Coupled grooving and migration of inclined grain boundaries: Regime II

This work studies the coupled grooving and migration of an initially straight, inclined grain boundary ending at a horizontal free surface with an inclination angle betamuch less than1. The coupled motion is separated into two time regimes. In Regime I, the grain boundary turns vertically at the groove root. In Regime II, the turning relaxes following two different paths depending on sigma/beta where sigma is the supplementary dihedral angle. For beta > sigma/6, the groove root positions (x(o), y(o)) similar to (t(1/2),t(1/6)) as time t-->infinity, whereas for beta < sigma/6, (x(o),y(o)) similar to (t(1/4),t(1/4)) as t-->infinity. These results come from asymptotic expansions and agree with a finite-difference solution of the coupled equations. They show that the grain boundary is never pinned. The asymptotic solutions also apply to the Sun-Bauer method of measuring mobility, and predict grain-boundary profiles that agree better with experiments. (C) 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.