Surface morphologies due to grooves at moving grain boundaries having stress-driven fluxes

We modify a previous steady-state description developed by Gènin [J. Appl. Phys. 77, 5130-5137 (1995)] for a grain boundary groove moving with a prescribed speed in a material subject to in-plane stress and a resultant grain boundary flux. The arbitrary assumption that the grain boundary flux is equally delivered to (or extracted from) the two adjacent free surfaces of the grains is replaced by a condition that requires continuity of surface chemical potentials at the grain boundary. Analytical results for the small-slope approximation as well as nonlinear results for large slopes are computed numerically for steady-state motion at a specified groove speed. We apply these results to a “partial loop” grain boundary geometry that moves by mean curvature induced by the groove conditions. In contrast to the ordinary effect that a grain boundary surface groove retards grain boundary motion, the presence of a compressive stress and resultant grain boundary flux toward the free surface can promote grain boundary motion.