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.     

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.     

Crack propagation rate as a function of crack tip characteristics

The dependence of crack growth rate on various crack tip parameters was studied. Experiments were performed on thin sheets of 6063-T6 Al-alloy having a central notch, to find crack tip opening displacement, total strain range, plastic strain range, crack opening stress and crack growth rate. Crack tip opening displacement and crack opening stress were measured, using a surface measurement technique, with small crack opening displacement gauges. The theoretical predictions of crack tip opening displacement compare fairly well with the experimental values. It is found that crack propagation rate vs total strain range-plastic strain range gives a straight-line fit on a log-log graph and, for positive stress ratios, the fatigue crack growth rates are found to be independent of R.

Experimental results show that the crack opening stress is not affected by the position of the gauge when it is mounted behind and near the crack tip.

The effect of mechanical properties and loading on crack growth were also studied. The specimens were fatigue cracked to a predetermined length and some specimens were annealed and again loaded cyclically. The application of cyclic loads to annealed specimens caused significant increase in crack propagation rates in comparison with the specimens having no heat-treatment. The load-displacement record was found to stabilize in about 10 cycles; the crack then extended slowly as a fatigue crack. Crack propagation rates for different values of R for annealed and work-hardened material were plotted against a crack tip parameter, ΔK*, based on notional crack lengths. Since the results of da/dN vs ΔK* for both states of material (as-received and annealed) seem to lie on the same straight line on a log-log graph, the study provides a hope that the results for a material tested in any state (annealed or work-hardened) for positive values of R (0·0≤R≤0·3) will lie on this line, thus eliminating fatigue tests on the same material under different work-hardening conditions for different values of R. Models for da/dN have been developed using various crack tip parameters.     

Experimental study of effects of prior overload on fracture toughness of A533B steel

This paper presents the results of an extensive study carried out to examine the effects of prior overloading over the entire fracture transition regime for 50-mm thick A533B steel. The main variables examined are temperature, crack orientation with respect to the rolling direction, level of prior overload, the initial crack length, and the statistical variation of prior overload effects. It is found that the effect of prior overload on fracture toughness at lower temperatures is dependent on orientation, so that in the L-T orientation for short and medium cracks (0·2 and 0·5 a/W) there is a benefit throughout the transition regime of 50-mm thick A533B steel. In the T-L orientation no benefit is obtained for temperatures greater than the initiation of tearing temperatures. Above these temperatures the prior overload sequence lowers the fracture toughness. For L-T orientation long cracks (a/W = 0·7) it is found for temperatures lower than −140°C that prior overload apparently increases the toughness. At higher temperatures there is a loss of toughness even though failure is cleavage dominated up to −80°C.

On the lower shelf at −170°C in the L-T orientation the fracture toughness variability after preloading is found (based on a sample of 14 specimens) to exhibit a bimodal distribution. This distribution is similar to that exhibited by non-preloaded material.     

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.     

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.     

Effects of crack depth and specimen size on ductile crack growth of SENT and SENB specimens for fracture mechanics evaluation of pipeline steels

A strong geometry dependence of ductile crack growth resistance emerges under large scale yielding. The geometry dependence is associated with different levels of crack tip constraint conditions. However, in a recent attempt to identify appropriate fracture mechanics specimens for pipeline steels, an “independent” relationship between the crack growth resistance curves and crack depths for SENT specimens has been observed experimentally. In this paper, we use the complete Gurson model to study the effects of crack depth and specimen size on ductile crack growth behavior. Crack growth resistance curves for plane strain, mode I crack growth under large scale yielding conditions have been computed. SENB and SENT specimens with three different specimen sizes, each specimen size with three different crack depths, have been selected. It has been found that crack tip constraint (Q-parameter) has a weak dependence on the crack depth for specimens in the low constraint regime.     

Finite element based evaluation of stress intensity factors for interactive semi-elliptic surface cracks

A finite thickness plate with two coplanar self-same shallow and deep semi-elliptical surface cracks subjected to remote tensile surface traction is considered for fracture analysis. Based on three-dimensional (3D) finite element solutions, stress intensity factors (SIFs) are evaluated along the entire crack front using a force method. The line spring model has also been used to evaluate crack depth point SIFs using shell finite element analysis. A wide range of geometric dimensions and crack configurations viz. crack shape aspect ratio (0.3≤a/c≤1.2), crack depth ratio (1.25≤t/a≤6), relative crack location (0.33≤2c/d≤0.9) and normalized location on the crack front (0≤2φ/π≤2) are considered for numerical estimation of crack interaction factors. SIFs evaluated at the depth point using the force method from the 3D finite element results are compared with SIFs evaluated using the line spring model. Finally, using finite element results, an empirical relation is proposed for the evaluation of crack interaction factors. For the ranges considered, the proposed empirical relation predicts crack interaction factors at critical locations within ±2% of the 3D finite element solutions.     

