Equilibrium pore surfaces, sintering stresses and constitutive equations for the intermediate and late stages of sintering. Part 1. Computation of equilibrium surfaces

The intermediate stage of sintering is characterized by equilibrium surfaces of the open pore space between the grains. These doubly curved surfaces are determined numerically for the three cubic arrangements of grains (simple cubic, b.c.c. and f.c.c). The numerical program constructs surfaces of constant mean curvature connected via the dihedral angle to grain boundaries having zero mean curvature. The pore morphologies resulting from the analysis are different from the conventional picture of interconnected pore channels along grain edges. According to the present results, open porosity rather consists of interconnected pillow-shaped gaps between next-nearest grain neighbors. The transition to closed porosity occurs when the connections between these gaps close, a process which leads to relatively large isolated pores on two-grain junctions between former next-nearest neighbors. The numerical results for the contact areas between grains and for the sintering stress are approximated b y quadratic functions of the pore volume fraction and of the dihedral angle, and the best-fit coefficients are tabulated. The results are used in a companion paper in which constitutive equations for the mechanical behavior during sintering are derived.