This paper describes an experimental validation of the enhanced reference stress method to calculate fatigue J-integral ranges, which are effective in predicting the fatigue crack propagation rate under low–cycle fatigue loadings. Although J-integral type fracture mechanics parameters can be calculated via elastic–plastic finite element analysis (FEA) of the crack geometry, performing such an analysis is costly and requires a high–end computer. A simplified method for estimating the elastic–plastic J-integral is therefore desired. Herein, several representative simplified methods for estimating the elastic–plastic J-integral were applied to crack propagation prediction and compared with each other. The experiments referred to was a previously performed cyclic bending tests using wide–plate specimens containing a semielliptical surface crack. Limit load correction factors to improve the accuracy of the reference stress method were estimated by performing an elastic–plastic FEA. The predicted crack propagation behaviors were compared against the test results.

Linear elastic fracture mechanics based flaw evaluation procedures in Section XI of the ASME Boiler and Pressure Vessel Code require calculation of the stress intensity factor (K I ). The 2015 Edition of ASME Section XI [1] implemented a number of significant improvements in Article A-3000, including closed-form equations for calculating stress intensity factor influence coefficients (G i ) for circumferential flaws on the inside surface of cylinders. In the 2017 Edition [2], closed-form equations for axial flaws on the inside and outside surfaces of cylinders have been implemented. In this paper, closed-form equations are developed for circumferential cracks on the OD surface of cylinders, based on tabular data from API 579 (2007 Edition) [3]. The equations presented, represent a complete set of R i / t , a / t , and a / ℓ ratios. The closed-form equations provide G 0 and G 1 coefficients while G 2 through G 4 are obtained using a weight function representation for the K I solutions for a surface crack. These equations permit the calculation of the G i coefficients without the need to perform tabular interpolation. The equations are complete up to a fourth order polynomial representation of the applied stress. The fourth-order representation for stress will allow for more accurate fitting of highly non-linear stress distributions, such as those depicting high thermal gradients and weld residual stress fields.

Nuclear reactor pressure vessels must be able to withstand thermal shock due to emergency cooling during a loss of coolant accident. Demonstrating structural integrity during thermal shock is difficult due to the complex interaction between thermal stress, residual stress, and stress caused by internal pressure. Finite element and analytic approaches exist to calculate the combined stress, but validation is limited. This study describes an experiment which aims to measure stress in a slice of clad reactor pressure vessel during thermal shock using time-resolved synchrotron X-ray diffraction. A test rig was designed to subject specimens to thermal shock, whilst simultaneously enabling synchrotron X-ray diffraction measurements of strain. The specimens were extracted from a block of SA508 Grade 4N reactor pressure vessel steel clad with Alloy 82 nickel-base alloy. Surface cracks were machined in the cladding. Electric heaters heat the specimens to 350°C and then the surface of the cladding is quenched in a bath of cold water, representing thermal shock. Six specimens were subjected to thermal shock on beamline I12 at Diamond Light Source, the UK’s national synchrotron X-ray facility. Time-resolved strain was measured during thermal shock at a single point close to the crack tip at a sample rate of 30 Hz. Hence, stress intensity factor vs time was calculated assuming K-controlled near-tip stress fields. This work describes the experimental method and presents some key results from a preliminary analysis of the data.

Stress intensity factor solutions are readily available for flaws found in pipe to pipe welds or shell to shell welds (i.e., circumferential/axial crack in cylinder). In some situations, flaws can be detected in locations where an appropriate crack model is not readily available. For instance, there are no practical stress intensity factor solutions for circular-arc cracks which can form in circular welds (e.g., nozzle to vessel shell welds and storage cask closure welds). In this paper, stress intensity factors for circular-arc cracks in finite plates were calculated using finite element analysis. As a first step, stress intensity factors for circular-arc through-wall crack under uniform tension and crack face pressure were calculated. These results were compared with the analytical solutions which showed reasonable agreement. Then, stress intensity factors were calculated for circular-arc semi-elliptical surface cracks under the lateral and crack face pressure loading conditions. Lastly, to investigate the applicability of straight crack solutions for circular-arc cracks, stress intensity factors for circular-arc and straight cracks (both through-wall and surface cracks) were compared.

