A constitutive model for stage 2 sintering of fine grained materials—I. Grain-boundaries act as perfect sources and sinks for vacancies

Abstract

In this paper, a constitutive model for stage 2 sintering of powder compacts by grain-boundary diffusion is established. A three-dimensional material model composed of a uniform array of tetrakaidecahedra shaped grains with spherical pores at each grain-boundary vertex is adopted. A bounding theorem described by Cocks for grain-boundary diffusion problems is used to obtain a lower bound to the scalar strain-rate potential, through which the macroscopic strain rates and macroscopic stresses are related. Use of the theorem requires a set of kinematically compatible fields of grain-boundary separation rates, matter flux along the grain-boundaries and macroscopic strain-rates to be proposed. In this paper, we focus our attention on the classical grain-boundary diffusion problem where grain-boundaries are assumed to act as perfect sources and sinks for vacancies. The effects of an interface-reaction are discussed in an accompanying paper.