Using analytical and numerical methods, the Raj–Ashby bicrystal model of diffusionally accommodated grain-boundary sliding was analysed for finite interface slopes. Two perfectly elastic layers of finite thickness were separated by a given fixed spatially periodic interface. Dissipation occurred by time-periodic shearing of the viscous interfacial region, and by time-periodic grain-boundary diffusion. Although two time scales govern these processes, of particular interest was the characteristic time tD for grain-boundary diffusion to occur over distances of order of the grain size. For seismic frequencies ωtD≫1, it was found that the spectrum of mechanical loss Q−1 was controlled by the local stress field near corners. For a simple piecewise linear interface having identical corners, this localization led to a simple asymptotic form for the loss spectrum: for ωtD≫1, Q−1∼constant x ω−α. The positive exponent α was determined by the structure of the stress field near the corners, but depended both upon the angle subtended by the corner and upon the orientation of the interface; the value of α for a saw-tooth interface having 120° angles differs from that for a truncated saw-tooth interface whose corners subtended the same 120° angle. When corners on an interface were not all identical, the behaviour was even more complex. This analysis suggested that the loss-spectrum of a fine-grained solid resulted from volume-averaging of the dissipation occurring in the neighbourhood of a randomly oriented three-dimensional network of grain boundaries and edges.

Stress Concentrations, Diffusionally Accommodated Grain Boundary Sliding and the Viscoelasticity of Polycrystals. L.C.Lee, S.J.S.Morris, J.Wilkening: Proceedings of the Royal Society A, 2011, 467[2130], 1624-44