Modeling of interdendritic strain and macrosegregation for dendritic solidification processes: Part I. Theory and experi
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I. INTRODUCTION
FOR almost 3 decades, metallurgists have modeled the various mechanisms of the macrosegregation phenomenon which are inherently associated with the majority of casting processes.[1–21] The displacement of segregated solid and liquid phases which accompanies the solidification process is the primary mechanism for macrosegregation. Floating or settling of free crystals can contribute to several types of observed segregation, based on their shape, location, or concentration.[2] However, the motion of interdendritic fluid during solidification is considered the most important and general cause of these heterogeneities.[1] This motion may be driven by thermal concentration or shrinkage, as well as by thermal and solutal buoyancy forces. Recognizing the significance of mushy-region fluid motion, Flemings and Nereo[3] developed analytical expressions for inverse segregation due to the flow of solute-rich interdendritic fluids feeding solidification contractions in systems exhibiting planar isotherms. This model has been applied theoretically and experimentally by Flemings et al.,[4,5,6] to describe quantitative effects on the macrosegregation of some solidification and mold-design variables. In these investigations,[3–6] local temperature gradients and solidification rates were presumed to be known, and macrosegregation was based on the assumption of negligible solute convection from interdendritic flow due to buoyancy. Mehrabian et al.[7] and Streat and Weinberg[8] refined Flemings’s model to consider the combined effect of the solidification M. EL-BEALY, formerly Research Associate, Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, is President, Materials Processing International, Toronto, ON, Canada M6J 3P3. Manuscript submitted June 9, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS B
shrinkage and gravity acting on a fluid of variable density on the macrosegregation under various assumptions concerning the interdendritic liquid. This basic approach, with physical and numerical improvements, was subsequently used to model and study macrosegregation in cylindrical remelted ingots[9–14] under thermal conditions in which the width of the mushy zone varies[12,13] and for multicomponent alloys.[12,14] Much attention has been given recently to the use of simulations of macrosegregation to improve the inner quality of continuously cast slabs and billets.[22,23] Rogberg[23] made a careful analysis of the variation in the carbon concentration from the surface and inwards in a continuously cast steel billet. He concluded that the concentration of carbon at the surface of the billets was always considerably higher than the calculated values obtained by using the theory of the inverse segregation. In addition, at distances closer to the surface (20 to 30 mm), the concentration fluctuates up and down with the distance from the surface as shown in Figure 1. Rogberg proposed that the solidified shell either contracts or expands due to the thermal strai
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