An experimental study of the fracture resistance of bimaterial interfaces

The fracture resistance of a model bimaterial interface has been measured for a wide range of phase angles: the measure of the relative crack face sliding and opening displacement near the crack tip. These experiments have revealed that the critical strain energy release rate increases with increase in phase angle, especially when the crack opening becomes small. The results are consistent with a model based on crack surface contact associated with non-planarity of the fracture interface.     

The nonlinear energy method for mixed mode fracture

In a linear elastic analysis of mixed mode fracture problem, a general G-K relation has been obtained based upon the maximum energy release rate criterion. The expression of nonlinear energy release rate for specimen with an arbitrarily oriented crack subjected to biaxial loading has been formulated. The numerical results which indicate the biaxial effect are presented.     

Numerical simulation of time-dependent fracture of graded bimaterial metallic interfaces

Stationary cracks along and near interfaces between two time-dependent materials are simulated using the finite element method (FEM) to examine crack tip fields and candidate driving force parameters for crack growth. Plane strain conditions are assumed. In some cases, a thin transition layer is included between the two materials. This transition layer features a functionally graded blend of properties of the two materials. An example of such a system is that of weld metal (WM) and base metal (BM) in a weldment, with the transition layer corresponding to the heat-affected zone (HAZ). Numerical solutions for the stress and strain fields of homogeneous and heterogeneous Compact Tension (C(T)-type) specimens are presented. The equivalent domain integral technique is employed to compute the J-integral for elastic-plastic cases as well as the C(t)-integral and transition times for creep behavior. Results from parametric studies are curve-fit in terms of transition layer thickness and crack position, inelastic property mismatches, and other independent model parameters. Results indicate that the incorporation of functionally graded transition layer regions leads to less concentrated stress and strain components along interfaces ahead of the crack tip. It is also shown that the computed fracture parameters are influenced by the transition layer properties.     

A method for calculating stress intensities in bimaterial fracture

A numerical method is presented for obtaining the values of K^* ₁,K ^* _II and K^* _III in the elasticity solution at the tip of an interface crack in general states of stress. The basis of the method is an evaluation of theJ-integral by the virtual crack extension method. Individual stress intensities can then be obtained from further calculations ofJ perturbed by small increments of the stress intensity factors. The calculations are carried out by the finite element method but minimal extra computations are required compared to those for the boundary value problem. Very accurate results are presented for a crack in the bimaterial interface and compared with other methods of evaluating the stress intensity factors. In particular, a comparison is made with stress intensity factors obtained by computingJ by the virtual crack extension method but separating the modes by using the ratio of displacements on the crack surface. Both techniques work well with fine finite element meshes but the results suggest that the method that relies entirely on J-integral evaluations can be used to give reliable results for coarse meshes.

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Résumé On présente une méthode numérique en vue d'obtenir les valeurs de K^* ₁, K^* _II et K^* _III relatives à la solution élastique d'application à l'extrémité d'une fissure d'interface sujette à un état de contraintes général. La méthode repose sur l'évaluation de l'intégraleJ par la technique d'extension virtuelle de la fissure. On peut ensuite obtenir les intensités de contraintes individuelles à partir de calculs deJ subséquents, correspondant à des perturbations introduites par de petits accroissements des facteurs d'intensité de contraintes.Les calculs sont accomplis par la méthode des éléments finis, mais, par rapport aux calculs à mettre en oeuvre dans le problème des valeurs aux limites, il ne faut procéder qu'à quelques calculs supplémentaires.On présente des résultats très précis pour le cas d'une fissure dans un interface entre deux matériaux, et on les compare avec ceux provenant d'autres méthodes d'évaluation des facteurs d'intensité de contraintes.En particulier, on fait une comparaison pour des facteurs d'intensité de contraintes obtenus en calculant J par la méthode d'extension virtuelle d'une fissure, mais en séparant les modes selon le rapport des déplacements de la surface de la fissure.Les deux techniques fonctionnent de manière satisfaisante avec des maillages fins d'éléments finis; cependant, les résultats suggèrent que la méthode qui repose entièrement sur les évaluations de l'intégraleJ peut être utilisée afin d'obtenir des résultats fiables dans les réseaux à mailles grossières.

