An investigation of the blunting line

Experimental evidence obtained on 3-point SENB specimens of carbon steel (St52-3) is used to compare ways of determining the slope of the “blunting line” in $\text{J}{}_{\mathrm{Ic}}$ testing. The results demonstrate that the slope of the blunting line obtained by the stretched zone width (SZW) method is steeper than the blunting line predicted by the ASTM method. This results in lower values for both $\text{J}{}_{\mathrm{Ic}}$ and $\text{(Δa)}{}_{\mathrm{c}}$ as determined with the SZW method, compared with those obtained by the ASTM method. The increased conservatism compared to the ASTM approach and the experimental evidence underlying it recommend the SZW method for further study. The subsequent widespread use expected for any recognized $\text{J}{}_{\mathrm{Ic}}$ determination seems to justify the additional effort and expenses associated with the SZW method.     

On the J-integral in periodically layered composites

When a heterogeneous elastic material is represented by an effective homogeneous elastic solid, average stress and strain fields are used. The meaning of the J-integral in the effective homogeneous solid is investigated. A periodically layered medium is considered. The relation between the J-integrals in the original layered medium and the effective medium is derived.     

On the decomposition of the J-integral for 3D crack problems

The extended J-integral for 3D linear elastostatic crack problems and its application to mixed mode problems is investigated. In 3D, the decomposition of the J-integral into its parts corresponding to the symmetric mode I and both antisymmetric modes II and III is derived explicitly. The range of validity of the decomposition method is also discussed in the framework of linear elastic fracture mechanics (LEFM). It is shown analytically that in a general mixed mode case the antisymmetric part of the J-integral can be split into the parts associated with mode II and mode III only in the crack near-field.     

On the cyclic J-integral applied to fatigue cracking

Currently on leave from Xian Jiaotong University, Xian, PRC     

On J-integral and potential energy variation

The divergence theorem has been used in a region containing the crack tip to derive the J-integral from the potential energy variation in most fracture mechanics books. Such a derivation is flawed because of the crack tip stress singularity. The present study describes a rigorous and straightforward derivation of the J-integral from the potential energy variation with crack extension by carefully addressing the effect of the crack tip singularity.     

On the energy release rate and the J-integral for 3-D crack configurations

In this paper an analytical expression for the energy release rate has been derived and put in a form suitable for a numerical analysis of an arbitrary 3-D crack configuration. The virtual crack extension method can most conveniently be used for such a derivation. This method was originally developed from finite element considerations and the resulting expressions were, therefore, based on the finite element matrix formulation [1–5]. In this paper the derivation of the energy release rate leads to an expression which is independent of any specific numerical procedure. The formulation is valid for general fracture behavior including nonplanar fracture and shear lips and applies to elastic materials as well as materials following the deformation theory of plasticity. The body force effect is also included. For 3-D fracture problems it is of advantage to use both an average and a local form of the energy release rate and definitions for both forms are suggested. For certain restrictions on the crack geometry it is shown that the energy release rate reduces to the 3-D form of the J-integral.

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Résumé Dans le mémoire, on a établi une expression analytique pour la vitesse de relaxation de l'énergie et on l'a mise sous une forme convenable pour une analyse numérique de configurations de fissures arbitrairement à trois dimensions. La méthode d'extension virtuelle de la fissure est celle qui convient le mieux pour un tel traitement. Cette méthode a été, à l'origine, développée à partir de considérations d'éléments finis et les expressions qui en résultaient ont dès lors été basées sur une formulation de matrice d'éléments finis [1, 5]. Dans le présent mémoire, la dérivation de la vitesse de relaxation de l'énergie conduit à une expression indépendante de toute procédure numérique spécifique. La formulation est applicable au comportement général à la rupture comprenant des ruptures non coplanaires et des lèvres de cisaillement, et s'applique à des matériaux aussi bien élastiques que redevables de la théorie des déformations en plasticité. On tient compte également de l'effet des forces appliquées sur un corps. Dans le cas de problèmes de rupture à trois dimensions, il est avantageux d'utiliser à la fois une forme moyenne et une forme locale de taux de relaxation d'énergie et l'on suggère des définitions pour ces deux formes. Dans le cas de certaines restrictions relatives à la géométrie de la fissure, on montre que le taux de relaxation de l'énergie se ramène à une expression générale à trois dimensions de l'intégrale J.

