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


A cellular automaton (CA)-finite element (FE) model and a phase field (PF)-FE model were used to simulate equiaxed dendritic growth during the solidification of hexagonal metals. In the CA-FE model, the conservation equations of mass and energy were solved in order to calculate the temperature field, 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 solidification 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 difficulty 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.


Materials Science and Engineering

Keywords and Phrases

Conservation equations; Cooling rates; Dendrite growth; Dendritic growth; Experimental data; FE model; Finite element; Finite element models; Hexagonal crystals; Hexagonal systems; Liquid phasis; Magnesium alloy AZ91; Melt undercooling; Phase field models; Phase fields; Phase-field model; Pure materials; Secondary dendrite arm spacing; Solute concentrations; Tip growth; Cellular automata; Magnesium alloys; Phase interfaces; Solidification; Finite element method; Cellular automaton; Dendrite growth; Finite element; Magnesium alloy; Phase-field model

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Article - Journal

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