Anelasticity and grain boundary sliding

Abstract

We describe a theoretical and numerical analysis of an existing model of anelasticity owing to grain boundary sliding. Two linearly elastic layers having finite thickness and identical material constants are separated by a given fixed spatially periodic interface across which the normal component of velocity is continuous, whereas the tangential component has a discontinuity determined by the shear stress σ * ns and the boundary sliding viscosity η *. We derive asymptotic forms giving the complex rigidity for the extremes of low-frequency forcing and of high-frequency forcing. Using those forms, we create master variables allowing results for different interface shapes, and arbitrary forcing frequency, to be collapsed (very nearly) into a single curve. We then analyse numerically, with finite interface slope, three proposed factors that may weaken and broaden the theoretical prediction of a single Debye peak in the loss spectrum. They are, namely, stress concentrations at interface corners, spatial variation in grain size and spatial variation in boundary sliding viscosity η *. Our results show that all these factors can, indeed, contribute to a moderate weakening of the loss peak. By contrast, the loss peak markedly broadens only when the boundary sliding viscosity η * differs by an order of magnitude across adjacent interface. The shape of the loss spectrum (self-similar to a single Debye peak) is insensitive to the other two factors.