Continuum model for predicting macrosegregation in dendritic alloys

“Macrosegregation” represents a class of defects in cast products of serious concern to both alloy producers and users. Many types of macrosegregation result from thermosolutal convection in the solid plus liquid and all-liquid regions of a solidifying alloy, and this has spurred modeling and simulations, which treat the solid plus liquid region (i.e., the mushy zone) as a porous medium of variable porosity and permeability. Simulations include scenarios in which the convection is strong enough to make channels in the mushy zone region, and these channels lead to localized segregates known as “freckles”. Using Pb-10 wt.% Sn as a model alloy, we simulated vertical solidification with various solidification rates. By sufficiently increasing the cooling rate at the bottom surface, convection can be suppressed enough to prevent the formation of freckles. The simulation is an example of relating microstructural metrics to a macroscopic property of the porous medium used in continuum theory. In this case, the property is the permeability, which is governed by two microstructural metrics: the volume fraction of liquid and a characteristic length in the dendritic microstructure. Permeability data, relevant to columnar dendritic solidification, are reviewed, and recommendations for future work on determining the permeability in terms of microstructural metrics are given.