STOCHASTIC MODELING OF SOLIDIFICATION GRAIN STRUCTURES

Stochastic models have been developed for the simulation of grain stru cture formation during the solidification of metallic alloys. Nucleati on is assumed to occur randomly in space according to a prescribed dis tribution 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-tr acking technique are used to follow the growth-impingement of dendriti c and eutectic grains, respectively. The influence of the local therma l conditions, namely the thermal gradient and the velocity of the isot herm, and of the nucleation parameters on the resulting grain structur es is assessed. In particular, it is shown that the asymmetry of the g rains along the thermal gradient is an increasing function of the ther mal gradient and nucleation undercooling and a decreasing function of the velocity and grain density. The presence of the outer equiaxed zon e and the transition from columnar to equiaxed microstructures can als o be explained using such models.