A mathematical model for surface segregation in aluminum direct chill casting
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I.
INTRODUCTION
THE surface quality of direct-chilled (DC) cast aluminium rolling sheet ingots is often reduced by a segregated layer of exudations (Figure 1). For example, on AA5182 ingots with a nominal magnesium concentration of 4.7 pct cast with the spout-and-pin regulating technology, the layer can be more than 1-mm thick and have an average magnesium concentration of up to about 10 pct.[1] The removal of the surface layer before further processing of the ingot entails high costs. The exudated layer is caused by interdendritic melt flow through a partly solidified (mushy) and remelting shell close to the mold. This remelting and the resulting metal flow are due to an air gap between the shell and the mold caused by the global solidification contraction of the ingot[2– 6] (Figure 2). The metallostatic head then forces interdendritic liquid through the mushy shell toward the ingot surface. In addition to exudation, the solidification shrinkage also leads to transport of interdendritic liquid.[7,8,9] While the latter flow phenomenon leads to positive macrosegregation (i.e., the solute concentration becomes larger than the nominal alloying concentration) close to the ingot surface, exudation results in negative segregation in the zone through which the interdendritic melt flow has taken place.[5,10] In the AA5182 example referred to previously, it should be noted that the negative macrosegregation in the solute-depleted zone caused by the exudation is much more severe than the positive contribution associated with the solidification shrinkage. On the other hand, when the exudation is very small, the solidification shrinkage becomes the leading mechanism behind the macrosegregation formation close to the surface.[11] This study is directed toward the mathematical modeling of the macrosegregation formation associated with exudaHAVARD J. THEVIK, formerly Research Scientist with SINTEF, Oslo, Norway, is now with Det Norske Veritas, N-1322, Hovik, Norway. ASBJØRN MO, Research Director, and TORGEIR RUSTEN, Senior Scientist, are with SINTEF, N-0314 Oslo, Norway. Manuscript submitted April 29, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS B
tion and solidification shrinkage. This segregation will be referred to as surface segregation. Former macrosegregation studies focusing on either exudation or solidification shrinkage can be found in References 5 and 10, and 8 and 9, respectively. Haug et al.[11] carried out a one-dimensional study in which both macrosegregation mechanisms were addressed, and a case study relevant for aluminum DC casting was incorporated. The purpose of the present article is to present an extension of the modeling concept in Reference 11 to a twodimensional situation relevant to the DC casting process. Section II describes briefly the physical basis of the model, the governing equations, and their numerical solution. In Section III, model predictions are compared to surface segregation measurements on full-scale castings, and weak points in the model are discussed. II.
MODEL DESCRIPTION
A half-ve
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