Thermomechanics of the cooling stage in casting processes: Three-dimensional finite element analysis and experimental va
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INTRODUCTION
THE complexity of phenomena encountered in casting processes makes numerical modeling a very useful tool to predict the final state of cast products and to optimize the process. Historically, the first attempts to model the solidification of industrial parts in casting processes were purely thermal.t~.2] As a matter of fact, it can be considered, as a first approximation, that the governing variable is the temperature, since much information can be deduced from the knowledge of the history of the temperature distribution in the part: simple calculations of microstructure evolution, empirical shrinkage criteria, or development of thermal stresses and deformations are based on thermal considerations. However, the reality departs significantly from this ideal situation for the following reasons. The cooling of a casting is not homogeneous: some regions of the part cool at different rates than others, leading to differential thermal strain and eventual air gap formation at the casting-mold interface. Also, those thermal strains are constrained by the presence of the mold, leading to the development of thermal stresses in the casting. For instance, direct investigations on heat transfer in the continuous casting process (Singh and Blazek~31and Samarasekera and Brimacombet41) showed the M. BELLET and F. BAY, Senior Scientists, and J.-L. CHENOT, Head, are with the CEMEF-Materials Forming Center, Ecole des Mines de Paris, 06904 Sophia Antipolis, Cedex, France. F. DECULTIEUX, Postdoctoral Student, formerly with the CEMEF-Materials Forming Center, Ecole des Mines de Paris, is with the Commissa.ri.'at~ l'Energie Atomique, Bruy~resle-Chatel, 91680 France. M. MENAI, Doctor, formerly with CEMEFMaterials Forming Center, Ecole des Mines de Paris, is with the Transvalor Company, 06904 Sophia Antipolis, Cedex, France. C. LEVAILLANT, Doctor, formerly with CEMEF-Materials Forming Center, Ecole des Mines de Paris, is Head, Materials Center, Ecole des Mines d'Albi-Carmaux, Albi, 81013 France. P. SCHMIDT, Doctor, formerly with the Royal Institute of Technology, is with Volvo Company, Gfteborg, 40508 Sweden. I.L. SVENSSON, Professor, is with the Royal Institute of Technology, 10044 Stockholm, Sweden. Manuscript submitted July 22, 1994. METALLURGICALAND MATERIALSTRANSACTIONS B
influence of the formation of an insulating air gap between the billet and the mold on the heat exchange. Moreover, numerous experimental works on instrumented laboratory tests pointed out the clear influence of the air gap width on the heat transfer at the interface between a solidified shell and a mold: let us quote, among others, Ho and Pehlke,tS] Nishida et r Harste et a L , m Schmidt and Svensson,[81 and Assar.tg] The influence of the normal stress (contact pressure) on the interfacial heat exchange has been much tess studied, but it can be expected that such a parameter should have a prominent influence, as shown by Peterson and Fletcher,tt~ who measured thermal contact conductance of anodized aluminum coatings. Thus, due to the inherent shri
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