Assessment for Fitness for Purpose of Cracked Piping Components-I: R6 Method
Rohit Rastogi Reactor Safety Division
Bhabha Atomic Research Center Mumbai
Indian Nuclear Society COURSE ON DESIGN OF COMPONENTS OPERATING AT HIGH TEMPERATURE
July 25-29, 2005
R6 Method
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1. Introduction
3
2. Assessment of a component with a crack
7
3. The R6 Method 3.1 Option 3 Curve and the assessed point 3.2 Option 2 Curve 3.3 Option 1 Curve 3.4 Unstable Crack Growth as Failure Criteria 3.5 Treatment of secondary stresses 3.6 Evaluation under Mode I, II, III loads 3.7 Flaw Characterization 3.8 Sensitivity Analysis 3.8 R6 Methodology
9 9 11 12 13 14 15 15 18 20
4 Sample Calculation [11]
20
5 References
27
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1. Introduction Defects in pressure vessels and piping components can be introduced during manufacturing (e.g. laminations), transportation (e.g. fatigue cracking), fabrication (e.g. weld defects) and installation (e.g. dents), and can occur both due to deterioration (e.g. corrosion) and due to external interference (e.g. gouges and dents). To ensure the integrity of these components, operators must be able to both detect and assess the significance of pipeline defects. The past 45 years has seen the development of 'fitness-for-purpose' methods for assessing the significance of these defects. A pressure retaining system must be operated safely and efficiently. There are four key issues in the operation of these systems: 1. Safety - the system must pose an acceptably low risk to the surrounding population. 2. Security of Supply - the system must deliver its product in a continuous manner, to satisfy the owners of the product (the 'shippers') and the shippers' customers (the 'end users'), and have low risk of supply failure. 3. Cost Effectiveness - the system must deliver the product at an attractive market price, and generate an acceptable rate of return on the investment. 4. Regulations - the operation of the system must satisfy all legislation and regulations. An operator must ensure that all risks associated with the pipeline are as low as is reasonably practicable. Occasionally an operator will detect, or become aware, of defects in their pipeline. In the past, this may have led to expensive shutdowns and repairs. However, recent years have seen the increasing use of fitness-for-purpose methods to assess these pipeline defects. Detailed procedures for assessing the significance of defects in structures are given in documents such as BS 7910: 1999 [1], API 579 [2], SINTAP [3], R6 [4], ASME [5] and others. For many engineers, the decision of whether to use fitness-for-service assessment procedures and which procedures to use can be difficult. While users and regulators across industry now increasingly accept defects and damage in equipment assessed as fit-for-service, the differences between the available procedures and the implied safety margins are not so well understood. There can be uncertainty about the data and technical skills required to make good assessments. As a result, the benefits from fitness-for-service assessment may not have been as widespread as might have been expected.
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Cosham and Kirkwood [6] have arranged the dilemma faced by an operator on detecting a flaw in his piping component. CAN I APPLY, AND DO I NEED TO USE, FITNESS-FOR PURPOSE METHODS? Any engineer with a potential defect problem should question the need for a fitnessfor-purpose assessment as follows: PHASE 1 – Appraisal •
Is it really there, and can I readily dismiss it? o Is it really a defect, or is it some feature of the inspection method? o Are the operating conditions able to create such a defect and can operational conditions be controlled to prevent growth (e.g. corrosion inhibition, re-coating)? o Is the defect within design and fabrication acceptance levels? o What is industry experience of similar defects? For example, have other companies faced this problem, and produced a solution that concludes that the defect is acceptable?
•
Is it a defect? o Do I know how the defect was formed, and how it may develop in the future? o Is the defect indicative of poor practice during construction or operation, and as such can be controlled by other methods?
•
Who is competent to assess the defect? o What are the legal ramifications (e.g. professional liability), what are the views of the regulatory body, and who would be responsible for the structure, and any defect assessment relating to it? o Is current staff capable and experienced enough to apply fitness-forpurpose methods?
•
Is it worth the effort? o Is it cheaper to repair than assess?
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PHASE 2 - Assessment •
Can fitness-for-purpose methods provide an answer? o Can fitness-for-purpose methods solve the problem? For example, are the methods robust for the particular defect and loading? o What data exists, and how reliable is it? If the data is sparse, what confidence is there in any engineering judgment, or are special tests required?
