Three-dimensional Cellular Automaton Model for the Prediction of Microsegregation in Solidification Grain Structures

A 3-D cellular automaton finite difference (3-D CAFD) model to predict the solidification grain structure and the microsegregation was developed. In the present model, a new approach to calculate the solute concentration distribution was developed. Moreover, the CA cell including the grain boundary was newly defined. The probabilistic approach was adopted as the nucleation model, and the decentered octahedron growth algorithm was adopted as the grain growth model. The growth kinetics of the dendrite tip to calculate the growth of the dendrite envelope was calculated by a 3-D Kurz-Giovanola-Trivedi (KGT) model. In the 3-D KGT model, the local undercooling estimated by the local temperature and local solute concentration was used. To evaluate the validity of the present model, we carried out simulations of the solidification grain structure under directional solidification. The different solidification grain structures were obtained by the different solute concentration distributions. In addition, we compared our model with the microsegregation predicted by Scheil's equation. The simulated results of microsegregation by the present model were in fairly good agreement with those by Scheil's equation. From these results, we confirmed that the calculation of solute concentrations has to be considered and that the present model can simultaneously simulate microstructure and microsegregation.