Relevance of plastic limit loads to reference stress approach for surface cracked cylinder problems

To investigate the relevance of the definition of the reference stress to estimate J and C* for surface crack problems, this paper compares finite element (FE) J and C* results for surface cracked pipes with those estimated according to the reference stress approach using various definitions of the reference stress. Pipes with part circumferential inner surface cracks and finite internal axial cracks are considered, subject to internal pressure and global bending. The crack depth and aspect ratio are systematically varied. The reference stress is defined in four different ways using (i) a local limit load, (ii) a global limit load, (iii) a global limit load determined from the FE limit analysis, and (iv) the optimised reference load. It is found that the reference stress based on a local limit load gives overall excessively conservative estimates of J and C*. Use of a global limit load clearly reduces the conservatism, compared to that of a local limit load, although it can sometimes provide non-conservative estimates of J and C*. The use of the FE global limit load gives overall non-conservative estimates of J and C*. The reference stress based on the optimised reference load gives overall accurate estimates of J and C*, compared to other definitions of the reference stress. Based on the present findings, general guidance on the choice of the reference stress for surface crack problems is given.     

Use of local and global limit load solutions for plates with surface cracks under tension

Some available experimental results for the ductile failure of plates with surface cracks under tension are reviewed. The response of crack driving force, J, and the ligament strain near the local and global limit loads are investigated by performing elastic-perfectly plastic finite element (FE) analysis of a plate with a semi-elliptical crack under tension. The results show that a ligament may survive until the global collapse load is reached when the average ligament strain at the global collapse load, which depends on the uniaxial strain corresponding to the flow stress of the material and the crack geometry, is less than the true fracture strain of the material obtained from uniaxial tension tests. The FE analysis shows that ligament yielding corresponding to the local limit load has little effect on J and the average ligament strain, whereas approach to global collapse corresponds to a sharp increase in both J and the average ligament strain. The prediction of the FE value of J using the reference stress method shows that the global limit load is more relevant to J-estimation than the local one.     

The effect of mechanical heterogeneity and limit load of a weld joint with longitudinal weld crack on the J-integral and failure assessment curve

According to the CEGB R6 (Rev.3) approach, the influence of strength mis-matching and the limit load of a weld joint with a longitudinal weld crack on the J-integral and failure assessment curve can be studied by using an elastic–plastic finite element method for Center-Cracked Panel (CCP) specimens. The results indicate that the values of the J-integral and the shapes and positions of the failure assessment curves are greatly affected by the strength mis-matching factor M, a ratio of weld metal yield strength to that of base metal. If the limit load of the base metal is adopted to normalize the applied load, then the greater the value of M, the larger the safe area is in the failure assessment curve (FAC). However, if the limit load of the weld metal is adopted to normalize the applied load, then the greater the value of M, the smaller the safe area is. Therefore, for the undermatched and evenmatched joints, it is safer to choose the limit load of the base metal as the normalized load, and for the overmatched joints, it is safer to choose the limit load of the weld metal as the normalized load. Moreover, when M is less than 0.8 for the former situation, the option 1 curve of the R6 is not a conservative assessment curve. Considering that there is no simple theoretical formula which is suitable for calculating the limit load of a mechanical heterogeneous weld joint under plane stress and a variety of crack geometries, it is recommended that no matter what the strength of the overmatched or undermatched weld joint is, it is safer to use the limit load of that metal which has the higher strength grade of base metal and weld metal as the normalized load.     

Elastic–plastic J and COD estimates for axial through-wall cracked pipes

This paper proposes engineering estimation equations of elastic–plastic J and crack opening displacement (COD) for axial through-wall cracked pipes under internal pressure. On the basis of detailed 3D finite element (FE) results using deformation plasticity, the plastic influence functions for fully plastic J and COD solutions are tabulated as a function of the mean radius-to-thickness ratio, the normalised crack length, and the strain hardening. On the basis of these results, the GE/EPRI-type J and COD estimation equations are proposed and validated against 3D FE results based on deformation plasticity. For more general application to general stress–strain laws or to complex loading, the developed GE/EPRI-type solutions are re-formulated based on the reference stress (RS) concept. Such a re-formulation provides simpler equations for J and COD, which are then further extended to combined internal pressure and bending. The proposed RS based J and COD estimation equations are compared with elastic–plastic 3D FE results using actual stress–strain data for Type 316 stainless steels. The FE results for both internal pressure cases and combined internal pressure and bending cases compare very well with the proposed J and COD estimates.     

