A finite elastic body with a curved crack loaded in anti-plane shear

Abstract

This paper presents a Boundary Integral Equation Method (BIEM) for an arbitrarily shaped, linearly elastic, homogeneous and isotropic body with a curved crack loaded in anti-plane shear. The crack must be modeled as an arc of a circle and wholly inside the solid—otherwise its position and orientation with respect to the boundary of the body is arbitrary.The effect of the crack on the stress field is incorporated in an augmented kernel developed for the mode III crack problem such that discretization of the cutout boundary is no longer necessary. This modification of the kernel of the integral equation leads to solutions on and near the cutout with great accuracy. An asymptotic analysis is conducted in order to derive the Stress Intensity Factor (SIF) KIII, at each crack tip, in closed form. In this formulation, a straight crack can be viewed as a particular case of the more general curved crack. In particular, attention is paid to the influence of crack curvature and edge effect on the stress intensity factors at the right and left crack tips. A rigorous mathematical formulation is developed, the main aspects of the numerical implementation are discussed and several representative numerical examples are presented in this paper.