J-integral Values Research Articles

Elastic J-integral solution for an elbow with axial through-wall crack at crown under in-plane bending

Piping elbows under bending moment are vulnerable to cracking at crown. The structural integrity assessment requires knowledge of the J-integral. The J-integral values for axially through-wall cracked thick elbows are not available in the open literature over a certain range. This paper presents a closed form expression for elastic J-integral for 90°, long radius elbows subjected to bending moment. The expression is derived, based on the results of a large number of finite element analyses covering a wide range of standard geometries. The analyses were performed using WARP3D software. The present study enables the estimation of the elastic J-integral over a range of R m/ t from 5 to 25 ( R m/ t = 5, 6, 7.5, 9, 12, 15, 20 and 25) and thus extends the range of earlier solution towards the thicker elbows used in nuclear industry. The crack angles considered were 9°, 18°, 27° and 36°.

C-Specimen Fracture Toughness Testing: Effect of Side Grooves and η Factor

Elastic-plastic crack front fields in arc-shaped tension specimens (C-specimens) were analyzed by a three-dimensional finite element method. The effect of side grooves on the ductile fracture behavior was investigated by studying the J-integral distribution, plane-strain constraint parameter, and development of plastic zones and comparing to experimental data. The applicability of the η factor (derived for use with compact tension specimens) for the calculation of J-integral values for the C-specimen was also investigated. The results show that side grooves promote and establish near plane strain conditions at the crack front in sub-size specimens. It was also found that a two-dimensional plane-strain analysis in conjunction with the standard American Society for Testing and Materials (ASTM) tests was sufficient to determine the fracture toughness values from side-grooved C-specimen. The results indicate the η factor for compact tension specimen as specified in the ASTM standards appears to produce reliable results for the calculation of J of C-specimens.

Application of the normalization method for the determination of J–R curves

Abstract The performance of the normalization method (NM) is evaluated and compared with the standard unloading-compliance method of fracture-toughness analysis for a broad spectrum of different materials and specimen geometries. The critical J-integral values based on the normalization method are summarized and compared with the results of unloading compliance tests. The results demonstrate the applicability of the normalization method for the J–R curve determination for a range of steels. The normalization method yields results, which deviate as much as 15% from the values obtained with the unloading compliance method, and thus results of acceptable accuracy can be attained with this method.

Elastic-plastic fracture mechanics based prediction of crack initiation load in through-wall cracked pipes

In order to evaluate the structural integrity of power plants, it is required to know the load carrying capacity of a piping system. J-integral based elastic-plastic fracture mechanics (EPFM) has become a useful analytical technique for dealing with ductile materials. It is important to see how accurately we can predict the stages of leak-before-break demonstration using EPFM. Current efforts are focussed on verifying previously developed J-estimation schemes for through-wall cracked (TWC) straight pipes with the calculated elastic-plastic J-integral values that are obtained by conducting a rigorous 3D non-linear finite element analysis using advanced fracture analysis code WARP3D. This includes the validation and benchmarking of J-estimation schemes with the present 3D non-linear finite element analysis results and with the experimental results at crack initiation stage. The results corresponding to crack initiation results calculated by estimation schemes are too conservative. Thus, in order to perform J-integral based EPFM analysis more accurately and conveniently, there is a need to develop an efficient estimation scheme that can represent material behaviour closely. The crack initiation load calculated by the present finite element analysis results is shown to provide a more reasonable prediction.

Study on J-integral with SENB specimens in a condenser material

A series of tests was performed with three-point single-edge-notched-bend (SENB) specimens in a condenser material (Titanium alloy). Results show that the J-integral values of welded joint and HAZ are obviously smaller than those of the base metal. It signifies that the welding process can result in a reduced toughness of Titanium alloy and the effect of crack orientation on toughness value is not negligible for engineering applications. Besides, the J-integral values of L-T direction specimens are much higher than those of L-S ones. The J-integral values of rolled ring are: JC-R>JC-L>JL-R.

New ` ηpl' and ` γ' functions to evaluate J– R curve from cracked pipes and elbows. Part II: experimental and numerical validation

Experimental evaluation of J– R curve in a crack growth situation requires ` η pl' and ` γ' functions that are specific to a cracked geometry and loading condition. In Part I [Engng. Fract. Mech., in press] of this paper, new η pl and γ functions, which are not available in the literature, for pipe and elbow geometry with various crack configurations under different loading conditions have been derived. In this paper, some of these newly proposed η pl and γ functions have been validated experimentally through comparison of crack initiation load and J– R curve. In few cases, numerical validation has also been provided by comparing the J-integral values calculated through η factor approach and finite element method.