Net-section limit moments and approximate J estimates for circumferential cracks at the interface between elbows and pipes

This paper firstly presents net-section limit moments for circumferential through-wall and part-through surface cracks at the interface between elbows and attached straight pipes under in-plane bending. Closed-form solutions are proposed based on fitting results from small strain FE limit analyses using elastic–perfectly plastic materials. Net-section limit moments for circumferential cracks at the interface between elbows and attached straight pipes are found to be close to those for cracks in the centre of elbows, implying that the location of the circumferential crack within an elbow has a minimal effect on the net-section limit moment. Accordingly it is also found that the assumption that the crack locates in a straight pipe could significantly overestimate the net-section limit load (and thus maximum load-carrying capacity) of the cracked component. Based on the proposed net-section limit moment, a method to estimate elastic–plastic J based on the reference stress approach is proposed for circumferential cracks at the interface between elbows and attached straight pipes under in-plane bending.     

Limit loads and fracture mechanics parameters for thick-walled pipes

In this paper, information on plastic limit loads and both elastic and elastic-plastic fracture mechanics parameters is given for cracked thick-walled pipes with mean radius-to-thickness ratios ranging from two to five. It is found that existing limit load expressions for thin-walled pipes can be applied to thick-walled pipes, provided that they are normalized with respect to the corresponding un-cracked thick-walled pipe values. For elastic fracture mechanics parameters, FE values of the influence functions for the stress intensity factor and the crack opening displacement are tabulated. For elastic-plastic J, it is shown that existing reference stress based J estimates can be applied, provided that a proper limit load for thick-walled pipes is used.     

A J integral estimation method for cracks in welds with mismatched mechanical properties

A J integral estimation method is proposed for a crack located in the middle of a weld with a mismatch in mechanical properties from the surrounding base material. The method covers both yield stress over/under-matching and differences in hardening behaviour between weld and base material. The method involves the definition of an ‘equivalent stress-strain relationship’ based on the mechanical properties of both the weld and base materials. The value of J is then estimated using the equivalent stress-strain relationship in conjunction with the EPRI method. An approximate solution for the equivalent stress-strain relationship has been obtained by assuming that the average resistance along a slip-line controls the plastic stress and strain fields near the crack tip. Detailed formulae for plane strain centre-cracked panel (CCP) specimens have been derived on the basis of limit load solutions.

Nonlinear finite element analysis of 26 cases with various degrees of mismatch in yield stress and hardening behaviour have been performed for plane strain CCP specimens. The results show good agreement with those estimated using the equivalent stress-strain relationship method. Traditional defect assessment methods based on the use of ‘weaker material’ properties in a mismatched weld are compared to the results of the finite element analyses. It is proposed that the equivalent stress-strain relationship may be used to define the R6 failure assessment diagram for particular weld defects using the Option 2 procedure of R6.     

Validation of BS7910:2005 failure assessment diagrams for cracked square hollow section T-, Y- and K-joints

This paper describes the usage of finite element (FE) analyses results to validate the standard BS7910 assessment procedure for the safe design of cracked square hollow section (SHS) T-, Y- and K-joints. In the study, the actual 3D surface cracks obtained from previous fatigue tests have been included in the FE models. An automatic mesh generation program is then developed and used to produce the failure assessment diagram (FAD) through the J-integral method. The ultimate strength of uncracked SHS joints with reduced load bearing areas have been referenced to derive the plastic collapse loads of cracked SHS joints for the development of FAD. These loads have been validated against the previous experimental results. In comparison with the existing standard BS7910 Level 2A/3A FAD curve and the proposed assessment procedure for circular hollow section joints, it is found that a plastic collapse load with a penalty factor of 1.05 will be sufficient for the safe assessment of cracked SHS T, Y, and K-joints under brace end axial loading.     

J-integral and local damage fracture analyses for a pump casing containing large weld repairs

Three-dimensional J-integral and two-dimensional Local Approach finite element studies are described for postulated crack-like defects in a large repair weld to the casing of a light water reactor circulation pump. The repair weld residual stress field is simulated and plant operating pressure and thermal transient loads are applied. Crack tip constraint effects are quantified through detailed analysis of the cracked structure and compact tension fracture toughness specimens. Fracture initiation crack sizes are shown to be larger than conceivable fabrication defects that are detectable using modern ultrasonic inspection techniques. The Local Approach study demonstrates the benefits of quantifying crack tip constraint conditions, compared with conventional J-estimation schemes and cracked body J-integral analysis. The method of introducing the crack into the finite element model is shown to have a large effect on calculated crack tip fracture parameters; a slowly developing crack in the residual stress field being more benign.     

