3D STOCHASTIC MODELING OF EQUIAXED SOLIDIFICATION IN THE PRESENCE OF GRAIN MOVEMENT

A three-dimensional stochastic model of equiaxed solidification of eutectic alloys in the presence of convection/sedimentation is proposed. Assuming uniform temperature, the heat balance is coupled to a microscopic description of grain evolution. Grain location is chosen randomly within the solidifying volume. Grain evolution is followed by mapping the interface of each grain with a large number of elementary surfaces. Each grain is fully described by its centre position, radius, and the status of its elementary surfaces (in contact with liquid or not). Grain movement is modelled by changing centre coordinates; evolution of the solid volume fraction is deduced by summing over all elementary surfaces which comprise the solid-liquid interface. A recursive method yields two-dimensional grain sections. Grain movements associated with convection and sedimentation are investigated, and their effects on the final grain structure, the solid-liquid interface, the impingement factor, and the cooling curve are shown.