Modeling and simulation of dendrite growth in solidification of Al-Si-Mg ternary alloys

Abstract

Based on a previously cellular automaton (CA) model for Al-Si binary alloys, a modified cellular automaton (MCA) model is developed to numerically simulate the dendrite growth and microsegregation of Al-Si-Mg ternary alloys. By direct coupling PanEngine, the MCA model can obtain thermodynamic data for dendrite growth of ternary alloys in real time, such as equilibrium liquidus temperature, partition coefficient and liquidus slope of two solute elements. In the model, the normal velocity of the interface cell can not be derived only by solving the solute conservation equation, and must be simultaneously coupled with dimensionless solute supersaturation equation for each alloying element and local equilibrium temperature equation at the S/L interface. All the equations of the MCA model are solved by finite difference method on a uniform mesh. By considering local curvature and constitutional undercooling, solute diffusion and solute redistribution at the S/L interface, the MCA model can simulate the columnar dendrite growth and the solidification path of the equiaxed dendrite growth.