Determination of the elastic-plastic fracture mechanics Z-factor for alloy 182 weld metal flaws

One of the ways that the ASME Section XI code incorporates elastic-plastic fracture mechanics (EPFM) in the Section XI Appendix C flaw evaluation procedures for circumferential cracks is through a parameter called Z-factor. This parameter allows the simpler limit-load (or Net-Section-Collapse) solutions to be used with a multiplier from EPFM analyses. This paper shows how 3-D finite element (FE) analyses were employed to investigate the sensitivity of the crack-driving force as a function of crack location (i.e., crack in the center of weld, or closer to the stainless or low alloy steel sides) in an Alloy 182 dissimilar metal weld (DMW), and how an appropriate (or equivalent) stress-strain curve was determined for use in the J-estimation schemes. The J-estimation schemes are then used to cover a wider range of variables, i.e., pipe diameters, cracks lengths, and also incorporate crack growth by ductile tearing. The Z-factor equations as a function of pipe diameter were calculated using the LBB.ENG2 J-estimation scheme along with the most conservative equivalent stress-strain curve from the FE analyses. The proposed Z-factor approach was then validated against an Alloy 182 DMW full-scale pipe test that had a circumferential through-wall crack in the fusion line. The predicted EPFM maximum load showed excellent agreement with the experimental result. Furthermore, it was shown that the proposed Z-factor equation is not sensitive to the location of the crack.     

Establishing a methodology to predict the crack initiation load in through-wall cracked components using tensile specimen test data

Among several other definitions, the crack initiation fracture toughness (J_i) based on critical stretch zone width (SZWc), called J_SZWc, is being considered as a geometry independent material property. The problem in SZWc experimental evaluation is in identifying the size of stretch zone on a blunted crack front as this requires a high degree of precision and expertise in measuring the SZW. The present study addresses finite element determination of SZWc value using tensile test data. The role of stress tri-axiality in standard fracture specimens and the smooth round tensile specimen is also studied. Based on the ASTM-E1820 standard, the present study also showed that fracture specimen thickness greater than the specified size is to be used for numerical prediction of valid SZWc value. The numerically predicted SZWc that leads to J_SZWc matches well with experimental values. Using J_SZWc, the crack initiation load is also determined in circumferentially through-wall cracked (TWC) elbows and compares well with experimental results. Thus the paper establishes the methodology to predict crack initiation in cracked piping components using numerically obtained valid J_SZWc from material’s tensile test data.     

Influence of weld misalignment and weld metal overmatch on the prediction of fracture in pipeline girth welds

$\text{J-}\text{integral}$ estimates using elastic-plastic finite element calculations, are shown to compare well with experimental results from single edge-notch bend (SENB) specimens made of X483 grade line pipe steel.The influence of weld misalignment and weld metal overmatch on fracture of cracked girth welds is predicted, also using elastic-plastic finite element calculations. Weld metal overmatch reduces plastic strain levels in the weld and appears beneficial in reducing $\text{J-}\text{integral}$ magnitudes. Predicted values of $\text{J-}\text{integral}$ are shown to increase with weld misalignment. However, $\text{J-}\text{integral}$ magnitudes near the critical value for crack growth initiation were only attained after considerable plastic straining at or near limit load. This result suggests that limit load calculations may be more appropriate for prediction of failure of cracked girth welds than conventional fracture techniques.     

Quantification of ductile crack growth in 18G2A steel at different constraint levels

A constraint theory in fracture mechanics is used to analyze the test data of 18G2A steels using single edge-notched bend (SENB) specimens with various crack depth to specimen width ratios (a/W). A bending correction factor is included in the two-parameter (J–A₂) asymptotic solution to improve the theoretical prediction of the stress field for deep cracks under large-scale yielding condition, where J is the J-integral and A₂ is the constraint parameter, which depends on the in-plane geometry of the cracked body (a/W). As a result, the valid region for a traditional J-controlled crack growth is extended, and the ASTM specimen size requirements for fracture toughness testing can be relaxed. In addition, it is shown that the functional dependence of J–R curves on A₂ for 18G2A steels is established with test data; and the predicted J–R curves agree very well with the experimental curves. This ensures the transferability of laboratory test data to an actual structure provided the constraint level (A₂) of the cracked structure is known or determined. This procedure allows an appropriate J–R curve with the same constraint level to be constructed and used in flaw stability analysis of any cracked body.     

Yield load solutions of heterogeneous welded joints

The aim of this paper is to establish yield load solutions when the materials inhomogeneity within the weld is present, which is usually the case in repair welding. The effect of yield strength mismatch of welded joints performed with different geometry on the yield load value has been investigated in the context of single edge notched fracture toughness specimen subjected to bending SE(B) using the finite element method. The crack was located in the center of the weld and the two most important geometrical parameters were identified as: crack length ratio a/W as well as slenderness of the welded joint, which were systematically varied. One practical and four additional combinations of filler materials, with the same portion of overmatched part and undermatched part of the weld, were analyzed, and plane strain FE solutions for the case when the crack is located in the overmatched half of the heterogeneous weld were obtained.     

