A two-dimensional study of coupled grain boundary motion using the level set method

The coupled motion of a closed non-circular grain boundary (GB) in a bicrystal, with both isotropic and anisotropic GB energies, is studied using the level set method. The kinetic relations, obtained within the framework of linear irreversible thermodynamics, govern the overall dynamics, including normal motion (migration) of the GB, viscous sliding along the GB and tangential motion of the grains which is geometrically coupled with the migration. The shape accommodation necessary to maintain coherency of relatively rotating and non-deforming grains is accomplished by allowing for diffusion along the GB. We solve the governing equations for the coupled motion in order to determine the shape and the misorientation evolution of an isolated GB under various constitutive assumptions. First, assuming both GB energy and kinetic coefficients to be isotropic, we study the interplay between kinetic coefficients for initially circular, near-circular and non-circular GBs, as well as the impact of stress and initial conditions on the GB dynamics. Next, we study the influence of anisotropy in the GB energy, mobility and geometric coupling for various combinations of parameters and initial conditions. Allowing for geometric coupling can in fact lead to shapes distinctly different to those that are usually predicted on the basis of migration alone. Our numerical scheme provides a general framework in which to study these and other related problems of GB motion.