual and Automated Microindentation Hardness Tests

FIG. X4.6 Comparison between Knoop 300 gf Manual and Automated Microindentation Hardness Tests

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FIG. X4.7 Compa Comparison rison between Vickers 100 gf Manual and Auto Automated mated Microindentatio Microindentation n Hardn Hardness ess Tests

FIG. X4.8 Compa Comparison rison between Vickers 300 gf Manual and Auto Automated mated Microindentatio Microindentation n Hardn Hardness ess Tests

X5. RECOMMEN RECOMMENDA DATIONS TIONS FOR LIGHT FORCE MICROINDE MICROINDENT NTA ATION HARDNE HARDNESS SS TESTING

X5.1 Introduction

more imp more impera erativ tivee as the ind indent entatio ations ns bec become ome sma smaller ller.. For example, consider a material with a Vickers hardness of 500, Table 5. 5. For a force of 100 gf, the diagonal length would be 19.258 µm. To maintain an error of  6 1 %, the accuracy of the diagonal diago nal measur measurement ement must be ≤   0.096 µm. Similarly for a material with a Knoop hardness of 500, when tested with a 20 gf force, the ideal diagonal length would be 23.86 µm,  Table 6. 6. To maintain an error of  6  1 %, the accuracy of the diagonal measurement has to be ≤  0.12 µm. Measurements to this level of accuracy are impossible to achieve by optical microscopy. Because of the inherent difficulties involved in obtaining and measuring indentations with diagonals less than 20 µm, and the increasi incr easing ng ef effect fect of pos possibl siblee ind indenta entation tion or meas measure uremen mentt errors, error s, light force microindentation microindentation hardness testing requires

X5.1.1 X5.1. 1 Micro Microindent indentation ation hardness hardness of materials can be determined using a variety of loads to force the indenter into the test piece. Testing is considered to be light force when the force in use produces indentations with a diagonal length of less than 20 µm. Both Knoop and Vickers hardness numbers increase in prop pr opor ortio tion n to th thee in inve vers rsee of th thee sq squa uare re of th thee in inde dent ntati ation on diagonal length, Eq length,  Eq 3 and 7. 7 .  Thus, hardness numbers obtained from indentations with diagonals measuring less than 20 µm are much more sensitive to variations of a few tenths of a micrometer in the actual or measured length of the diagonals than tha n ha hard rdnes nesss nu numbe mbers rs ob obtai taine ned d by mea measu surin ring g lar larger ger indentations, Eq indentations,  Eq 13 and 17. 17 .  Creation of valid indentations, and the accurate measurement measurement of their diago diagonals, nals, becomes even 33

E384 − 11 precautio precau tions ns in add additio ition n to tho those se nor normall mally y nec necess essary ary.. Sma Small ll indentations may be due to high test piece hardness or the use of light forces. In either case, some of the concerns involved with obtaining accurate hardness results are addressed in this appendix.

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X5.4.1.3 X5.4.1 .3 The surfaces surfaces to be tested should should be as clea clean n as possible. Care must be taken to avoid surface contaminants that may be absorbed into the surfaces of some materials such as polymers or ceramics. Microstructuree of Specim Specimen—  en— If X5.4.2   Microstructur If the micros microstructu tructure re of the ma mater teria iall tes testt pi piec ecee is on the sa same me size sc scale ale as th thee indentation diagonal length, an increase in the variability of the hardness data should be expected. Indentations placed within a single grain will experience resistance to deformation somewhatt dep wha depend endent ent on the orientati orientation on of that gra grain in to the test surface. Since these orientations are normally random, variability of results is increa increased. sed. Indentation Indentation diago diagonal nal lengths can vary depending upon the number of grain boundaries transversed by the inden indentation. tation. Multiphase Multiphase material system systemss will provide indentation diagonal lengths that may be proportional to the volume percentage of each phase included within the volume of deformation caused by the indentation. In the above cases, an increase in the number of measurements taken will be necessary to provide meaningful results.

X5.2 Scope X5.2.1 These recommendation X5.2.1 recommendationss prov provide ide guidance and suggest additional precautions for microindentation hardness testing when the measured diagonals of indentations are less than 20 µm. X5.3   Environment  : X5.3.1   Vibration: X5.3.1.1 X5.3. 1.1 Vibratio ibration n of the micro microindent indentation ation hardness tester during a light force test can cause a large percentage increase in the measured diagonals. Reasonable Reasonable accura accuracy cy and precision can only be achieved when the test instrument is isolated from vibr vi brat atio ion n as mu much ch as po poss ssib ible le du duri ring ng te testi sting ng.. Us Usee of an isolation isolatio n table or isolati isolation on platfo platform rm is manda mandatory tory.. Airborne vibrations in the vicinity of the test instrument, such as air currents and loud noises, are to be avoided. X5.3.1 X5. 3.1.2 .2 It is rec recomm ommend ended ed tha thatt tes testt ins instru trumen ments ts not be locat lo cated ed ab abov ovee th thee gr grou ound nd flo floor or of th thee bu build ildin ing g du duee to th thee increase in vibration usually experienced by the upper floors. Test instruments should be located in areas away from machinery that may cause low (<20 Hz) frequency vibrations, since low frequencies are more easily transmitted through isolation tables and platforms.

X5.5 Instr Instrument umentss Magnificatio ification n of Micr Microscop oscope—  e— Classic X5.5.1 Magn Classic microi microindenndentation hardness testers make use of optics that provide magnification fica tionss of up to 800 800X. X. Hig Higher her mag magnifi nificati cations ons are rec recomommended when performing light force testing. Specimens may be removed from the test instru instrument ment following the indentation operati ope ration, on, and the dia diagon gonals als of the ind indent entatio ations ns meas measure ured d using a separa separate te high quality light or SEM micros microscope cope capable of providing higher magnifications.

X5.3.2   Level— Microinden Microindentation tation hardness testers must be level in order to obtain usable information. Errors due to minor unle un leve velin ling g be beco come me mo more re im impo port rtan antt as th thee fo forc rces es be beco come me lighter.

X5.5.2  Optical Quality of Microscope— Use Use of highly corrected objectives with numerical apertures of 0.9 or greater is recommended recomm ended.. Use of dark field illumin illumination ation or dif differen ferential tial interference contrast may improve the contrast of the image and also enhance the users ability to detect the ends of the indentations.

X5.3.3   Temperature— Cont C ontro roll of th thee tem tempe pera ratu ture re of th thee specimen, testing instrumentation, and surrounding area should be considered. It is recommended that these temperatures be maintain main tained ed at 23 6   3°C. 3°C. As th thee len lengt gth h of th thee me meas asur ured ed diagona diag onall bec become omess sma smaller ller,, it may be nec necess essary ary to inc increa rease se control of temperature to reduce variability.

Diagonal nal Meas Measurin uring g Devic Device—  e— The X5.5.3   Diago The measu measuremen rementt technique and the devices used to perform the measurements should be capable of discerning differences in length of 0.1 µm or le less ss.. In so some me ca case ses, s, it ma may y be pr pref efer erab able le to ob obta tain in a photom pho tomicr icrogr ograph aph of the ind indent entatio ation n firs first, t, and meas measure ure the length of the diagonal as seen in the photomicrograph. In all cases, calibration of magnifications and measuring devices is necessary.

X5.4 Specimens X5.4.1   Specimen Preparation: X5.4.1.1 X5.4. 1.1 Usuall Usually y, test pieces requir requiree moun mounting. ting. Care must be taken to ensure that the specimens are well supported in the mounting material, and that the surface to be tested can be placed into the test instrument such that it will be normal to both the loading and optical axes. X5.4.1.2 X5.4. 1.2 The surface properties properties of the test specimen must not be alte altered red due to spe specim cimen en pre prepar paratio ation. n. Met Metallo allogra graphi phicc polish pol ishing ing,, whe when n app applica licable ble,, sho should uld be per perfor formed med usi using ng accepted cep ted tec techni hnique quess kno known wn to min minimi imize ze the def deform ormed ed lay layer er remai re maini ning ng on th thee su surf rface ace of th thee sp spec ecime imen. n. Li Ligh ghtt etc etchi hing ng followed by light repolishing may be used to further decrease the thic thickne kness ss of any def deform ormed ed laye layerr. Elec Electro tropol polish ishing ing can provide surfaces essentially free of deformation due to preparation. Areas to be tested must appear flat in the field of focus of th thee mi micr cros osco cope pe us used ed to mea measu sure re th thee di diag agon onals als of th thee indentations.

X5.5.4  Accuracy of Forces— Often, Often, small indentation diagonal lengths are the result of the use of very light forces, in many cases less than 10 g. Force accuracy of  6 1.5 % is required in accordance with Table with  Table A1.2. A1.2.  For light forces, this requires that no oil oils, s, dus dust, t, or oth other er min minor or con contami taminan nants ts be pre presen sent. t. For example, when using a force of 2.0 g, contaminants with a total mass of more than 0.03 g render the results of the test invalid. X5.5.5   Loading Rates— When When using light forces, the impact of th thee in inde dent nter er on th thee su surf rface ace of th thee tes testt pi piece ece can ca caus usee significant inaccuracies to occur. Use of the slowest loading rate available for each instrument is recommended. X5.5.6   Indenters— Greater Greater repeatability, accuracy, and precision may be obtained by the careful selection of indenters. 34

E384 − 11 Verification of the included angles of the faces, the degree of  mismatch at the vertex, and the sharpness of the edges are appropriate appro priate criteria for the selectio selection n of indent indenters. ers. Using the manufacturer’s certification, the exact indenter constant should be calculated and used to minimize errors, Eq errors,  Eq 14, 14, Eq 18 and 18  and Eq  Eq 19.. 19

´1

bration of the SEM photographic image at the exact magnification cati on to be use used d is ess essent ential. ial. For the these se meas measure uremen ments, ts, the specimen should be perpendicular to the beam, that is, the tilt angl an glee sh shou ould ld be 0° 0°.. Th Thee ac accel celer erati ating ng vo volta ltage ge,, an and d ot othe herr parameters should remain as they were for calibration. (The SEM should be calibrated in both the  X  and  Y  directions; refer to Pra Practic cticee   E766. E766.   Indent Indentatio ations ns to be meas measure ured d sho should uld not extend to the periphery of the SEM field of view, as the video signal can be distorted at the edges of the video monitor.

X5.6 Measu Measuremen rementt of Indent Indentation ationss X5.6.1 X5.6. 1 Inden Indentation tationss that do not appear symmetrical symmetrical should not be consid considered ered valid for diagonal measurement. measurement. A dif differenc ferencee in sy symm mmetr etry y gr grea eater ter th than an 10 % sh shou ould ld be ad addr dres esse sed d wi with th concern con cern.. If con consist sistentl ently y asy asymmet mmetrica ricall ind indenta entation tionss are obtained, the alignment of the specimen to the indenter should be adj adjust usted. ed. If the pro proble blem m per persis sists, ts, the mic microi roinde ndentat ntation ion hardness instrument should be serviced by a qualified technician.

X5.8 Vid Video eo and Automatic Automatic Measur Measuring ing Systems X5.8.1 Typical video or compu computerized terized measuring measuring system systemss lack the necessary resolution for obtaining acceptable results when indentation diagonal lengths are less than 20 µm. Loss of  resolution within the digitized image can cause a substantial decrease in the accuracy of the measurement. Extremely high resolution resolu tion video camera camerass and monitors, when appro appropriatel priately y asse as semb mbled led in into to a me measu asuri ring ng sy syst stem, em, ma may y be cap capab able le of  resolution sufficient to provide accurate results.

X5.7 Scann Scanning ing Electron Microscope Microscope X5.7.1 Measur X5.7.1 Measurement ement of indentation diagonals diagonals using a scanning electron microscope is possible. However, careful cali-

X6. HK AND HV VALUES FOR A1 gf TEST LOAD X6.1 Refe X6.1 Referr to Table to  Table X6.1 for X6.1  for the Knoop hardness numbers for load of 1 gf. Refer to  Table X6.2 for X6.2  for the Vickers hardness numbers for load of 1 gf. TABLE X6.1 Knoop Hardness Numbers for Load of 1 gf Knoop Hardness Number for Diagonal Measured to 0.1 µm

