Transient and asymptotic kinetics of mass transfer by coupled surface and grain boundary diffusion in sintering under strain rate control

An original procedure is developed for simulating pore surface evolution during sintering at high strain rate while distinguishing two types of diffusion fluxes: transient surface fluxes governed by short-range curvature gradients and coupled fluxes at surface and grain boundary governed by strain rate. The latter fluxes become dominant asymptotically, i.e. after damping-out of transient fluxes. The procedure aims at allowing the prediction of the strain rate dependence of macroscopic viscosity, a concept which is meaningful only during the asymptotic stage. The problem is addressed in two-dimension. It is shown that the asymptotic solution of the general partial differential equation of the problem can be obtained as the solution of an ordinary differential equation, of which the resolution lends itself to a semi-analytical procedure. An estimate is also proposed for the rate of convergence of the general solution towards the asymptotic solution. The accuracy of the mathematical procedure is validated by a comparison of the evolution of asymptotic profiles and exact profiles calculated fully numerically during densification or expansion of the system. A method is proposed for mapping the conditions of existence of an asymptotic stage. The method can account for the dependence of average grain coordination on relative density.