UC Davis

The topological transitions of the grain boundary network during grain growth under uniform grain boundary energies are believed to be known. However, this is not true for more realistic materials with varying grain boundary energies that, in principle, allow many different grain boundary configurations. A grain growth simulation for such a material therefore requires a procedure to enumerate all possible topological transitions and select the most energetically favorable one. Such a procedure is developed and implemented here for a microstructure represented by a volumetric finite element mesh. The method is implemented as a C++ library called VDlib based on SCOREC, an open source massively parallelizable library for finite element simulations with adaptive meshing. To test the implementation, a Voronoi tessellated microstructure composed of one hundred grains is generated and evolved under constant grain boundary properties until half of the grains remained. The evolution of the individual grains is compared to what is expected from the MacPherson-Srolovitz relation and is found to be in good match.

As with all numerical techniques, it is important to identify systematic sources of error. Such studies for grain growth simulations are either missing from or not uniform across the literature. To address this issue and enable comparison across grain growth simulations, a set of benchmark cases, one for each boundary type of surfaces, lines, and points with analytical solutions are identified. These are used to compare a recently developed discrete-interface method for microstructure evolution to a state of the art diffuse interface (multiphase field method). In each case, the discrete method is found to meet or outperform the multiphase field method in terms of accuracy for comparable levels of refinement, demonstrating its potential efficacy as a numerical approach for microstructure evolution.

Last, a novel invariant of ideal grain growth process is defined that ideally can be used to calculate the number of topological entities in a microstructure and only changes as the topology changes. VDlib is used to test the invariant on a simulated microstructure composed of a periodic arrangement of Kelvin cells. A convergence study reveals that the invariant converges to the ideal case with increasing levels of refinement, however predicting the number of entities without bounds on number of entities proves unpractical. Two error measures based on this novel invariant are proposed which can potentially be used to quantitavely measure how much simulations deviate from ideal grain growth process and experimental microstructures.