Simulation of freckles during vertical solidification of binary alloys.

Abstract

The formation of channel segregates or freckles during vertical solidification of Pb-Sn alloys is simulated. The simulation is based on a mathematical model of dendritic solidification, in which the solid plus liquid zone is modeled as an anisotropic porous medium of variable porosity. The alloy solidifies from an initial melt and proceeds until the alloy is completely solidified, and the final macrosegregation can be predicted. The growth process is calculated by solving the fully coupled equations of momentum, energy and solute transport, as well as by maintaining the thermodynamic constraints dictated by the equilibrium phase diagram of the alloy. It is found that the thermosolutal convection that occurs during solidification, under certain growth conditions, can produce localized segregation zones, varying in shape from short streaks or pockets to long and narrow channels or freckles rich in solute. Several numerical examples show how these defects originate and why they subsist or die, depending on whether they face a favorable or adverse convection pattern ahead of the solidification front. The response, in both appearance and location, of channels to the variation of the cooling conditions is in good agreement with experiments, although the preference of channels to form on the outer surface of the casting, rather than in the interior, is greater than what is normally observed in Pb-Sn alloys. A mechanism that favors the formation of freckles within the body of the casting, because of defects in the dendritic mushy zone, is proposed and illustrated numerically.