Analytic Solution for a Line Edge Dislocation in a Bimaterial System Incorporating Interface Elasticity

Abstract

We examine the plane strain deformations of a bimaterial system consisting of a line edge dislocation interacting with a flat interface between two dissimilar isotropic half-planes in which the additional effects of interface elasticity are incorporated into the model of deformation. The entire system is assumed to be free of any external loading. Despite the fact that it is generally accepted that the separate interface modulus describing interface elasticity is permitted to take negative values, we show that simple closed-form solutions for the dislocation-induced stress field and the image force acting on the dislocation are available only when the interface modulus is assumed to be positive; the corresponding system admits no valid solutions when the interface modulus is negative. We present several numerical examples to illustrate our solutions. Additionally, we show that the influence of interface elasticity on the dislocation-induced interfacial stress field decays with increasing hardness of the adjoining half-plane (free of the dislocation). Moreover, we find that for a given (positive) in-plane interface modulus, the corresponding interface effects on the image force (acting on the dislocation) can reach maximum or minimum values when the Burgers vector of the dislocation is either parallel or perpendicular to the interface.