Multi-scale modeling of shape distortions during sintering of bi-layers

Models for deformational behaviors of porous bodies during sintering often rely on limited number of internal variables as they are formulated based on simplified or ideal microstructures. Considering realistic microstructures can improve the predictive capabilities of the already established theories like the continuum theory of sintering. A new multi-scale numerical approach for modeling of shape distortions during sintering of macroscopically inhomogeneous structures combined with a microstructure model is developed. The microstructures of the porous body are described by unit cells based on kinetic Monte Carlo (kMC) model of sintering. During the sintering process the shrinkage rate is calculated from the kMC model. With the help of computational homogenization, the effective viscosity of the powder compact is also estimated from a boundary value problem defined on the microstructures of unit cells simulated by the kMC model. Examples of simulation of sintering of bi-layers based on different material systems are presented to illustrate the multi-scale model. The approach can be considered as an extension to the continuum theory of sintering combined with the meso-scale kinetic Monte Carlo model.