Modeling of solute redistribution in the mushy zone during solidification of aluminum-copper alloys
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I.
INTRODUCTION
SOLIDIFICATION o f alloys is characterized by the existence o f a mushy z o n e , in w h i c h the solid phase and liquid phase coexist. It has been reported that transport phenomena (i.e., heat and mass transfer and fluid flow) in the mushy zone are the major cause for the formation o f casting defects, such as segregation, porosity, and hot tears, tL2] In particular, the formation o f macrosegregation (i.e., a large-scale nonuniformity in composition) in castings is understood to be caused by two mechanisms occurring in the mushy zone.Lm] The f i r s t mechanism corresponds to the floating or settling o f precipitated phases during solidification. The precipitated phases could be the equiaxed grains and/or broken dendrites in the mushy zone. The other mechanism is related to the flow o f soluterich o r solute-poor liquid in the m u s h y z o n e . The fluid flow can be caused by solidification contraction a n d / o r thermala n d / o r solutal gradients. A higher concentration o f solute is frequently found near the bottom surface o f a casting unidirectionally solidified from the bottom, which is commonly called inverse segregation. Inverse segregation is a kind o f macrosegregation that has been reported to be caused by solidification contraction. [1] In the past, many experimer, tal and theoretical studies on the formation o f inverse segregation have been reported. Scheilt3] developed an expression w h i c h can predict the "maximum segregation" at the chill surface as a function o f alloy composition in a unidirectionally solidified ingot. Kirkaldy and Youdelis t4] extended Scheil's equation to predict not only the maximum segregation but the positional variation o f the segregation. Their model, however, is limited to one dimension, and the Q.Z. DIAO, Graduate Student, and H.L. TSAI, Associate Professor of Mechanical Engineering, are with the Department of Mechanical and Aerospace Engineering and Engineering Mechanics, University of Missouri-Rolla, Rolla, MO 65401. Manuscripts submitted September 1 7 , 1992. METALLURGICAL TRANSACTIONS A
momentum, energy, and species equations are not completely coupled. Perhaps the first rigorous m o d e l to predict the formation o f macrosegregation was described in the pioneering articles by Flemings and co-workers.[5,6.7] The well known "local solute redistribution equation" was derived, w h i c h predicted successfully the formation o f inverse segregation, centerline segregation, and segregation resulting from changes o f cross section for unidirectional solidification o f AI-Cu alloys. However, the solute diffusion was neglected, and the thermal gradients and velocity distributions used in the equation were measured o r assumed. Kato and Cahoon t81 studied the inverse segregation in directionally solidified A1-Cu-Ti alloys with equiaxed grains based on the theory proposed by Kirkaldy and Youdelis and reported that the theoretical predictions were consistent with the experimental measurements. Ohnaka and Matsumoto t9,1°] have analyzed the unidirecti
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