The J-resistance curve leak-before-break test program on material for the darlington nuclear generating station

The Darlington Leak-Before-Break (DLBB) approach has been developed for large diameter (21, 22, 24 inch) SA106B heat transport (HT) piping and SA105 fittings as a design alternative to pipewhip restraints and in recognition of the questionable benefits of providing such restraints. Ontario Hydro's DLBB approach is based on the elastic plastic fracture mechanics (EPFM) method. In this test program, J-resistance curves were determined from actual pipe heats that were used in the construction of the Darlington heat transport systems (Units 1 and 2). Test blocks were prepared using four different welding procedures for nuclear Class I piping.

The test program was designed to take into account the effect of various factors such as test temperature, crack plane orientation, welding effects, etc., which have influence on fracture properties. A total of 91 tests were conducted. An acceptable lower bound J-resistance curve for the piping steels was obtained by machining maximum thickness specimens from the pipes and by testing side grooved compact tension specimens.

Test results showed that all pipes, welds and heat-affected zone materials within the scope of the DLBB program exhibited uppershelf toughness behaviour. All specimens showed high crack initiation toughness J_Ic, rising J-resistance curve and stable and ductile crack extension. Toughness of product forms depended on the direction of crack extension (circumferential versus axial crack orientation). Toughness of DLBB welds and parent materials at 250°C was lower than that at 20°C.     

Effect of constraint on ductile crack growth and ductile-brittle fracture transition of a carbon steel

Ductile-brittle fracture transition was investigated using compact tension (CT) specimens from −70 to 40°C for a carbon steel. Large deformation finite element analysis was carried out to simulate the stable crack growth in the compact tension (CT, a/W = 0.6), three point-point bend [SE(B), a/W = 0.1] and centre-cracked tension [M(T), a/W = 0.5] specimens. An experimental crack tip opening displacement (CTOD) resistance curve was employed as the crack growth criterion. Ductile tearing is sensitive to constraint and tearing modulus increases with reduced constraint level. The finite element analysis shows that path-dependence of the J-integral occurs from the very beginning of crack growth and ductile crack growth elevates the opening stress on the remaining ligament. Cleavage may occur after some ductile crack growth due to the increase of opening stress. For both stationary and growing cracks, the magnitude of opening stress increases with increasing in-plane constraint. The ductile-brittle transition takes place when the opening stress ahead of the crack tip reaches the local cleavage stress as the in-plane constraint of the specimen increases.     

EFFECT OF THERMAL RESIDUAL STRESS ON THE INTERLAMINAR CRACK EXTENSION BEHAVIOR IN CROSS-PLY LAMINATES DUE TO TRANSVERSE LOADING

The effect of thermal residual stress on the two-dimensional interlaminar crack extension behavior in a cross-ply laminate subjected to transverse loading is estimated. Attention is focused on the contribution of thermal residual stress to the local energy release rate along the interlaminar crack front. Computational simulations are carried out on the basis of constant critical energy release rates in order to examine implicitly how the two-dimensional size and shape would be changed by the presence of thermal residual stress. A considerably large amount of energy is found to be supplied for the interlaminar crack extension by thermal residual stress, while little influence is perceived with respect to the apparent extension behavior including the shape of the interlaminar crack.     

Modeling for ductile-to-brittle transition under ductile crack growth for reactor pressure vessel steels

The local stress–strain state (SSS) near the crack tip is investigated by the finite element method in the finite strain statement (with regard to a change of the crack tip blunting) for both stationary cracks and crack growing by a ductile mechanism. Using the revealed particularities of SSS near the stationary and growing crack tips and the local cleavage fracture criterion the phenomenon of the ductile-to-brittle transition is explained for reactor pressure vessel steels. The model is proposed to predict the amount of ductile crack extension preceding the ductile-to-brittle transition as a function of the test temperature. The procedure for calculation of the cleavage fracture toughness is also elaborated with regard to ductile crack extensions. Analysis of the obtained calculated results and available experimental data is made. Alternative approaches for the interpretation of the ductile-to-brittle transition are discussed.     

