Size effects in polycrystalline thin films analyzed by discrete dislocation plasticity

Stress development and relaxation in polycrystalline thin films perfectly bonded to a stiff substrate is analyzed numerically. The calculations are carried out within a two-dimensional plane strain framework. The film-substrate system is subject to a prescribed temperature decrease, with the coefficient of thermal expansion of the metal film larger than that of the substrate. Plastic deformation arises solely from the glide of edge dislocations. The dislocations nucleate from pre-existing Frank-Read sources, with the grain boundaries and film-substrate interface acting solely as impenetrable barriers to dislocation glide. At each stage of loading, a boundary value problem is solved to enforce the boundary conditions and the stress field and the dislocation Structure are obtained. The results of the simulations show both film-thickness and a am size dependent strengthening of polycrystalline films. Limited plasticity occurs in films with a sufficiently small grain-size, mainly due to a reduced nucleation rate in the constrained grain geometry.