大型石油備蓄タンクの高レベル地震に対する疲労き裂成長予測手法の開発(J02-1 タンク構造,J02 シェル構造の計算力学と先端アプリケーション)

Since the past decade, diagnostics evaluation method for the oil tank under ultra low cycle fatigue was continuously discussed at several committees in Japan High Pressure Institute (JHPI). This paper reports the summary of the activity of the committees toward the establishment of the method to estimate crack growth life under repeated large plastic loading. Crack growth behaviors under large cyclic plastic strains were examined experimentally under both axial loadings and bending loadings of a plate with a surface flaw. A series of three-dimensional FEM analyses was also carried out to obtain J-integral value for shell-to-annular joint with various crack sizes.

Zr-2.5Nb 압력관의 휘어진 CT시편으로 측정한 J 저항곡선의 정확도에 관한 연구

In this study, the difference of J integral values between the standard CT specimens satisfying plane strain condition and the nonstandard curved CT with limited thickness (4.2mm) is estimated using finite element analysis. The fracture resistance curves of Zr-2.5Nb obtained previously by other authors are critically discussed. Various finite element analysis were conducted such as 20 analysis under plane stress and plane strain conditions and 3D analysis for nat CT, curved CT with straight crack and curved CT with slant crack front. J-integral values were determined by local contour integration near the crack tip, which was considered as accurate J-values. J value was also determined from the load versus load line displacement curve and the J estimation equation in the ASTM standard. Discrepancies between the two values were shown and suggestion was made for obtaining accurate J values from the load line displacement curves obtained by the curved CT specimens.

Mixed-mode fatigue crack propagation in thin T-sections under plane stress

Data that can be used in the fatigue analysis of flat T-section bars subjected to axial loading and local restraint are presented. The paper describes how finite element analysis has been used to obtain stress fields in the vicinity of a crack or crack-like flaw introduced into the fillet (i.e. high-stress) region of the component. The effect of both the position and inclination of the crack has been investigated. The inclination of the crack to the transverse direction is varied in such a way that a combination of mode I (tension opening) and mode II (in-plane shear) crack tip conditions are created in the component when subjected to axial loading which is applied to the entire flat shoulder of the projection. Linear elastic fracture mechanics finite element analyses have been performed, and the results are presented in the form of J integrals and notch and crack configuration factors for a wide range of component and crack geometric parameters. These parameters are chosen to be representative of typical practical situations and have been determined from evidence presented in the open literature. The extensive range of notch and crack configuration factors obtained from the analyses are then used to obtain equivalent prediction equations using a statistical multiple non-linear regression model. The accuracy of this model is measured using a multiple coefficient of determination, R2, where 0 < R2 < 1. This coefficient is found to be greater than or equal to 0.98 for all cases considered in this study, demonstrating the quality of the model fit to the data. Predictive equations for stress intensity factors and J-integral values, which are based on the elastic stress concentration factor, are also developed. A crack propagation methodology, based on existing theory coupled with these predictive equations, is then presented for this type of component and loading.

Prediction of ductile fracture initiation using micromechanical analysis

In the paper ductile fracture initiation analysis of low-alloyed ferritic steel has been made by application of two micromechanical models: the Rice–Tracey void growth model and the Gurson–Tvergaard–Needleman (GTN) model. The aim of the study was to analyse transferability of micromechanical parameters determined on specimens without initial crack to pre-cracked specimens. A significant part of the research has been carried out through participation in the round robin project organised by the European Structural Integrity Society (ESIS). Tensile tests have been performed on cylindrical smooth specimens and CT specimens. Critical values of micromechanical parameters determined on smooth specimen for both applied models, have been used for prediction of the crack growth initiation in CT specimen. Modelling of the first phase of ductile fracture––void nucleation––has been carried out using quantitative metallographic analysis of non-metallic inclusion content in tested steel. For determination of critical values of model parameters corresponding to ductile fracture initiation a simple procedure has been applied based on a combination of experimental and numerical results. Evaluated J-integral values corresponding to onset of crack growth, J i, are in good agreement with experimental result and both models have proved to be suitable for determination of the ductile fracture initiation in tested steel. The effect of FE size at a crack tip on J i-value has been particularly analysed: it has been established that the calculation with FE size corresponding to the mean free path λ between inclusions in steel gives results that are in accordance with the experimental ones.