Crack-tip opening displacement (CTOD) and J -integral have been used for elastic-plastic fracture parameters as a crack driving force (CDF) and crack resistance curve to evaluate tensile strain capacity (TSC) of cracked pipelines based on strain-based design (SBD). The TSC can be determined by using two kinds of failure criteria. One is based on the limit state corresponding to an onset of stable crack growth and the other is tangency approach which determines an onset of unstable crack growth by comparing crack driving force and resistance curve. For this reason, the accurate calculation of crack driving force and crack resistance curve is highly required to determine TSC. In the present study, the TSCs for X70 pipelines with a circumferential semi-elliptical surface crack were estimated based on both crack initiation and ductile tearing criteria using crack driving force diagram (CDFD) method. The CDF curves of cracked pipelines were calculated through the detailed elastic-plastic finite element (FE) analyses. Crack resistance curves were obtained from experimental data of single edged notch tension (SENT) specimens. Both the CDF and crack resistance curves were represented using CTOD and J -integral, respectively. As for loading conditions, axial strain and internal pressure were considered. The TSCs based on CTOD were compared with those based on J -integral to investigate the effect of choice of the fracture parameters on TSC. From the FE results, the TSCs based on ductile tearing allowed higher TSCs than those based on crack initiation. Although there were some differences between the TSCs using CTOD and J -integral, the effect of choice of fracture parameter on TSC with internal pressure was not significant.

Due to the interaction of welding residual stress (WRS) and salt environment, cracks can be generated and grow in the Spent Nuclear Fuel (SNF) Canisters. In this paper, two fracture mechanics parameters, stress intensity factor and J-integral, for the canisters with axial cracks subjected to the mechanical loading are calculated by finite element analysis. The structural integrity assessment codes, API 579-1 and R6, are used to verify the procedure. For every external surface crack and through-wall crack, the stress intensity factor follows well the existing evaluation codes, API 579-1. The reference stress-based J-integral prediction of R6 procedure is the most accurate to use the tresca-based limit load as the reference stress.

In this paper, a redefined three-dimensional J-integral for the quadratic tetrahedral element along with some numerical examples are presented. It is known that the J-integral represents the energy release rate and can be computed on an arbitrary path or a domain of integration. This feature is called the “path-independent property”. It requires the assumption of proportional loading in the case of elastic-plastic material. Because of this assumption, when the J-integral is applied to a problem under a non-proportional loading condition, the computed J-integral value depends on the integral path or the integral domain. To overcome this problem, the authors have proposed a formula to evaluate the energy dissipation inside a finite domain in the vicinity of the crack front, which is an extension of the conventional three-dimensional J-integral. The energy dissipating into a small but finite domain in the vicinity of crack front includes the energy released due to the opening of new crack faces and the deformation energy in the process zone. The numerical evaluation is carried out by the domain integral. In this formula, it is not necessary to evaluate any non-integrable terms at the crack front. Furthermore, the proposed formula has the feature of integral domain independence for any material models without any assumptions in their deformation histories. Therefore, it is possible to evaluate the J-integral for problems with non-proportional loads by using the proposed method. In this paper, computational method using the quadratic tetrahedral element for the redefined J-integral under non-proportional loading is presented first. Some results of three-dimensional semi-circular surface crack problem are presented as numerical examples.

In this paper, the results of evaluations of the stress intensity factor and of natural SCC (stress corrosion cracking) growth simulations under weld residual stresses are presented. The results reveal some characteristic SCC propagation behaviors. A surface crack is assumed at the welded joint of a mock-up of a pressurized water reactor (PWR) pressurizer nozzle. SCC propagation law for the weld metal is assumed to be anisotropic. SCC propagation in the surface direction is assumed to be 10 times slower than that in the thickness direction of the welded joint. The anisotropy is caused by different solidification rates of the weld metal in these directions. The material in terms of mechanical properties is set to be homogeneous as differences in the Young’s moduli and the Poisson’s ratios are not large between the weld and the mother metal. The analytical procedures based on the finite element method with an automatic mesh generation scheme for cracked structures, the results of analyses under a various residual stress distributions and some discussions are presented in this paper.

