A CONSTITUTIVE MODEL FOR STAGE-2 SINTERING OF FINE-GRAINED MATERIALS .2. EFFECTS OF AN INTERFACE REACTION

In this paper, a nonlinear constitutive model is developed for stage 2 sintering of powder compacts by grain-boundary diffusion where energy is dissipated not only in driving the flux of material around the gra ins but also in overcoming an interface reaction. A three dimensional material model composed of a uniform array of tetrakaidecahedra shaped grains with spherical pores at each grain-boundary vertex is adopted. The interface reaction is assumed to be a function of the grain-bound ary separation rate in a power law form as suggested by Cocks [A. C. F . Cocks, Mech. Mater. 13, 165 (1992)]. The set of kinematically compat ible fields of grain-boundary separation rates, matter flux along grai n-boundaries and macroscopic strain-rate proposed in the first part of this paper [J. Pan and A. C. F. Cocks, Acta metall. mater. 42, 1215 ( 1994)] are used to obtain a lower bound to the scalar macroscopic stra in rate potential using the lower bound theorem described by Cocks (to be published) for the coupled grain-boundary diffusion and interface reaction problem. The optimum magnitudes of the adjustable parameters used to describe the kinematic fields are determined numerically and s uitable analytic forms of the strain-rate potential are proposed, base d on the results of these computations.