Modelling and experimental characterisation of a residual stress field in a ferritic compact tension specimen

The aim of the work is to elucidate the influence of plasticity behaviour on the residual stress field in a ferritic reactor pressure vessel steel. To this end, we investigate two compressively pre-loaded compact tension (CT) specimens to generate a mechanical residual stress field. One specimen was subsequently pre-cracked by fatigue before both specimens were measured using high-energy synchrotron X-ray diffraction. A fine grain size microstructure (∼5–10 μm grain size) allowed a small X-ray beam slit size and therefore gauge volume. The results provide an excellent data set for validation of finite element (FE) modelling predictions against which they have been compared. The results of both mechanical testing and modelling suggest that the use of a combined hardening model is needed to accurately predict the residual stress field present in the specimen after pre-loading. Some discrepancy between the modelled crack tip stress values and those found by X-ray diffraction remain which can be partly explained by volume averaging effects in the presence of very high stress/strain gradients.     

Tearing–fatigue interactions in 316L(N) austenitic stainless steel

This paper presents the results from a programme of tearing, fatigue and tearing–fatigue tests performed on specimens from a 316L(N) stainless steel plate. All tests were carried out at ambient temperature. The experimental results have been compared with assessments performed using current guidance within the R6 defect assessment method. The work has shown that there is some evidence that fatigue cycling modifies the JR-curve behaviour of this material. In most cases, the data lie approximately 20–30% above the base-line JR-curve. However, whilst there may be a modest influence of fatigue crack growth on the ductile tearing characteristics, it is difficult to separate this from experimental scatter. In tearing–fatigue tests performed at a stress ratio, R=0.2, ductile tearing reduces the fatigue crack growth rates by up to 50%. This is likely to result from the presence of a residual compressive zone at the crack-tip, and increased crack closure due to the irregular and non-matching fracture surfaces generated by the ductile crack growth mechanisms. For R=0.1 tearing–fatigue tests, fatigue crack growth rates are apparently enhanced by a factor up to of 10, particularly during the latter stages of the tests when ΔK>60 MPam. This is likely to result from: (i) loading being in the elastic–plastic regime where the J-integral (rather than K) characterises the crack-tip fields, (ii) increments of ductile tearing which may occur during each fatigue cycle, and (iii) crack blunting which reduces crack closure effects. For the R=0.2 tearing–fatigue tests, the linear summation approach described in R6 provides a consistently conservative prediction of ductile, fatigue and total crack growth during the tests. However, for the R=0.1 tearing–fatigue tests, the Paris law under-predicts fatigue crack growth rates. This may be corrected by using the Kaiser equation, which acknowledges loading in the elastic–plastic regime and incorporates incremental growth due to tearing as well as fatigue. R6 provides conservative predictions of instability for the CT specimen geometry tested in the current programme, both in terms of the critical crack growth and load required for instability to occur.     

The effect of ductile crack growth on the temperature dependence of cleavage fracture toughness for a RPV steel with various degrees of embrittlement

The basic properties of cleavage fracture after ductile crack growth are studied on the basis of a probabilistic model for cleavage fracture and a deterministic model for ductile fracture, proposed earlier by the authors. Investigations are applied to a 2Cr–Ni–Mo–V reactor pressure vessel steel in the initial (as-received) and embrittled states. For various temperatures, the dependencies of brittle fracture probability on stress intensity factor and extent of ductile tearing are calculated. For various states of a material, the temperature dependencies of cleavage fracture toughness are predicted with and without regard for ductile crack growth. The basic factors controlling the above dependencies are analysed. The calculated results obtained are compared with test results from CT specimens.     

The influence of side-grooving on pre-cracked Charpy specimens in bending

Fatigue pre-cracked Charpy specimens are sometimes used to measure the fracture toughness of steels. For most steels the dimensions of the Charpy specimens are insufficient to prevent significant plastic yielding ahead of the crack during a test. A feature of the tests is that stable crack growth results in significant crack front curvature. Side-grooving compact tension specimens has been found to inhibit crack front curvature and promote straight fronted crack growth. This paper investigates the effect of side-groove depth on the fracture behaviour of pre-cracked Charpy specimens.Elastic three-dimensional finite element analyses have been performed to assess the effect of side-groove depth on the compliance, stress state and stress intensity factor.The load displacement behaviour of Charpy specimens has been measured to determine the effect of side-groove depth on the limit load and fracture resistance.Using the finite element and experimental results an expression is derived for calculating the fracture resistance of side-grooved Charpy specimens. The expression is used to determine the critical fracture resistance of 1CrMoV steel at two temperatures using Charpy specimens with and without side-grooves.     

Residual stress due to welding and its effect on the assessment of cracks near the weld interface

An experimental/analytical hybrid-type investigation of the effects of residual stress on crack propagation due to welding has been performed. The residual stresses in the SAW welded A533B plates and electron beam welded plates that consist of HT80 and A533B steels were detected by an acoustoelastic technique. The measured residual stress was incorporated into a finite element procedure, which simulated stable crack growth in 1T compact specimens, where the effects on far-field crack parameters and on near-field crack parameters were examined. Also investigated was the effect on fatigue crack propagation with the hypothetical residual stress of the identical distribution to that in the electron beam weld. The significance of the residual stress distribution ahead and behind the crack tip in relation to the plastic zone size was identified.     

