Solutions for Edge Dislocation in Anisotropic Film–substrate System by the Image Method

Abstract

In this paper, the problem of an edge dislocation in an elastically anisotropic dissimilar film-substrate is formulated exactly using the method of continuously distributed image dislocations. The resulting singular Cauchy integral equations are transformed into non-singular Fredholm integral equations, and the solutions are given in the form of series. The formulation and solution are greatly facilitated by the use of certain integral transforms and their iterative operations which are developed in this paper. The numerical solutions are verified by convergence study, direct checking of the governing equations and comparison with previous results. The technique of transforming singular to non-singular integral equations can be used for other physical problems. The truncated solutions can be employed as Green functions for solving problems involving cracks and dislocations and in the boundary element method. The image method can also be generalized for the analysis of multilayered composites. Numerical results for an edge dislocation located in film–substrate systems and strips demonstrate the importance of elastic anisotropy and material inhomogeneity in determining the image forces and the stress components.