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 macr osegregation result from thermosolutal convection in the solid plus li quid and all-liquid regions of a solidifying alloy, and this has spurr ed modeling and simulations, which treat the solid plus liquid region (i.e., the mushy zone) as a porous medium of variable porosity and per meability. Simulations include scenarios in which the convection is st rong enough to make channels in the mushy zone region, and these chann els lead to localized segregates known as ''freckles.'' Using Pb-10 wt . % Sn as a model alloy, we simulated vertical solidification with var ious 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 m icrostructural metrics to a macroscopic property of the porous medium used in continuum theory. In this case, the property is the permeabili ty, which is governed by two microstructural metrics: the volume fract ion of liquid and a characteristic length in the dendritic microstruct ure. 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.