For steady-state deformation caused by grain-boundary diffusion in hexagonal microstructures, the stress distribution on grain boundaries and the macroscopic strain rates were analysed by taking the effects of viscous grain-boundary sliding into account. The maximum normal stress and the extent of stress concentration were shown to decrease as the grain-boundary viscosity increased. For infinite viscosity and/or extremely small grain sizes, the distribution of the normal stress became uniform on grain boundaries. The strain rates were predicted by both the stress analysis and the energy balance method, and the two strain rates were consistent with each other. The predicted strain rates also decrease as the grain-boundary viscosity increased. The present analysis revealed that the grain-size exponent was dependent on the grain size and the grain-boundary viscosity: the exponent became unity for small grain sizes and/or high viscosity, while it was three for large grain sizes and/or low viscosity. Recent experimental observations that the strain rates of nano-sized grain were much lower than those predicted by grain-boundary diffusion were explained by the increasing contribution of viscous grain-boundary sliding with decreasing grain size.

Analysis of Creep due to Grain-Boundary Diffusion in Hexagonal Microstructures. B.N.Kim, K.Hiraga, K.Morita, B.W.Ahn: Philosophical Magazine, 2004, 84[30], 3251-62