PHASE 3 - Safety Factors and Probabilistic Aspects •
What safety margins should be used? o If fitness-for-purpose methods are applied, what safety factors should be used? o How should the safety factors be set, and would it be better to conduct a probabilistic analysis?
PHASE 4 - Consequence •
What are the consequences of getting it wrong? o Is a risk analysis required?
Having decided that a defect assessment can be conducted, it is now necessary to determine the level of detail and complexity that is required. Different levels of defect assessment, ranging from simple screening methods to very sophisticated three-dimensional elastic-plastic finite element stress analyses, are available. The method used depends upon the type of defect detected, the loading conditions, the objective of the assessment, and the type and quality of data that is available. Figure 1 summarizes the differing levels of defect assessments, and the required data. Generally, defect assessments are conducted up to stage 3. If defects still remained ‘unacceptable’ at this stage, a higher-level assessment, or repair would be necessary. A sensible approach to adopt in any fitness for purpose assessment is to use the most conservative data and assessment method to demonstrate that the defect is acceptable, and apply more accurate (less conservative) methods only as required. More accurate assessment methods generally require more data, and are more difficult to apply. The higher levels may require risk analyses. Risk is a function of the probability of failure and the consequences of failure. Such analyses are becoming increasingly popular, but are also very complicated.
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A fitness-for-purpose analysis of defects does not entail a risk analysis, although due account of the consequences of failure will be taken in a qualitative manner, and the recommended safety factor will reflect this.
Figure 1: Stages in Defect Assessment
A fitness-for-purpose assessment will usually involve a deterministic assessment of the defects, to determine whether or not the defect is acceptable. Probabilistic methods are useful when dealing with uncertainty over the data used in the assessment or future conditions, such as corrosion rates. These methods can be used as an aid to deciding future inspection and maintenance requirements. Underlying such probabilistic analyses are fitness-for-purpose methods for assessing defects (i.e. the limit states).
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2. Assessment of a component with a crack In the common design philosophy, the applied stresses are compared with a limit stress such as the yield strength of the material. As long as the latter exceeds the applied stresses, the component is regarded as safe. A failure function or the limit state function can be defined by eq. (1). g = σ y −σ g > 0 : Safe g ≤ 0 : Unsafe σ y = yield stress
(1)
σ = applied stress The implicit background assumption is that the component is defect-free. If a real or assumed crack or crack-like flaw affects the load carrying capacity, fracture mechanics has to be applied. Then the comparison between the applied and the material side has to be carried out on the basis of crack tip parameters such as the linear elastic stress intensity factor KI, the J integral or the crack tip opening displacement . As a result, the fracture behavior of the component can be predicted in terms of a critical applied load or a critical crack size. These critical load or crack size values are obtained by comparing the applied crack tip parameter with the material limit. Thus in presence of cracks the limit state function can be given by eq. (2). g = K mat − K I g = J mat − J g = δ mat − δ g > 0 : Safe g ≤ 0 : Unsafe K mat , J mat , δ mat are material parameters
(2)
K , J , δ are applied parameters Standardized solutions for the crack tip parameters are available for test specimens, which are used for measuring the material's resistance to fracture. As long as the deformation behavior of the structural component is linear elastic, then the relevant applied parameter in the component is KI. Comprehensive compendia of KI factor solutions exist in handbook format [7-9] and as computer programs. The linear elastic handbook solutions are usually approximations of finite element solutions, which have been generated for arrange of component and crack dimensions. If the component behaves in an elastic-plastic manner, the situation is much more complex because the crack tip loading is additionally influenced by the deformation pattern of the material as given by its stress-strain curve. This makes the generation of handbook solutions an expensive task. To a limited extent this task has been realized for a few component configurations, for example, in the Electric Power Research Institute (EPRI) handbook [10]. More generally, however, individual finite element R6 Method
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analyses have to be carried out. These analyses require a high level of experience personnel, which is not always available. Fig. 1 gives an overview of the crack tip parameters.
Figure 2: Principles of analytical determination of the crack tip loading. Due to the inherent uncertainties in the determination of the crack tip loading parameter analytical flaw assessment methods are aimed at providing conservative results. Consequently, an assessment leading to the result unsafe does not necessarily mean that the component will fail. The R6 defect assessment procedure has been continually developed since 1976. It is currently at Revision 4. R6 has had a major influence on the development of other codes and standards, including the new API 579 [2], BS guide BS7910:1999 [1] and the SINTAP [3] procedure.
