A discrete dislocation plasticity analysis of plastic deformation in metal thin films caused by thermal stress was carried out. The calculations use a two-dimensional plane-strain formulation with only edge dislocations. Single crystal films with a specified set of slip systems were considered. The film-substrate system was subjected to a prescribed temperature history and a boundary value problem was formulated and solved for the evolution of the stress field and for the evolution of the dislocations structure in the film. A hard boundary layer formed at the interface between the film and the substrate, which did not scale with the film thickness and thus gave rise to a size effect. It was found that a reduction in the rate of dislocation nucleation could occur abruptly, which gave rise to a two-stage hardening behavior.

Discrete Dislocation Analysis of Size Effects in Thin Films. L.Nicola, E.Van der Giessen, A.Needleman: Journal of Applied Physics, 2003, 93[10], 5920-8