Modeling dendritic solidification of Al-3%Cu using cellular automaton and phase-field methods

摘要

We compared a cellular automaton (CA)-finite element (FE) model and a phase-field (PF)-FE model to simulate equiaxed dendritic growth during the solidification of cubic crystals. The equations of mass and heat transports were solved in the CA-FE model to calculate the temperature field, solute concentration, and the dendritic growth morphology. In the PF-FE model, a PF variable was used to identify solid and liquid phases and another PF variable was considered to determine the evolution of solute concentration. Application to Al-3.0 wt.% Cu alloy illustrates the capability of both CA-FE and PF-FE models in modeling multiple arbitrarily-oriented dendrites in growth of cubic crystals. Simulation results from both models showed quantitatively good agreement with the analytical model developed by Lipton-Glicksman-Kurz (LGK) in the tip growth velocity and the tip equilibrium liquid concentration at a given melt undercooling. The dendrite morphology and computational time obtained from the CA-FE model are compared to those of the PF-FE model and the distinct advantages of both methods are discussed.