Anti-Plane Interaction of a Coated Circular Inclusion with a Crack Located in Matrix

Abstract

In this study, the interaction between a coated circular inclusion with an anti-plane crack located in matrix is considered. The solution procedures for solving this problem consist of two parts. In the first part, based on the method of analytical continuation in conjunction with the alternating technique, the complex potential functions of screw dislocation interacting with multi-layered composites are obtained. The second part consists of the derivation of logarithmic singular integral equations by introducing the complex potential functions of screw dislocation along the crack border together with superposition technique. The logarithmic singular integral equations is the solved numerically by modeling a crack in place of several segments. Linear interpolation formulae with undetermined coefficients are applied to approximate the dislocation distribution along the elements, except at vicinity of crack tip where the dislocation distribution preserves a square-root singularity. The stress intensity factors are then obtained numerically in terms of the values of the dislocation density functions of the logarithmic singular integral equations.