Diagonal of Indentation, µm

0 .0

0. 1

0. 2

0 .3

0 .4

0. 5

0 .6

0. 7

0 .8

0 .9

1 2 3 4 5

14 2 30 35 57 15 81 8 8 9. 3 5 6 9. 2

11760 322 7 148 1 8 4 6 .5 5 4 7 .1

9 88 1 29 4 0 13 9 0 8 0 6 .6 5 2 6 .2

8 4 20 2 69 0 1 30 7 7 6 9 .5 5 0 6 .2

7 26 0 24 7 0 12 3 1 7 3 5 .0 4 8 8 .0

6 32 4 22 7 7 1162 7 0 2 .7 4 7 0 .4

5 55 8 2 1 05 1 0 98 6 7 2 .4 4 5 3 .7

4 9 24 1 95 2 1 03 9 6 4 4 .1 4 3 7 .9

43 92 1 81 5 9 8 5 .4 61 7. 6 42 3. 0

3 94 2 1 6 92 9 3 5 .5 5 9 2 .6 4 0 8 .8

6 7 8 9 10

3 9 5. 2 2 9 0. 4 2 2 2. 3 1 7 5. 7 1 4 2 .3

3 8 2 .4 2 8 2 .3 2 1 6 .9 1 7 1 .8 1 3 9 .5

3 7 0 .2 2 7 4 .5 211.6 1 6 8 .1 1 3 6 .8

3 5 8 .5 2 6 7 .0 2 0 6 .5 1 6 4 .5 1 3 4 .1

3 4 7 .4 2 5 9 .8 2 0 1 .7 1 6 1 .0 1 3 1 .6

3 3 6 .8 2 5 3 .0 1 9 6 .9 1 5 7 .7 1 2 9. 1

3 2 6 .7 2 4 6 .3 1 9 2 .4 1 5 4 .4 1 2 6. 6

3 1 7 .0 2 4 0 .0 1 8 8 .0 1 5 1 .2 1 2 4. 3

30 7. 7 23 3. 9 18 3. 7 14 8. 2 1 2 2. 0

2 9 8 .9 2 2 8 .0 1 7 9 .6 1 4 5 .2 119.8

11 12 13 14 15

117.6 98 . 81 84 . 20 72 . 60 63 . 24

115.5 9 7. 19 8 2. 91 7 1. 57 6 2. 40

113.4 9 5. 60 8 1. 66 7 0. 57 6 1. 59

111.4 9 4. 05 8 0. 44 6 9. 58 6 0. 78

1 0 9 .5 9 2 .5 4 7 9 .2 4 6 8 .6 2 6 0 .0 0

1 0 7. 6 9 1 .0 7 7 8 .0 7 6 7 .6 8 5 9 .2 3

1 0 5. 7 8 9 .6 3 7 6 .9 3 6 6 .7 5 5 8 .4 7

1 0 3. 9 8 8 .2 2 7 5 .8 1 6 5 .8 5 5 7 .7 3

1 0 2. 2 8 6 .8 5 7 4 .7 2 6 4 .9 6 5 7 .0 0

10 0. 5 8 5 .5 1 7 3 .6 5 6 4 .0 9 5 6 .2 8

16 17 18 19 20

55 . 58 49 . 24 43 . 92 39 . 42 35 . 57

5 4. 89 4 8. 66 4 3. 43 3 9. 00 3 5. 22

5 4. 22 4 8. 10 4 2. 96 3 8. 60 3 4. 87

5 3. 55 4 7. 54 4 2. 49 3 8. 20 3 4. 53

5 2 .9 0 4 7 .0 0 4 2 .0 3 3 7 .8 1 3 4 .1 9

5 2 .2 6 4 6 .4 6 4 1 .5 7 3 7 .4 2 3 3 .8 6

5 1 .6 4 4 5 .9 4 4 1 .1 3 3 7 .0 4 3 3 .5 3

5 1 .0 2 4 5 .4 2 4 0 .6 9 3 6 .6 6 3 3 .2 1

5 0 .4 1 4 4 .9 1 4 0 .2 6 3 6 .2 9 3 2 .8 9

4 9 .8 2 4 4 .4 1 3 9 .8 3 3 5 .9 3 3 2 .5 7

21 22 23 24 25

32 . 27 29 . 40 26 . 90 24 . 70 22 . 77

3 1. 96 2 9. 13 2 6. 67 2 4. 50 2 2. 59

3 1. 66 2 8. 87 2 6. 44 2 4. 30 2 2. 41

3 1. 36 2 8. 61 2 6. 21 2 4. 10 2 2. 23

3 1 .0 7 2 8 .3 6 2 5 .9 9 2 3 .9 0 2 2 .0 5

3 0 .7 8 28.11 2 5 .7 7 2 3 .7 1 2 1 .8 8

3 0 .5 0 2 7 .8 6 2 5 .5 5 2 3 .5 1 2 1 .7 1

3 0 .2 2 2 7 .6 1 2 5 .3 3 2 3 .3 2 2 1 .5 4

2 9 .9 4 2 7 .3 7 2 5 .1 2 2 3 .1 4 2 1 .3 8

2 9 .6 7 2 7 .1 3 2 4 .9 1 2 2 .9 5 2 1 .2 1

26 27 28 29 30

21 . 05 19 . 52 18 . 15 16 . 92 15 . 81

2 0. 89 1 9. 37 1 8. 02 1 6. 80 1 5. 71

2 0. 73 1 9. 23 1 7. 23 1 6. 89 1 5. 60

2 0. 57 1 9. 09 1 7. 77 1 6. 57 1 5. 60

2 0 .4 2 1 8 .9 5 1 7 .6 4 1 6 .4 6 1 5 .4 0

2 0 .2 6 1 8 .8 2 1 7 .5 2 1 6 .3 5 1 5 .3 0

20.11 1 8 .6 8 1 7 .4 0 1 6 .2 4 1 5 .2 0

1 9 .9 6 1 8 .5 4 1 7 .2 7 1 6 .1 3 1 5 .1 0

1 9 .8 1 1 8 .4 1 1 7 .1 5 1 6 .0 1 1 5 .0 0

1 9 .6 6 1 8 .2 8 1 7 .0 4 1 5 .9 2 1 4 .9 0

31

14 . 81

1 4. 71

1 4. 62

1 4. 52

1 4 .4 3

1 4 .3 4

1 4 .2 5

1 4 .1 6

1 4 .0 7

1 3 .9 8

35

E384 − 11

´1

TABLE TA BLE X6.1   Continued  Knoop Hardness Number for Diagonal Measured to 0.1 µm

