Comparison of Cellular Automaton and Phase Field Models to Simulate Dendrite Growth in Hexagonal Crystals

Abstract

A cellular automaton (CA){flnite element (FE) model and a phase fleld (PF){FE model were used to simulate equiaxed dendritic growth during the solidiflcation of hexagonal metals. In the CA{FE model, the conservation equations of mass and energy were solved in order to calculate the temperature fleld, solute concentration, and the dendritic growth morphology. CA{FE simulation results showed reasonable agreement with the previously reported experimental data on secondary dendrite arm spacing (SDAS) vs cooling rate. In the PF model, a PF variable was used to distinguish solid and liquid phases similar to the conventional PF models for solidiflcation of pure materials. Another PF variable was considered to determine the evolution of solute concentration. Validation of both models was performed by comparing the simulation results with the analytical model developed by Lipton{Glicksman{Kurz (LGK), showing quantitatively good agreement in the tip growth velocity at a given melt undercooling. Application to magnesium alloy AZ91 (approximated with the binary Mg{8.9 wt% Al) illustrates the di‐culty of modeling dendrite growth in hexagonal systems using CA{FE regarding mesh-induced anisotropy and a better performance of PF{FE in modeling multiple arbitrarily-oriented dendrites growth.