Modeling freckle formation in three dimensions during solidification of multicomponent alloys
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TRODUCTION
MATHEMATICAL modeling of alloy solidification with a ‘‘mushy zone’’ (solid plus liquid region) involves the simultaneous solution to the equations of momentum, energy, and mass transport. Analysis of transport phenomena during dendritic solidification is a prerequisite for understanding macrosegregation in cast products. One of the most severe forms of macrosegregation is manifested as defects known as ‘‘freckles,’’ which develop in directional solidification (DS) processes effected vertically. Vertical DS provides an effective means of controlling the grain shape, producing a columnar microstructure with all the grain boundaries parallel to the longitudinal direction of the casting. In conjunction with a grain selector or a preoriented seed at the bottom of the casting, directional solidification is used to make entire castings that are dendritic single crystals.[1] Unfortunately, freckles can form during DS that are sufficient cause to scrap these expensive castings. Freckles are observed as long and narrow trails, aligned roughly parallel to the direction of gravity, enriched in the normally segregating elements and depleted of the inversely segregating elements. Several experimental works with nonmetallic transparent systems have provided conclusive evidence that freckles are a direct consequence of upward flowing liquid plumes that emanate from channels within the mushy zone (e.g., Copley et al.[2] and Chen and Chen[3]). Observation of freckles in quenched Pb-Sn alloys (Tewari et al.[4] and S.D. FELICELLI, Research Scientist, is with Centro Ato´mic Bariloche, 8400 S.C. de Bariloche, Argentina. D.R. POIRIER, Professor, Department of Materials Science and Engineering, and J.C. HEINRICH, Professor, Department of Aerospace and Mechanical Engineering, are with the University of Arizona, Tucson, AZ 85721. Manuscript submitted August 1, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS B
Sarazin and Hellawell[5]) and Ni-base superalloys (Giamei and Kear[6]) suggests that freckles in metallic alloys also form by the same mechanism. The channels that form in the mushy zone during solidification and that lead to freckling in the solidified casting are a manifestation of localized remelting produced by thermosolutal convection. Because of the technological importance of the DS process, there have been many works on simulating transport phenomena in directionally solidified castings using the full set of conservation equations. In 1991, the authors simulated channels and freckles in directionally solidified Pb-Sn alloys,[7] and several numerical works dealing with binary alloys followed.[8,9,10] The prediction of macrosegregation in alloys with two or more solutes dates back to 1970, when Fujii et al.[11] considered a simplified model of convection in the mushy zone. Models for multicomponent alloys that include thermosolutal convection, both in the liquid and mushy zone, started appearing in 1995[12–15] and will probably be widely applied in the near future due to the fact that most alloys of practical interest c
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