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3. The R6 Method 3.1 Option 3 Curve and the assessed point R6 method is basically a method developed to simplify the elastic plastic fracture analysis. Calculation of the plastic part of the J integral is difficult. R6 methodology helps in performing a detailed elastic plastic fracture analysis using the stress intensity factor only. The method is double criteria approach. It simultaneously checks for failure against plastic collapse too. Consider fig. 3, the x-axis represents a ratio between the applied load M and the limit load Ml. The failure based on net section collapse criteria is when this ratio exceeds 1. The y-axis represents the ratio between the applied J and the fracture toughness Jc. The failure based on fracture mechanics (crack growth initiation) will happen when this ratio is greater than 1. Thus the safe and the unsafe region can be defined. It can be seen that the applied J has elastic and a plastic part. The elastic part contribution to the J decreases as the load increases. R6 method envisages a failure assessment line (FAL), which joins all the points that demarcates the elastic and the plastic part of the J integral. If such a line is obtained, only the elastic part of the J may be evaluated and then a check for safe condition is made such that the ratio Je/Jc is within the FAL at the given applied load. R6 method uses two ratios Kr’ and Lr’. Kr’ is a measure of nearness to brittle fracture. Kr’ is defined by eq. (3). 1 Jp/Jmat J/Jmat
SAFE UNSAFE
Je/Jmat
M/Ml
1
Figure 3: Normalizing fracture and the collapse criteria
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K r' =
Je K = J mat K mat
J mat , K mat = fracture toughness
(3)
K mat = J mat E and K = J e E E = Young's Modulus Lr’ is a measure of nearness to plastic collapse. Lr’ is defined by eq. (4). L'r =
M Ml
M = applied load
(4)
M l = yield stress based limit load
The basic equation of FAL can be written as in eq.(5) Je for Lr ≤ Lmax r Kr = Je + J p 0 for Lr > Lmax r J e = elastic part of J
(5)
J p = platic part of J J = Je + J p This is termed in the R6 document as Option 3 curve. This represents the basic definition of FAL. The limit to plastic collapse is set by a ratio Lrmax, which is defined by eq. (6). Lmax = r
σf =
σf σy
σu +σ y
(6)
2 σ f = flow stress
σ y = yield stress A typical R6 diagram popularly known as “Failure Assessment Diagram” FAD is shown in figure 4.
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Figure 4: FAD in R6 method
Steps to plot R6 Option 3 FAD for a given cracked component: A number of points are taken on the Lr axis in between 0 and Lrmax. 1. For each of these points, limit load Ml will remain same. Corresponding to each value of Lr, applied load M, is determined. 2. Now for each M, The FAL is plotted as a ratio of the elastic J (Je) to the total J at different loads corresponding to Lr values. 3. For the component to be analyzed, Kr’ and Lr’ are calculated, and plotted on the FAD. This point is termed as the assessed point. If this point lies with in the region enclosed by the axes and the FAL, the crack growth initiation does not happen. 4. The safety margin on load can be determined by the ration OB/OA. Since the plotting of FAL requires calculation of Je and Jp, this makes FAL, dependent on the geometry and the material of the component being analyzed.
3.2 Option 2 Curve To avoid calculation of the J integral, this FAL is modified by approximating the J solutions given in the EPRI report by Kumar et.al. [10]. Approximations were made on the conservative side to remove the geometry dependence of FAL. It was however
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still dependent on the material of the component. This FAL is termed as Option 2 FAL in R6. The FAL in Option 2 is defined by eq. (7). −1 Eε 3 2 L σ ref + r y K r = Lrσ y 2 Eε ref 0 E = Young's modulus
for
Lr ≤ Lmax r
for
Lr > Lmax r
(7)
σ y = Yield stress ε ref = true strain at true stress = Lrσ y Steps to plot R6 Option 2 FAD for a given cracked component: 1. A number of points are taken on the Lr axis in between 0 and Lrmax. 2. For each of these points, reference stress σref is determined from Lrσy, and corresponding true strain εref is read from the true-stress strain curve of the material of the component. 3. Now for each chosen Lr point, The FAL is plotted using eq. (7). 4. For the component to be analyzed, Kr’ and Lr’ are calculated, and plotted on the FAD. This point is termed as the assessed point. If this point lies with in the region enclosed by the axes and the FAL, the crack growth initiation does not happen. The safety margin on load is also obtained. Since the plotting of FAL requires calculation of σref and εref, this makes FAL, dependent on the stress- strain data of the material of the component being analyzed.