Diagonal of Indentation, µm

0 .0

0. 1

0. 2

0 .3

0 .4

0. 5

0 .6

0. 7

0 .8

0 .9

32 33 34 35

13 . 90 13 . 07 12 . 31 11.62

1 3. 81 1 2. 99 1 2. 24 11.55

1 3. 72 1 2. 91 1 2. 17 11.48

1 3. 64 1 2. 83 1 2. 09 11.42

1 3 .5 5 1 2 .7 5 1 2 .0 2 11.35

1 3 .4 7 1 2 .6 8 11.95 11.29

1 3 .3 9 1 2 .6 0 11.89 11.23

1 3 .3 1 1 2 .5 3 11.82 11.16

1 3 .2 3 1 2 .4 5 11.75 11.10

1 3 .1 5 1 2 .3 8 11.68 11.04

36 37 38 39 40

10 . 98 10 . 39 9. 8 54 9. 3 55 8. 8 93

1 0. 92 1 0. 34 9 .8 0 2 9 .3 0 7 8 .8 4 9

1 0. 86 1 0. 28 9 .7 5 1 9 .2 6 0 8 .8 0 5

1 0. 80 1 0. 23 9 .7 0 0 9 .2 1 3 8 .7 6 1

1 0 .7 4 1 0 .1 7 9. 65 0 9. 16 6 8. 71 8

1 0 .6 8 1 0 .1 2 9 .6 0 0 9 .1 2 0 8 .6 7 5

1 0 .6 2 1 0 .0 6 9 .5 5 0 9 .0 7 4 8 .6 3 2

1 0 .5 6 1 0 .0 1 9 .5 0 1 9 .0 2 8 8 .5 9 0

1 0 .5 1 9 .9 5 8 9 .4 5 2 8 .9 8 3 8 .5 4 8

1 0 .4 5 9. 90 6 9. 40 3 8. 93 8 8. 50 6

41 42 43 44 45

8. 4 65 8. 0 66 7. 6 95 7. 3 50 7. 0 27

8 .4 2 3 8 .0 2 8 7 .6 6 0 7 .3 1 6 6 .9 9 6

8 .3 8 3 7 .9 9 0 7 .6 2 4 7 .2 8 3 6 .9 6 5

8 .3 4 2 7 .9 5 2 7 .5 8 9 7 .2 5 0 6 .9 3 4

8. 30 2 7. 91 5 7. 55 4 7. 21 8 6. 90 3

8 .2 6 2 7 .8 7 8 7 .5 2 0 7 .1 8 5 6 .8 7 3

8 .2 2 2 7 .8 4 1 7 .4 8 5 7 .1 5 3 6 .8 4 3

8 .1 8 3 7 .8 0 4 7 .4 5 1 7 .1 2 1 6 .8 1 3

8 .1 4 4 7 .7 6 8 7 .4 1 7 7 .0 9 0 6 .7 8 3

8. 10 5 7. 73 1 7. 38 3 7. 05 8 6. 75 4

46 47 48 49 50

6. 7 24 6. 4 41 6. 1 76 5. 9 26 5. 6 92

6 .6 9 5 6 .4 1 4 6 .1 5 0 5 .9 0 2 5 .6 6 9

6 .6 6 6 6 .3 8 7 6 .1 2 5 5 .8 7 8 5 .6 4 6

6 .6 3 8 6 .3 6 0 6 .0 9 9 5 .8 5 4 5 .6 2 4

6. 60 9 6. 33 3 6. 07 4 5. 83 1 5. 60 2

6 .5 8 1 6 .3 0 6 6 .0 4 9 5 .8 0 7 5 .5 7 9

6 .5 5 2 6 .2 8 0 6 .0 2 4 5 .7 8 4 5 .5 5 7

6 .5 2 4 6 .2 5 4 6 .0 0 0 5 .7 6 1 5 .5 3 6

6 .4 9 7 6 .2 2 8 5 .9 7 5 5 .7 3 7 5 .5 1 4

6. 46 9 6. 20 2 5. 95 1 5. 71 4 5. 49 2

51 52 53 54 55

5. 4 71 5. 2 62 5. 0 65 4. 8 80 4. 7 04

5 .4 4 9 5 .2 4 2 5 .0 4 6 4 .0 8 2 4 .6 8 7

5 .4 2 8 5 .2 2 2 5 .0 2 7 4 .8 4 4 4 .6 7 0

5 .4 0 7 5 .2 0 2 5 .0 0 9 4 .8 2 6 4 .6 5 3

5. 38 6 5. 18 2 4. 99 0 4. 80 8 4. 63 6

5 .3 6 5 5 .1 6 2 4 .9 7 1 4 .7 9 0 4 .6 1 9

5 .3 4 4 5 .1 4 3 4 .9 5 3 4 .7 7 3 4 .6 0 3

5 .3 2 3 5 .1 2 3 4 .9 3 4 4 .7 5 6 4 .5 8 6

5 .3 0 3 5 .1 0 4 4 .9 1 6 4 .7 3 8 4 .5 7 0

5. 28 2 5. 08 5 4. 89 8 4. 72 1 4. 55 4

56 57 58 59 60

4. 5 37 4. 3 79 4. 2 30 4. 0 88 3. 9 52

4 .5 2 1 4 .3 6 4 4 .2 1 5 4 .0 7 4 3 .9 3 9

4 .5 0 5 4 .3 4 9 4 .2 0 1 4 .0 6 0 3 .9 2 6

4 .4 8 9 4 .3 3 4 4 .1 8 8 4 .0 4 6 3 .9 1 3

4. 47 3 4. 31 9 4. 17 2 4. 03 3 3. 90 0

4 .4 5 7 4 .3 0 4 4 .1 5 8 4 .0 1 9 3 .8 8 7

4 .4 4 2 4 .2 8 9 4 .1 4 4 4 .0 0 6 3 .8 7 5

4 .4 2 6 4 .2 7 4 4 .1 2 9 3 .9 9 2 3 .8 6 2

4 .4 1 0 4 .2 5 9 4.115 3 .0 7 0 3 .8 4 9

4. 39 5 4. 24 4 4. 10 2 3. 96 6 3. 83 7

61 62 63 64 65

3. 8 24 3. 7 02 3. 5 85 3. 4 74 3. 3 68

3.811 3 .6 9 0 3 .5 7 4 3 .4 6 3 3 .3 5 7

3 .7 9 9 3 .6 7 8 3 .5 6 2 3 .4 5 2 3 .3 4 7

3 .7 8 7 3 .6 6 6 3 .5 5 1 3 .4 4 2 3 .3 3 7

3. 77 4 3. 65 4 3. 54 0 3. 43 1 3. 32 7

3 .7 6 2 3 .6 4 3 3 .5 2 9 3 .4 2 0 3 .3 1 7

3 .7 5 0 3 .6 3 1 3 .5 1 8 3 .4 1 0 3 .3 0 6

3 .7 3 8 3 .6 1 9 3 .5 0 7 3 .3 9 9 3 .2 9 6

3 .7 2 6 3 .6 0 8 3 .4 9 6 3 .3 8 9 3 .2 8 6

3. 71 4 3. 59 6 3. 48 5 3. 37 8 3. 27 6

66 67 68 69 70

3. 2 67 3. 1 70 3. 07 7 2. 98 9 2. 90 4

3 .2 5 7 3 .1 6 0 3 .0 6 8 2 .9 8 0 2 .8 9 6

3 .2 4 7 3 .1 5 1 3 .0 5 9 2 .9 7 1 2 .8 8 7

3 .2 3 7 3 .1 4 2 3 .0 5 0 2 .9 6 3 2 .8 7 9

3. 22 7 3. 13 2 3. 04 1 2. 95 4 2. 87 1

3 .2 1 8 3 .1 2 3 3 .0 3 2 2 .9 4 6 2 .8 6 3

3 .2 0 8 3.114 3 .0 2 4 2 .9 3 7 2 .8 5 5

3 .1 9 8 3 .1 0 5 3. 015 2. 929 2. 846

3 .1 8 9 3.095A † 3 .0 0 6 2 .9 2 1 2 .8 3 9

3. 17 9 3 .0 8 6 2. 99 7 2. 91 2 2. 83 1

71 72 73 74 75

2. 82 3 2. 74 5 2. 67 0 2. 59 8 2. 53 0

2 .8 1 5 2 .7 3 7 2 .6 6 3 2 .5 9 1 2 .5 2 3

2 .8 0 7 2 .7 3 0 2 .6 5 6 2 .5 8 4 2 .5 1 6

2 .7 9 9 2 .7 2 2 2 .6 4 8 2 .5 7 7 2 .5 0 9

2. 79 1 2. 71 5 2. 64 1 2. 57 1 2. 50 3

2 .7 8 3 2 .7 0 7 2 .6 3 4 2 .5 6 4 2 .4 9 6

2 .7 7 6 2 .7 0 0 2 .6 2 7 2 .5 5 7 2 .4 9 0

2. 768 2. 692 2. 620 2. 550 2. 483

2 .7 6 0 2 .6 8 5 2 .6 1 3 2 .5 4 3 2 .4 7 6

2. 75 2 2. 67 7 2. 60 5 2. 53 6 2. 47 0

76 77 78 79 80

2. 46 3 2. 40 0 2. 33 9 2. 28 0 2. 22 3

2 .4 5 7 2 .3 9 4 2 .3 3 3 2 .2 7 4 2 .2 1 8

2 .4 5 1 2 .3 8 7 2 .3 2 7 2 .2 6 8 2 .2 1 2

2 .4 4 4 2 .3 8 1 2 .3 2 1 2 .2 6 3 2 .2 0 7

2. 43 8 2 .. 3 7 5 2. 31 5 2. 25 7 2. 20 1

2 .4 3 1 2 .3 6 9 2 .3 0 9 2 .2 5 1 2 .1 9 6

2 .4 2 5 2 .3 6 3 2 .3 0 3 2 .2 4 6 2 .1 9 0

2. 419 2 .3 5 7 2. 297 2. 240 2. 185

2 .4 1 2 2 .3 5 1 2 .2 9 2 2 .2 3 4 2 .1 7 9

2. 40 6 2 .3 4 5 2. 28 6 2. 22 9 2. 17 4

81 82 83 84 85

2. 16 9 2.116 2. 06 5 2. 01 7 1. 96 9

2 .1 6 3 2.111 2 .0 6 0 2 .0 1 2 1 .9 6 5

2 .1 5 8 2 .1 0 6 2 .0 5 6 2 .0 7 7 1 .9 6 0

2 .1 5 3 2 .1 0 1 2 .0 5 1 2 .0 0 2 1 .9 5 6

2. 14 7 2. 09 6 2. 04 6 1. 99 8 1. 95 1

2 .1 4 2 2 .0 9 1 2 .0 4 1 1 .9 9 3 1 .9 4 6

2 .1 3 7 2 .0 8 6 2 .0 3 6 1 .9 8 8 1 .9 4 2

2. 132 2 .0 8 0 2. 031 1. 983 1. 937

2 .1 2 7 2 .0 7 5 2 .0 2 6 1 .9 7 9 1 .9 3 3

2. 12 1 2. 07 0 2. 02 1 1. 97 4 1. 92 8

86 87 88 89 90

1. 92 4 1. 88 0 1. 83 7 1. 79 6 1. 75 7

1 .9 1 9 1 .8 7 6 1 .8 3 3 1 .7 9 2 1 .7 5 3

1 .9 1 5 1 .8 7 1 1 .8 2 9 1 .7 8 8 1 .7 4 9

1.911 1 .8 6 7 1 .8 2 5 1 .7 8 4 1 .7 4 5

1. 90 6 1. 86 3 1. 82 1 1. 78 0 1. 74 1

1 .9 0 2 1 .8 5 8 1 .8 1 7 1 .7 7 6 1 .7 3 7

1 .8 9 7 1 .8 5 4 1 .8 1 3 1 .7 7 2 1 .7 3 3

1. 893 1. 850 1. 809 1. 768 1. 730

1 .8 8 9 1 .8 4 6 1 .8 0 4 1 .7 6 5 1 .7 2 6

1. 88 4 1. 84 2 1. 80 0 1. 76 1 1. 72 2

91 92 93

1. 71 8 1. 68 1 1. 65 4

1 .7 1 5 1 .6 7 7 1 .6 4 2

1.711 1 .6 7 4 1 .6 3 8

1 .7 0 7 1 .6 7 0 1 .6 3 5

1. 70 3 1. 66 7 1. 63 1

1 .7 0 0 1 .6 6 3 1 .6 2 8

1 .6 9 6 1 .6 5 9 1 .6 2 4

1. 692 1. 656 1. 621

1 .6 8 8 1 .6 5 2 1 .6 1 7

1. 68 5 1. 64 9 1. 61 4

36

E384 − 11

´1

TABLE TA BLE X6.1   Continued  Knoop Hardness Number for Diagonal Measured to 0.1 µm

