Numerical simulations were used to investigate the influence of heterogeneity, in grain-boundary diffusivity and sliding resistance, upon the creep response of a polycrystal. The polycrystal was modelled as being a two-dimensional assembly of elastic grains separated by sharp grain boundaries. The crystal deformed plastically by stress-driven mass transport along the grain boundaries; together with grain-boundary sliding. Heterogeneity was treated by assigning, to each grain boundary, one of two possible values of diffusivity and sliding viscosity. Steady-state and transient creep rates were computed as functions of the diffusivity mismatch and the relative fractions of grain boundaries exhibiting fast and slow diffusion. In addition, the results showed that, under transient conditions, flux divergences developed at the intersections between grain boundaries having fast and slow diffusivities. These generated high local stress concentrations. The latter concentrations developed at a rate which was governed by the fast-diffusion coefficient, and subsequently relaxed at a rate which was governed by the slow-diffusion coefficient. The influence of the mismatch in diffusion coefficient, loading conditions and material properties upon the magnitude of the stress concentration was investigated in detail by using a simple model involving a planar grain boundary. The strain energy associated with these stress concentrations also made recoverable a small fraction of the plastic strain, due to diffusion and sliding, upon unloading.

Recoverable Creep Deformation and Transient Local Stress Concentration due to Heterogeneous Grain-Boundary Diffusion and Sliding in Polycrystalline Solids. Y.Wei, A.F.Bower, H.Gao: Journal of the Mechanics and Physics of Solids, 2008, 56[4], 1460-83