Stress relaxation in thin film/substrate systems by grain boundary diffusion: A discrete dislocation framework

The relaxation of stress in a thin film due to grain boundary diffusion is investigated in terms of a new discrete dislocation framework. Discrete dislocations along grain boundaries are nucleated from the free surface and are then driven to 'climb' by the Peach-Koehler force, with a mobility that is determined by the grain boundary diffusivity. Application to a planar film/substrate problem with (sub-) micrometer scale columnar grains shows that the amount of relaxation is dependent on the initial stress and on the grain aspect ratio. For thin columnar grains the relaxation is faster and more effective and the opening displacements along the grain boundary are more uniform, an effect that is not captured by current continuum models. When the initial stress is low and and the grain size is small, it is necessary to account for variations in the threshold stress for diffusion among different grain boundaries to achieve realistic results.