Diagonal of Indentation, µm

0 .0

0. 1

0. 2

0 .3

0 .4

0. 5

0 .6

0. 7

0 .8

0 .9

94 95

1. 6 10 1. 5 77

1 .6 0 7 1 .5 7 3

1 .6 0 4 1 .5 7 0

1 .6 0 0 1 .5 6 7

1. 59 7 1. 56 3

1 .5 9 3 1 .5 6 0

1 .5 9 0 1 .5 5 7

1 .5 8 7 1 .5 5 4

1 .5 8 3 1 .5 5 0

1. 58 0 1. 54 7

96 97 98 99 10 0

1. 5 44 1. 5 12 1. 4 82 1. 4 52 1. 42 3

1 .5 4 1 1 .5 0 9 1 .4 7 9 1 .4 4 9 1 .4 2 0

1 .5 3 8 1 .5 0 6 1 .4 7 6 1 .4 4 6 1. 41 7

1 .5 3 4 1 .5 0 3 1 .4 7 3 1 .4 4 3 1 .4 1 3

1. 53 1 1. 50 0 1. 47 0 1. 44 0 1 .4 1 2

1 .5 2 8 1 .4 9 7 1 .4 6 7 1 .4 3 7 1. 40 9

1 .5 2 5 1 .4 9 4 1 .4 6 4 1 .4 3 4 1 .4 0 6

1 .5 2 2 1 .4 9 1 1 .4 6 1 1 .4 3 1 1 .4 0 3

1 .5 1 9 1 .4 8 8 1 .4 5 8 1 .4 2 9 1 .4 0 0

1. 51 5 1. 48 5 1. 45 5 1. 42 6 1 .3 9 8

10 1 10 2 10 3 10 4 10 5

1. 39 5 1. 36 8 1. 34 1 1. 31 6 1. 29 1

1 .3 9 2 1 .3 6 5 1 .3 3 9 1 .3 1 3 1 .2 8 8

1. 38 9 1. 36 2 1. 33 6 1.311 1. 28 6

1 .3 8 7 1 .3 6 0 1 .3 3 3 1 .3 0 8 1 .2 8 3

1 .3 8 4 1 .3 5 7 1 .3 3 1 1 .3 0 5 1 .2 8 1

1. 38 1 1. 35 4 1. 32 8 1. 30 3 1. 27 8

1 .3 7 8 1 .3 5 2 1 .3 2 6 1 .3 0 1 1 .2 7 6

1 .3 7 6 1 .3 4 9 1 .3 2 3 1 .2 9 8 1 .2 7 4

1 .3 7 3 1 .3 4 6 1 .3 2 1 1 .2 9 6 1 .2 7 1

1 .3 7 0 1 .3 4 4 1 .3 1 8 1 .2 9 3 1 .2 6 9

10 6 10 7 10 8 10 9 110

1. 26 6 1. 24 3 1. 22 0 1. 19 8 1. 17 6

1 .2 6 4 1 .2 4 0 1 .2 1 8 1 .1 9 5 1 .1 7 4

1. 26 2 1. 23 8 1. 21 5 1. 19 3 1. 17 2

1 .2 5 9 1 .2 3 6 1 .2 1 3 1 .1 9 1 1 .1 7 0

1 .2 5 7 1 .2 3 4 1.211 1 .1 8 9 1 .1 6 7

1. 25 5 1. 23 1 1. 20 9 1. 18 7 1. 16 5

1 .2 5 2 1 .2 2 9 1 .2 0 6 1 .1 8 5 1 .1 6 3

1 .2 5 0 1 .2 2 7 1 .2 0 4 1 .1 8 2 1 .1 6 1

1 .2 4 7 1 .2 2 4 1 .2 0 2 1 .1 8 0 1 .1 5 9

1 .2 4 5 1 .2 2 2 1 .2 0 0 1 .1 7 8 1 .1 5 7

111 112 113 114 115

1. 15 5 1. 13 4 1.114 1. 09 5 1. 07 6

1 .1 5 3 1 .1 3 2 1.112 1 .0 9 3 1 .0 7 4

1. 15 1 1. 13 0 1.110 1. 09 1 1. 07 2

1 .1 4 9 1 .1 2 8 1 .1 0 8 1 .0 8 9 1 .0 7 0

1 .1 4 7 1 .1 2 6 1 .1 0 6 1 .0 8 7 1 .0 6 8

1. 14 5 1. 12 4 1. 10 5 1. 08 5 1. 06 7

1 .1 4 2 1 .1 2 2 1 .1 0 3 1 .0 8 3 1 .0 6 5

1 .1 4 0 1 .1 2 0 1 .1 0 1 1 .0 8 2 1 .0 6 3

1 .1 3 8 1.118 1 .0 9 9 1 .0 8 0 1 .0 6 1

1 .1 3 6 1.116 1 .0 9 7 1 .0 7 8 1 .0 5 9

116 117 118 119 12 0

1. 05 7 1. 03 9 1. 02 2 1. 00 5 0 .9 8 8 1

1 .0 5 6 1 .0 3 8 1 .0 2 0 1 .0 0 3 0. 98 6 5

1. 05 4 1. 03 6 1. 01 8 1. 00 1 0. 98 4 8

1 .0 5 2 1 .0 3 4 1 .0 1 7 0 .9 9 9 8 0 .9 8 3 2

1 .0 5 0 1 .0 3 2 1 .0 1 5 0. 99 8 1 0 .9 8 1 6

1. 04 8 1. 03 1 1. 01 3 0 .9 9 6 4 0 .9 7 9 9

1 .0 4 7 1 .0 2 9 1 .0 1 2 0 .9 9 4 7 0 .9 7 8 3

1 .0 4 5 1 .0 2 7 1 .0 1 0 0. 99 3 1 0 .9 7 6 7

1 .0 4 3 1 .0 2 5 1 .0 0 8 0 .9 9 1 4 0 .9 7 5 1

1 .0 4 1 1 .0 2 4 1 .0 0 6 0 .9 8 9 8 0 .9 7 3 5

12 1 12 2 12 3 12 4 12 5

0 .9 7 1 9 0 .9 5 6 0 0 .9 4 0 5 0 .9 2 5 4 0 .9 1 0 7

0. 97 0 3 0. 95 4 4 0. 93 9 0 0. 92 3 9 0. 90 9 2

0. 96 8 7 0. 95 2 9 0. 93 7 5 0. 92 2 4 0. 90 7 8

0 .9 6 7 1 0 .9 5 1 3 0 .9 3 5 9 0 .9 2 0 9 0 .9 0 6 3

0 .9 6 5 5 0 .9 4 9 8 0 .9 3 4 4 0 .9 1 9 5 0 .9 0 4 9

0 .9 6 3 9 0 .9 4 8 2 0 .9 3 2 9 0 .9 1 8 0 0 .9 0 3 4

0 .9 6 2 3 0 .9 4 6 7 0 .9 3 1 4 0 .9 1 6 5 0 .9 0 2 0

0 .9 6 0 7 0 .9 4 5 1 0 .9 2 9 9 0 .9 1 5 0 0 .9 0 0 5

0 .9 5 9 1 0 .9 4 3 6 0 .9 2 8 4 0 .9 1 3 6 0 .8 9 9 1

0 .9 5 7 6 0 .9 4 2 0 0 .9 2 6 9 0 .9 1 2 1 0 .8 9 7 7

12 6 12 7 12 8 12 9 13 0

0 .8 9 6 3 0 .8 8 2 2 0 .8 6 8 5 0 .8 5 5 1 0 .8 4 2 0

0. 89 4 8 0. 88 0 8 0. 86 7 1 0. 85 3 7 0. 84 0 7

0. 89 3 4 0. 87 9 4 0. 86 5 8 0. 85 2 4 0. 83 9 4

0 .8 9 2 0 0 .8 7 8 0 0 .8 6 4 4 0.8511 0 .8 3 8 1

0 .8 9 0 6 0 .8 7 6 7 0 .8 6 3 1 0 .8 4 9 8 0 .8 3 6 8

0 .8 8 9 2 0 .8 7 5 3 0 .8 6 1 7 0 .8 4 8 5 0 .8 3 5 5

0 .8 8 7 8 0 .8 7 3 9 0 .8 6 0 4 0 .8 4 7 2 0 .8 3 4 3

0 .8 8 6 4 0 .8 7 2 6 0 .8 5 9 1 0 .8 4 5 9 0 .8 3 3 0

0 .8 8 5 0 0 .8 7 1 2 0 .8 5 7 7 0 .8 4 4 6 0 .8 3 1 7

0 .8 8 3 6 0 .8 6 9 8 0 .8 5 6 4 0 .8 4 3 3 0 .8 3 0 4

13 1 13 2 13 3 13 4 13 5

0 .8 2 9 1 0 .8 1 6 6 0 .8 0 4 4 0 .7 9 2 4 0 .7 8 0 7

0. 82 7 9 0. 81 5 4 0. 80 3 2 0. 79 1 3 0. 77 9 6

0. 82 6 6 0. 81 4 2 0. 80 2 0 0. 79 0 1 0. 77 8 4

0 .8 2 5 4 0 .8 1 2 9 0 .8 0 0 8 0 .7 8 8 9 0 .7 7 7 3

0 .8 2 4 1 0.8117 0 .7 9 9 6 0 .7 8 7 7 0 .7 7 6 1

0 .8 2 2 9 0 .8 1 0 5 0 .7 9 8 4 0 .7 8 6 6 0 .7 7 5 0

0 .8 2 1 6 0 .8 0 9 3 0 .7 9 7 2 0 .7 8 5 4 0 .7 7 3 8

0 .8 2 0 4 0 .8 0 8 0 0 .7 9 6 0 0 .7 8 4 2 0 .7 7 2 7

0 .8 1 9 1 0 .8 0 6 8 0 .7 9 4 8 0 .7 8 3 1 0 .7 7 1 6

0 .8 1 7 9 0 .8 0 5 6 0 .7 9 3 6 0 .7 8 1 9 0 .7 7 0 4

13 6 13 7 13 8 13 9 14 0

0 .7 6 9 3 0 .7 5 8 1 0 .7 4 7 2 0 .7 3 6 5 0 .7 2 6 0

0. 76 8 2 0. 75 7 0 0. 74 6 1 0. 73 5 4 0. 72 4 9

0. 76 7 0 0. 75 5 9 0. 74 5 0 0. 73 4 3 0. 72 3 9

0 .7 6 5 9 0 .7 5 4 8 0 .7 4 3 9 0 .7 3 3 3 0 .7 2 2 9

0 .7 6 4 8 0 .7 5 3 7 0 .7 4 2 9 0 .7 3 2 2 0 .7 2 1 8

0 .7 6 3 7 0 .7 5 2 6 0 .7 4 1 8 0 .7 3 1 2 0 .7 2 0 8

0 .7 6 2 6 0 .7 5 1 5 0 .7 4 0 7 0 .7 3 0 1 0 .7 1 9 8

0 .7 6 1 4 0 .7 5 0 4 0 .7 3 9 6 0 .7 2 9 1 0 .7 1 8 8

0 .7 6 0 3 0 .7 4 9 3 0 .7 3 8 6 0 .7 2 8 1 0 .7 1 7 7

0 .7 5 9 2 0 .7 4 8 3 0 .7 3 7 5 0 .7 2 7 0 0 .7 1 6 7

14 1 14 2 14 3 14 4 14 5

0 .7 1 5 7 0 .7 0 5 7 0 .6 9 5 8 0 .6 8 6 2 0 .6 7 6 8

0. 71 4 7 0. 70 4 7 0. 69 4 9 0. 68 5 2 0. 67 5 8

0. 71 3 7 0. 70 3 7 0. 69 3 9 0. 68 4 3 0. 67 4 9

0 .7 1 2 7 0 .7 0 2 7 0 .6 9 2 9 0 .6 8 3 4 0 .6 7 4 0

0.7117 0 .7 0 1 7 0 .6 9 2 0 0 .6 8 2 4 0 .6 7 3 1

0 .7 1 0 7 0 .7 0 0 7 0 .6 9 1 0 0 .6 8 1 5 0 .6 7 2 1

0 .7 0 9 7 0 .6 9 9 7 0 .6 9 0 0 0 .6 8 0 5 0 .6 7 1 2

0 .7 0 8 7 0 .6 9 8 8 0 .6 8 9 1 0 .6 7 9 6 0 .6 7 0 3

0 .7 0 7 7 0 .6 9 7 8 0 .6 8 8 1 0 .6 7 8 6 0 .6 6 9 4

0 .7 0 6 7 0 .6 9 6 8 0 .6 8 7 2 0 .6 7 7 7 0 .6 6 8 4

14 6 14 7 14 8 14 9 15 0

0 .6 6 7 5 0 .6 5 8 5 0 .6 4 9 6 0 .6 4 0 9 0 .6 3 2 4

0. 66 6 6 0. 65 7 6 0. 64 8 7 0. 64 0 1 0. 63 1 6

0. 66 5 7 0. 65 6 7 0. 64 7 9 0. 63 9 2 0. 63 0 7

0 .6 6 4 8 0 .6 5 5 8 0 .6 4 7 0 0 .6 3 8 3 0 .6 2 9 9

0 .6 6 3 9 0 .6 5 4 9 0 .6 4 6 1 0 .6 3 7 5 0 .6 2 9 0

0 .6 6 3 0 0 .6 5 4 0 0 .6 4 5 2 0 .6 3 6 6 0 .6 2 8 2

0 .6 6 2 1 0 .6 5 3 1 0 .6 4 4 4 0 .6 3 5 8 0 .6 2 7 4

0 .6 6 1 2 0 .6 5 2 3 0 .6 4 3 5 0 .6 3 4 9 0 .6 2 6 5

0 .6 6 0 3 0 .6 5 1 4 0 .6 4 2 6 0 .6 3 4 1 0 .6 2 5 7

0 .6 5 9 4 0 .6 5 0 5 0 .6 4 1 8 0 .6 3 3 2 0 .6 2 4 9