Simulation of JR-curves for reactor pressure vessels steels on the basis of a ductile fracture model

A procedure for the prediction of J_R-curves for reactor pressure vessels (RPVs) steels in the initial and embrittled states is presented. Prediction of the J_R-curves is performed over the ductile fracture temperature range on the basis of a ductile fracture model. A procedure for the determination of ductile fracture model parameters based on tests of smooth and notched cylindrical specimens is proposed. The stress and strain fields near the stationary and growing crack tip are analyzed by FEM. Approximate analytical solutions for stress and strain fields near a growing crack tip are proposed. Comparison of the predicted J_R-curves and experimental 2T–CT data for the initial and embrittled RPV 2Cr–Ni–Mo–V steels for WWER-1000 is performed.     

Finite element analysis on relationships between the J-integral and CTOD for stationary cracks in welded tensile specimens

In this study the effects of weld strength mismatching and geometry parameters on the relationship between the J-integral and the crack tip opening displacement (CTOD) are investigated. Numerical analysis was carried out by an ABAQUS two-dimensional elastic–plastic analysis mode. The work was performed for center-cracked welded specimens with uniform tensile load. In the specimens the weld strength mismatch, M, was from 0.8 to 1.2, the crack length, a/W, from 0.1 to 0.5, the weld width, h/c, from 0.1 to 0.5. The main results indicate that weld strength mismatching has only a weak influence on the relationship between the J-integral and CTOD at low load levels, but there is a strong effect at high load levels. The yield strength of weld metal may be used for low load levels and the yield strength of base metal may be used for high load levels, when the basic relationship of J-integral versus CTOD is utilized to treat the problem of welded joints. The results also show that the crack size and weld width have an influence on the relationship between the J-integral and CTOD at high load levels. Because the equivalence between the J-integral and CTOD breaks down at high load levels, the relationship between J-integral and CTOD becomes more complex, and the weld strength and geometry mismatching factors must be included.     

Evaluation of leak-before-break assessment methodology for pipes with a circumferential through-wall crack. Part II: J-integral estimation

Evaluation of the J-integral plays a central part in evaluation of the critical crack length for unstable fracture for piping systems. Simplified evaluation methods for the J-integral for a circumferential through-wall crack in pipes subjected to axial and bending loading or their combination is reviewed in this paper. Use of the LBB.ENG2 method and a similar approach based on the η-factor concept were found to result in significant underestimation of the J-integral for small and medium crack angles. On the other hand, the reference stress method based on the solutions for stress intensity factor and limit load recommended in the companion paper (Part I) provides solutions which agree well with the available non-linear finite-element solutions and can be utilized as a powerful tool for J-integral evaluation for arbitrary materials, not restricted to simple power-law hardening.     

The estimation of J in three-point-bend specimens with a crack in a mismatched weld

The J integral is estimated by using an equivalent stress-strain relationship approach for three-point-bend specimens containing a weld with mismatched mechanical properties. Elastic-plastic finite element analyses are performed to verify the use of this approach. The results show that satisfactory precision can be obtained provided a suitable limit load solution is used. A limit load solution suggested by Burstow is suitable for over-matching situations and a solution due to Joch et al. for under-matching ones.     

Evaluation of fracture mechanics parameters for bimaterial compact tension specimens

Abstract

The elastic–plastic fracture mechanics parameter J and its analogous creep fracture parameter C* are widely used to measure the fracture resistance of a material. The non-linear component of the J and C* parameters can be evaluated experimentally using the η factor. For weldments, the η factor is dependent on the relative properties of the base (parent) and weld materials, particularly the mismatch in their yield strengths. In this work, the η factor has been evaluated using non-linear finite element analyses in a standard compact tension C(T) specimen for a power law material. A range of mismatches in base/weld material properties have been considered. A through thickness strip of weld material, of height 2h, has been modelled, which was positioned at the mid height of the specimen. The η factor has been evaluated for a range of crack lengths and power law hardening exponents under both plane stress and plane strain conditions and the results compared with literature where available. For a given crack length and weld width, the η solutions of the undermatched and overmatched conditions examined show a maximum variation of 12% from the mean value. A relationship has been proposed with respect to crack length for the C(T) specimen to describe the decrease in the η factor with an increase in mismatch ratio.     

Evaluation of leak-before-break assessment methodology for pipes with a circumferential through-wall crack. Part I: stress intensity factor and limit load solutions

The J-integral and the crack opening area are the main parameters required for a leak-before-break evaluation of a piping system. Stress intensity factor and limit load solutions have been widely used for evaluating these parameters in a simplified way. Solutions for the stress intensity factor and limit load for a pipe with a circumferential through-wall crack subjected to axial and bending loads are reviewed and compared in this study. Based on the comparisons, recommendations are then made on expressions for calculating these parameters.