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

Using analytical and numerical methods, we analyze the Raj–Ashby bicrystal model of diffusionally accommodated grain–boundary sliding for finite interface slopes. In that model, two perfectly elastic layers of finite thickness are separated by a given fixed spatially periodic interface. Dissipation occurs by two processes: time–periodic shearing of the interfacial region; and time–periodic diffusion of matter along the interface. Though two timescales govern these processes, of particular interest is the characteristic time tD taken for matter to move by grain–boundary diffusion over distances of order the grain size. Two previously unrecognized features of the loss spectrum in the seismic frequency band ωtD ≫ 1 are established here. First, we show that if all corners on the interface are geometrically identical, the mechanical loss Q depends on angular frequency ω by a strict power law Q = const.ω. For two sliding surfaces found in a regular array of hexagonal grains, the exponent α ∼ −0.3. Second, our analysis shows that α decreases slowly as ω is increased if corner angle varies along the interface. Ultimately Q is controlled by the corner having the most singular stress behaviour. Though these results are obtained from the idealized bicrystal model, we argue physically that similar behaviour will be found in numerical models of polycrystals. Viscoelasticity of polycrystals 1