15 1 15 2 15 3 15 4 15 5

0 .6 2 4 1 0 .6 1 5 9 0 .6 0 7 8 0 .6 0 0 0 0 .5 9 2 3

0. 62 3 2 0. 61 5 1 0. 60 7 1 0. 59 9 2 0. 59 1 5

0. 62 2 4 0. 61 4 3 0. 60 6 3 0. 59 8 4 0. 59 0 7

0 .6 2 1 6 0 .6 1 3 4 0 .6 0 5 5 0 .5 9 7 6 0 .5 9 0 0

0 .6 2 0 8 0 .6 1 2 6 0 .6 0 4 7 0 .5 9 6 9 0 .5 8 9 2

0 .6 1 9 9 0.6118 0 .6 0 3 9 0 .5 9 6 1 0 .5 8 8 5

0 .6 1 9 1 0.6110 0 .6 0 3 1 0 .5 9 5 3 0 .5 8 7 7

0 .6 1 8 3 0 .6 1 0 2 0 .6 0 2 3 0 .5 9 4 6 0 .5 8 6 9

0 .6 1 7 5 0 .6 0 9 4 0 .6 0 1 5 0 .5 9 3 8 0 .5 8 6 2

0 .6 1 6 7 0 .6 0 8 6 0 .6 0 0 8 0 .5 9 3 0 0 .5 8 5 4

37

E384 − 11

´1

TABLE TA BLE X6.1   Continued 

A

Knoop Hardness Number for Diagonal Measured to 0.1 µm

Diagonal of Indentation, µm

0 .0

0. 1

0. 2

0 .3

0 .4

0. 5

0 .6

0. 7

0 .8

0 .9

15 6 15 7 15 8 15 9 16 0

0 .5 8 4 7 0 .5 7 7 3 0 .5 7 0 0 0 .5 6 2 8 0 .5 5 5 8

0. 58 3 9 0. 57 6 5 0. 56 9 3 0. 56 2 1 0. 55 5 1

0. 58 3 2 0. 57 5 8 0. 56 8 5 0. 56 1 4 0. 55 4 4

0 .5 8 2 5 0 .5 7 5 1 0 .5 6 7 8 0 .5 6 0 7 0 .5 5 3 7

0 .5 8 1 7 0 .5 7 4 3 0 .5 6 7 1 0 .5 6 0 0 0 .5 5 3 1

0 .5 8 1 0 0 .5 7 3 6 0 .5 6 6 4 0 .5 5 9 3 0 .5 5 2 4

0 .5 8 0 2 0 .5 7 2 9 0 .5 6 5 7 0 .5 5 8 6 0 .5 5 1 7

0 .5 7 9 5 0 .5 7 2 2 0 .5 6 5 0 0 .5 5 7 9 0 .5 5 1 0

0 .5 7 8 7 0 .5 7 1 4 0 .5 6 4 3 0 .5 5 7 2 0 .5 5 0 3

0 .5 7 8 0 0 .5 7 0 7 0 .5 6 3 5 0 .5 5 6 5 0 .5 4 9 6

16 1 16 2 16 3 16 4 16 5

0 .5 4 8 9 0 .5 4 2 2 0 .5 3 5 6 0 .5 2 9 0 0 .5 2 2 6

0. 54 8 3 0. 54 1 5 0. 53 4 9 0. 52 8 4 0. 52 2 0

0. 54 7 6 0. 54 0 8 0. 53 4 2 0. 52 7 8 0. 52 1 4

0 .5 4 6 9 0 .5 4 0 2 0 .5 3 3 6 0 .5 2 7 1 0 .5 2 0 8

0 .5 4 6 2 0 .5 3 9 5 0 .5 3 2 9 0 .5 2 6 5 0 .5 2 0 1

0 .5 4 5 5 0 .5 3 8 9 0 .5 3 2 3 0 .5 2 5 8 0 .5 1 9 5

0 .5 4 4 9 0 .5 3 8 2 0 .5 3 1 6 0 .5 2 5 2 0 .5 1 8 9

0 .5 4 4 2 0 .5 3 7 5 0 .5 3 1 0 0 .5 2 4 6 0 .5 1 8 2

0 .5 4 3 5 0 .5 3 6 9 0 .5 3 0 3 0 .5 2 3 9 0 .5 1 7 6

0 .5 4 2 9 0 .5 3 6 2 0 .5 2 9 7 0 .5 2 3 3 0 .5 1 7 0

16 6 16 7 16 8 16 9 17 0

0 .5 1 6 4 0 .5 1 0 2 0 .5 0 4 1 0 .4 9 8 2 0 .4 9 2 4

0. 51 5 7 0. 50 9 6 0. 50 3 5 0. 49 7 6 0. 49 1 8

0. 51 5 1 0. 50 9 0 0. 50 3 0 0. 49 7 0 0. 49 1 2

0 .5 1 4 5 0 .5 0 8 4 0 .5 0 2 4 0 .4 9 6 4 0 .4 9 0 6

0 .5 1 3 9 0 .5 0 7 8 0 .5 0 1 8 0 .4 9 5 9 0 .4 9 0 0

0 .5 1 3 3 0 .5 0 7 2 0 .5 0 1 2 0 .4 9 5 3 0 .4 8 9 5

0 .5 1 2 7 0 .5 0 6 6 0 .5 0 0 6 0 .4 9 4 7 0 .4 8 8 9

0 .5 1 2 0 0 .5 0 6 0 0 .5 0 0 0 0 .4 9 4 1 0 .4 8 8 3

0.5114 0 .5 0 5 4 0 .4 9 9 4 0 .4 9 3 5 0 .4 8 7 8

0 .5 1 0 8 0 .5 0 4 7 0 .4 9 8 8 0 .4 9 2 9 0 .4 8 7 2

17 1 17 2 17 3 17 4 17 5

0 .4 8 6 6 0 .4 8 1 0 0 .4 7 5 4 0 .4 7 0 0 0 .4 6 4 6

0. 48 6 0 0. 48 0 4 0. 47 4 9 0. 46 9 4 0. 46 4 1

0. 48 5 5 0. 47 9 9 0. 47 4 3 0. 46 8 9 0. 46 3 6

0 .4 8 4 9 0 .4 7 9 3 0 .4 7 3 8 0 .4 6 8 4 0 .4 6 3 0

0 .4 8 4 3 0 .4 7 8 7 0 .4 7 3 2 0 .4 6 7 8 0 .4 6 2 5

0 .4 8 3 8 0 .4 7 8 2 0 .4 7 2 7 0 .4 6 7 3 0 .4 6 2 0

0 .4 8 3 2 0 .4 7 7 6 0 .4 7 2 1 0 .4 6 6 8 0 .4 6 1 5

0 .4 8 2 7 0 .4 7 7 1 0 .4 7 1 6 0 .4 6 6 2 0 .4 6 0 9

0 .4 8 2 1 0 .4 7 6 5 0.4711 0 .4 6 5 7 0 .4 6 0 4

0 .4 8 1 5 0 .4 7 6 0 0 .4 7 0 5 0 .4 6 5 2 0 .4 5 9 9

17 6 17 7 17 8 17 9 18 0

0 .4 5 9 4 0 .4 5 4 2 0 .4 4 9 1 0 .4 4 4 1 0 .4 3 9 2

0. 45 8 8 0. 45 3 7 0. 44 8 6 0. 44 3 6 0. 43 8 7

0. 45 8 3 0. 45 3 2 0. 44 8 1 0. 44 3 1 0. 43 8 2

0 .4 5 7 8 0 .4 5 2 6 0 .4 4 7 6 0 .4 4 2 6 0 .4 3 7 7

0 .4 5 7 3 0 .4 5 2 1 0 .4 4 7 1 0 .4 4 2 1 0 .4 3 7 2

0 .4 5 6 8 0 .4 5 1 6 0 .4 4 6 6 0 .4 4 1 6 0 .4 3 6 7

0 .4 5 6 2 0.4511 0 .4 4 6 1 0.4411 0 .4 3 6 3

0 .4 5 5 7 0 .4 5 0 6 0 .4 4 5 6 0 .4 4 0 6 0 .4 3 5 8

0 .4 5 5 2 0 .4 5 0 1 0 .4 4 5 1 0 .4 4 0 1 0 .4 3 5 3

0 .4 5 4 7 0 .4 4 9 6 0 .4 4 4 6 0 .4 3 9 7 0 .4 3 4 8

18 1 18 2 18 3 18 4 18 5

0 .4 3 4 3 0 .4 2 9 6 0 .4 2 4 9 0 .4 2 0 3 0 .4 1 5 8

0. 43 3 9 0. 42 9 1 0. 42 4 4 0. 41 9 8 0. 41 5 3

0. 43 3 4 0. 42 8 6 0. 42 4 0 0. 41 9 4 0. 41 4 9

0 .4 3 2 9 0 .4 2 8 2 0 .4 2 3 5 0 .4 1 8 9 0 .4 1 4 4

0 .4 3 2 4 0 .4 2 7 7 0 .4 2 3 0 0 .4 1 8 5 0 .4 1 4 0

0 .4 3 1 9 0 .4 2 7 2 0 .4 2 2 6 0 .4 1 8 0 0 .4 1 3 5

0 .4 3 1 5 0 .4 2 6 8 0 .4 2 2 1 0 .4 1 7 6 0 .4 1 3 1

0 .4 3 1 0 0 .4 2 6 3 0 .4 2 1 7 0 .4 1 7 1 0 .4 1 2 6

0 .4 3 0 5 0 .4 2 5 8 0 .4 2 1 2 0 .4 1 6 7 0 .4 1 2 2

0 .4 3 0 0 0 .4 2 5 4 0 .4 2 0 7 0 .4 1 6 2 0.4117

18 6 18 7 18 8 18 9 19 0

0.4113 0 .4 0 6 9 0 .4 0 2 6 0 .3 9 8 3 0 .3 9 4 2

0. 41 0 9 0. 40 6 5 0. 40 2 2 0. 39 7 9 0. 39 3 7

0. 41 0 4 0. 40 6 0 0. 40 1 7 0. 39 7 5 0. 39 3 3

0 .4 1 0 0 0 .4 0 5 6 0 .4 0 1 3 0 .3 9 7 1 0 .3 9 2 9

0 .4 0 9 5 0 .4 0 5 2 0 .4 0 0 9 0 .3 9 6 7 0 .3 9 2 5

0 .4 0 9 1 0 .4 0 4 7 0 .4 0 0 5 0 .3 9 6 2 0 .3 9 2 1

0 .4 0 8 7 0 .4 0 4 3 0 .4 0 0 0 0 .3 9 5 8 0 .3 9 1 7

0 .4 0 8 2 0 .4 0 3 9 0 .3 9 9 6 0 .3 9 5 4 0 .3 9 1 3

0 .4 0 7 8 0 .4 0 3 4 0 .3 9 9 2 0 .3 9 5 0 0 .3 9 0 9

0 .4 0 7 3 0 .4 0 3 0 0 .3 9 8 8 0 .3 9 4 6 0 .3 9 0 5

19 1 19 2 19 3 19 4 19 5

0 .3 9 0 0 0 .3 8 6 0 0 .3 8 2 0 0 .3 7 8 1 0 .3 7 4 2

0. 38 9 6 0. 38 5 6 0. 38 1 6 0. 37 7 7 0. 37 3 8

0. 38 9 2 0. 38 5 2 0. 38 1 2 0. 37 7 3 0. 37 3 4

0 .3 8 8 8 0 .3 8 4 8 0 .3 8 0 8 0 .3 7 6 9 0 .3 7 3 1

0 .3 8 8 4 0 .3 8 4 4 0 .3 8 0 4 0 .3 7 6 5 0 .3 7 2 7

0 .3 8 8 0 0 .3 8 4 0 0 .3 8 0 0 0 .3 7 6 1 0 .3 7 2 3

0 .3 8 7 6 0 .3 8 3 6 0 .3 7 9 6 0 .3 7 5 7 0 .3 7 1 9

0 .3 8 7 2 0 .3 8 3 2 0 .3 7 9 2 0 .3 7 5 4 0 .3 7 1 5

0 .3 8 6 8 0 .3 8 2 8 0 .3 7 8 9 0 .3 7 5 0 0 .3 7 1 2

0 .3 8 6 4 0 .3 8 2 4 0 .3 7 8 5 0 .3 7 4 6 0 .3 7 0 8

19 6 19 7 19 8 19 9 20 0

0 .3 7 0 4 0 .3 6 6 3 0 .3 6 3 0 0 .3 5 9 3 0 .3 5 5 7

0. 37 0 0 0. 36 6 3 0. 36 2 6 0. 35 9 0 0. 35 5 4

0. 36 9 6 0. 36 5 9 0. 36 2 2 0. 35 8 6 0. 35 5 0

0 .3 6 9 3 0 .3 6 5 5 0 .3 6 1 9 0 .3 5 8 2 0 .3 5 4 7

0 .3 6 8 9 0 .3 6 5 2 0 .3 6 1 5 0 .3 5 7 9 0 .3 5 4 3

0 .3 6 8 5 0 .3 6 4 8 0.3611 0 .3 5 7 5 0 .3 5 4 0

0 .3 6 8 1 0 .3 6 4 4 0 .3 6 0 8 0 .3 5 7 2 0 .3 5 3 6

0 .3 6 7 8 0 .3 6 4 1 0 .3 6 0 4 0 .3 5 6 8 0 .3 5 3 3

0 .3 6 7 4 0 .3 6 3 7 0 .3 6 0 0 0 .3 5 6 4 0 .3 5 2 9

0 .3 6 7 0 0 .3 6 3 3 0 .3 5 9 7 0 .3 5 6 1 0 .3 5 2 5

† Corrected.

TABLE X6.2 Vickers Hardness Numbers for Load of 1 gf Vickers Hardness Number for Diagonal Measured to 0.1 µm

