3-DIMENSIONAL PROBABILISTIC MODELING OF EQUIAXED EUTECTIC SOLIDIFICATION IN THE PRESENCE OF CONVECTION

A three-dimensional probabilistic model describing the solidification of a small specimen containing a metallic alloy of eutectic compositio n has been developed. For a uniform temperature, the heterogeneous nuc leation of the grains is assumed to be randomly distributed within the domain. The growth kinetics of the grain interface may be that of eit her a coupled regular or irregular eutectic (i.e. Jackson-Hunt type of model) or given by the diffusion of carbon through the austenite shel l for the case of nodular cast iron. The grains are allowed to move wi thin the liquid according to different convection models, such as no m ovement, random movement of the grains associated with turbulent effec ts, inhomogeneous fluid now velocity or sedimentation. In order to tra ce the position of the grain interface, each grain surface is subdivid ed into a given number of elementary surfaces. The grain impingement, the volume fraction of solid, the effective solid-liquid interface, th e average number of nearest neighbours, the grain size distribution an d stereological relationships may all be calculated by means of such m odels. The effect on the cooling curve may also be deduced.