     

An end-notched beam test for specific fracture energy in mixed mode in timber

A simple method for achieving stable crack propagation in a beam notched at a support is presented. The method allows the measurement of fracture energy in mixed modeG _f,mix. Results from a small number of laminated veneer lumber specimens suggest that there is a relationship betweenG _f,mix and density and that the ratioG _f,mix/(G _f,I+G _f,II) is about 0.35. Calculations of fracture energy in mode IG _f,I and mode, IIG _f,II did not coincide with values from mode-specific tests, indicating that an adjustment is necessary to take account of the interaction between the modes.     

An energy method for calculating the stress intensities in orthotropic bimaterial fracture

An energy based numerical method has been developed for extracting stress intensities at the tip of an interface crack bounded by two orthogonal dissimilar materials and subjected to a general state of stress. The method is most suitable for mixed mode delamination fracture studies often observed in brittle matrix composite laminates. After obtaining the near-tip finite element solution for a given laminated geometry, the elastic energy release rate, i.e., J is computed via the stiffness derivative method. The individual orthotropic stress intensities, K _I ^*, K _II ^* are then calculated at a minimum computational expense from further J calculations perturbed by reciprocal stress intensity increments. Results obtained using the Crack Surface Displacement (CSD) method were found to be in good agreement with those obtained using the energy method. Comparisons with theoretical solutions indicate that the energy method can be used accurately even when relatively coarse finite element meshes containing approximately 200 eight noded isoparametric elements are used. The method provides an effective and reliable tool for studying via the method of finite elements delamination phenomena in composite anisotropic laminates.     

A mixed mode fracture specimen for mode II dominant deformation

Several theories have been proposed for the failure of metals, as well as for the angle of crack propagation in mixed mode loading. In order to demonstrate the validity of these theories, the majority of tests have been carried out with an oblique crack placed in a uniaxial stress field. Better testing conditions may be achieved by placing a crack in a uniform bidimensional stress field. A specimen which was recently developed for $\text{K}{}_{\mathrm{IIC}}$ measurement may be readily adapted to achieve a bidimensional stress field and be used for mixed mode testing for the case in which shear deformation is dominant. The main aims of this study are to examine both the cracked and uncracked specimen by means of photoelasticity and finite elements in order to analyze the capabilities and limitations of this specimen for mixed mode testing. It will be demonstrated that there exists a nearly uniform biaxial field in the uncracked specimen. Moreover, calibration formulas will be presented for $\text{K}{}_{\mathrm{I}}$ and $\text{K}{}_{\mathrm{II}}$.     

An interaction integral method for computing mixed mode stress intensity factors for curved bimaterial interface cracks in non-uniform temperature fields

In finite element analysis the interaction integral has been a useful tool for computing the stress intensity factors for fracture analysis. This work extends the interaction integral to account for non-uniform temperatures in the calculation of stress intensity factors for three dimensional curvilinear cracks either in a homogeneous body or on a bimaterial interface. First, the derivation of the computational algorithm, which includes the additional terms developed by the non-zero gradient of the temperature field, is presented in detail. The algorithm is then implemented in conjunction with commercial finite element software to calculate the stress intensity factors of a crack undergoing non-uniform temperatures on both a homogeneous and a bimaterial interface. The numerical results displayed path independence and showed excellent agreement with available analytical solutions.     

On the interaction of cracks with bimaterial interfaces

Mechanical properties of engineering materials are primarily controlled by interfaces that they contain, i.e., free surfaces, grain boundaries, and phase boundaries. The fracture and fatigue properties, in particular, are a function of the interaction of such boundaries with cracks. In the present paper, we review the various types of interaction between cracks propagating at or near such bimaterial interfaces. Indeed, the nature of these interactions is critical in determining trajectories of cracks in both homogeneous and layered structures, which in turn has a direct influence on their fracture toughness and resistance to subcritical crack growth. Material Sciences Division, Lawrence Berkeley National Laboratory, and Department of Material Science and Mineral Engineering, University of California, Berkeley, CA 94720, USA. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 1, pp. 119–132, January–February, 1996.     

