STOCHASTIC MODELING OF SOLIDIFICATION GRAIN STRUCTURES

Stochastic models have been developed for the simulation of grain structure formation during the solidification of metallic alloys. Nucleation is assumed to occur randomly in space according to a prescribed distribution of nucleation sites. For dendritic alloys, the hypothesis of a random orientation of the [100] crystallographic directions of the new nuclei is also made. A cellular automaton (CA) and an interface-tracking technique are used to follow the growth-impingement of dendritic and eutectic grains, respectively. The influence of the local thermal conditions, namely the thermal gradient and the velocity of the isotherm, and of the nucleation parameters on the resulting grain structures is assessed. In particular, it is shown that the asymmetry of the grains along the thermal gradient is an increasing function of the thermal gradient and nucleation undercooling and a decreasing function of the velocity and grain density. The presence of the outer equiaxed zone and the transition from columnar to equiaxed microstructures can also be explained using such models.