A phase field model with arbitrary misorientation dependence of grain boundary energy

TL;DR

This paper introduces a modified phase field model for grain growth that allows arbitrary misorientation dependence of grain boundary energy, overcoming limitations of previous orientation-field models.

Contribution

The authors propose a non-local modification to the Kobayashi-Warren-Carter model enabling flexible misorientation dependence in grain boundary energy.

Findings

The modified model can embed arbitrary misorientation dependence.

It demonstrates a sharp cusp in grain boundary free energy.

Extension to three dimensions is proposed.

Abstract

Grain growth in polycrystals is often simulated using orientation-field models, which employ a field to represent the local orientation of the crystal lattice. These models can be challenging to represent a realistic misorientation dependence of grain boundary free energy. We prove that existing orientation-field models, in general, cannot reproduce a decrease in the grain boundary free energy with a increasing misorientation angle, demonstrating a significant limitation of previous models in applications to polycrystalline materials. To overcome this limitation, we propose a modification to the Kobayashi-Warren-Carter model for grain growth wherein the coefficients of the free-energy functional become functions of the misorientation between the grains, which is a non-local quantity. Due to this modification, an arbitrary dependence of the grain boundary free energy on the misorientation can be embedded in the model. We propose calculating the non-local misorientation by interpolating the orientation field at a fixed distance in both directions along the local grain boundary normal vector. The capabilities of the model are demonstrated by introduction of a sharp cusp to the misorientation dependent grain boundary free energy. Finally, we propose an extension of the model to three dimensions.