Stress field due to a dislocation loop in a heterogeneous thin film–substrate system

Abstract

In this paper, a superposition method is proposed to compute the stress field due to a dislocation loop in a heterogeneous thin film–substrate system. The problem is decomposed into two sub-problems: the stresses due to a dislocation loop in an infinitely extended bi-material space and the stresses induced by equivalent tractions on the free surface. The area-integral expression of the former is further reformulated in a line-integral form. Taking advantage of the Galerkin potential method and the Fourier transform, this paper then derives the elastic field in a heterogeneous thin film–substrate system due to surface loading. Numerical results demonstrate that both the free surface and the material heterogeneity have great influence on the stress field due to a dislocation loop.