3-D elastic-plastic finite element analysis of interface cracks under mixed mode load

A three-dimensional finite element computation was performed for a throughedge cracked bimaterial steel specimen under mixed mode loadings in which the crack was lying on an interface between an elastic-plastic material and a perfectly rigid substratum. In order to take account of the average effect of microvoid nucleation and growth in the deformation, the modified Gurson's constitutive equation suggested by Tvergaard and Needleman was used. It was found that due to the interaction between the singularity along the crack front and that along the interface on the specimen surface, the distributions of stresses, plastic deformations, J-integral and void volume fraction in a bimaterial specimen were significantly different from those in a homogeneous specimen. Based on the numerical results on the distributions of void volume fraction and J-integral, the locations of fracture initiation in bimaterial and homogeneous specimens under mixed mode loadings are discussed.     

The influence of the stress state on fracture toughness

Conventional fracture mechanics treatments usually disregard biaxial loading modes, even though several authors have discussed the biaxiality effect of an additional load in the crack extension direction. Another biaxial effect, that related to an additional load parallel to the crack front, has not been investigated until now. This paper describes experiments and three-dimensional (3D) FE stress analyses which have been performed with plate-shaped cracked specimens under biaxial bending. In relation to stresses around the blunted crack tip, a fracture criterion based on achieving a critical stress is discussed.     

Three-dimensional fully plastic solutions for semi-elliptical surface cracks

Nonlinear finite element analyses of semi-elliptical surface cracks are performed with the fully plastic condition, where the power-law hardening materials and the deformation theory of plasticity are assumed. To satisfy the incompressibility condition of a plastic material, two kinds of numerical techniques (the penalty function method and the Uzawa algorithm) are employed. The local distributions and the global values of the J-integral are obtained using the virtual crack extension technique for various configurations of semi-elliptical surface crack in plate subjected to uniform tension and bending, respectively. These solutions are given in the form of polynomials with geometric parameters of crack and the strain hardening exponent. Finally, an estimation scheme for the J-integral of surface crack in a plate subjected to mixed loading of tension and bending is proposed.     

Analytical and numerical crack growth prediction for a leak-before-break assessment of a nuclear pressure vessel

Extending the safety analysis of a nuclear reactor pressure vessel beyond the requirements of the regulations which were first laid down in the ASME-Code, the behavior of two crack sizes (1/4-t axial, 3/4-t circumferential, a/2c = 1/6) in the upper shelf region is analyzed to demonstrate the capability of a reactor pressure vessel for Leak-Before-Break. The postulated load is a monotonic increase of pressure, ending when the crack penetrates through the wall.

The conditions for re-initiation and ductile extension of the conservatively postulated largest possible axial and circumferential crack geometries resulting from initiation and arrest during a thermal shock are evaluated on the basis of the J-integral concept. Three-dimensional finite element models simulating large amounts of crack growth are employed as well as analytical approximations. The results demonstrate that very high internal pressure far beyond the capacity of the plant and also far beyond the strength of the other components of the primary circuit would be required to initiate and grow the cracks, and that Leak-Before-Break behavior is confirmed.     

French experimental studies of circumferentially through-wall cracked austenitic pipes under static bending

This paper describes experimental studies performed on cracked pipes made of austenitic steel and subjected to a bending load. The studies concern the characterization of conditions for which an initial crack (fatigue precracked) initiates and then propagates along the circumference of the tube. The influences of different parameters were obtained: crack length, crack tip radius, tube geometry (radius, thickness), temperature and weldment. The predictive criteria checked in these studies are limit analysis (or net-section stress criterion) and J estimation.     

Removal of the influence of stress triaxiality on crack tip opening displacement fracture toughness by continuum damage mechanics approach

Experimental data for AS 1405-180, AS 1204-350, HY 80 and C-Mn steels shows that the crack tip opening displacement (CTOD) elastic-plastic fracture toughness at initiation δ_c decreases with increasing crack tip stress trifaxiality. This trend is confirmed by the continuum damage analysis in this paper. The dependence of the CTOD parameter at initiation on the local constraint, i.e. the stress triaxiality, provides the motivation to seek parameters that could rank the toughness of steels. Since the local effective plastic strain can be related to the CTOD, a relationship is described between the initiation CTOD toughness and the crack tip constraint, i.e. the stress triaxiality, on the basis of a new local damage theory for ductile fracture. Furthermore, a new constraint corrected toughness parameter δ_dc (and corresponding criterion) for ductile fracture is proposed, in which both crack tip deformation and crack tip constraint intensity are taken into account. Several series of experimental data have shown that the parameter δ_dc is nearly a constant or independent of the local constraint. It is found that the toughness variation with constraint changes can effectively be removed by use of the constraint correction procedure proposed in this paper.     

