Modelling microstructural evolution of porous polycrystalline materials and a numerical study of anisotropic sintering

This paper presents a numerical scheme for computer simulation of microstructural evolution of porous polycrystalline materials at elevated temperatures. The scheme is then applied to study the sintering behaviour of polycrystalline solid containing elongate pores. In a previous paper [J. Comput. Phys. 196 (2004) 724], we presented a set of finite element formulations to model surface diffusion, grain-boundary diffusion and grain-boundary migration, and their interactions. A range of numerical examples were provided for which analytical solutions are available to verify the finite element formulations. All these examples had to be simple and contained at most two grains for the analytical solutions to be possible. In this paper, we complete the numerical scheme and address the numerical issues which have to be resolved when applying the finite element formulations to material models consisted of many grains and pores. In particular, we demonstrate how the joining conditions at triple junctions are achieved in the finite element solution and how the microstructure is updated according to the velocities obtained from the finite element solution. The numerical scheme is then used to study the problem of anisotropic sintering. A series of computer simulations were carried out to study microstructural evolution around an elongate pore. The numerical results show that an elongate pore leads to anisotropic shrinkage and that the shrinkage is always larger in the direction of the longer axis of the pore. The numerical results also show that the shrinkage anisotropy can be controlled by manipulating the ratios between the kinetic mobilities of surface diffusion, grain-boundary diffusion and grain-boundary migration. Increasing the grain-boundary migration mobility increases the shrinkage anisotropy. Increasing the surface diffusion mobility, on the other hand, reduces the shrinkage anisotropy. These numerical findings are not obvious and remain to be verified by future experiment.