Finite element simulation of Zener pinning behavior

The axi-symmetric finite element method is developed in order to simulate the three-dimensional migration behavior of a grain boundary around a spherical particle, called Zener pinning. The formulation of the method is conducted on the basis of the energy principle during the boundary motion. The validity of the method is confirmed by comparing the results of the shrinkage behavior of an isolated spherical grain with the theoretical predictions. A spherical grain boundary shrinks in keeping its original shape, and the velocity is consistent with the theoretical prediction. In the simulation of the interaction between a curved grain boundary and a spherical particle, the velocity of the grain boundary varies during the interaction process depending on the location against a particle. Since the velocity of the grain boundary near the particle varies more intensively than that away from the particle, the shape of the grain boundary is considerably deformed during the Zener pinning process. The simulated boundary shape during the interaction shows large differences from that in the equilibrium state. The lowered velocity of the grain boundary motion due to the existence of a particle is evaluated by comparing with the motion of the unperturbed boundary. The entire moving velocity decreases with increasing particle radius with respect to the radius of the grain boundary.