The evolution of macrosegregation in statically cast binary ingots
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I.
INTRODUCTION
PRODUCT inhomogeneities which result from the uncontrolled macroscopic redistribution of constituents during solidification continue to plague engineers and scientists in disciplines such as casting, welding, and crystal growth. The displacement of segregated solid and liquid phases which accompanies solidification is the primary mechanism responsible for macrosegregation. While the floating or settling of unattached or detached solid grains can contribute to several types of observed segregation, liquid motion within the mushy region is considered the most important and general cause of macrosegregation, l This motion may be driven by thermal and solutal buoyancy forces, as well as by thermal contractions or shrinkage. Recognizing the significance of mushy region fluid motion, Flemings and c o w o r k e r s 2'3'4 developed-analytical expressions for macrosegregation due to the flow of solute-rich interdendritic fluids feeding solidification and thermal contractions in systems exhibiting planar isotherms. In these models, local temperature gradients and solidification rates were presumed known, and macrosegregation was based on assuming, without explicit hydrodynamic considerations, the nature of the interdendritic flow. Experiments designed to eliminate thermal and solutal advection were effected by inducing upward solidification in an AI-4.5 pct Cu solution, and, in several cases, good agreement was obtained between measured and predicted results. Hydrodynamic considerations of interdendritic flows influenced by buoyancy, as well as by thermal solidification contractions, were later reported by Mehrabian et al. 5 In this study, the mushy region was viewed as a porous medium, and velocities were determined from Darcy's law. Solutions were limited to unidirectional solidification and, as with previous efforts, temperature gradients and solidification rates were prescribed without explicit consideration of energy transport mechanisms. An extension of this work to cylindrical geometries was reported by Kou et al. 6 In each of the previous investigations, mushy region temperature fields were assumed or measured and used as inputs to the fluid flow calculations. The first attempt to predict transient mushy region temperature fields, and thereby couple the energy and momentum equations, was reported by Fujii et al. 7 In this study, planar solidus and liquidus interW.D. BENNON, on supported technical leave of absence at Purdue University, is Senior Engineer, Alcoa Technical Center, Alcoa Center, PA. F. P. INCROPERA is Professor, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907. Manuscript submitted April 13, 1987.
METALLURGICAL TRANSACTIONS B
faces were assumed and, since the mushy region was uncoupled from the solid and bulk liquid regions, an a p r i o r i knowledge of the transient progression of these interfaces was required. Ridder et al. 8 presented a two-dimensional model of energy and momentum transport in solidifying axisymmetric ingots. The model accounted for ad
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