3.3 Option 1 Curve In many real engineering analyses, the full stress strain data is not available. For such cases R6 has defined an Option 1 FAL. To obtain this curve, Option 2 equation was applied to a number of materials to generate a material independent lower bound curve, which is the more conservative. This lower bound curve is given in eq.(8). (1 − 0.14 L2r ) 0.3 + 0.7 exp ( −0.65L6r ) Kr = 0
for
Lr ≤ Lmax r
for
Lr > L
(8)
max r
In order to plot this FAL, only the engineering values of lower yield or 0.2% proof stress and the flow stress need to be known. This curve is reasonably conservative for most materials. However in certain circumstances when initial rate of hardening in stress-strain is high, the underestimation may be excessive. For the special case of strain aging C-Mn(mild) steels, if Option 1 curve is to be used, and alternate equation has been provided. A typical Option 1 curve is shown in fig. 5. R6 Method
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1.2
FAL
1
Lr
0.8
B
0.6
0.4 A 0.2
0 O
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Kr
Figure 5: R6 Option 1 Curve
3.4 Unstable Crack Growth as Failure Criteria The condition when the assessed point crosses the FAL can cause the crack growth initiation. R6 also considers the unstable crack growth as failure criteria. In evaluating the margin on unstable crack growth, J-Resistance curve is required. The J-Resistance curve is converted into fracture toughness Kmat vs. crack extension a data. Once the assessed point is outside the safe region, small increment to crack size a, is given. This modifies the assessed point. Because of increase in crack size, K increases while the limit load decreases. The main change is in the value of Kmat, which increases appreciably. Hence the, assessed point has a lower Kr’ value and a marginally increased Lr’ value. This process is repeated to check if the assessed point enters the safe region. In such a case, the crack arrest takes place. If the assessed point fails to enter the safe region, the unstable crack growth occurs. The unstable crack growth load is the load at which the locus of the Lr’-Kr’ just touches the R6 FAL. This analysis of unstable crack growth in R6 is termed as Category 3 analysis. The analysis done for checking crack growth initiation is termed as Category 1 analysis. Consider Fig. 6. The procedure for estimating load to cause unstable crack growth is as follows. 1. The original assessed point is A. 2. The load is increased, the crack growth initiation occurs at point B. 3. On further increasing the load, crack growth initiation occurs. Consider point L1. As the stable crack growth takes place, the assessed point is updated based on increased crack size and increased Kmat. The locus followed is L1-L1’. The R6 Method
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assessed point re-enters the safe region and the crack is arrested. The amount of crack extension done is decided by the availability of J-Resistance data. 4. Now consider the load L3. Here, after exhausting the J-Resistance, still the assessed point is in the unsafe region. The unstable crack growth takes place at this load. 5. The objective now is to find a load L2 such that the locus L2-L2’ is tangent to the FAL. This is the limiting load for unstable crack growth. 1.2
FAL
1
L3 L1 L2
Lr
0.8
B L3'
0.6 L1'
L2'
0.4 A 0.2
0 O
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Kr
Figure 6: Category 3 Analysis in R6
3.5 Treatment of secondary stresses In presence of secondary stresses, R6 considers the interaction between the primary and secondary stress levels. Secondary loads do not have any effect on FAL and Lr’ values. Kr’ is the only parameter that is affected. The Kr’ in presence of secondary stress is defined as eq. (9). K r' = K rp' + K rs' + ρ K rp' = K r' because of primary stress
(9)
K rs' = K r' because of secondary stress
ρ = interaction parameter The factor in eq. (9) takes account of plasticity corrections required to cover interactions between the primary and secondary stresses. Value of depends on the crack size and on the magnitude of primary stress. It is calculated using the eq. (10).
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0.1x 0.714 − 0.007 x 2 + 0.00003x 5 , x ≤ 5.2
ρ1 =
0.5, x > 5.2 S K Lr x= KP ρ1 , Lr ≤ 0.8 ρ = 4 ρ1 (1.05 − Lr ) , 0.8 < Lr ≤ 1.05 0, 1.05
(10)
K P = Stress intensity factor for primary load
The effect of secondary load is negligible in the plastic zone, i.e. the interaction parameter is negative. However, R6 specifies a value of = 0 for Lr > 1.05 as a conservative estimate.
