Strain in the mesoscale kinetic Monte Carlo model for sintering

TL;DR

This paper analyzes and improves a mesoscale kinetic Monte Carlo model for solid state sintering, specifically addressing anisotropic strain issues by introducing a new annihilation algorithm that ensures isotropic shrinkage.

Contribution

It introduces a novel annihilation algorithm that corrects strain anisotropy in the existing mesoscale kMC sintering model, ensuring isotropic shrinkage regardless of sample aspect ratio.

Findings

Existing models produce anisotropic strains for non-cubic samples.

The new algorithm achieves isotropic strains across all sample geometries.

Microstructural evolution remains consistent with previous models.

Abstract

Shrinkage strains measured from microstructural simulations using the mesoscale kinetic Monte Carlo (kMC) model for solid state sintering are discussed. This model represents the microstructure using digitized discrete sites that are either grain or pore sites. The algorithm used to simulate densification by vacancy annihilation removes an isolated pore site at a grain boundary and collapses a column of sites extending from the vacancy to the surface of sintering compact, through the center of mass of the nearest grain. Using this algorithm, the existing published kMC models are shown to produce anisotropic strains for homogeneous powder compacts with aspect ratios different from unity. It is shown that the line direction biases shrinkage strains in proportion the compact dimension aspect ratios. A new algorithm that corrects this bias in strains is proposed; the direction for collapsing the column is determined by choosing a random sample face and subsequently a random point on that face as the end point for an annihilation path with equal probabilities. This algorithm is mathematically and experimentally shown to result in isotropic strains for all samples regardless of their dimensions. Finally, the microstructural evolution is shown to be similar for the new and old annihilation algorithms.