The role of grain boundary mobility in diffusional deformation

Abstract

The model of diffusional deformation is revisited by accounting for the dependence of the diffusion potential on grain boundary curvature. The issue is developed through the analysis of two case-studies: the deformation of a lattice of columnar grains in conditions of Coble creep, and the rotation of a grain embedded in a polycrystal in conditions of either Nabarro-Herring creep or Coble creep. The analysis reveals that, unless grain boundary mobility is infinite, grain boundary curvature is dynamically induced by strain rate. A link is established between the curvature distribution and the transfer of diffusion fluxes across grain boundaries. For the two case-studies, the equation expressing the balance of grain boundary motions at steady-state is solved for calculating, within a range of grain boundary mobilities, the grain boundary profiles, the diffusion fluxes, and the contributions to power dissipation arising from curvature. The latter contributions are found to scale closely as the square of grain size. It follows that the dissipation contribution due to curvature is larger in conditions of Nabarro-Herring creep. In conditions of Coble creep, the dissipation contribution due to curvature translates into a lower bound for the apparent boundary viscosity parameter to be used in numerical simulations. This lower bound is consistent with previous identifications of the parameter in the literature. The classical model assuming flat grain boundaries with transfer of fluxes via triple junctions emerges as a particular case involving the implicit assumption of an infinite grain boundary mobility.