Abstract
This paper is a review of the marvelous development of mathematical and computer models that describe the fundamentals of microstructure evolution during the solidification of cast alloys, from the 1966 seminal paper by Oldfield, the first to attempt computational modeling of microstructure evolution during solidification, to the current prediction of mechanical properties. The latest analytical models for irregular eutectics such as cast iron, as well as numerical models with microstructure output, to include cellular automaton, will be discussed. Phase field models will not be discussed because of their inapplicability to casting solidification at the present time.
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