A numerical study of grain boundary motion in bicrystals

We study the motion of a grain boundary in a bicrystal which is attached at a groove root to an exterior surface in a “quarter loop” geometry. Our study is based on a fully nonlinear model for which stationary travelling wave solutions were recently proven to exist [Adv. Diff. Eqns. 9 (2004) 299] for all values of m, 0 ⩽ m < 2, where m denotes the ratio of the surface energy of the grain boundary to the surface energy of the exterior surface. In the present paper, these travelling waves are calculated numerically and are compared with the predictions of earlier “linearized” models. We demonstrate that the nonlinear theory yields deeper groove depths, larger dihedral angles, and more tilted grain boundaries than the “linear” theory. Moreover, when m is sufficiently large, the predicted profiles are no longer single-valued. We show that experimental measurements based on the linearized theory may cause misinterpretation of data, and we call attention to several phenomena which appear worthy of experimental investigation.