Some components of the main primary circuit of PWR nuclear power plants contain nickel-base alloy 600 parts (steam generator (SG) tubes, steam generator partition plates, lower internal radial supports). It is well known that this alloy is prone to stress corrosion cracking in the primary water environment. In 2002, surface cracks were discovered for the first time in SG partition plates of EDF 900 MWe NPP. The integrity of the SG containing these cracks must be demonstrated for all operating conditions, including accidental conditions. Due to the high tensile consolidation rate and the high fracture toughness of alloy 600, this was proved using limit load analysis. However, for a thorough demonstration, an experimental program was launched at EDF/R&D to better understand the behaviour of cracks in this high fracture toughness material. Centre Cracked Tensile (CCT) specimens were selected for this experimental program, being closer to the industrial case than conventional CT specimens. Two tests have been conducted at room temperature on large CCT specimens containing a semi-elliptical crack. The paper presents the design of the CCT tests, the material characterisation, the main results of the tests and their numerical interpretation.

To perform the integrity assessment of a reactor pressure vessel (RPV) related to Pressurized Thermal Shock (PTS), we model the RPV using the 3D finite element method (FEM). Accurate prediction of temperature and stress fields is determined by using 2-Phase computational fluid dynamics (CFD) simulation in combination with an appropriate finite element discretization of the RPV wall. The cladding and the ferritic low alloy steel are considered as two separated layers, which can be intersected by superficial cracks. The calculation of the stress intensity factor (SIF) in mode I is based on the linear fracture mechanics theory (LEFM) and hypothetical cracks are located in different locations to consider the most critical cases. In the present study, the sub-modeling technique is implemented to refine the mesh required by the fracture analysis in the region of interest. Three types of cracks are considered: axial, circumferential and inclined. The performed integrity assessment uses the master curve approach. The stress intensity factor in the deepest point of a surface crack was compared with the material’s fracture toughness. In previous studies the integrity of the RPV subjected to medium and small break Loss-of-Coolant Accident (MBLOCA and SBLOCA, respectively) has been evaluated, therefore the concern in this contribution is the large break of Loss-Of-Coolant Accident (LBLOCA). The combination of 3D FEM with CFD simulations allows us to study the influence of the dynamic cooling plume on the stress intensity in more detail than with the conventional one dimensional method.

In this paper, the burst pressure estimation equations for steam generator tubes with multiple axial surface cracks are proposed based on the local collapse load approach concept. The proposed equations are for a single axial surface crack, two collinear axial surface cracks and two non-aligned axial surface cracks. The proposed equations are validated against experimental tube burst test results and finite element damage analysis for twin cracks. Predicted burst pressures agree well with the experimental results and FE analysis results, suggesting validity of the proposed equations to estimate burst pressures for twin axial surface cracks.

In oil and gas pipelines, cracks can initiate from regions of high stress concentration or from defects due to either manufacturing or corrosion or both. The cracks under service may grow due to applied load and form stable through-thickness cracks causing leak prior to catastrophic failure. If this leak-before-break (LBB) takes place, then there is a possibility of preventing catastrophic failure. Therefore, LBB analysis is an important requirement for the safe design and re-assessment of pipelines life. This paper presents a simplified approach for the failure assessment utilizing LBB concept of pressurized pipes having an axial crack.

This paper summarizes the design calculations performed by Framatome, EDF, KIWA INSPECTA and VTT for three large scale tests on ferritic pipes made of material WB 36 (15 NiCuMoNb 5). The large scale tests will be performed on a 4-point bending test facility provided by EDF under displacement control at room temperature. The overall goal of the planned large scale tests is to demonstrate the effect of the crack tip constraint on the fracture toughness at the component level. Results of those tests will be utilized to develop and validate advanced tools for structural integrity assessment within WP 3 particularly with respect to the transferability of material properties from small scale specimens to large scale components as well as for the development and validation of a procedure for the determination of component fracture resistance curves. Three configurations of the initial defect with different constraint conditions (one through-wall and two surface cracks) are considered. The design calculations are divided into two parts. In the first part an optimization of three different crack shapes is performed on basis of the standard fracture mechanics approach (based on J-Integral) without consideration of the constraint effect. In the second part a quantification of the crack tip constraint for the selected crack configurations from part I is performed. The effect of the constraint on the crack initiation and propagation for the selected crack configurations shall be assessed and compared between each other. Based on these calculations the final flaw configuration for each large scale experiment is selected.

