A model for macrosegregation and its application to Al-Cu castings
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I.
BACKGROUND
SOLUTE redistribution, fluid flow, and transport of solid fragments occurring during solidification of casting alloys generate compositional nonuniformity at the macroscopic level. The resulting chemical anisotropy is called macrosegregation. It may result in significant variation of physical and mechanical properties throughout the entire casting, preventing the casting to perform as expected in specific applications. Complete elimination of macrosegregation is extremely difficult. To control the degree of macrosegregation, an in-depth understanding of the variables involved is necessary. Since the mechanism of formation of macrosegregation is very complicated, computer modeling can be successfully used to provide useful insights. The physics of macrosegregation formation can be summarized as follows. Segregation starts at the microscopic level as solidification proceeds. During solidification, solute is rejected (k0 < 1) or depleted (k0 > 1) continuously from the precipitated solid and the composition of the surrounding liquid is consequently affected. The redistribution of solute at the microscopic level is controlled by diffusion transport. Since the local solidification conditions determine the diffusion time, the degree of microsegregation depends on solidification, too. On the other hand, if significant concentration gradients are developed at the interface, the interdendritic liquid can be driven simultaneously by thermal
S. CHANG, Graduate Research Assistant, and D.M. STEFANESCU, University Research Professor and Director of the Solidification Laboratory, are with the Department of Metallurgical and Materials Engineering, The University of Alabama, Tuscaloosa, AL 35487. Manuscript submitted September 7, 1994. 2708--VOLUME 27A, SEPTEMBER 1996
and solutal buoyancy, as well as by solidification contraction. The induced flow will wash away the liquid next to the interface, resulting in segregation at the macroscopic level (macrosegregation). The study of the formation of macrosegregation was initiated in the late 1940s. Inverse segregation in nonferrous ingots was first treated in unidirectional solidification by Scheil.t~] An expression was developed to predict the maximum segregation at the chill surface as a function of alloy composition. Kirkaldy and Youdelist2] extended the Scheil model to predicted the variation of solute distribution along a bottom-chilled unidirectionally solidified casting, based on the difference between solid and liquid specific volumes during solidification. Flemings et a/. [3,4,5]proposed a model for macrosegregation based on liquid convection in the interdendritic region, driven only by solidification contraction. Mass transport in or out of the element by diffusion and solid movement were ignored, and thermal gradients and velocity distribution were measured or assumed. Mehrabian et al. [61proposed a model that considered both shrinkage and thermal buoyancy effects on liquid flow. The mushy region was treated as a porous medium. The liquid velocity in the inter
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