Model of the effect of alloy content on shell strength during solidification of binary alloys

A thermomechanical model of unidirectional solidification of binary alloy systems is presented. The goal of the model is to begin to explore the effect of alloy content on the mechanical behavior of the solidifying shell by first examining the effect on lateral strength. The shell solidifies onto a semi-infinite mold proceeding behind a mushy zone that grows into an initially quiescent fluid Deformation of the shell is modeled with a thermolypoelastouiscous constitutive law that allows for examination of the idealized case of elastic deformation of the casting as well as the case where strain rate relaxation due to viscous creep predominates. Any effects of alloy content on the coefficients in the constitutive model are ignored so that the calculated effects on strength arise entirely from the size of the mushy zone. Aluminum-magnesium alloys solidifying onto a copper mold are considered as specific examples using a linearized portion of the Al-Mg phase diagram. The material with the smallest alloy content exhibits the greatest shell strength for the same cooling histories. That material with the widest freezing range has the lowest strength. For the elastic model, the average strength always increases with time, whereas for the elastoviscous case it can decrease with time to the point where the alloy content has virtually no effect on strength.