In Japan, a probabilistic fracture mechanics (PFM) analysis code PASCAL has been developed by Japan Atomic Energy Agency for structural integrity assessment of reactor pressure vessels (RPVs). The most recent release is PASCAL Version 4 (hereafter, PSACAL4) which can be used to evaluate the failure frequency of RPVs considering neutron irradiation embrittlement and pressurized thermal shock events. For the integrity assessment of RPVs, development of crack evaluation models is important. In this study, finite element analyses are performed firstly to verify the stress intensity factor calculations of cracks in PASCAL4. In addition, the applicability of the crack evaluation models in PASCAL4 such as the location of embedded cracks, crack shape and depth of surface cracks, and the increment of crack propagation is investigated. Based on sensitivity analyses of crack evaluation models for Japanese RPVs using PASCAL4, the effects of these evaluation models on failure frequency are clarified. From the analysis results, crack evaluation models recommended to the failure frequency evaluation for a Japanese model RPV are discussed.

The reciprocal effect between a quarter-circle corner crack and a non-aligned surface crack of comparable size is addressed in the present study. The significance of understanding the reciprocal effect between the non-aligned parallel cracks is to assist in the evaluation of non-aligned multiple cracks as required in various fitness-for-service codes. For non-aligned parallel cracks, on-site inspection needs to decide whether the cracks should be treated as coalesced or separate multiple cracks. In the existing literature, criteria and standards for the adjustment of multiple non-aligned cracks are very source dependent, and those criteria and standards are often derived from on-site service experience without rigorous and systematic verification. Based on this observation, the authors previously reported on the effect of an embedded parallel crack on an edge crack in 2-D scenarios and, more recently, in 3-D scenarios of a circular corner crack influenced by a parallel surface crack. It may be just as important to evaluate the mutual effect of a quarter-circle corner crack on a non-aligned surface crack as reflected in their stress intensity factors (SIFs). In the present study, the quarter-circle corner crack and the non-aligned surface crack are assumed to be of the same length a 2 = a 1 = 15mm. While keeping throughout the entire analysis the geometry of the quarter-circle corner crack unchanged, the relative depth of the semi-elliptical surface crack is varied so that b 1 /a 1 = 0.2–1.0. For each particular case a pair of horizontal (H) and vertical (S) separation distances between the two cracks is chosen (H/a 2 = 0.4–2 and S/a 2 = −0.5–2) and the SIFs along the 3D crack fronts are extracted for both the corner and the surface crack. The reciprocal effect on the SIFs for both cracks are discussed. It is found that the mutual influence between the corner crack and the surface crack are equally important, and each may dominate the decision making based on present criteria and standards in Fitness-for-Service.

The reference stress for axial (longitudinal) surface cracks in cylinders is compared using equations from the 2016 API 579-1/ASME FFS-1 and BS 7910:2013 engineering standards, and by using J-integral values from elastic-plastic Finite Element Analysis of three-dimensional crack meshes to compute crack front reference stress. The cylinder axial surface crack reference stress solutions from the two standards differ, and further examination and comparison is desired. To evaluate if a crack is unstable and may cause catastrophic structural failure, the Failure Assessment Diagram method provides an evaluation using two ratios: brittle fracture and plastic collapse. The FAD vertical axis gives the Kr stress intensity to toughness ratio, and the FAD horizontal axis gives the Lr reference stress to yield strength ratio. The details of the FAD method are described in both standards, along with stress intensity and reference stress solutions for various geometries and crack shapes. Since the cylinder axial surface crack reference stress solutions from API 579 and BS 7910 differ, J-integral values are used to compute reference stress trends that provide additional insight and reveal if there is agreement with one or the other or neither standard. Computing reference stress from crack front J-integral results is described in API 579 Annex 9G Section 9G.4. A 3D crack mesh is created for each crack and cylinder size. Along the crack front the focused mesh pattern uses initially coincident groups of nodes at each crack front position. The group of nodes at each location on the crack front are initially coincident and can separate to help model the blunting at the crack front as the loading increases and local plasticity occurs. Post processing calculations use the J-integral versus load trend and the material specific Kr at Lr = 1 ratio to determine the reference stress geometry factor. The reference stress is computed at each crack front node to find the maximum crack front reference stress value for comparison to the engineering standards’ reference stress solutions. A range of surface crack sizes in thin to thick wall cylinders with internal pressure are used to examine reference stress trends. Standard pipe sizes and typical pipeline steel material is used in the analysis. The difference in reference stress solutions was found during an engineering critical assessment, so the J-integral approach was used to improve the solution to reduce conservatism and allow the component to remain in service.