Experiences using three-dimensional finite element analysis for leak-before-break assessment

Because of practical limitations, analytical problems in fracture mechanics have often been solved using simplified geometries (e.g. plane stress/strain, shell models). We have applied the Leak-Before-Break approach extensively to the large diameter piping of a new nuclear power plant. Various piping components such as elbows, tee and branch connections with postulated cracks were analyzed. Since no credible geometric simplification was possible, fully three-dimensional (3D) analytical models were found to be essential.

The paper describes our experiences in performing 3D Finite Element (FE) analysis of these components. Included are comparisons of numerical and test results of compact specimens, material modeling considerations, handling of 3D effects, such as the variation of the J-integral along a crack front, and especially, the effects of plasticity.

The overall intent of the paper is not simply to present specific numerical results, but rather to give some perspective on the effort required and results attainable.     

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.     

Linear elastic analysis of semi-elliptical axial surface cracks in a hollow cylinder

The variation of the stress intensity factor along the front of two semi-elliptical axial surface cracks in a hollow cylinder subject to temperature and pressure loading is analysed. A three-dimensional elastic finite element analysis is performed using twenty noded isoparametric elements employing the quarter point singularities at the crack front and calculating the energy release rate. The solution is compared with analytical results as well as with results from other authors.     

Numerical simulation of tearing–fatigue interactions in 316l(N) austenitic stainless steel

The loading history of engineering components can influence the behaviour of defects in service. This paper presents, the results of a numerical study aimed at using the Gurson ductile damage model, calibrated against J R-curve data, to simulate load-history effects on ductile tearing behaviour in austenitic materials. The work has demonstrated that ductile crack growth resistance is influenced by sub-critical crack growth by an intervening mechanism such as fatigue. Fatigue crack growth under a positive R-ratio leads to increase in subsequent tearing resistance through three main mechanisms: (i) re-sharpening of the crack tip; (ii) crack extension through the fracture process zone; and (iii) cyclic loading effects on void development. The ratio of minimum to maximum stress during fatigue loading (R-ratio) has been shown to influence subsequent tearing resistance, with an R-ratio of 0.2 generally leading to a greater enhancement in tearing resistance than an R-ratio of 0.1. This behaviour is due to the influence of R-ratio on void development ahead of the fatigue crack tip. Finally, relevant experimental data compare favourably with the predicted J R-curves.     

Failure assessment of cracked square hollow section T-joints

Three full-scale static strength tests were carried out on pre-cracked square hollow section (SHS) T-joints. In accordance with the experimental results, an accurate crack model for welded SHS joints is proposed in this paper. Based on this numerical model, the load–displacement curves and the stress intensity factors (SIFs) along the crack front are calculated. It is found that the SIF varies greatly along the crack front, and the highest value is located at the brace corner. From Charpy V-notch impact test results, anisotropic fracture toughness was found, and influenced the failure behavior of the damaged joints. Ductile tearing was found to initiate from the crack front parallel to the chord side wall where the fracture toughness was smaller, and not from the crack front at the corner where the SIF value was the highest. Using the plastic collapse load obtained via the twice elastic compliance technique and the fracture toughness obtained from the Crack tip opening displacement (CTOD) tests, the BS7910 Level 2A Failure Assessment Diagrams (FAD) for the three cracked joints are plotted. It is confirmed that the standard BS7910 Level 2A curve gives a conservative assessment for cracked SHS T-joints under brace end axial loads.     

