TY - JOUR
T1 - Anelasticity and grain boundary sliding
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
M3 - 10.1098/rspa.2009.0624
AU - Lee, L. C.
AU - Morris, S. J. S.
Y1 - 2010/03/24
UR - http://rspa.royalsocietypublishing.org/content/early/2010/03/23/rspa.2009.0624.abstract
N2 - 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. © 2010 The Royal Society
ER -