Anisotropic viscosities and shrinkage rates in sintering of particles arranged in a simple orthorhombic structure

Macroscopic shrinkage in sintering is described as a linear function of the sintering stress tensor and the viscosity tensor, which is determined by taking into account the grain boundary diffusion mechanism and the anisotropy in the microstructure. For a simple orthorhombic structure in equilibrium, the anisotropic shrinkage rate is dominated by the deviatoric component of the viscosity tensor, which is approximately proportional to the logarithm of the aspect ratio of a volume element, and acts so as to deform the elongated structure to be more isotropic.