DENSIFICATION AND CREEP IN THE FINAL STAGE OF SINTERING

Densification and creep by grain boundary diffusion is modelled for th e late stage of sintering. The grain structure is described as a regul ar array of tetrakaidekahedra with pores at each grain boundary betwee n next-nearest neighbors. The diffusion problem on the surface of the tetrakaidekahedron is solved numerically using the heat-conduction opt ion of the finite element code ANSYS. From the calculated normal stres ses on the boundary facets one assembles the macroscopic constitutive behavior. Since the assumed grain shape is the Wigner-Seitz cell of th e body-centered cubic lattice, the resulting viscosity tensor has cubi c symmetry. Isotropic bulk and shear viscosities are obtained by apply ing the procedures developed for the elasticity theory of polycrystals . The resulting bulk viscosity is well approximated by a closed-form s olution developed previously. Due to the pronounced cubic anisotropy o f the model, the isotropic shear viscosity cannot be determined unambi guously. The model includes the effect of viscous grain boundary slidi ng. The influence of surface diffusion on the sintering rate is also e xplored.