3D PROBABILISTIC MODELING OF EQUIAXED EUTECTIC SOLIDIFICATION

The equiaxed solidification of eutectic alloys is modelled by a probab listic method. The volume of the specimen is divided into a regular ne twork of cubic cells and the temperature is assumed to be uniform. The temperature of the specimen is calculated in a time-stepping scheme f rom 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-t o-solid transition of the cells is calculated by considering the mecha nisms of heterogeneous nucleation and grain growth, but the grain impi ngement is already accounted for by this probabilistic method. Althoug h the number of new grains which form during each time step is calcula ted from a deterministic nucleation site distribution, their location is chosen randomly among the cells. Once a nucleus has formed at a giv en cell location, it grows with a velocity given by the model of Jacks on and Hunt and thus captures neighbouring cells. While producing grai n structures similar to those previously reported by Mahin et al for s olid state transformations, the present three-dimensional method gives direct access to the effective solid liquid interface or to the impin gement factor, PSI. This factor is important because it directly modif ies the undercooling, the growth rate, the end of solidification and t he 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 analytic al result predicted by Meijering for instantaneous nucleation and cons tant growth rate situations are also in very good agreement.