Calculation of a constitutive potential for isostatic powder compaction

A macroscopic constitutive potential has been developed for the deformation of a powder compact of cylindrical particles during pressure sintering. The derivation is based on finite-element simulations of the densification process that proceeds under the synergistic action of power-law creep deformation in the particles, evolution of the nonlinearly developing contact area between the particles, and interparticle and pore free-surface diffusional mass transport. Solution to this initial/boundary-value problem as deformation proceeds with time provides all necessary information for the calculation of the constitutive potential. The associated constitutive law predicts the densification rate of the powder compact at a given temperature and pressure in terms of material parameters, such as creep constants and diffusion coefficients, and reflects the role played in the densification process by various micromechanical features at the microscale such as the pore surface curvature. The model predictions are compared with the existing analytical models for plane strain densification and experimental data from sintering of copper wires by grain boundary and curvature-driven pore surface diffusion.