Stability of a crack in a cantilever beam undergoing large plastic deformation after impact

A simple model is employed to determine the dynamic response of a rigid-perfectly plastic cantilever beam with an attached tip mass and a crack, taking into account the weakening effect of the crack. The crack is assumed to be located at the base of the beam, and an initial velocity is imparted to the tip mass. The subsequent stability of the crack is considered by calculating the tearing modulus based on the J-integral associated with the deflecting beam. For the example of circumferential cracks in thin-walled piping, whose idealized geometry models some stress corrosion cracks found in service, radial propagation and instability are found to be more likely than circumferential. Once a crack penetrates the wall, however, stability in the circumferential direction is found to depend in a complex way upon loading and crack geometry.     

Probabilistic fracture analysis of cracked pipes with circumferential flaws

This paper describes the development of a probabilistic fracture-mechanics model for analyzing circumferential through-walled-cracked pipes subject to bending loads. It involves elastic-plastic finite element analysis for estimating energy release rates, J-tearing theory for characterizing ductile fracture, and standard structural reliability methods for conducting probabilistic analysis. The evaluation of the J-integral is based on the deformation theory of plasticity and power-law idealizations of stress-strain and fracture toughness curves. This allows J to be expressed in terms of non-dimensional influence functions (F- and h₁-functions) that depend oncrack size, pipe geometry, and material hardening constant. New equations were developed to represent these functions. Both analytical and simulation methods were formulated to determine the probabilistic characteristics of J. The same methods were used later to predict the failure probability of pipes as a function of applied load. Numerical examples are provided to illustrate the proposed methodology. The validity of the J-integral based on the proposed equations for predicting the crack driving force in a through-wall-cracked pipe was evaluated by comparison with available results in the current literature. Probability densities of the J-intergral were predicted as a function of applied loads. Failure probabilities corresponding to three different performance criteria were evaluated for stanless steel nuclear piping from a boiling water reactor plant. The results suggest that large differences may exist in the failure probability estimates produced by these performance criteria.     

Elastic stress and deformation analyses on an all-steel cylinder without defects and with axial cracks

Using the three-dimensional elastic finite element method, stress analyses and the deformation analyses on an all-steel cylinder without defects and with axial cracks were carried out. The severe effect of the defects on an all-steel cylinder was shown through comparisons of the stress analyses and the deformation analyses on the cylinder without defects and with an axial crack. The analyses show that there appear both the inhomogeneous deformation and the stress singularities around the defects. The influences of defect size, internal pressure and defect types (internal crack or external crack), on the stress distributions and on the deformation distributions were discussed. The crack mouth opening displacement and the stress intensity factor K_I for the cylinders containing the axial deep cracks, which was detected in a practical applied cylinder, were presented and discussed. The effects of the location of the cracks (whether external or internal) and the shape of the through-thickness crack front (whether elliptical or straight front) on the crack driving forces are quantified. All the results of the stress analysis, the deformation analyses and the fracture analyses are supported by each other very well.     

Fracture behaviors of all-steel gas cylinder with different axial cracks

Using the three-dimensional finite element method, the researches on the linear elastic and the nonlinear elasto-plastic fracture behaviors of all-steel gas cylinders with different axially oriented cracks were carried out. The crack mouth opening displacement CMOD and the crack driving forces for the cylinders containing axial deep cracks, which have the crack depth of 25%–100% of the wall thickness, and the crack length of ten times the wall thickness, were obtained. The effects of the location of the cracks (whether external or internal) and the shape of the through-thickness crack front (whether elliptical or straight front) on the crack driving forces are respectively quantified in the linear elastic deformation state and in the elasto-plastic deformation state.     

A new J-integral estimation scheme and its relation to existing schemes

The paper outlines a new, and very simple, J-integral estimation scheme which is based on the representation of J_DP, the plastic component of the deformation J-integral J_D, as a linear combination of the plastic energy and complementary plastic energy integrals, and the use of eta factors. A characteristic of the scheme is that it is exact at the two extremes: small-scale yielding and extensive deformation at limit load conditions. Determination of the eta factors requires only a knowledge of the limit load solution and the crack tip stress intensity. The paper shows how the new scheme relates to existing schemes: the GE-EPRI scheme and the CEGB-R6 scheme.