Incorporation of fragmentation into a volume average solidification model

In this study, a volume average solidification model was extended to consider fragmentation as a source of equiaxed crystals during mixed columnar-equiaxed solidification. The formulation suggested for fragmentation is based on two hypotheses: the solute-driven remelting is the dominant mechanism; and the transport of solute-enriched melt through an interdendritic flow in the columnar growth direction is favorable for solute-driven remelting and is the necessary condition for fragment transportation. Furthermore, a test case with Sn-10 wt%Pb melt solidifying vertically downward in a 2D domain (50 × 60 mm²) was calculated to demonstrate the model's features. Solidification started from the top boundary, and a columnar structure developed initially with its tip growing downward. Furthermore, thermo-solutal convection led to fragmentation in the mushy zone near the columnar tip front. The fragments transported out of the columnar region continued to grow and sink, and finally settled down and piled up in the bottom domain. The growing columnar structure from the top and pile-up of equiaxed crystals from the bottom finally led to a mixed columnar-equiaxed structure, in turn leading to a columnar-to-equiaxed transition (CET). A special macrosegregation pattern was also predicted, in which negative segregation occurred in both columnar and equiaxed regions and a relatively strong positive segregation occurred in the middle domain near the CET line. A parameter study was performed to verify the model capability, and the uncertainty of the model assumption and parameter was discussed. (paper)