Diagonal of Indentation, µm

0 .0

0 .1

0. 2

0. 3

0 .4

0. 5

0 .6

0 .7

0 .8

0 .9

1 2 3 4 5

18 5 4. 6 4 6 3. 0 2 0 6. 9 115.17 74

15 3 3. 5 4 2 0. 0 1 9 3. 3 110.29 71

1 2 88 3 8 3. 1 1 8 1. 1 1 0 5. 58 68

1 0 9 7 .5 3 5 0 .3 1 7 0 .3 1 0 0 .0 1 66

9 4 6. 1 3 2 1 .9 1 6 0 .4 9 5 .7 8 6 3 .5 9

8 2 4 .2 29 6. 7 15 1. 4 9 1 .5 7 6 1 .3 0

7 2 4 .4 2 7 4 .3 1 4 3 .1 8 7 .6 4 5 9 .1 3

6 4 1. 6 2 5 4 .4 1 3 5 .5 8 3. 95 5 7 .0 7

5 7 2 .3 2 3 6 .5 1 2 8 .4 8 0 .4 8 5 5 .1 2

5 1 3 .7 2 2 0 .5 1 2 1 .9 7 7 .2 3 5 3 .2 7

6 7 8 9 10

5 1 .5 1 3 7 .8 4 2 8 .9 7 2 2 .8 9 18 . 54

4 9 .8 3 3 6 .7 9 2 8 .2 6 2 2 .3 9 1 8 .1 8

4 8 .2 4 3 5 .7 7 2 7 .5 8 2 1 .9 1 1 7. 82

4 6 .7 2 3 4 .8 0 2 6 .9 2 2 1 .4 4 1 7 .4 8

4 5. 27 3 3. 86 2 6. 28 2 0. 99 1 7 .1 4

4 3 .8 9 3 2 .9 7 2 5 .6 7 2 0 .5 5 1 6 .8 2

4 2 .5 7 3 2 .1 0 2 5 .0 7 2 0 .1 2 1 6 .5 0

4 1. 31 3 1. 28 2 4. 50 1 9. 71 1 6 .2 0

4 0 .1 0 3 0 .4 8 2 3 .9 5 1 9 .3 1 1 5 .9 0

3 8 .9 5 2 9 .7 1 2 3 .4 1 1 8 .9 2 1 5 .6 1

11

15 . 33

1 5 .0 5

1 4. 78

1 4 .5 2

1 4 .2 7

1 4 .0 2

1 3 .7 8

1 3 .5 5

1 3 .3 2

1 3 .0 9

38

E384 − 11

´1

TABLE X6.2   Continued  Vickers Hardness Number for Diagonal Measured to 0.1 µm

Diagonal of Indentation, µm

0 .0

0 .1

0. 2

0. 3

0 .4

0. 5

0 .6

0 .7

0 .8

0 .9

12 13 14 15

12 . 88 10 . 97 9. 4 61 8. 2 42

1 2 .6 7 1 0 .8 1 9. 32 7 8. 13 3

1 2. 46 1 0. 64 9 .1 9 6 8 .0 2 6

1 2 .2 6 1 0 .4 8 9. 06 8 7. 92 2

1 2 .0 6 1 0 .3 3 8. 94 3 7. 81 9

11.87 1 0 .1 7 8 .8 2 0 7 .7 1 8

11.68 1 0 .0 3 8 .6 9 9 7 .6 2 0

11.50 9. 88 0 8. 58 1 7. 52 3

11.32 9. 73 7 8. 46 6 7. 42 8

11.14 9. 59 8 8. 35 3 7. 33 5

16 17 18 19 20

7. 2 44 6. 4 16 5. 7 23 5. 1 37 4. 6 36

7. 15 4 6. 34 2 5. 66 0 5. 08 3 4. 59 0

7 .0 6 6 6 .2 6 8 5 .5 9 8 5 .0 3 0 4 .5 4 5

6. 97 9 6. 19 6 5. 53 7 4. 97 8 4. 50 0

6. 89 5 6. 12 5 5. 47 7 4. 92 7 4. 45 6

6.811 6 .0 5 5 5 .4 1 8 4 .8 7 7 4 .4 1 3

6 .7 2 9 5 .9 8 6 5 .3 6 0 4 .8 2 7 4 .3 7 0

6. 64 9 5. 91 9 5. 30 3 4. 77 8 4. 32 8

6. 57 0 5. 85 3 5. 24 7 4. 73 0 4. 28 6

6. 49 3 5. 78 7 5. 19 1 4. 68 3 4. 24 5

21 22 23 24 25

4. 2 05 3. 8 31 3. 5 05 3. 2 19 2. 9 67

4. 16 5 3. 79 7 3. 47 5 3. 19 3 2. 94 3

4 .1 2 6 3 .7 6 3 3 .4 4 5 3 .1 6 6 2 .9 2 0

4. 08 7 3. 72 9 3. 41 6 3. 14 0 2. 89 7

4. 04 9 3. 69 6 3. 38 7 3.115 2. 87 4

4 .0 1 2 3 .6 6 3 3 .3 5 8 3 .0 8 9 2 .8 5 2

3 .9 7 5 3 .6 3 1 3 .3 2 9 3 .0 6 4 2 .8 3 0

3. 93 8 3. 59 9 3. 30 1 3. 03 9 2. 80 8

3. 90 2 3. 58 7 3. 27 4 3. 01 5 2. 78 6

3. 86 6 3. 53 6 3. 24 6 2. 99 1 2. 76 4

26 27 28 29 30

2. 7 43 2. 5 44 2. 3 65 2. 2 05 2. 0 60

2. 72 2 2. 52 5 2. 34 8 2. 19 0 2. 04 7

2 .7 0 1 2 .5 0 6 2 .3 3 2 2 .1 7 5 2 .0 3 3

2. 68 1 2. 48 8 2. 31 5 2. 16 0 2. 02 0

2. 66 1 2. 47 0 2. 29 9 2. 14 5 2. 00 7

2 .6 4 1 2 .4 5 2 2 .2 8 3 2 .1 3 1 1 .9 9 3

2 .6 2 1 2 .4 3 4 2 .2 6 7 2.116 1 .9 8 0

2. 60 1 2. 41 7 2. 25 1 2. 10 2 1. 96 8

2. 58 2 2. 39 9 2. 23 6 2. 08 8 1. 95 5

2. 56 3 2. 38 2 2. 22 0 2. 07 4 1. 94 2

31 32 33 34 35

1. 9 30 1.811 1. 7 03 1. 6 04 1. 5 14

1. 91 7 1. 80 0 1. 69 3 1. 59 5 1. 50 5

1 .9 0 5 1 .7 8 8 1 .6 8 2 1 .5 8 5 1 .4 9 7

1. 89 3 1. 77 7 1. 67 2 1. 57 6 1. 48 8

1. 88 1 1. 76 6 1. 66 2 1. 56 7 1. 48 0

1 .8 6 9 1 .7 5 6 1 .6 5 2 1 .5 5 8 1 .4 7 1

1 .8 5 7 1 .7 4 5 1 .6 4 3 1 .5 4 9 1 .4 6 3

1. 84 5 1. 73 4 1. 63 3 1. 54 0 1. 45 5

1. 83 4 1. 72 4 1. 62 3 1. 53 1 1. 44 7

1. 82 2 1. 71 3 1. 61 4 1. 52 2 1. 43 9

36 37 38 39 40

1. 4 31 1. 3 55 1. 2 84 1. 2 19 1. 1 59

1. 42 3 1. 34 7 1. 27 7 1. 21 3 1. 15 3

1 .4 1 5 1 .3 4 0 1 .2 7 1 1 .2 0 7 1 .1 4 7

1. 40 7 1. 33 3 1. 26 4 1. 20 1 1. 14 2

1. 40 0 1. 32 6 1. 25 8 1. 19 5 1. 13 6

1 .3 9 2 1 .3 1 9 1 .2 5 1 1 .1 8 9 1 .1 3 1

1 .3 8 4 1 .3 1 2 1 .2 4 5 1 .1 8 3 1 .1 2 5

1. 37 7 1. 30 5 1. 23 8 1. 17 7 1.119

1. 36 9 1. 29 8 1. 23 2 1. 17 1 1.114

1. 36 2 1. 29 1 1. 22 5 1. 16 5 1. 10 9

41 42 43 44 45

1. 1 03 1. 0 51 0. 0 03 0. 95 78 0. 91 57

1. 09 8 1. 04 6 0. 99 8 3 0 .9 5 3 5 0.9117

1 .0 9 2 1 .0 4 1 0 .9 9 3 6 0 .9 4 9 2 0 .9 0 7 7

1. 08 7 1. 03 6 0. 98 91 0 .9 4 4 9 0 .9 0 3 6

1. 08 2 1. 03 1 0 .9 8 4 5 0 .9 4 0 7 0 .8 9 9 7

1 .0 7 7 1 .0 2 7 0. 98 0 0 0. 93 64 0. 89 57

1 .0 7 2 1 .0 2 2 0 .9 7 5 5 0 .9 3 2 2 0 .8 9 1 8

1. 06 6 1. 01 7 0. 97 10 0. 92 81 0. 88 79

1. 06 1 1. 01 2 0 .9 6 6 6 0. 92 39 0. 88 40

1. 05 6 1. 00 8 0. 96 2 2 0. 91 98 0. 88 02

46 47 48 49 50

0. 87 64 0. 83 95 0. 80 48 0. 77 23 0. 74 17

0 .8 7 2 6 0 .8 3 5 9 0 .8 0 1 5 0 .7 6 9 2 0 .7 3 8 8

0 .8 6 8 8 0 .8 3 2 4 0 .7 9 8 2 0 .7 6 6 1 0 .7 3 5 9

0 .8 6 5 0 0 .8 2 8 8 0 .7 9 4 9 0 .7 6 3 0 0 .7 3 2 9

0 .8 6 1 3 0 .8 2 5 4 0 .7 9 1 6 0 .7 5 9 9 0 .7 3 0 0

0. 85 76 0. 82 19 0. 78 83 0. 75 68 0. 72 71

0 .8 5 3 9 0 .8 1 8 4 0 .7 8 5 1 0 .7 5 3 8 0 .7 2 4 3

0. 85 03 0. 81 50 0. 78 19 0. 75 07 0. 72 14

0. 84 67 0.8116 0. 77 87 0. 74 77 0. 71 86

0. 84 30 0. 80 82 0. 77 55 0. 74 47 0. 71 58

51 52 53 54 55

0. 71 29 0. 68 58 0. 66 02 0. 63 59 0. 61 30

0 .7 1 0 2 0 .6 8 3 2 0 .6 5 7 7 0 .6 3 3 6 0 .6 1 0 8

0 .7 0 7 4 0 .6 8 0 5 0 .6 5 5 2 0 .6 3 1 2 0 .6 0 8 6

0 .7 0 4 6 0 .6 7 7 9 0 .6 5 2 7 0 .6 2 8 9 0 .6 0 6 4

0 .7 0 1 9 0 .6 7 5 4 0 .6 5 0 3 0 .6 2 6 6 0 .6 0 4 2

0. 69 92 0. 67 28 0. 64 79 0. 62 43 0. 60 20

0 .6 9 6 5 0 .6 7 0 2 0 .6 4 5 5 0 .6 2 2 0 0 .5 9 9 9

0. 69 38 0. 66 77 0. 64 31 0. 61 98 0. 59 77

0.6911 0. 66 52 0. 64 07 0. 61 75 0. 59 56

0. 68 84 0. 66 27 0. 63 83 0. 61 53 0. 59 34

56 57 58 59 60

0. 59 13 0. 57 08 0. 55 12 0. 53 27 0. 51 51

0 .5 8 9 2 0 .5 6 8 8 0 .5 4 9 3 0 .5 3 0 9 0 .5 1 3 4

0 .5 8 7 1 0 .5 6 6 8 0 .5 4 7 5 0 .5 2 9 1 0.5117

0 .5 8 5 0 0 .5 6 4 8 0 .5 4 5 6 0 .5 2 7 3 0 .5 1 0 0

0 .5 8 3 0 0 .5 6 2 8 0 .5 4 3 7 0 .5 2 5 6 0 .5 0 8 3

0. 58 09 0. 56 09 0. 54 19 0. 52 38 0. 50 66

0 .5 7 8 8 0 .5 5 8 9 0 .5 4 0 0 0 .5 2 2 0 0 .5 0 5 0

0. 57 68 0. 55 70 0. 53 82 0. 52 03 0. 50 33

0. 57 48 0. 55 51 0. 53 63 0. 51 86 0. 50 16

0. 57 28 0. 55 31 0. 53 45 0. 51 68 0. 50 00

61 62 63 64 65

0. 49 84 0. 48 24 0. 46 72 0. 45 27 0. 43 89

0 .4 9 6 7 0 .4 8 0 9 0 .4 6 5 7 0 .4 5 1 3 0 .4 3 7 6

0 .4 9 5 1 0 .4 7 9 3 0 .4 6 4 3 0 .4 4 9 9 0 .4 3 6 2

0 .4 9 3 5 0 .4 7 7 8 0 .4 6 2 8 0 .4 4 8 5 0 .4 3 4 9

0 .4 9 1 9 0 .4 7 6 2 0 .4 6 1 3 0 .4 4 7 1 0 .4 3 3 6

0. 49 03 0. 47 47 0. 45 99 0. 44 57 0. 43 22

0 .4 8 8 7 0 .4 7 3 2 0 .4 5 8 4 0 .4 4 4 4 0 .4 3 0 9

0. 48 71 0. 47 17 0. 45 70 0. 44 30 0. 42 96

0. 48 55 0. 47 02 0. 45 56 0. 44 16 0. 42 83

0. 48 40 0. 46 87 0. 45 41 0. 44 03 0. 42 70

66 67 68 69 70

0. 42 57 0. 41 31 0. 40 10 0. 38 95 0. 37 84

0 .4 2 4 4 0.4119 0 .3 9 9 9 0 .3 8 8 4 0 .3 7 7 4

0 .4 2 3 1 0 .4 1 0 6 0 .3 9 8 7 0 .3 8 7 2 0 .3 7 6 3

0 .4 2 1 9 0 .4 0 9 4 0 .3 9 7 5 0 .3 8 6 1 0 .3 7 5 2

0 .4 2 0 6 0 .4 0 8 2 0 .3 9 6 4 0 .3 8 5 0 0 .3 7 4 2

0. 41 93 0. 40 70 0. 39 52 0. 38 39 0. 37 31

0 .4 1 8 1 0 .4 0 5 8 0 .3 9 4 1 0 .3 8 2 8 0 .3 7 2 0

0. 41 68 0. 40 46 0. 39 29 0. 38 17 0. 37 10

0. 41 56 0. 40 34 0. 39 18 0. 38 06 0. 36 99

0. 41 43 0. 40 22 0. 39 06 0. 37 95 0. 36 89

71 72 73

0. 36 79 0. 35 77 0. 34 80

0 .3 6 6 8 0 .3 5 6 7 0 .3 4 7 0

0 .3 6 5 8 0 .3 5 5 7 0 .3 4 6 1

0 .3 6 4 8 0 .3 5 4 8 0 .3 4 5 1

0 .3 6 3 8 0 .3 5 3 8 0 .3 4 4 2

0. 36 27 0. 35 28 0. 34 33

0 .3 6 1 7 0 .3 5 1 8 0 .3 4 2 3

0. 36 07 0. 35 09 0. 34 14

0. 35 97 0. 34 99 0. 34 05

0. 35 87 0. 34 89 0. 33 96

39

E384 − 11

´1

TABLE X6.2   Continued  Vickers Hardness Number for Diagonal Measured to 0.1 µm

Diagonal of Indentation, µm

0 .0

0 .1

0. 2

0. 3

0 .4

0. 5

0 .6

0 .7

0 .8

0 .9

74 75

0. 33 86 0. 32 97

0 .3 3 7 7 0 .3 2 8 8

0 .3 3 6 8 0 .3 2 7 9

0 .3 3 5 9 0 .3 2 7 0

0 .3 3 5 0 0 .3 2 6 2

0. 33 41 0. 32 53

0 .3 3 3 2 0 .3 2 4 5

0. 33 23 0. 32 36

0. 33 14 0. 32 27

0. 33 05 0. 32 19

76 77 78 79 80

0.3211 0. 31 28 0. 30 48 0. 29 71 0. 28 97

0 .3 2 0 2 0 .3 1 2 0 0 .3 0 4 0 0 .2 9 6 4 0 .2 8 9 0

0 .3 1 9 4 0.3111 0 .3 0 3 2 0 .2 9 5 6 0 .2 8 8 3

0 .3 1 8 5 0 .3 1 0 3 0 .3 0 2 5 0 .2 9 4 9 0 .2 8 7 6

0 .3 1 7 7 0 .3 0 9 5 0 .3 0 1 7 0 .2 9 4 1 0 .2 8 6 9

0. 31 69 0. 30 87 0. 30 09 0. 29 34 0. 28 62

0 .3 1 6 0 0 .3 0 7 9 0 .3 0 0 2 0 .2 9 2 7 0 .2 8 5 5

0. 31 52 0. 30 72 0. 29 94 0. 29 19 0. 28 47

0. 31 44 0. 30 64 0. 29 86 0. 29 12 0. 28 40

0. 31 36 0. 30 56 0. 29 79 0. 29 05 0. 28 33

81 82 83 84 85

0. 28 26 0. 27 58 0. 26 92 0. 26 28 0. 25 67

0 .2 8 1 9 0 .2 7 5 1 0 .2 6 8 5 0 .2 6 2 2 0 .2 5 6 1

0 .2 8 1 2 0 .2 7 4 4 0 .2 6 9 7 0 .2 6 1 6 0 .2 5 5 5

