3D PROBABILISTIC MODELING OF EQUIAXED EUTECTIC SOLIDIFICATION

The equiaxed solidification of eutectic alloys is modelled by a probablistic method. The volume of the specimen is divided into a regular network of cubic cells and the temperature is assumed to be uniform. The temperature of the specimen is calculated in a time-stepping scheme from a simple heat balance and a knowledge of the heat flux leaving the metal. However, unlike the classical deterministic models describing equiaxed solidification, the evolution of the volume fraction of solid associated with the latent heat release is directly obtained from the cells of the network which have already been solidified. The liquid-to-solid transition of the cells is calculated by considering the mechanisms of heterogeneous nucleation and grain growth, but the grain impingement is already accounted for by this probabilistic method. Although the number of new grains which form during each time step is calculated from a deterministic nucleation site distribution, their location is chosen randomly among the cells. Once a nucleus has formed at a given cell location, it grows with a velocity given by the model of Jackson and Hunt and thus captures neighbouring cells. While producing grain structures similar to those previously reported by Mahin et al for solid state transformations, the present three-dimensional method gives direct access to the effective solid liquid interface or to the impingement factor, PSI. This factor is important because it directly modifies the undercooling, the growth rate, the end of solidification and the possible appearance of metastable phases in between the grains. It is shown that the PSI value obtained with this probabilistic method is close to that predicted by the Kolmogorov-Johnson-Mehl Avrami model. The calculated average number of facets of each grain and the analytical result predicted by Meijering for instantaneous nucleation and constant growth rate situations are also in very good agreement.