Analysis of near interface cracks by weakly singular boundary integral equation method

Abstract

This thesis presents a weakly singular boundary integral equation method for analysis of sub-interface cracks in a three-dimensional, linearly elastic, multi-material domain. The formulation is established in a general framework allowing finite bodies, general material anisotropy and loading conditions, arbitrarily shaped cracks, and curved material interface to be treated. A system of integral equations governing the unknown data on the boundary, the crack surface and the material interface are established using a pair of weakly singular, weak-form displacement and traction integral equations and the continuity along the material interface. A symmetric Galerkin boundary element method together with the standard finite element technique is implemented to solve the governing integral equations. Special near-front approximation is employed to enhance the approximation of the relative crack-face displacement in the neighborhood of the crack front. The solved crack-face data is then used to post-process for the stress intensity factors and the T-stress along the crack front. A selected set of results is presented not only to demonstrate the accuracy, convergence and capability of the proposed technique but also to explore the influence of the material stiffness and the distance to the material interface on the fracture data along the crack front.