S-PFM model for ideal grain growth

Abstract The phase-field method is increasingly used for studying grain growth in metallic alloys. Such an approach offers a thermodynamically consistent framework for studying microstructure evolution during grain growth without the need to explicitly track the interface positions. However, the numerical solution of the models requires a grid spacing much smaller than the interface width. This leads to computationally very intensive simulations, especially when a large number of grains is required to accurately measure statistical quantities. The recently proposed S-PFM approach provides a new inherently discrete formulation of phase field models where the interface width can be as small as the grid spacing, thus drastically improving the numerical performances of the method. Here, we show that this approach can be extended to a multi-phase field model for ideal grain growth. Then, we perform two dimensional simulations to analyse in detail the kinetics of both grain boundaries and triple junctions. We compare our model to a classical phase field formulation and we demonstrate that, for a prescribed accuracy, the memory requirement and simulation times are both reduced by a factor of 4 D , where D is the space dimension. Finally, we perform a large-scale simulation of grain growth in two dimensions and show that the method is able to reveal the specific shape of the grain size distribution in the scale-invariant regime displaying two peaks around the mean grain size and quantitative measurements of the underlying topological classes are performed.