Bounds for shear viscosity in Nabarro–Herring–Coble creep

At high homologous temperature, plastic flow of a polycrystalline material can be mediated by self-diffusion and grain boundary sliding, rather than by dislocation glide. The effective viscosity of the polycrystal depends on the underlying mechanisms as well as on the microstructure. Simple expressions relating the shear viscosity to lattice and grain boundary diffusion coefficients were proposed in pioneering contributions by Nabarro (1948), Herring (1950) and Coble (1963). While these models remain widely used today to deduce the dominant mechanism based on the observed dependence of viscosity on grain size, a number of questions remain open. The present work revisits Nabarro–Herring–Coble creep using a micromechanical approach and variational principles. We focus on a random polycrystal of equiaxed grains deforming by coupled lattice and grain boundary diffusion and grain boundary sliding. We show that the classical results of Herring and Coble correspond to upper bounds on the shear viscosity, and obtain complementary lower bounds. Our results shed new light on these classical results and question the validity of the common interpretation of the dependence of viscosity on grain size