The extended finite element method (XFEM) has recently become a very effective method to investigate the propagation of cracks in various structures under complex loading conditions. However, its use in the pipeline industry has been limited. This paper aims to apply XFEM to model our previous experimental results on NPS 12 grade of X52 steel pipes in which circumferential cracks with different sizes were pre-machined near the middle length and then eccentric tension was applied to the pressurized pipe specimens. Our previous experiments showed that the propagation of a surface crack was affected by the original crack configuration, the internal pressure level, and the external loading applied. The crack depth showed greater influence than the crack length on the burst load and the tensile strain capacity of the pipe. In this paper, the fracture criterion for modelling crack propagation using XFEM was defined by two damage parameters, the maximum principle stress and the fracture energy. The values of the damage parameters were varied until excellent agreement was obtained between one of our previous experiments and its numerical model. Then, this set of damage parameters was used to model another one of the experiments for verification. This paper describes our methodology for validation of XFEM and the adequate values of the damage parameters required to model crack propagation in X52 pipes.

Materials made of Alloy 82/182/600 used in light-water reactors are known to be susceptible to stress corrosion cracking. It is known that the depth a of some cracks due to primary water stress corrosion cracking is larger than the half-length c . The stress intensity factor solution for cracks plays an important role to predict crack propagation and failure. However, Section XI of the ASME Boiler and Pressure Vessel Code does not provide the solutions for cracks with large aspect ratios a/c . In this study, closed-form stress intensity factor influence coefficients for deep surface cracks in plates are discussed. The crack tip stress distribution is represented by a fourth degree polynomial equation. Influence coefficient tables obtained by using finite element analysis in previous studies are used for curve fitting. The closed-form solutions for the coefficient were developed at the surface points and the deepest points of the cracks with aspect ratio a/c ranged from 1.0 to 8.0. The solutions for the points where the stress intensity factor reaches maximum were also investigated.

Three-dimensional finite element models are used to analyze a reactor pressure vessel with an axial semi-elliptical surface crack subjected to pressurized thermal shock. During the thermal shock event, the J-A 2 two-parameter fracture theory is used to investigate the temperature-dependent constraint effect at the deepest point and the surface point of the crack. Using the R6 methodology, a series of constraint-based crack failure assessment curves during the thermal shock can be obtained. It was found that the crack tip constraint should be considered for developing a more realistic failure criterion.

In this study, some benchmark problems on fracture tests for circumferentially through-wall/surface cracked pipes were provided. The participants predicted the ductile crack propagation behavior by their own approaches, including nucleation, growth, and coalescence of voids simulated by Gurson model, ductile crack propagation using stress modified fracture strain (SMFS) model, J-integral based ductile crack propagation using XFEM, CTOA based ductile crack propagation using FEM, stress triaxiality and plastic strain (STPS) based ductile crack propagation using FEM, and ductile crack propagation using peridynamics. Among them, GTN, CTOA and STPS models were not applied to surface crack problems. Discrepancies between the experimental maximum loads and calculated maximum loads were within 10% in most cases and 25% in the maximum case. Element size dependency of analysis parameters were considered in SMFS and GTN models while those were determined from independent material tests. Gurson model can predict slanting crack propagation directions. XFEM which did not need analysis fitting parameters cannot analyze beyond the peaks of load-LPD curves. Crack propagation directions were given and fixed in both CTOA and STPS models. Parameters in Gurson model and peridynamics were optimized to reproduce load-LPD curve in one of the benchmark problems.