Micro–macro simulation of sintering process by coupling Monte Carlo and finite element methods

Abstract

A micro–macro method for simulating a sintering process of ceramic powder compacts based on the Monte Carlo and finite element methods is proposed. Macroscopic non-uniform shrinkage during the sintering is calculated by the viscoplastic finite element method. In the microscopic approach using the Monte Carlo method, powder particles and pores among the particles are divided into many cells, and the growth of grains in the particles and the disappearance of pores are simulated by means of the Potts model.The shrinkage strain rate required as a materials constant in the macroscopic method is calculated by the microscopic approach. The microscopic and macroscopic approaches are coupled by exchanging microscopic and macroscopic results in each finite element step. In the Monte Carlo method, the effect of macroscopic viscoplastic deformation on the microstructural change is taken into consideration by including viscoplastic strain rate calculated by the finite element method in the disappearance frequency of pore cells. The shrinkage behaviour in the sintering of circular two-layer compacts is simulated by the proposed micro–macro method.