     

On the J-integral and energy-release rates in dynamical fracture

Summary The apparent contradiction between the Eshelby formulation (consideration of a material force on the material manifold) and the more usual global-dissipation analysis (essentially, the balance of energy about the moving singular point represented by the tip of the crack) of theJ-integral and energy-release rate in dynamical fracture is resolved in both pure finite-strain elasticity and Galilean-invariant electrodynamics of electro-magneto-elastic media. The solution uses the notions of mechanical and electromagnetic pseudomomenta (canonical momenta) in finitely deformable continua with cracks.     

On the thermal blunting of crack tips in polymers

The analysis of crack tip blunting in the impact test is reviewed and the results for polymethylmethacrylate at room temperature are presented, together with more recent data for which loading times have been measured. A successful comparison is drawn between the results of impact tests at various strain rates and those of static single edge notched tests where the crack tip region is heated. Such a correlation confirms the suspected suppression of crack tip crazing owing to thermal effects.     

Plastic eta factor and blunting line for characterization of fracture toughness of dissimilar metal weld

This paper addresses the fracture toughness evaluation procedure of different zones of dissimilar metal weld (DMW). Experiments have been conducted on compact tension specimens from DMW joint having initial notch in centre of weld and fusion boundaries. Plastic eta factors (η_p) and slope of blunting line (bl) for above specimens have been evaluated numerically. Experimental load, load line displacement, and crack growth data along with numerically evaluated η_p and bl have been used for calculation of fracture resistance curve and initiation fracture toughness, and finally, it has been compared with that evaluated as per ASTM E1820 and ESIS standard.     

Effects of microvoids on crack blunting and initiation in ductile materials

Effects of microvoid nucleation and growth on the stress and strain fields near a crack tip are studied by employing the Gurson's constitutive model of porous plastic solids and by using a finite element method suitably formulated to admit large geometry change. It is shown that microvoids nucleate and grow rapidly in the region at a distance less than the blunted tip diameter away from the crack tip and have a great influence on the stress fields therein. Effects of a large void near a crack tip on crack initiation are also investigated by taking the shear localization into account. The critical value of the crack tip opening displacement predicted by the present investigation is shown to coincide with the published experimental data.

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Résumé On examine les effets d'une nucléation et d'une croissance de micro-cavités sur les champs de contrainte et de déformation au voisinage de l'extrémité d'une fissure en recourant au modèle constitutif de Gurson pour les solides poreux plastiques, et en utilisant une méthode par éléments finis formulée de manière à admettre des modifications importantes de géométrie. On montre que les microcavités coalescent et croissent rapidement en avant de la fissure sur une distance inférieure au diamètre qu'atteint l'arrondissement de la fissure et qu'elles ont une grande influence sur le champ de contrainte qui règne dans cette région. On étudie également l'influence d'une grande lacune au voisinage de l'extrémité d'une fissure sur l'amorçage de la cassure, en prenant en compte le cisaillement local. On montre que la valeur critique du COD à l'extrémité de la fissure telle que prédite par la présente étude coïncide avec les données expérimentales de la littérature.

     

Mixed-mode J-integral formulation and implementation using graded elements for fracture analysis of nonhomogeneous orthotropic materials

The path-independent J_k^*-integral, in conjunction with the finite element method (FEM), is presented for mode I and mixed-mode crack problems in orthotropic functionally graded materials (FGMs) considering plane elasticity. A general procedure is presented where the crack is arbitrarily oriented, i.e. it does not need to be aligned with the principal orthotropy directions. Smooth spatial variations of the independent engineering material properties are incorporated into the element stiffness matrix using a “generalized isoparametric formulation”, which is natural to the FEM. Both exponential and linear variations of the material properties are considered. Stress intensity factors and energy release rates for pure mode I and mixed-mode boundary value problems are numerically evaluated by means of the equivalent domain integral especially tailored for orthotropic FGMs. Numerical results are discussed and validated against available theoretical and numerical solutions.