Prediction of Solidification Microstructure and Columnar-to-equiaxed Transition of Al–Si Alloy by Two-dimensional Cellular Automaton with “Decentred Square” Growth Algorithm

Abstract

A Cellular Automaton (CA) -Finite Difference (FD) coupling model was developed to analyze the evolution of solidification microstructure and the columnar-to-equiaxed transition (CET) in Al–Si alloy. Kobayashi's microsegregation equation was adopted to describe the solute diffusion in solid phase, and a “decentred square” growth algorithm with coordinate transformation was performed to describe the grain growth and the entrapment of neighbor cells. Through the examination on the effects of operation parameters and nucleation parameters on solidification morphologies, it was found that the length of columnar grains is controlled by the dendrite tip growth kinetics, and that the width of columnar grains is controlled by the implicit relationship between nucleation density and cooling rate at ingot surface. It was also found that the size of equiaxed grains is controlled by the competition of the nucleation and the grain growth. With the controllability of nucleation density in the bulk of liquid for equiaxed grain size, the nucleant and the nucleation density in actual Al–Si alloy were estimated. Both of the CET criteria based on the solidification path by CA-FD coupling model and the one based on the curves of critical temperature gradient conditions by Hunt's model were strongly dependent on nucleation undercooling and Si concentration. A good agreement was obtained between these two.