Transient Stress Concentration in Diffusional Creep of a Thin Foil with Heterogeneous Grain Boundary Diffusivity

Abstract

Coble creep in thin films with heterogeneous grain boundary (GB) diffusivity and non-uniform grain size is investigated in the model problem of a thin foil with a high diffusivity GB joined with a low diffusivity GB of unequal length and subjected to a far field uniaxial tensile stress. It is found that a transient stress peak emerges near the GB junction on the characteristic time scale of the high diffusivity boundary and then disappears when the system reaches steady-state on the characteristic time scale of the low diffusivity boundary. We show that for a given GB size ratio, this stress depends logarithmically on the GB diffusivity ratio. Based on the GB diffusivity and size ratios, we present a diagram demarcating the regime in which peak stress is determined by the steady state solution and that determined by the transient stress solution.