0 .2 8 0 6 0 .2 7 3 8 0 .2 6 7 2 0 .2 6 0 9 0 .2 5 4 9

0 .2 7 9 9 0 .2 7 3 1 0 .2 6 6 6 0 .2 6 0 3 0 .2 5 4 3

0. 27 92 0. 27 25 0. 26 60 0. 25 97 0. 25 37

0 .2 7 8 5 0 .2 7 1 8 0 .2 6 5 3 0 .2 5 9 1 0 .2 5 3 1

0. 27 78 0.2711 0. 26 47 0. 25 85 0. 25 25

0. 27 71 0. 27 05 0. 26 41 0. 25 79 0. 25 19

0. 27 65 0. 26 98 0. 26 34 0. 25 73 0. 25 13

86 87 88 89 90

0. 25 07 0. 24 50 0. 23 95 0. 23 41 0. 22 89

0 .2 5 0 1 0 .2 4 4 4 0 .2 3 8 9 0 .2 3 3 6 0 .2 2 8 4

0 .2 4 9 6 0 .2 4 3 9 0 .2 3 8 4 0 .2 3 3 1 0 .2 2 7 9

0 .2 4 9 0 0 .2 4 3 3 0 .2 3 7 8 0 .2 3 2 5 0 .2 2 7 4

0 .2 4 8 4 0 .2 4 2 8 0 .2 3 7 3 0 .2 3 2 0 0 .2 2 6 9

0. 24 78 0. 24 22 0. 23 68 0. 23 15 0. 22 64

0 .2 4 7 3 0 .2 4 1 7 0 .2 3 6 2 0 .2 3 1 0 0 .2 2 5 9

0. 24 67 0.2411 0. 23 57 0. 23 05 0. 22 54

0. 24 61 0. 24 06 0. 23 52 0. 23 00 0. 22 49

0. 24 56 0. 24 00 0. 23 46 0. 22 94 0. 22 44

91 92 93 94 95

0. 22 39 0. 21 91 0. 21 44 0. 20 99 0. 20 55

0 .2 2 3 4 0 .2 1 8 6 0 .2 1 3 9 0 .2 0 9 4 0 .2 0 5 0

0 .2 2 3 0 0 .2 1 8 1 0 .2 1 3 5 0 .2 0 9 0 0 .2 0 4 6

0 .2 2 2 5 0 .2 1 7 7 0 .2 1 3 0 0 .2 0 8 5 0 .2 0 4 2

0 .2 2 2 0 0 .2 1 7 2 0 .2 1 2 6 0 .2 0 8 1 0 .2 0 3 8

0. 22 15 0. 21 67 0. 21 21 0. 20 77 0. 20 33

0 .2 2 1 0 0 .2 1 6 3 0.2117 0 .2 0 7 2 0 .2 0 2 9

0. 22 05 0. 21 58 0.2112 0. 20 68 0. 20 25

0. 22 00 0. 21 53 0. 21 08 0. 20 63 0. 20 21

0. 21 96 0. 21 49 0. 21 03 0. 20 59 0. 20 16

96 97 98 99 10 0

0. 20 12 0. 19 71 0. 19 31 0. 18 92 0 .1 8 5 4

0 .2 0 0 8 0 .1 9 6 7 0 .1 9 2 7 0 .1 8 8 8 0. 18 5 1

0 .2 0 0 4 0 .1 9 6 3 0 .1 9 2 3 0 .1 8 8 4 0 .1 8 4 7

0 .2 0 0 0 0 .1 9 5 9 0 .1 9 1 9 0 .1 8 8 1 0 .1 8 4 3

0 .1 9 9 5 0 .1 9 5 5 0 .1 9 1 5 0 .1 8 7 7 0 .1 8 4 0

0. 19 91 0. 19 51 0.1911 0. 18 73 0 .1 8 3 6

0 .1 9 8 7 0 .1 9 4 7 0 .1 9 0 7 0 .1 8 6 9 0 .1 8 3 2

0. 19 83 0. 19 43 0. 19 04 0. 18 66 0 .1 8 2 9

0. 19 79 0. 19 39 0. 19 00 0. 18 62 0 .1 8 2 5

0. 19 75 0. 19 35 0. 18 96 0. 18 58 0 .1 8 2 1

10 1 10 2 10 3 10 4 10 5

0 .1 8 1 8 0 .1 7 8 2 0 .1 7 4 8 0 .1 7 1 5 0 .1 6 8 2

0. 18 1 4 0. 17 7 9 0. 17 4 5 0.1711 0. 16 7 9

0.1811 0 .1 7 7 5 0 .1 7 4 1 0 .1 7 0 8 0 .1 6 7 6

0 .1 8 0 7 0 .1 7 7 2 0 .1 7 3 8 0 .1 7 0 5 0 .1 6 7 2

0 .1 8 0 4 0 .1 7 6 9 0 .1 7 3 4 0 .1 7 0 1 0 .1 6 6 9

0 .1 8 0 0 0 .1 7 6 5 0 .1 7 3 1 0 .1 6 9 8 0 .1 6 6 6

0 .1 7 9 6 0 .1 7 6 2 0 .1 7 2 8 0 .1 6 9 5 0 .1 6 6 3

0 .1 7 9 3 0 .1 7 5 8 0 .1 7 2 4 0 .1 6 9 2 0 .1 6 6 0

0 .1 7 8 9 0 .1 7 5 5 0 .1 7 2 1 0 .1 6 8 8 0 .1 6 5 7

0 .1 7 8 6 0 .1 7 5 1 0 .1 7 1 8 0 .1 6 8 5 0 .1 6 5 4

10 6 10 7 10 8 10 9 110

0 .1 6 5 0 0 .1 6 2 0 0 .1 5 9 0 0 .1 5 6 1 0 .1 5 3 3

0. 16 4 7 0. 16 1 7 0. 15 8 7 0. 15 5 6 0. 15 3 0

0 .1 6 4 4 0 .1 6 1 4 0 .1 5 8 4 0 .1 5 5 5 0 .1 5 2 7

0 .1 6 4 1 0 .1611 0 .1 5 8 1 0 .1 5 5 2 0 .1 5 2 4

0 .1 6 3 8 0 .1 6 0 8 0 .1 5 7 8 0 .1 5 4 9 0 .1 5 2 1

0 .1 6 3 5 0 .1 6 0 5 0 .1 5 7 5 0 .1 5 4 7 0 .1 5 1 9

0 .1 6 3 2 0 .1 6 0 2 0 .1 5 7 2 0 .1 5 4 4 0 .1 5 1 6

0 .1 6 2 9 0 .1 5 9 9 0 .1 5 6 9 0 .1 5 4 1 0 .1 5 1 3

0 .1 6 2 6 0. 15 96 0 .1 5 6 7 0 .1 5 3 8 0.1511

0 .1 6 2 3 0 .1 5 9 3 0 .1 5 6 4 0 .1 5 3 5 0 .1 5 0 8

111 112 113 114 115

0 .1 5 0 5 0 .1 4 7 8 0 .1 4 5 2 0 .1 4 2 7 0 .1 4 0 2

0. 15 0 2 0. 14 7 6 0. 14 5 0 0. 14 2 4 0. 14 0 0

0 .1 5 0 0 0 .1 4 7 3 0 .1 4 4 7 0 .1 4 2 2 0 .1 3 9 7

0 .1 4 9 7 0 .1 4 7 0 0 .1 4 4 5 0 .1 4 1 9 0 .1 3 9 5

0 .1 4 9 4 0 .1 4 6 8 0 .1 4 4 2 0 .1 4 1 7 0 .1 3 9 3

0 .1 4 9 2 0 .1 4 6 5 0 .1 4 4 0 0 .1 4 1 4 0 .1 3 9 0

0 .1 4 8 9 0 .1 4 6 3 0 .1 4 3 7 0 .1 4 1 2 0 .1 3 8 8

0 .1 4 8 6 0 .1 4 6 0 0 .1 4 3 4 0 .1 4 1 0 0 .1 3 8 5

0 .1 4 8 4 0 .1 4 5 7 0 .1 4 3 2 0 .1 4 0 7 0 .1 3 8 3

0 .1 4 8 1 0 .1 4 5 5 0 .1 4 2 9 0 .1 4 0 5 0 .1 3 8 1

116 117 118 119 12 0

0 .1 3 7 8 0 .1 3 5 5 0 .1 3 3 2 0 .1 3 1 0 0 .1 2 8 8

0. 13 7 6 0. 13 5 2 0. 13 3 0 0. 13 0 7 0. 12 8 6

0 .1 3 7 3 0 .1 3 5 0 0 .1 3 2 7 0 .1 3 0 5 0 .1 2 8 4

0 .1 3 7 1 0 .1 3 4 8 0 .1 3 2 5 0 .1 3 0 3 0 .1 2 8 1

0 .1 3 6 9 0 .1 3 4 5 0 .1 3 2 3 0 .1 3 0 1 0 .1 2 7 9

0 .1 3 6 6 0 .1 3 4 3 0 .1 3 2 1 0 .1 2 9 9 0 .1 2 7 7

0 .1 3 6 4 0 .1 3 4 1 0 .1 3 1 8 0 .1 2 9 6 0 .1 2 7 5

0 .1 3 6 2 0 .1 3 3 9 0 .1 3 1 6 0 .1 2 9 4 0 .1 2 7 3

0 .1 3 5 9 0 .1 3 3 6 0 .1 3 1 4 0 .1 2 9 2 0 .1 2 7 1

0 .1 3 5 7 0 .1 3 3 4 0 .1 3 1 2 0 .1 2 9 0 0 .1 2 6 9

12 1 12 2 12 3 12 4 12 5

0 .1 2 6 7 0 .1 2 4 6 0 .1 2 2 6 0 .1 2 0 6 0.1187

0. 12 6 5 0. 12 4 4 0. 12 2 4 0. 12 0 4 0.1185

0 .1 2 6 2 0 .1 2 4 2 0 .1 2 2 2 0 .1 2 0 2 0.1183

0 .1 2 6 0 0 .1 2 4 0 0 .1 2 2 0 0 .1 2 0 0 0.1181

0 .1 2 5 8 0 .1 2 3 8 0 .1 2 1 8 0.1198 0.1179

0 .1 2 5 6 0 .1 2 3 6 0 .1 2 1 6 0.1196 0.1177

0 .1 2 5 4 0 .1 2 3 4 0 .1 2 1 4 0.1194 0.1176

0 .1 2 5 2 0 .1 2 3 2 0 .1 2 1 2 0.1193 0.1174

0 .1 2 5 0 0 .1 2 3 0 0 .1 2 1 0 0.1191 0.1172

0 .1 2 4 8 0 .1 2 2 8 0 .1 2 0 8 0.1189 0.1170

12 6 12 7 12 8 12 9 13 0

0.1168 0.1150 0.1132 0.1114 0 .1 0 9 7

0.1166 0.1148 0.1130 0.1113 0. 10 9 6

0.1164 0.1146 0.1128 0.1111 0 .1 0 9 4

0.1163 0.1144 0.1127 0.1109 0 .1 0 9 2

0.1161 0.1143 0.1125 0.1108 0 .1 0 9 1

0.1159 0.1141 0.1123 0.1106 0 .1 0 8 9

0.1157 0.1139 0.1121 0.1104 0 .1 0 8 7

0.1155 0.1137 0.1120 0.1102 0 .1 0 8 6

0.1153 0.1135 0.1118 0.1101 0 .1 0 8 4

0.1152 0.1134 0.1116 0 .1 0 9 9 0 .1 0 8 2

13 1 13 2 13 3 13 4 13 5

0 .1 0 8 1 0 .1 0 6 4 0 .1 0 4 8 0 .1 0 3 3 0 .1 0 1 8

0. 10 7 9 0. 10 6 3 0. 10 4 7 0. 10 3 1 0. 10 1 6

0 .1 0 7 7 0 .1 0 6 1 0 .1 0 4 5 0 .1 0 3 0 0 .1 0 1 5

0 .1 0 7 6 0 .1 0 5 9 0 .1 0 4 4 0 .1 0 2 8 0 .1 0 1 3

0 .1 0 7 4 0 .1 0 5 8 0 .1 0 4 2 0 .1 0 2 7 0 .1 0 1 2

0 .1 0 7 2 0 .1 0 5 6 0 .1 0 4 1 0 .1 0 2 5 0 .1 0 1 0

0 .1 0 7 1 0 .1 0 5 5 0 .1 0 3 9 0 .1 0 2 4 0 .1 0 0 9

0 .1 0 6 9 0 .1 0 5 3 0 .1 0 3 7 0 .1 0 2 2 0 .1 0 0 7

0 .1 0 6 8 0 .1 0 5 2 0 .1 0 3 6 0 .1 0 2 1 0 .1 0 0 6

0 .1 0 6 6 0 .1 0 5 0 0 .1 0 3 4 0 .1 0 1 9 0 .1 0 0 4

40

E384 − 11

´1

TABLE X6.2   Continued  Vickers Hardness Number for Diagonal Measured to 0.1 µm

Diagonal of Indentation, µm

0 .0

0 .1

0. 2

0. 3

0 .4

0. 5

0 .6

0 .7

0 .8

0 .9

13 6 13 7 13 8 13 9 14 0

0 .1 0 0 3 0 .0 9 8 8 0 .0 9 7 4 0 .0 9 6 0 0 .0 9 4 6

0. 10 0 1 0. 09 8 7 0. 09 7 2 0. 09 5 8 0. 09 4 5

0 .1 0 0 0 0 .0 9 8 5 0 .0 9 7 1 0 .0 9 5 7 0 .0 9 4 3

0 .0 9 9 8 0 .0 9 8 4 0 .0 9 7 0 0 .0 9 5 6 0 .0 9 4 2

0 .0 9 9 7 0 .0 9 8 2 0 .0 9 6 8 0 .0 9 5 4 0 .0 9 4 1

0 .0 9 9 5 0 .0 9 8 1 0 .0 9 6 7 0 .0 9 5 3 0 .0 9 3 9

0 .0 9 9 4 0 .0 9 7 9 0 .0 9 6 5 0 .0 9 5 2 0 .0 9 3 8

0 .0 9 9 2 0 .0 9 7 8 0 .0 9 6 4 0 .0 9 5 0 0 .0 9 3 7

0 .0 9 9 1 0 .0 9 7 7 0 .0 9 6 3 0 .0 9 4 9 0 .0 9 3 5

0 .0 9 8 9 0 .0 9 7 5 0 .0 9 6 1 0 .0 9 4 8 0 .0 9 3 4

14 1 14 2 14 3 14 4 14 5

0 .0 9 3 3 0 .0 9 2 0 0 .0 9 0 7 0 .0 8 9 4 0 .0 8 8 2

0. 09 3 1 0. 09 1 8 0. 09 0 6 0. 08 9 3 0. 08 8 1

0 .0 9 3 0 0 .0 9 1 7 0 .0 9 0 4 0 .0 8 9 2 0 .0 8 8 0

0 .0 9 2 9 0 .0 9 1 6 0 .0 9 0 3 0 .0 8 9 1 0 .0 8 7 8

0 .0 9 2 8 0 .0 9 1 5 0 .0 9 0 2 0 .0 8 8 9 0 .0 8 7 7

0 .0 9 2 6 0 .0 9 1 3 0 .0 9 0 1 0 .0 8 8 8 0 .0 8 7 6

0 .0 9 2 5 0 .0 9 1 2 0 .0 8 9 9 0 .0 8 8 7 0 .0 8 7 5

0 .0 9 2 4 0.0911 0 .0 8 9 8 0 .0 8 8 6 0 .0 8 7 4

0 .0 9 2 2 0 .0 9 0 9 0 .0 8 9 7 0 .0 8 8 4 0 .0 8 7 2

0 .0 9 2 1 0 .0 9 0 8 0 .0 8 9 6 0 .0 8 8 3 0 .0 8 7 1

14 6 14 7 14 8 14 9 15 0

0 .0 8 7 0 0 .0 8 5 8 0 .0 8 4 7 0 .0 8 3 5 0 .0 8 2 4

0. 08 6 9 0. 08 5 7 0. 08 4 5 0. 08 3 4 0. 08 2 3

0 .0 8 6 8 0 .0 8 5 6 0 .0 8 4 4 0 .0 8 3 3 0 .0 8 2 2

0 .0 8 6 6 0 .0 8 5 5 0 .0 8 4 3 0 .0 8 3 2 0 .0 8 2 1

0 .0 8 6 5 0 .0 8 5 4 0 .0 8 4 2 0 .0 8 3 1 0 .0 8 2 0

0 .0 8 6 4 0 .0 8 5 2 0 .0 8 4 1 0 .0 8 3 0 0 .0 8 1 9

0 .0 8 6 3 0 .0 8 5 1 0 .0 8 4 0 0 .0 8 2 9 0 .0 8 1 8

0 .0 8 6 2 0 .0 8 5 0 0 .0 8 3 9 0 .0 8 2 8 0 .0 8 1 7

0 .0 8 6 1 0 .0 8 4 9 0 .0 8 3 8 0 .0 8 2 6 0 .0 8 1 5

0 .0 8 5 9 0 .0 8 4 8 0 .0 8 3 6 0 .0 8 2 5 0 .0 8 1 4

15 1 15 2 15 3 15 4 15 5

0 .0 8 1 3 0 .0 8 0 3 0 .0 7 9 2 0 .0 7 8 2 0 .0 7 7 2

0. 08 1 2 0. 08 0 2 0. 07 9 1 0. 07 8 1 0. 07 7 1

0.0811 0 .0 8 0 1 0 .0 7 9 0 0 .0 7 8 0 0 .0 7 7 0

0 .0 8 1 0 0 .0 8 0 0 0 .0 7 8 9 0 .0 7 7 9 0 .0 7 6 9

0 .0 8 0 9 0 .0 7 9 8 0 .0 7 8 8 0 .0 7 7 8 0 .0 7 6 8

0 .0 8 0 8 0 .0 7 9 7 0 .0 7 8 7 0 .0 7 7 7 0 .0 7 6 7

0 .0 8 0 7 0 .0 7 9 6 0 .0 7 8 6 0 .0 7 7 6 0 .0 7 6 6

0 .0 8 0 6 0 .0 7 9 5 0 .0 7 8 5 0 .0 7 7 5 0 .0 7 6 5

0 .0 8 0 5 0 .0 7 9 4 0 .0 7 8 4 0 .0 7 7 4 0 .0 7 6 4

0 .0 8 0 4 0 .0 7 9 3 0 .0 7 8 3 0 .0 7 7 3 0 .0 7 6 3

15 6 15 7 15 8 15 9 16 0

0 .0 7 6 2 0 .0 7 5 2 0 .0 7 4 3 0 .0 7 3 4 0 .0 7 2 4

0. 07 6 1 0. 07 5 1 0. 07 4 2 0. 07 3 3 0. 07 2 4

