Discrete dislocation analysis of size effects in thin films

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Abstract
A discrete dislocation plasticity analysis of plastic deformation in metal thin films caused by thermal stress is 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 are considered. The film-substrate system is subjected to a prescribed temperature history and a boundary value problem is 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 forms at the interface between the film and the substrate, which does not scale with the film thickness and thus gives rise to a size effect. It is found that a reduction in the rate of dislocation nucleation can occur abruptly, which gives rise to a two-stage hardening behavior.