ANALYTICAL AND NUMERICAL PREDICTIONS OF DENDRITIC GRAIN ENVELOPES

An analytical model is developed for the prediction of the shape of de ndritic grain envelopes during solidification of a metallic alloy in a Bridgman configuration (i.e. constant thermal gradient and cooling ra te). The assumptions built into the model allow a direct comparison of the results with those obtained from a previously developed cellular automaton-finite element (CAFE) model. After this comparison, the CAFE model is applied to the study of the extension of a single grain into an open region of liquid after passing a re-entrant corner. The simul ation results are compared with experimental observations made on a di rectionally solidified succinonitrile-acetone alloy. Good agreement is found for the shape of the grain envelopes when varying the orientati on of the primary dendrites with respect to the thermal gradient direc tion, the velocity of the isotherms or the thermal gradient.