3.6 Evaluation under Mode I, II, III loads R6 advises only Category 1 analysis for mixed mode loading. However, not much validation of the cases under mixed mode loading has been done in R6 method, hence the formulation should be done with conservative data. The Kr’ calculation is given by eq (11). if K C σ y ≥ 0.2 m
(
)
2 K eff = K I2 + K II2 + K III 1 −ν
1
2
if K C σ y < 0.2 m
(11)
no general definition available K eff K eff K r' = + +ρ K mat Pr imary K mat Seconadry
Formulations for limit load under mixed mode loading are available for selected geometries in the literature.
3.7 Flaw Characterization Flaw characterization is the name given to the process of modeling an existing crack by a geometrically simpler one, more amenable for analysis. Characterization rules have built in conservatism. ASME Pressure Vessel Code, Section XI and A16 guide has published guidelines for flaw characterization. A postulated or an observed flaw should be subjected to a recursive treatment before arriving at the final crack size. Some sample characterization of flaws is given in following figures.
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Figure 7: Flaw Sizing
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Figure 8: Characterizing embedded defect a to larger of b or c in Brittle Mechanism
Figure 9: Characterizing Surface Defect a to larger of b or c in Brittle Mechanism
Figure 10: Characterizing Defects in ductile Mechanism
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a = max(a1,a2) l = l1 + l2 +b
a=a1 + a2 + b l = max(l1, l2)
a = max(a1, a2) l = l1 + l2 + b
a = a1 + a 2 + a 3 l = max(l1, l2)
Figure 11: Planar Defect Interaction Criteria
3.8 Sensitivity Analysis R6 method suggests a detailed sensitivity analysis before the results could be used. It defines the margins on different input parameters in terms of reserve factors. If the assessed point lies on FAL, it is the limiting condition. The various reserve factors are evaluated based on this condition.
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Reserve Factors: The most significant reserve factor is the one on applied load. load to cause limiting condition FL = applied load in assessed condition
(12)
Similarly load factors for crack size (a), fracture toughness (K) and yield stress (σ) can be expressed as: crack to cause limiting condition Fa = crack in assessed condition fracture toughness of the material being assessed (13) FK = fracture toughness to provide limiting condition yield stress of the material being assessed Fσ = yield stress to provide limiting condition
The sensitivity analysis can be performed by plotting a reserve load factor against the corresponding input parameter.
Figure 12 Locus of Kmat, crack size and σy
In fig. 12, if the fracture toughness is decreased then the path followed is X-A. Thus the reserve factor is the toughness at the assessed point X divided by the toughness value at A. Similarly if crack size is increased, the path followed is X-B and the reserve factor on crack is given as the crack size at B divided by the crack size at X. Similarly reserve factor on yield stress can be obtained from the path X-C.
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3.8 R6 Methodology The step-by-step procedure to perform R6 analysis is given here. 1. Define and categorize all loads and stress. 2. Determine material tensile properties. 3. Define and select FAD (Option). 4. Characterize the shape of the flaw. 5. Select category of analysis. 6. Define fracture toughness parameters. 7. Define relevant crack size. 8. Calculate Lr. 9. Calculate Kr. 10. Plot all points on FAD. 11. Assess the significance of results and perform sensitivity analysis.
4 Sample Calculation [11] On insetting the cylindrical section of a pressure vessel after post weld heat treatment a number of indications of defects were observed in a longitudinal seam weld. The largest string of these were parallel to the weld within a depth of 17 mm of the outer surface over a length of 200 mm, and though it was concluded that they were not crack like defects and did not impair the integrity of the vessel, a fracture mechanics analysis was required to demonstrate that the margin on pressure against failure is high. The normal operating temperature of the vessel is above 20oC, where the material is ductile. Proof pressure testing in works may be conducted at temperatures as cold as 5oC. Perform the analysis assumed level of residual stresses of magnitude 0.2σy. Basic Data Internal Radius ‘R’: 508mm Wall thickness ‘t’: 77mm Design Pressure: 30MPa Normal Operating Pressure: 26MPa Proof Pressure: 40MPa Defect depth ‘a’: 17mm Defect length ‘l’: 200mm Material: Ferritic Steel Tensile properties: Parent Material σy = 390MPa σu = 590Mpa E = 210GPa Weld Metal σy = 420MPa σu = 610MPa E = 210GPa o o Fracture properties: (same at 5 C and 20 C) Weld Metal
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Table 1: Fracture data
a (mm) 0.2 1.0 2.0 2.45 3.0 4.0 4.4 R6 analysis:
Kmat (MPa√m) 178.3 228.7 254.5 262.7 271.0 283.3 287.5
1. Define and categorize all loads and stress. The crack is in the longitudinal direction and the only load of interest is the internal pressure. Hence the hoop stress caused by internal pressure is to be used for fracture analysis. The analysis is performed for two levels of pressure, 26 MPa and 40 MPa. Residual stresses of magnitude 0.2σy are also considered acting normal to the crack plane. 2. Determine material tensile properties. The tensile properties of weld metal and parent material has been provided. For conservative analysis, the tensile properties of parent material which are lower are used in the analysis. Hence σy used is 390 MPa and σu used is 590 MPa. Corresponding σf is (390+590)/2 = 490 MPa. 3. Define and select FAD (Option). Since full stress strain curve is not known, Option 1 FAL is used to perform the fracture analysis. The cut off value for plastic collapse (Lrmax) is given by 490/390 = 1.26 4. Characterize the shape of the flaw. The flaw will be characterized as semi-elliptical surface flaw. This is shown in figure 13.
