Relationship between shrinkage-induced macrosegregation and the sump profile upon direct-chill casting

A simple analytical model for predicting shrinkage-induced macrosegregation during direct-chill casting is suggested. The model links the macrosegregation to the local slope of the coherency isotherm, the thickness of the mushy zone, and the solidification path of an alloy. The derived expression is applied to a direct-chill casting of an Al–Cu alloy and shows good semi-quantitative agreement with experimentally measured macrosegregation.