Phase field modeling of anisotropic grain growth using a Spherical-Gaussian-based 5-D computational approach
Yeo, Lenissongui Cedric
Citations
Abstract
Studies have shown that specific grain boundaries (GBs) greatly influence the properties of materials, indicating that material performance can be enhanced through deliberate GB engineering. Twin boundaries, for instance, have been found to significantly improve properties like corrosion resistance and electrical conductivity. Given that GBs exhibit five degrees of freedom for anisotropy and that current methods to incorporate both misorientation and inclination dependencies are either insufficient or complex to implement, there is a need for further research and advanced modeling techniques. In this study, a previously developed Spherical-Gaussian method is employed to incorporate 5-D anisotropy in two phase field models, originally developed by Moelans, referred to as the epsilon and gamma models. Orientations are assigned to individual grains using quaternions, which are then used to compute quaternion misorientations at each GB, driving ongoing mesoscale changes. To account for specific low-energy boundaries, such as twin boundaries, local minima or specific grain boundaries are stored in a minima library and used in the phase field models through a developed gaussian switch. The 2-D gaussian switches compare the system’s misorientations between pairs of grains to the list of minima misorientations, inducing a spherical-Gaussian effect that adjusts the GB energy to the desired value from a pre-specified base GB energy. This method allows GB energy to change dynamically as the GB plane and grain misorientations evolve. Simulations are performed using the Multiphysics Object-Oriented Simulation Environment (MOOSE) with both models. Results from bicrystal simulations across six different cases showed that the models could accurately reproduce validated GB energy, irrespective of initial conditions, as long as a library misorientation is recognized. Complex phenomena, such as faceting due to two minima near the GB typically observed at the atomistic scale, were also observed at the mesoscale with the improved models. Additional tricrystal simulations demonstrated significant variation from the isotropic model when anisotropy was introduced through GB energy alone, with only slight deviation when adding anisotropy through GB mobility, a trend noted in prior studies. The effective application of these models presents numerous opportunities for designing superior materials for industrial use.