Multigrain and Multiphase Mathematical Model for Equiaxed Solidification

Abstract

A deterministic multigrain and multiphase model of equiaxed solidification of binary alloys is proposed, implemented, and analyzed. An important feature of the present model is the creation of classes of dendritic and globulitic grains according to their instantaneous sizes during solidification. Globulitic and dendritic grain growth, coarsening of secondary dendrite arms, distribution of nucleation undercoolings, and equiaxed eutectic growth are consistently included in the model equations. Important model assumptions are uniform temperature, negligible liquid convection, and negligible grain movement. Calculated cooling curves, solid fraction evolution, average grain sizes, and eutectic fractions agree well with predictions of previous models for dendritic and globulitic equiaxed grains. Predicted grain sizes decrease with an increase in cooling rate for an Al-2.12 pct Cu alloy and with an increase in Si concentration up to 3 pct for Al-Si alloys, agreeing quantitatively with experimental results. Simulations for an Al-7 pct Si alloy predict that an increase in grain size correlates with an increase in the magnitude of the recalescence observed in cooling curves. These calculations agree well with experimental results when the transition from a globulitic to a dendritic morphology occurs in the model before the minimum temperature of recalescence is reached.