Stochastic modeling of solidification grain structures of Al-Cu crystalline ribbons in planar flow casting

A stochastic model has been developed for the prediction of polycrystalline microstructure formation in planar flow casting. The present model was based on the coupling of the finite volume (FV) method for macroscopic heat flow calculation and a two-dimensional cellular automaton (CA) model for treating microstructural evolution in planar flow casting. The CA model takes into account nucleation and growth kinetics. Heterogeneous nucleation can occur on nucleation sites both at the wheel surface and in the bulk liquid with random crystallographic orientations. The growth kinetics of a dendrite tip was evaluated using the Lipton-Kurz-Trivedi (LKT) model by which the relationship between the growth velocity of a dendrite tip and the local undercooling was calculated. At each time interval, the latent heat released by the growing cells in the CA model was fed back into the control volume containing those cells in order to calculate the temperature distribution for the following step of calculation. The present model has been applied to predict the cooling curves and the resultant microstructures of AI-Cu polycrystalline ribbons spun by planar flow casting. The effects of wheel speed, alloy composition, and superheat of the melt on grain structures were investigated. Variation in interface velocity of the growing cell with distance from the wheel surface was also analyzed in order to investigate microstructural transition in ribbons. The calculated grain structures were in good agreement with those obtained experimentally.