Figure 13: Characterization of the flaw
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5. Select category of analysis. A category 3 analysis is performed as the full J-Resistance curve is available. 6. Define fracture toughness parameters. The fracture data is defined in Table 1. The fracture toughness, Kmat is taken as 178.3 MPa√m. 7. Define relevant crack size. The crack configuration defined in fig. 13 is used. The Category 3 analysis is performed for a crack extension of 4.4 mm. 8. Calculate Lr’. The limit load for the geometry defined is given by eq.(14).
Py =
(1 − a t )σ y (1 − a (mt )) R
t (14)
l2 m = 1 + 1.05 4 Rt 2
The value of Lr’ is given by P/Py. Table 2: Lr’ at Normal operating condition and proof test
P (MPa) 26 40
1. 2.
Lr’ 0.46 0.70
9. Calculate Kr’. The K for this configuration is given by eq. (15). In this equation ‘c’ is half crack length (l/2) and Ro is the outer radius. K I = σ h (π a)0.5 F
σ h = p( Ro2 + R 2 ) /( Ro2 − R 2 )
( 0.4759α + 0.1262α ) F = 0.25 + 2
Ri 0.102 t − 0.02
α = (a t ) (a c) The Kr’ = (Krp’+ Krs’+
(15)
0.1
0.58
)
Table 3: Kr’ at Normal operating condition and proof test
P
R6 Method
Krp’
Krs’
Kr’
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1. 2.
26 40
0.28 0.44
0.12 0.12
0.03 0.03
0.43 0.59
To estimate the load to cause crack growth initiation, the values of Lr’ and Kr’ were plotted for increasing applied pressures. These are listed in Table 4.
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Table 17.4: Lr’ and Kr’ for increased load
Pressure MPa Lr’ 40 0.70 41 0.72 42 0.74 43 0.75 44 0.77 45 0.79 46 0.81 47 0.82 48 0.84 49 0.86 50 0.88 51 0.89 52 0.91 53 0.93 54 0.95 55 0.96 56 0.98 57 1.00 58 1.02 59 1.03 60 1.05
Krp’ 0.44 0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61 0.62 0.63 0.64 0.66
Krs’ 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12
0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.00
Kr’ 0.59 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78
10. Plot all points on FAD. Figure 14 gives the R6 FAD in the absence of residual stresses. The initiation point corresponds to an internal pressure of 56 MPa. Hence the reserve factor is 56/26 = 2.15 on operating load and 56/40 = 1.4 on proof pressure. The FAD in presence of residual stress is shown in fig. 15. The initiation point corresponds to an internal pressure of 52 MPa. Hence the reserve factor on load is 52/26 = 2 on operating load and 52/40 = 1.3 on proof pressure.
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1 0.9 0.8
INITIATION POINT
0.7
Kr
0.6
(0.98,0.61)
PROOF TEST
0.5 0.4
(0.70, 0.44)
NOC
Lrmax
0.3 (0.46,0.28)
0.2 0.1 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
Lr
Figure 14: Failure assessment diagram, without secondary load 1
Lr = 0.8
0.9 0.8
INITIATION POINT
0.7
PROOF TEST
0.6 Kr
Lr = 1.05
(0.9,0.7) NOC
0.5 0.4
(0.70, 0.59) (0.45,0.43) max
0.3
Lr
0.2
Krs = 0.12
0.1 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
Lr
Figure 15: Failure assessment diagram, with secondary load
The flawed structure has a reserve margin on normal operating load equal to 2 against crack growth initiation. The calculations for margin against unstable crack growth using Category 3 analysis of R6, is shown in Table 5 In these calculations, for loads in the unsafe region, tearing analysis is applied by increasing the crack depth. The points for each load are plotted on the FAD (Fig. 16).
