A size interval-by-size interval marching algorithm for modelling grain growth in the intermediate stage of sintering

Abstract

An accurate and efficient numerical algorithm is presented for solving the grain population balance equation which describes the evolution of micro-structure as a function of time in solid-state sintering. The solution scheme is based on the postulate that in a class of physically realistic deterministic systems, the queue or the relative order of particles in size is maintained intact as they grow and or decay in time. The resulting size interval-by-size interval marching algorithm has been validated with the available asymptotic steady-state analytical solutions of grain growth/ripening model equations. It can be employed to simulate the sintering process in a more quantitative and realistic manner than what has been possible hitherto, especially in the intermediate stage of sintering, which is of practical interest in ceramic systems. A variety of simulations showing the effects of initial grain size distribution and sintering time are presented. Potential applications for optimizing the sintering process are discussed.