A superposition method was proposed to compute the stress field due to a dislocation loop in a heterogeneous thin film–substrate system. The problem was decomposed into 2 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 was further reformulated in a line-integral form. Taking advantage of the Galerkin potential method and the Fourier transform, the elastic field in an heterogeneous thin-film/substrate system due to surface loading was derived. Numerical results demonstrated that both the free surface and heterogeneity of the material had a great influence upon the stress field due to a dislocation loop.

Stress Field due to a Dislocation Loop in a Heterogeneous Thin Film–Substrate System. E.H.Tan, L.Z.Sun: Modelling and Simulation in Materials Science and Engineering, 2006, 14[6], 993-1013