Modeling of casting solidification stochastic or deterministic?

Solidification modeling has had a phenomenal impact on metalcasting in the last decade. Following its initial success in predicting the occurrence of porosity defects, it has grown to be an essential casting engineering tool. As more complex models have been developed (in response to the realization that simple heat how models were not adequate to serve the shrinkage probl em), they are being used to design more efficient gating and risering syste ms, which minimize the amount of metal poured to produce a good casting. Mo dels today include predictions of fluid how during mold filling, casting di stortion, mold-metal interface reactions and cast structure. Until a few years ago solidification simulation was based only on determini stic models. As prediction of microstructural evolution became a contempora ry problem, the limitation of deterministic models in predicting such featu res as dendrite coherency, columnar-to-equiaxed transition, dendrite fragme ntation and movement of dendrites by the liquid, became evident. Recently d eveloped stochastic models for solidification are capable of simulating and displaying the growth of columnar and equiaxed grains. However, the physic s of dendritic growth is rather approximate. The growth of dendrite arms an d their branching are ignored, and only a bulk representation of the grain growth is provided. A micro-scale approach for more accurate dendritic growth simulation in cas ting processes is presented in this paper. The model couples stochastic mod eling at a length scare of 10(-6) m, with deterministic modeling at a lengt h scale of 10(-4) m. A deterministic tip-velocity model is used to calculat e the advance of the dendrite tip. Arm thickening is also calculated with a deterministic law derived from the dendrite tip Velocity law and crystallo graphic considerations in combination with a deterministic coarsening model . However, the overall growth of dendrite arms is derived from probabilisti c calculations. Branching of dendrites arm is allowed to occur based on mor phologic instability. Thus the dendrite morphology, rather than the gain st ructure can be simulated. A discussion on the advantages and limitations of contemporary deterministi c and stochastic models is also included. (C) 1998 Canadian Institute of Mi ning and Metallurgy. Published by Elsevier Science Ltd. All rights reserved .