Axisymmetric model of pore-grain boundary separation

In the final stage of ceramic sintering, pores can either move with, or separate from, grain boundaries. The outcome is critical to the resulting ceramics. This paper studies an axisymmetric model of a single pore on a moving grain boundary. Two rate processes, grain boundary migration and surface diffusion, are concomitant. Surfaces move to reduce the total surface and grain boundary energy. A finite element method is formulated to simulate the transient separation process. Using an independent method, we also obtain steady state solutions of the pore moving with the grain boundary. The steady state problem has multiple solutions with a surprisingly rich mathematical structure. Finite element simulations show that some steady state solutions are stable, and others unstable. We find that the pore-grain boundary separation condition is insensitive to the dihedral angle.