Stress concentrations, diffusionally accommodated grain boundary sliding and the viscoelasticity of polycrystals

Abstract

Using analytical and numerical methods, we analyse the Raj–Ashby bicrystal model of diffusionally accommodated grain-boundary sliding for finite interface slopes. Two perfectly elastic layers of finite thickness are separated by a given fixed spatially periodic interface. Dissipation occurs 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 is the characteristic time t D for grain-boundary diffusion to occur over distances of order of the grain size. For seismic frequencies ωt D ≫1, we find that the spectrum of mechanical loss Q −1 is controlled by the local stress field near corners. For a simple piecewise linear interface having identical corners, this localization leads to a simple asymptotic form for the loss spectrum: for ωt D ≫1, Q −1 ∼const. ω − α . The positive exponent α is determined by the structure of the stress field near the corners, but depends both on the angle subtended by the corner and on the orientation of the interface; the value of α for a sawtooth interface having 120 ° angles differs from that for a truncated sawtooth interface whose corners subtend the same 120 ° angle. When corners on an interface are not all identical, the behaviour is even more complex. Our analysis suggests that the loss spectrum of a finely grained solid results from volume averaging of the dissipation occurring in the neighbourhood of a randomly oriented three-dimensional network of grain boundaries and edges.