Boundary element method for J-integral and stress intensity factor computations in three-dimensional interface cracks

A general numerical tool for the analysis of three–dimensional bimaterial interface cracks is presented in this paper. The proposed tool is based on a multidomain formulation of the Boundary Element Method (BEM), with the crack located at the interface of the domain. Mixed mode stress intensity factors are computed along the three-dimensional crack fronts using the Energy Domain Integral (EDI) methodology and decoupled via the Interaction Integral. The capability of the procedure is demonstrated by solving a number of examples. The last of these examples consists in a thick centre cracked panel for which the behaviour of the J-integral and the mixed-mode stress intensity factors along the crack front is studied as a function of the material mismatch.

[1]  T. K. Hellen On the method of virtual crack extensions , 1975 .

[2]  Vladimir Sladek,et al.  EVALUATIONS OF THE T-STRESS FOR INTERFACE CRACKS BY THE BOUNDARY ELEMENT METHOD , 1997 .

[3]  John E. Dolbow,et al.  Domain integral formulation for stress intensity factor computation along curved three-dimensional interface cracks , 1998 .

[4]  J. Rice A path-independent integral and the approximate analysis of strain , 1968 .

[5]  P. K. Banerjee,et al.  Computation of stress intensity factors for interfacial cracks , 1991 .

[6]  P. C. Paris,et al.  The Stress Analysis of Cracks Handbook, Third Edition , 2000 .

[7]  J. Dundurs Discussion: ``Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading'' (Bogy, D. B., 1968, ASME J. Appl. Mech., 35, pp. 460-466) , 1969 .

[8]  A boundary element for crack analysis at a bimaterial interface , 1994 .

[9]  R. Shield,et al.  Conservation laws in elasticity of the J-integral type , 1977 .

[10]  James R. Rice,et al.  Elastic Fracture Mechanics Concepts for Interfacial Cracks , 1988 .

[11]  Tzi-Kang Chen,et al.  Three-dimensional surface singularity of an interface crack , 1991 .

[12]  David B. Bogy,et al.  Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading , 1968 .

[13]  A. Cisilino Linear and Nonlinear Crack Growth Using Boundary Elements , 1999 .

[14]  Toru Ikeda,et al.  Stress intensity factor analysis of interface crack using boundary element method (Application of contour-integral method) , 1993 .

[15]  M. Aliabadi,et al.  BEM Implementation of the Energy Domain Integral for the Elastoplastic Analysis of 3D Fracture Problems , 1999 .

[16]  C. F. Shih,et al.  Corner Singularities of Three-Dimensional Planar Interface Cracks , 1992 .

[17]  Yuuki Ryoji,et al.  Determination of stress intensity factors and boundary element analysis for interface cracks in dissimilar anisotropic materials , 1992 .

[18]  R. Yuuki,et al.  Boundary element analysis of dissimilar materials and interface crack , 1994 .

[19]  Y. L. Gao,et al.  Treatment of bimaterial interface crack problems using the boundary element method , 1990 .

[20]  J. Dundurs,et al.  Discussion of Edge-Bonded Dissimilar Orthogonal Elastic Wedges under Normal and Shear Loading , 1969 .

[21]  D. T. Read,et al.  Comparison of several path independent integrals including plasticity effects , 1986 .

[22]  Zhigang Suo,et al.  MECHANICS AND 1HERMODYNAMICS OF BRITILE IN1ERFACIAL FAILURE IN BIMATERIAL SYSTEMS , 1990 .

[23]  B. Moran,et al.  A general treatment of crack tip contour integrals , 1987 .

[24]  Marcelo J. Vénere,et al.  Shape sensitivity analysis for energy release rate evaluation and its application to the study of three-dimensional cracked bodies , 2000 .

[25]  Steven L. Crouch,et al.  Prediction of interfacial crack path: a direct boundary integral approach and experimental study , 1994 .

[26]  J. Varna,et al.  The effect of crack-face contact on fiber/matrix debonding in transverse tensile loading , 1997 .

[27]  Toshio Nakamura,et al.  Three-Dimensional Stress Fields of Elastic Interface Cracks , 1991 .

[28]  Maria Comninou,et al.  The Interface Crack , 1977 .

[29]  M. H. Aliabadi,et al.  Energy domain integral applied to solve center and double-edge crack problems in three-dimensions , 1998 .

[30]  Gernot Beer An efficient numerical method for modelling initiation and propagation of cracks along material interfaces , 1993 .

[31]  Toshio Nagashima,et al.  Stress intensity factor analysis of interface cracks using X‐FEM , 2003 .

[32]  Adrián P. Cisilino,et al.  Boundary element analysis of three-dimensional mixed-mode cracks via the interaction integral , 2005 .

[33]  G. Sun,et al.  A study of the interaction between matrix crack and matrix-fibre interface , 1995 .

[34]  C. Brebbia,et al.  Boundary Element Techniques , 1984 .

[35]  Nan Xu,et al.  Modeling of interface cracks in fiber-reinforced composites with the presence of interphases using the boundary element method , 2000 .

[36]  M. Williams The stresses around a fault or crack in dissimilar media , 1959 .

[37]  S. Atluri,et al.  CALCULATION OF FRACTURE MECHANICS PARAMETERS FOR AN ARBITRARY THREE-DIMENSIONAL CRACK, BY THE ‘EQUIVALENT DOMAIN INTEGRAL’ METHOD , 1987 .

[38]  J. Varna,et al.  The fiber-matrix interface crack — A numerical analysis using Boundary Elements , 1996 .

[39]  D. M. Parks A stiffness derivative finite element technique for determination of crack tip stress intensity factors , 1974 .

[40]  Yuuki Ryoji,et al.  Efficient boundary element analysis of stress intensity factors for interface cracks in dissimilar materials , 1989 .

[41]  Z. Bažant,et al.  Surface singularity and crack propagation , 1979 .

[42]  Boundary element analysis of cracks normal to bimaterial interfaces , 1991 .

[43]  John W. Hutchinson,et al.  Crack Paralleling an Interface Between Dissimilar Materials , 1987 .

[44]  David M. Parks,et al.  Antisymmetrical 3-D stress field near the crack front of a thin elastic plate , 1989 .

[45]  B. Moran,et al.  Domain integrals for axisymmetric interface crack problems , 1993 .

[46]  M. Aliabadi,et al.  Evaluation of the stress intensity factors for a three-dimensional interfacial crack by the boundary element method , 1999 .