Linear bubble model of abnormal grain growth

Abstract

A linear bubble model of grain growth is introduced to study the conditions under which an isolated grain can grow to a size much larger than the surrounding matrix average (abnormal growth). We first consider the case of bubbles of two different types such that the permeability of links joining unlike bubbles is larger than that of like bubbles (a simple model of grain boundary anisotropy). Stable abnormal growth is found both by mean field analysis and direct numerical solution. We next study the role of grain boundary pinning (e.g., due to impurities or precipitate phases) by introducing a linear bubble model that includes lower and upper thresholds in the driving force for bubble growth. The link permeability is assumed finite for driving forces above the upper threshold, zero below the lower threshold, and hysteretic in between. Abnormal growth is also observed in this case.