A phase–field paradigm for grain growth and recrystallization

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Abstract
A new model is presented for the mesoscale modelling of grain–boundary motion. Grain boundaries are treated as regions of disorder across which orientation parameters change. The framework uses a set of lattice parameters to track grain orientation, and this is done with fewer equations than the more standard approach, which requires one equation for each grain orientation. An asymptotic analysis relates the theory to classical sharp–interface kinetics. A class of equilibrium states is analytically derived. The theory is numerically implemented in one dimension in order to illustrate the existence of stable grain structures. An ad hoc dislocation substructure energy is also used to demonstrate how the associated driving force causes grain boundaries to move, an essential ingredient in simulating recrystallization.