Densification and creep in the final stage of sintering

Abstract

Densification and creep by grain boundary diffusion is modelled for the late stage of sintering. The grain structure is described as a regular array of tetrakaidekahedra with pores at each grain boundary between next-nearest neighbors. The diffusion problem on the surface of the tetrakaidekahedron is solved numerically using the heat-conduction option of the finite element code ANSYS. From the calculated normal stresses on the boundary facets one assembles the macroscopic constitute behavior. Since the assumed grain shape is the Wigner-Seitz cell of the body-centered cubic lattice, the resulting viscosity tensor has cubic symmetry. Isotropic bulk and shear viscosities are obtained by applying the procedures developed for the elasticity theory of polycrystals. The resulting bulk viscosity is well approximated by a closed-form solution developed previously. Due to the pronounced cubic anisotropy of the model, the isotropic shear viscosity cannot be determined unambiguously. The model includes the effect of viscous grain boundary sliding. The influence of surface diffusion on the sintering rate is also explored.