Constrained grain-boundary diffusion in thin polycrystalline metal films on substrates was studied as a strongly-coupled, elasticity plus grain-boundary diffusion, problem in which no sliding and no diffusion were allowed at the film/substrate interface. Surface diffusion and grain-boundary grooving were neglected. It was shown that such a diffusion process led to the formation of crack-like grain-boundary wedges which caused the normal traction along the grain boundary to decay exponentially with time. A mathematical analysis was used to derive transient solutions for diffusion along a single grain boundary and along a periodic array of grain boundaries. An approximate closed-form solution was also derived for the simple description of constrained grain-boundary diffusion. An interesting feature of the solution was that the diffusion wedges produced crack-like singular stress concentrations which could enhance dislocation plasticity processes in metal films.

Crack-Like Grain-Boundary Diffusion Wedges in Thin Metal Films. H.Gao, L.Zhang, W.D.Nix, C.V.Thompson, E.Arzt: Acta Materialia, 1999, 47[10], 2865-78