Under steady-state deformation, caused by grain-boundary diffusion in hexagonal microstructures, the stress distribution on grain boundaries and the macroscopic strain rates were analyzed by taking account of the effects of viscous grain-boundary sliding. 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 the grain boundaries. The strain rates were predicted by using both the stress analysis and the energy balance methods, and the 2 strain-rates were consistent with each other. The predicted strain rates also decreased as the grain-boundary viscosity increased. The analysis revealed that the grain-size exponent depended upon the grain size and the grain-boundary viscosity. The exponent became unity for small grain sizes and/or high viscosities. It was equal to 3 for large grain sizes and/or low viscosity. Experimental observations, that the strain rates of nano-sized grains were much lower than those predicted by grain-boundary diffusion, were attributed to an 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