Crack-like grain-boundary diffusion wedges in thin metal films

Constrained grain-boundary diffusion in polycrystalline thin metal films on substrates is studied as a strongly coupled elasticity and grain-boundary diffusion problem in which no sliding and no diffusion are allowed at the film/substrate interface. Surface diffusion and grain-boundary grooving are neglected in the present analysis. We show that such a diffusion process leads to the formation of crack-like grain-boundary wedges which cause the normal traction along the grain boundary to decay exponentially with time. A rigorous mathematical analysis is performed to derive and calculate the transient solutions for diffusion along a single grain boundary and along a periodic array of grain boundaries. An approximate closed-form solution is also given as a simple description of constrained grain-boundary diffusion. A most remarkable feature of the solution is that the diffusion wedges induce crack-like singular stress concentrations which could also enhance dislocation plasticity processes in a metal film.