0 .0 7 6 0 0 .0 7 5 0 0 .0 7 4 1 0 .0 7 3 2 0 .0 7 2 3

0 .0 7 5 9 0 .0 7 4 9 0 .0 7 4 0 0 .0 7 3 1 0 .0 7 2 2

0 .0 7 5 8 0 .0 7 4 9 0 .0 7 3 9 0 .0 7 3 0 0 .0 7 2 1

0 .0 7 5 7 0 .0 7 4 8 0 .0 7 3 8 0 .0 7 2 9 0 .0 7 2 0

0 .0 7 5 6 0 .0 7 4 7 0 .0 7 3 7 0 .0 7 2 8 0 .0 7 1 9

0 .0 7 5 5 0 .0 7 4 6 0 .0 7 3 6 0 .0 7 2 7 0 .0 7 1 8

0 .0 7 5 4 0 .0 7 4 5 0 .0 7 3 5 0 .0 7 2 6 0 .0 7 1 7

0 .0 7 5 3 0 .0 7 4 4 0 .0 7 3 4 0 .0 7 2 5 0 .0 7 1 6

16 1 16 2 16 3 16 4 16 5

0 .0 7 1 5 0 .0 7 0 7 0 .0 6 9 8 0 .0 6 9 0 0 .0 6 8 1

0. 07 1 5 0. 07 0 6 0. 06 9 7 0. 06 8 9 0. 06 8 0

0 .0 7 1 4 0 .0 7 0 5 0 .0 6 9 6 0 .0 6 8 8 0 .0 6 8 0

0 .0 7 1 3 0 .0 7 0 4 0 .0 6 9 5 0 .0 6 8 7 0 .0 6 7 9

0 .0 7 1 2 0 .0 7 0 3 0 .0 6 9 5 0 .0 6 8 6 0 .0 6 7 8

0.0711 0 .0 7 0 2 0 .0 6 9 4 0 .0 6 8 5 0 .0 6 7 7

0 .0 7 1 0 0 .0 7 0 1 0 .0 6 9 3 0 .0 6 8 4 0 .0 6 7 6

0 .0 7 0 9 0 .0 7 0 1 0 .0 6 9 2 0 .0 6 8 4 0 .0 6 7 5

0 .0 7 0 8 0 .0 7 0 0 0 .0 6 9 1 0 .0 6 8 3 0 .0 6 7 5

0 .0 7 0 8 0 .0 6 9 9 0 .0 6 9 0 0 .0 6 8 2 0 .0 6 7 4

16 6 16 7 16 8 16 9 17 0

0 .0 6 7 3 0 .0 6 6 5 0 .0 6 5 7 0 .0 6 4 9 0 .0 6 4 2

0. 06 7 2 0. 06 6 4 0. 06 5 6 0. 06 4 9 0. 06 4 1

0 .0 6 7 1 0 .0 6 6 3 0 .0 6 5 6 0 .0 6 4 8 0 .0 6 4 0

0 .0 6 7 1 0 .0 6 6 3 0 .0 6 5 5 0 .0 6 4 7 0 .0 6 3 9

0 .0 6 7 0 0 .0 6 6 2 0 .0 6 5 4 0 .0 6 4 6 0 .0 6 3 9

0 .0 6 6 9 0 .0 6 6 1 0 .0 6 5 3 0 .0 6 4 5 0 .0 6 3 8

0 .0 6 6 8 0 .0 6 6 0 0 .0 6 5 2 0 .0 6 4 5 0 .0 6 3 7

0 .0 6 6 7 0 .0 6 5 9 0 .0 6 5 2 0 .0 6 4 4 0 .0 6 3 6

0 .0 6 6 7 0 .0 6 5 9 0 .0 6 5 1 0 .0 6 4 3 0 .0 6 3 6

0 .0 6 6 6 0 .0 6 5 8 0 .0 6 5 0 0 .0 6 4 2 0 .0 6 3 5

17 1 17 2 17 3 17 4 17 5

0 .0 6 3 4 0 .0 6 2 7 0 .0 6 2 0 0 .0 6 1 3 0 .0 6 0 6

0. 06 3 3 0. 06 2 6 0. 06 1 9 0. 06 1 2 0. 06 0 5

0 .0 6 3 3 0 .0 6 2 5 0 .0 6 1 8 0.0611 0 .0 6 0 4

0 .0 6 3 2 0 .0 6 2 5 0 .0 6 1 7 0 .0 6 1 0 0 .0 6 0 3

0 .0 6 3 1 0 .0 6 2 4 0 .0 6 1 7 0 .0 6 1 0 0 .0 6 0 3

0 .0 6 3 1 0 .0 6 2 3 0 .0 6 1 6 0 .0 6 0 9 0 .0 6 0 2

0 .0 6 3 0 0 .0 6 2 3 0 .0 6 1 5 0 .0 6 0 8 0 .0 6 0 1

0 .0 6 2 9 0 .0 6 2 2 0 .0 6 1 5 0 .0 6 0 8 0 .0 6 0 1

0 .0 6 2 8 0 .0 6 2 1 0 .0 6 1 4 0 .0 6 0 7 0 .0 6 0 0

0 .0 6 2 8 0 .0 6 2 0 0 .0 6 1 3 0 .0 6 0 6 0 .0 5 5 9

17 6 17 7 17 8 17 9 18 0

0 .0 5 9 9 0 .0 5 9 2 0 .0 5 8 5 0 .0 5 7 9 0 .0 5 7 2

0. 05 9 8 0. 05 9 1 0. 05 8 5 0. 05 7 8 0. 05 7 2

0 .0 5 9 7 0 .0 5 9 1 0 .0 5 8 4 0 .0 5 7 8 0 .0 5 7 1

0 .0 5 9 7 0 .0 5 9 0 0 .0 5 8 3 0 .0 5 7 7 0 .0 5 7 0

0 .0 5 9 6 0 .0 5 8 9 0 .0 5 8 3 0 .0 5 7 6 0 .0 5 7 0

0 .0 5 9 5 0 .0 5 8 9 0 .0 5 8 2 0 .0 5 7 6 0 .0 5 6 9

0 .0 5 9 5 0 .0 5 8 8 0 .0 5 8 1 0 .0 5 7 5 0 .0 5 6 9

0 .0 5 9 4 0 .0 5 8 7 0 .0 5 8 1 0 .0 5 7 4 0 .0 5 6 8

0 .0 5 9 3 0 .0 5 8 7 0 .0 5 8 0 0 .0 5 7 4 0 .0 5 6 7

0 .0 5 9 3 0 .0 5 8 6 0 .0 5 7 9 0 .0 5 7 3 0 .0 5 6 7

18 1 18 2 18 3 18 4 18 5

0 .0 5 6 6 0 .0 5 6 0 0 .0 5 5 4 0 .0 5 4 8 0 .0 5 4 2

0. 05 6 5 0. 05 5 9 0. 05 5 3 0. 05 4 7 0. 05 4 1

0 .0 5 6 5 0 .0 5 5 9 0 .0 5 5 3 0 .0 5 4 7 0 .0 5 4 1

0 .0 5 6 4 0 .0 5 5 8 0 .0 5 5 2 0 .0 5 4 6 0 .0 5 4 0

0 .0 5 6 4 0 .0 5 5 7 0 .0 5 5 1 0 .0 5 4 5 0 .0 5 4 0

0 .0 5 6 3 0 .0 5 5 7 0 .0 5 5 1 0 .0 5 4 5 0 .0 5 3 9

0 .0 5 6 2 0 .0 5 5 6 0 .0 5 5 0 0 .0 5 4 4 0 .0 5 3 8

0 .0 5 6 2 0 .0 5 5 6 0 .0 5 5 0 0 .0 5 4 4 0 .0 5 3 8

0 .0 5 6 1 0 .0 5 5 5 0 .0 5 4 9 0 .0 5 4 3 0 .0 5 3 7

0 .0 5 6 0 0 .0 5 5 4 0 .0 5 4 8 0 .0 5 4 2 0 .0 5 3 7

18 6 18 7 18 8 18 9 19 0

0 .0 5 3 6 0 .0 5 3 0 0 .0 5 2 5 0 .0 5 1 9 0 .0 5 1 4

0. 05 3 5 0. 05 3 0 0. 05 2 4 0. 05 1 9 0. 05 1 3

0 .0 5 3 5 0 .0 5 2 9 0 .0 5 2 4 0 .0 5 1 8 0 .0 5 1 3

0 .0 5 3 4 0 .0 5 2 9 0 .0 5 2 3 0 .0 5 1 8 0 .0 5 1 2

0 .0 5 3 4 0 .0 5 2 8 0 .0 5 2 2 0 .0 5 1 7 0 .0 5 1 2

0 .0 5 3 3 0 .0 5 2 8 0 .0 5 2 2 0 .0 5 1 6 0.0511

0 .0 5 3 3 0 .0 5 2 7 0 .0 5 2 1 0 .0 5 1 6 0 .0 5 1 0

0 .0 5 3 2 0 .0 5 2 6 0 .0 5 2 1 0 .0 5 1 5 0 .0 5 1 0

0 .0 5 3 1 0 .0 5 2 6 0 .0 5 2 0 0 .0 5 1 5 0 .0 5 0 9

0 .0 5 3 1 0 .0 5 2 5 0 .0 5 2 0 0 .0 5 1 4 0 .0 5 0 9

19 1 19 2 19 3 19 4 19 5

0 .0 5 0 8 0 .0 5 0 3 0 .0 4 9 8 0 .0 4 9 3 0 .0 4 8 8

0. 05 0 8 0. 05 0 3 0. 04 9 7 0. 04 9 2 0. 04 8 7

0 .0 5 0 7 0 .0 5 0 2 0 .0 4 9 7 0 .0 4 9 2 0 .0 4 8 7

0 .0 5 0 7 0 .0 5 0 2 0 .0 4 9 6 0 .0 4 9 1 0 .0 4 8 6

0 .0 5 0 6 0 .0 5 0 1 0 .0 4 9 6 0 .0 4 9 1 0 .0 4 8 6

0 .0 5 0 6 0 .0 5 0 0 0 .0 4 9 5 0 .0 4 9 0 0 .0 4 8 5

0 .0 5 0 5 0 .0 5 0 0 0 .0 4 9 5 0 .0 4 9 0 0 .0 4 8 5

0 .0 5 0 5 0 .0 4 9 9 0 .0 4 9 4 0 .0 4 8 9 0 .0 4 8 4

0 .0 5 0 4 0 .0 4 9 9 0 .0 4 9 4 0 .0 4 8 9 0 .0 4 8 4

0 .0 5 0 4 0 .0 4 9 8 0 .0 4 9 3 0 .0 4 8 8 0 .0 4 8 3

19 6

0 .0 4 8 3

0. 04 8 2

0 .0 4 8 2

0 .0 4 8 1

0 .0 4 8 1

0 .0 4 8 0

0 .0 4 8 0

0 .0 4 7 9

0 .0 4 7 9

0 .0 4 7 8

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TABLE X6.2   Continued  Vickers Hardness Number for Diagonal Measured to 0.1 µm

Diagonal of Indentation, µm

0 .0

0 .1

0. 2

0. 3

0 .4

0. 5

0 .6

0 .7

0 .8

0 .9

19 7 19 8 19 9 20 0

0 .0 4 7 8 0 .0 4 7 3 0 .0 4 6 8 0 .0 4 6 4

0. 04 7 7 0. 04 7 3 0. 04 6 8 0. 04 6 3

0 .0 4 7 7 0 .0 4 7 2 0 .0 4 6 7 0 .0 4 6 3

0 .0 4 7 6 0 .0 4 7 2 0 .0 4 6 7 0 .0 4 6 2

0 .0 4 7 6 0 .0 4 7 1 0 .0 4 6 6 0 .0 4 6 2

0 .0 4 7 5 0 .0 4 7 1 0 .0 4 6 6 0 .0 4 6 1

0 .0 4 7 5 0 .0 4 7 0 0 .0 4 6 5 0 .0 4 6 1

0 .0 4 7 4 0 .0 4 7 0 0 .0 4 6 5 0 .0 4 6 0

0 .0 4 7 4 0 .0 4 6 9 0 .0 4 6 5 0 .0 4 6 0

0 .0 4 7 4 0 .0 4 6 9 0 .0 4 6 4 0 .0 4 5 9

REFERENCES (1)  Campbell, R.F., et al., “A New Design of Microhardness Tester and

(5) Tarasov, L.P., L.P., and Thibault, N.W N.W., ., “Determination of Knoop Hardness

Some Factors Affecting the Diamond Pyramid Hardness Number at Light Loads,” Trans. ASM, Vol 40, 1948 , pp. 954-982. (2)   Kennedy, Kennedy, R.G., and Marro Marrotte, tte, N.W., N.W., “The Effect of Vibratio ibration n on Research ch and Stand Standard ardss, Vol 9, Microhardness Testing,”  Materials Resear November 1969, pp. 18-23. (3) Brow Brown, n, A.R.G., A.R.G., and Ineson, E., “Exper “Experiment imental al Surve Survey y of Low-L Low-Load oad Hardness Testing Instruments,” Journal of the Iron and Steel Inst., Vol 169, 1951, pp. 376-388. (4)   Thibault, N.W., and Nyquist, H.L., “The Measured Knoop Hardness of Hard Substances and Factors Affecting Its Determination,” Trans. ASM, Vol 38, 1947, pp. 271-330.

Numberss Ind Number Indepe epende ndent nt of Loa Load,” d,” Tr Trans ans.. ASM ASM,, Vol 38, 194 1947, 7, pp. 331-353. (6)  Vander Voort, G.P.,“Results of an ASTM E04 Round Robin on the Precision and Bias of Measurements of Microindentation Hardness,” Factorss that Affect the Prec Factor Precision ision of Mecha Mechanical nical Tests, Tests, ASTM STP 1025, ASTM, Philadelphia, 1989, pp. 3-39. (7)  Vander Voort, G.F.,“Operator Errors In the Measurement of MicroinAccreditation Practices for Inspections, Tests, dentation Hardness,”   Accreditation and Laboratories, ASTM STP 1057 , ASTM, Philadelphia, 1989, pp. 47-77.

SUMMARY OF CHANGES Committ Comm ittee ee E0 E04 4 ha hass id iden entifi tified ed th thee lo loca catio tion n of se selec lected ted ch chan ange gess to th this is st stan anda dard rd si sinc ncee th thee la last st is issu suee 2 (E384 – 10 ) that may impact the use of this standard. (Approved August 1, 2011.) ε

(1)  1.2  was revised. (2)  6.4  was revised. (3)  6.4.4  6.4.4 was  was revised. (4)  7.1.5   was revised and   Table 2 and   Table 3   were added added,, subsequent subseq uent tables were renum renumbered bered..

 8.9.2 was  was revised. (5)  8.9.2 (6)  Eq A1.1 was A1.1  was revised and  Annex A1  was revised to reflect that change. (7)  A1.5 and and Table  Table A1.1  A1.1   were revised. (8)  Table A1.5 a A1.5  and nd Table  Table A1.6   were revised.

Committee E04 has identified the location of selected changes to this standard since the last issue (E384–09) that may impact the use of this standard. (Approved February 1, 2010.) (1)  Revisions were made throughout Sections 1–12 and all of  the Annexes.

Committ Comm ittee ee E0 E04 4 ha hass id iden entifi tified ed th thee lo loca catio tion n of se selec lected ted ch chan ange gess to th this is st stan anda dard rd si sinc ncee th thee la last st is issu suee 1 (E384–08a ) that may impact the use of this standard. (Approved May 1, 2009.) ε

(1)  Added  Added Table  Table 7 and and Table  Table 8 (2)  Added  Added 10.8.3  10.8.3

(3)  Revised  Revised A2.5.2  A2.5.2 and and A2.5.4  A2.5.4 (4)  Deleted A2.5.1.

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