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It is seen that for pressure value greater than 59 MPa, crack arrest does not take place. Thus the margin on load against unstable crack growth is 59/26 = 2.27. Table 17.5: Calculation for unstable crack growth
Pressure a mm Kmat MPa√m 17.20 178.3 18.00 228.7 19.00 254.5 19.45 262.7 20.00 271 21.00 283.3 21.40 287.5
52 MPa Lr’ 0.91 0.91 0.91 0.91 0.91 0.92 0.92
Kr’ 0.71 0.56 0.52 0.51 0.49 0.48 0.48
60 MPa Lr’ 1.05 1.05 1.05 1.05 1.05 1.06 1.06
59 MPa Lr’ 1.03 1.03 1.03 1.04 1.04 1.04 1.04
Kr’ 0.78 0.62 0.56 0.55 0.54 0.52 0.52
Kr’ 0.77 0.61 0.56 0.54 0.53 0.52 0.51
1 0.9
P = 59
0.8 0.7
PROOF TEST
Kr
0.6 0.5
P = 60 P = 52
NOC
0.4 0.3 0.2 0.1 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
Lr
Figure 16: Calculation of load for unstable crack growth
11. Assess the significance of results and perform sensitivity analysis. Based on the analysis performed following observations can be made. a. If residual stress is ignored, a reserve margin of 2.14 is obtained on the operating pressure and a margin of 1.4 on proof pressure. b. If residual stress is considered, these margins fall to 2 and 1.3. Thus a residual stress of magnitude 0.2 σy results in 7% decrease in margins. If exact value of residual stresses is not know, a variation of these safety margins with respect to different stress value can be performed to assess their significance. c. Unstable crack growth occurs at a load of 59 MPa. Giving a margin of 2.27 on operating pressure compared to 2 in Category 1.
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d. It is observed that with increased ∆a for tearing analysis, the assessed points on the FAD are close together. Hence, further extension will not result is increased safety margins.
5 References 1. BS. “Guide on methods for assessing the acceptability of flaws in fusion welded structures”. BS 7910 : 1999, British Standards Institute, London, UK, 1999. 2. API. “Recommended practice for fitness-for-service”. API 579. Washington, DC: American Petroleum Institute, 2000. 3. SINTAP. “Structural integrity assessment procedure for European industry”. Final Procedure, 1999. Brite-Euram Project No. BE95- 1426, British Steel. 4. Milne I, Ainsworth RA, Dowling AR, Stewart AT. “Assessment of the integrity of structures containing defects”. CEGB Report R/H/R6-Revision 3. Latest ed. 1986; latest ed. British Energy, 1999. 5. ASME Boiler and Pressure Vessel Code, 1998 Edition. Section XI – Rules for Inservice Inspection of Nuclear Power Plant Components 6. Andrew Cosham and Mike Kirkwood, “Best practice in pipeline defect assessment”, Proceedings of IPC 2000: International Pipeline Conference October 2000; Calgary, Alberta, Canada. Also, www.penspenintegrity.com 7. Zahoor, A., 1989. Ductile Fracture Handbook. Electric Power Research Institute, Palo Alto, EPRI NP6301-D, Vol 1-3. 8. A16, 1995. Guide for Defect Assessment and leak before break analysis, Rapport DMT 96.096, EPAC 5450, Fiche Cooperative 4557. 9. Raju, I.S., Newman, J.C., 1982. Stress intensity factors for internal and external surface cracks in cylindrical vessels. Transactions of ASME Journal of Pressure Vessel Technology 104, 293–298. 10. Kumar V, German MD, Shih CF. An engineering approach for elastic-plastic fracture analysis. EPRI-Report NP-1931, EPRI, Palo Alto, 1981. 11. Milne I, “Problems on the use of R6”, in Assessment of Cracked Components by Fracture Mechanics, EGF4 (ed. LH Larsson), 1989, Mechanical Engineering Publications, London, pp 263-265, 457-472.
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