Fracture toughness of rubber-modified epoxy adhesives: effect of plastic deformability of the matrix phase

The fracture toughness of adhesively bonded compact tension (CT) and bulk single-edge notched bend (SENB) specimens using rubber-modified epoxy resins was investigated in terms of the relation between the J-integral value and crack extension, whereby the rubber-modified epoxy resins allow to alter the plastic deformability by changing curing temperature. For the SENB specimen, the crack extension is very small and the J-integral value increases with enhanced plastic deformability. On the other hand, for the CT specimen, a considerable crack extension is observed, furthermore, when the crack extension is nearly equal to 0.2 mm, the J-integral value does not vary with curing temperature; however, the slope of the J–Δ a curve slightly decrease with enhanced plastic defomablity. To elucidate these behaviors, assuming that the resins are governed by the Gurson's constitutive equation, the void–volume fractions near the crack tip of both the specimens were calculated by finite element method. It was found that the characteristics of J–R curves can be explained from the results of calculated void–volume fraction.

A J-integral-based approach to predict the fatigue strength of components weakened by sharp V-shaped notches

In the present paper, Rice's J-integral is applied to sharp V-shaped notches subjected to mixed mode loading. The material is thought of as obeying a linear elastic or a power hardening law. J, which is no longer an invariant, as it was in the crack-case, is analytically given as a function of the relevant Mode I-II Notch Stress Intensity Factors (N-SIFs). As soon as a convenient choice of the integration path is made, J is demonstrated to be able to summarise the fatigue properties of steel and aluminium welded joints of different geometry. By imposing the coincidence between elastic and plastic J-integral values, both the degree of singularity and the plastic N-SIF value are evaluated on the basis of the relevant linear elastic values. When N-SIF's are unknown, a general method suitable for determining J is reported. Finally, a new operator, JL, has been defined for sharp V-shaped notches. It is an invariant in the ambit of validity of the asymptotic stress distributions and in the presence of Mode I loading. In the linear elastic case, JL coincides with Rice's J-integral when the notch opening angle is null (i.e. when the notch becomes a crack).

Micromechanical analysis of fatigue cracks in cord–rubber composites

Analyses of two different types of cracks due to fatigue of cord–rubber composites is carried out using micromechanical two-dimensional (2D) and three-dimensional (3D) finite element analysis. The fracture parameter, tearing energy (TE)/ J-integral that characterizes the severity of crack tip stresses in rubber composites, is computed from the finite element results of stresses and strains. The results obtained are validated with existing analytical methods in the literature. Numerical results of J-integral values are presented for two crack types, and crack sizes under transverse strain and shear strain loading conditions. The results presented illustrate that crack type, loading, and crack size have a strong effect on the values of J-integral. The results of the J-integral should help our understanding in estimating the severity of local failures in cord–rubber composites.

Residual stress effects on fracture energies of cement–bone and cement–implant interfaces

The effects of residual stresses, which are caused by the temperature difference arising after polymerisation of bone cement, on the fracture energies of cement–bone and cement–implant interfaces have been examined by using both experimental and numerical works. Only fracture loads of the test specimen having interfacial cracks have been measured in the experimental stage. The values of fracture loads and temperature difference after polymerisation have been applied to finite element models of the test specimens to calculate critical J-integral values of these both interfaces in the numerical stage. In addition, fracture energies of bone and cement, have been obtained by experimentally, using three-point bending test method The results have shown that residual stresses can produce changes in the fracture energies of these bimaterial systems, especially in cement-implant interface and J IC values of interfaces are considerably smaller than the experimentally determined J IC values of cement and bone.

Influences of some materials on J-estimation methods for pipes with circumferential surface cracks

The approximate calculation methods (SC.ENG1 and SC.ENG2) for the J-integral for pipes with circumferential surface cracks are discussed and three-dimensional elastic–plastic finite element models for circumferentially surface-cracked pipe are conducted to evaluate the accuracy of these methods for different pipe materials used in China. The numerical studies verify that the SC.ENG2 method provides more accurate estimates of J than SC.ENG1. Based on three-dimensional elastic–plastic fracture analysis, the distribution of the local J-integral along the front of a circumferential constant-depth internal surface crack is investigated and the influences of different pipe materials with different yield plateaux on J-integral values are discussed. The validity of SC.ENG1 and SC.ENG2 J-integral estimation methods for pipe steel materials with different yield plateaux used in China are examined in detail and the SC.ENG2 method is found to provide reasonable estimates of J for materials with yield plateaux.

