A theoretical and numerical analysis of an existing model of anelasticity due to grain-boundary sliding was described. Two linearly elastic layers having finite thickness and identical material constants were separated by a given fixed spatially periodic interface across which the normal component of velocity was continuous, whereas the tangential component had a discontinuity which was determined by the shear stress and the boundary sliding viscosity. Asymptotic forms were derived which gave the complex rigidity for the extremes of low-frequency forcing and high-frequency forcing. Using those forms, master variables were created which allowed the results for different interface shapes, and arbitrary forcing frequency, to be almost exactly collapsed into a single curve. A numerical analysis, with finite interface slope, was then made of three proposed factors that might weaken or broaden the theoretical prediction of a single Debye peak in the loss spectrum. They were: stress concentrations at interface corners, spatial variations in grain size and spatial variations in the boundary sliding viscosity. The results showed that all of these factors could indeed contribute to a moderate weakening of the loss peak. By contrast, the loss peak broadened markedly only when the boundary sliding viscosity differed by an order of magnitude across the adjacent interface. The shape of the loss spectrum (self-similar to a single Debye peak) was insensitive to the other two factors.

Anelasticity and Grain Boundary Sliding. L.C.Lee, S.J.S.Morris: Proceedings of the Royal Society A, 2010, 466[2121], 2651-71