An extended equivalent domain integral method for mixed mode fracture problems by the p-version of FEM

A new path-independent contour integral formula is presented to estimate the crack-tip integral parameter, J-value, for two-dimensional cracked elastic bodies which may quantify the severity of the crack-tip stress fields. The conventional J-integral method based on a line integral has been converted to an equivalent area or domain integral (EDI) by the divergence theorem. It is noted that the EDI method is very attractive because all the quantities necessary for computation of domain integrals are readily available in a finite element analysis. The details and its implementation are extended to the p-version FE model with hierarchic elements using integrals of Legendre polynomials. By decomposing the displacement field obtained from the p-version finite element analysis into symmetric and antisymmetric displacement fields with respect to the crack line, the Mode-I and Mode-II non-dimensional stress intensity factors can be determined by using the decomposition method. The example problems for validating the proposed techniques are centrally oblique cracked plates under tensile loading. The numerical results associated with the variation of oblique angles show very good agreement with the existing solutions. Also, the selective distribution of polynomial orders and the corner elements for automatic mesh generation are applied to improve the numerical solution in this paper. © 1998 John Wiley & Sons, Ltd.     

Verification of a non-local stress criterion for mixed mode fracture in wood

An extension of a non-local stress fracture criterion to orthotropic materials based on the damage model of an elastic solid containing growing microcracks was presented in this paper. By taking this approach, a new fracture condition expressed in terms of the mixed mode stress intensity factors for orthotropic materials was proposed and its applicability to predict of a crack initiation and propagation in wood was validated. Predicted values of the stress intensity factors at failure were compared to experimental observations carried out on wood specimens for cracks arbitrarily oriented with respect to the orthotropy axes. Special considerations were applied to the comparison of the non-local stress fracture criterion with some classical fracture criteria for orthotropic materials.     

Interface fracture properties of a bimaterial ceramic composite

In this investigation, the interface fracture toughness is measured for a pair of ceramic clays which are joined together. The Brazilian disk specimen, which provides a wide range of mode mixity, is employed to measure these properties. Calibration equations relating the stress intensity factors to the applied load and geometry are determined by means of the finite element method and the M-integral. The effect of residual stresses is accounted for by employing a weight function to obtain the contribution to the stress intensity factors. Total stress intensity factors are obtained by superposition. These are employed to determine the critical interface energy release rate as a function of mode mixity from critical data obtained from tests carried out on the Brazilian disk specimens. An energy release rate fracture criterion is compared to the experimental results for .     

Analysis of mixed mode fracture and crack closure using the boundary integral equation method

A multi-domain boundary integral equation method, employing an isoparametric quadratic representation of geometries and functions, is developed for the analysis of two-dimensional linear elastic fracture mechanics problems. The multi-domain approach allows the two faces of a crack to be modelled in independent sub-regions of the body, avoiding singularity difficulties and making it possible to analyse crack closure problems with contact stresses over part of the cracked faces. Problems solved include slanted cracked plate mixed mode and crack closure examples, also crack closure situations involving fully reversed bending of an edge cracked strip, both with and without a superimposed tensile loading.

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Résumé Pour analyser les problèmes de mécanique de rupture linéaire et élastique en deux dimensions, on a développé une formulation sur plusieurs domaines de la méthode d'équation intégrale aux limites, en recourant à une représentation quadratique isoparamétrique des géométries et des fonctions.L'approche multidomaine permet de modéliser les deux faces d'une fissure dans des sous-régions indépendantes, ce qui évite des difficultés de singularité, et rend possible l'analyse des problèmes de fermeture d'une fissure avec des contraintes de contact agissant sur une partie des faces de la fissure.Les problèmes auxquels on trouve solution sont notamment la plaque fissurée sur un bord et sollicitée suivant un mode mixte, avec aussi fermeture de la fissure, ou des situations de fermeture de fissure où se trouve une bande fissurée sur un de ses bords et soumise à flexion complète réversible, avec ou sans sollicitations de traction

     

On the analysis of a mixed mode bending sandwich specimen for debond fracture characterization

The mixed mode bending specimen originally developed for mixed mode delamination fracture characterization of unidirectional composites has been extended to the study of debond propagation in foam cored sandwich specimens. The compliance and strain energy release rate expressions for the mixed mode bending sandwich specimen are derived based on a superposition analysis of solutions for the double cantilever beam and cracked sandwich beam specimens by applying a proper kinematic relationship for the specimen deformation combined with the loading provided by the test rig. This analysis provides also expressions for the global mode mixities. An extensive parametric analysis to improve the understanding of the influence of loading conditions, specimen geometry and mechanical properties of the face and core materials has been performed using the derived expressions and finite element analysis. The mixed mode bending compliance and energy release rate predictions were in good agreement with finite element results. Furthermore, the numerical crack surface displacement extrapolation method implemented in finite element analysis was applied to determine the local mode mixity at the tip of the debond.