Very fast simulation of growth competition between columnar dendritic grains during melt pool solidification

This paper presents a very fast numerical approach to simulate microstructures resulting from melt pool solidification including growth competition of columnar dendritic grains, and equiaxed grains nucleated from the melt. To reduce computation time, the key contribution is the development of an upscaling strategy, which instead of considering each dendrite individually consists in defining an average solidification front based on physically-informed dendritic growth velocity. The proposed approach also relies on dendritic preferred growth direction, and favorably oriented grain criterion to determine which grain survives the competition. To significantly reduce the total number of degrees of freedom Voronoi tessellations are used instead of regular grids for numerical implementation. Indeed, 3D regular grids typically leads to N³ degrees of freedom while Voronoi tessellations lead to only 3N, which dramatically reduces computation cost. This work is therefore a high-throughput approach enabling large data set generation to explore statistical features of microstructures with respect to melt pool properties. Results have been compared to experimental data, and to phase field and cellular automaton simulations in 2D only. Simulated microstructures are similar as those obtained with cellular automaton. Comparisons in 3D are left for future work. In addition, a convergence analysis is provided for 3D simulations, with thermal conditions corresponding to metal additive manufacturing to demonstrate how the present work can be used in practice.