A Cellular Automaton Technique for the Modeling of Solidification Microstructure in Multi-Component Alloys

Abstract

A two-dimensional model for the simulation of solidification microstructure in multi-component alloy systems has been developed. The model is based on a cellular automaton (CA) technique for the calculation of the evolution of solid/liquid (S/L) interface. The dynamics of the interface is controlled by temperature, solute diffusion and Gibbs-Thomson effects. The diffusion equation for the temperature with release of latent heat on the S/L interface is valid in the entire domain, and the solute diffusion equation is also used in the entire domain through potential functions. Two methods are proposed to calculate the increment of the solid fraction. The first method is based on the level rule method similar to the one proposed by Jacot et al., but without the assumption of uniform temperature on the scale of the calculation domain. The second one is based on the calculation of the S/L interface velocity, which generalizes the results of Nastac and Beltran-Sanchez et al. for two-component alloy systems. If the concentration of one of the solutes tends to zero, both proposed methods reduce to the methods in Jacot et al. and Beltran-Sanchez et al. for two component alloy systems. Mesh independency is achieved by both methods and the dendritic morphologies obtained are the same if the mesh is fine enough. However, the morphologies of equiaxed dendrites calculated by using the interface velocity tends to the stable form more easily than those calculated using the level rule method as the mesh size is refined. For two-component alloy systems, the predictions of LGK theory for the steady-state tip velocity are compared with simulated values as a function of melt undercooling, which shows good agreement at very large range of undercooling. The simulated primary arm spacing in directional solidification is compared with experimental results for Fe-Si-Mg alloys and good agreement is also observed. It is noted that both methods for computing the solid fraction can be used for any multi-component alloy systems provided that the thermodynamic data are given