The fracture properties of aged 316 austenitic steel

The fracture properties of 316 austenitic steel aged at 700°C are assessed in this paper. Charpy impact energy, crack growth fracture resistance, J-Δa, and tensile properties were compared with the unaged properties at four different ageing times. The J-Δa curves were measured from pre-cracked Charpy and 25 mm compact specimens using the unloading compliance technique.

The degradation in fracture properties with ageing is explained in terms of the microstructural behaviour of the steel.     

Creep crack growth data and prediction for a P91 weld at 650 °C

Creep crack growth tests have been carried out on compact tension (CT) specimens machined from a P91 weldment. Four of these specimens were cut from the parent material side of the weld and another seven specimens were cut across the weld. For the cross-weld specimens, starter cracks were positioned into (or close to) the Type IV region. The creep tests were carried out under constant loads, at 650 °C. The results obtained showed that, the creep crack growth rates for parent material specimens are about ten times lower than those for the cross-weld specimens and that the scatter in the data is relatively high. In this respect, the accuracy of the crack tip location, in the cross-weld CT specimens, plays an important role. Finite Element (FE) analyses were carried out, on notched bar and CT models, using damage mechanics material behaviour models. These analyses were used to estimate the triaxial stress factor, α, for the parent material (PM), the weld metal (WM) and the heat affected zone (HAZ). FE analyses were then used to predict the creep crack growth in the CT specimens. Results from the FE analyses for both the PM and the cross-weld CT specimens were in good agreement with the corresponding experimental results. The effect of the potential drop versus crack length calibration on the calculated C* values was also investigated.     

Effect of plastic prestrain on the crack tip constraint of pipeline steels

Before and during operation, pipelines may suffer from plastic pre-deformation due to accidental loading, cold bending and ground movement. Plastic prestrain not only modifies steel's yield and flow properties but also influences its fracture performance. This paper focuses on the effect of prestrain history on crack driving force and crack tip constraint. A single-edge notched tension specimen has been selected for the study and the crack is assumed to exist before a prestrain history was applied. The results show that prestrain history has a strong effect on the crack tip stress field. A new parameter has been proposed to characterize the prestrain-induced crack tip constraint. For the same crack tip opening displacement level, prestrain history will elevate the crack tip stress field. The prestrain-induced constraint decreases with the increase of loading.     

3D simulation of hydride-assisted crack propagation in zircaloy-4 using XFEM

Influence of hydride precipitated at the tip of the crack on crack propagation in zircaloy-4 is numerically investigated using the extended finite element method (XFEM). Numerical simulation is performed on compact tension specimen to understand the effects of crack and hydride lengths on crack propagation in terms of stress intensity factor and J-integral. The values of stress intensity factor and J-integral indicate that hydride induces the crack instability. The stress intensity factor decreases with the precipitation of brittle hydride phase at the crack tip, resulting in hydride-assisted crack propagation. A comparison of crack propagation behaviour with different hydride lengths is also presented. The crack remains stable in the absence of the hydride while it propagates when hydride is considered at its tip for the same applied load. The crack arrests only after reaching to the zircaloy metal matrix causing complete fracture of hydride.     

A study on three-dimensional crack tip fields

In this paper several kinds of crack problems are numerically analyzed by the three-dimensional finite element method. They are (1) CT specimens with different thicknesses; (2) stable crack growth in CT specimens: (3) surface cracked plate subjected to bending: (4) pipe with surface crack subjected to bending: (5) CT and surface cracked specimens made of welded plate. The crack tip singular fields are compared with HRR solutions and the Q-factor is evaluated. The effects of the J-integral and Q-factor on the crack growth behavious are discussed with the comparison of the experimental results. It is concluded that the J-integral does not uniquely control the stable crack growth behaviors in many three-dimensional crack problems. It is also found that both J-integral and Q-factor play important roles in the stable crack growth especially in the welded plate.     

Analysis of biaxial loading effect on fracture toughness of reactor pressure vessel steels

The local stress–strain state (SSS) near the crack tip and its connection with the crack tip opening displacement and J-integral under biaxial loading have been studied by finite element methods in elastic–plastic finite strain statement. Numerical investigations have been performed for various crack lengths and two types of biaxial loading (tension and bending) under conditions of small- and large-scale yielding. To predict the biaxial loading effect on cleavage fracture toughness, the procedure has been elaborated, this being based on the revealed regularities for SSS near the crack tip under biaxial loading and brittle fracture criterion proposed earlier. Prediction of the biaxial loading effect on cleavage fracture toughness has been performed as applied to reactor pressure vessel steel. The calculated results have been compared with available experimental data. Alternative approaches for prediction of the biaxial loading effect on fracture toughness have been discussed.