Weathering Effects on the Fracture Properties of Polyvinyl Chloride Pipes

Abstract Polyvinyl chloride (PVC) pipes were weathered naturally for periods of up to two years. The effect of weathering on the mechanical properties was investigated by compressing unnotched and radially notched ring specimens in a parallel-plate test. Disregarding the scatter existing among the test results, the general trend indicates deteriorating fracture properties due to exposure. The application of fracture mechanics concepts, explicitly the J-integral value, to the test results helps to reveal the susceptibility of weathered PVC pipe material to brittle fracture compared to its as-received condition.

J-integral analysis of the interaction between an interface crack and parallel subinterface cracks in dissimilar anisotropic materials

The J-integral analysis is presented for the interaction problem between a macro-interface crack and subinterface microcracks parallel to the former in the near-tip process zone in dissimilar anisotropic composite materials. Elementary solutions respectively considering an interface crack and a subinterface crack subjected to different loads are given from which the interaction problem is deduced to a system of integral equations with the aid of superimposing technique (i.e., the so called `Pseudo-Traction Method' abbreviated as PTM). After the integral equations are solved numerically, a consistent relation among three kinds of the J-integral values is obtained. They are induced from the macro-interface crack tip, the microcracks, and the remote field, respectively. This consistent relation of the J-integral can be used to confirm the numerical results derived by using whatever kind of technique. With the aid of J-integral analysis, the interaction behaviors between an interface crack and parallel subinterface cracks are investigated in detail, and some special physical phenomena are obtained.

Effect of Hydrostatic Testing on Ductile Tearing of X-65 Line Pipe Steel with Stress Corrosion Cracks

Abstract Hydrostatic testing is one method to confirm the integrity of pipelines containing colonies of stress corrosion cracks. Although this technique is widely used, a concern of the pipeline industry is the potential for ductile tearing damage of subcritical flaws. Objectives of the current study were to evaluate the influence of hydrostatic testing on the crack tip morphology and to determine the amount of ductile tearing that may occur for different hydrostatic testing conditions. Stress corrosion cracks were grown in compact tension specimens of X-65 line pipe steel in a near-neutral-pH stress corrosion cracking (SCC) environment. Simulated hydrostatic tests were performed at loads that corresponded to hoop stresses at and above the specified minimum yield strength (SMYS), resulting in applied J-integral values near to and above the J(Q) fracture toughness value of the material. Some specimens ruptured; some did not fail. Crack tip blunting occurred and the tearing extent was small and proportional...

Fracture Behavior of Notched Unidirectional Boron/Aluminum Metal Matrix Composite under Bending

The fracture behavior of continuous fiber reinforced boron/aluminum composite under bending is analyzed based on the measured full-field high resolution moire fringe patterns at the notch tip region of composites' specimen under three point bending. The mechanism of interfacial fiber/matrix sliding and debonding in bending is found to be quite different from those reported earlier for the case of uniform tension. In case of bending, after some initial crack growth, excessive shear deformation in other regions (other than notch tip) of the specimen makes the presence of notch irrelevant. Experimental results are compared with the results obtained from finite element analysis. J-integral values are evaluated using the displacements obtained experimentally and also by using finite element. It is realized that any numerical simulation should be based on elasto-plastic analysis and consider friction between fiber and matrix when excessive shear deformation occurs and sliding is initiated.

Elastic–plastic analysis of off-center cracks in cylindrical structures

This paper presents new elastic and elastic–plastic finite element solutions of the J-integral for a pipe containing off-center through-wall cracks under pure bending. The analysis is based on a three-dimensional nonlinear finite element method and small-strain theory. One hundred and five analyses were performed using the ABAQUS commercial code for a wide variety of crack sizes, off-center crack angles, and material hardening exponents. The results from these analyses show that the J-integral values at the two crack fronts of an off-center crack are unequal due to the loss of symmetry with respect to the bending plane of the pipe. In addition, the J-integral is larger, and hence, critical at the crack front which is farther away from the bending axis of the pipe. This is because, at that crack front, the tensile stress is larger and the component of the applied bending moment about the crack centerline has a further crack-opening effect. Also at this crack front, the J values can be lower or slightly higher than those of a symmetrically centered crack, depending on the crack size and off-centered angle. For the crack front that is closer to the bending axis, the J values are always lower than those of a symmetrically centered crack. This implies that the load-carrying capacity of a pipe is usually larger for an off-center crack than that for a symmetrically centered crack. Finally, based on these finite element solutions, new analytical expressions of J-integral were developed for fracture analysis of pipes containing off-center cracks.