On the effect of natural convection on the thermal-microstructural evolution in gray cast-iron solidification
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I. INTRODUCTION
THE modeling of casting processes is still nowadays a major area of research due to the different interdependent physical phenomena involved in it, e.g., fluid flow (mold filling and natural convection), heat transfer, phase-change microstructural evolution, shrinkage formation, and thermal residual stress development. Several multiphysics formulations have been proposed during the last decades for the analysis of different solidification processes involving a great variety of materials. Even the more recent works encompass a wide range of developments, e.g., macroscopic (i.e., only temperature dependent) phasechange thermally coupled fluid dynamics studies accounting for natural convection,[1–4] filling simulations,[5–8] models for microstructural formation during phase change,[9–15] solute conservation,[16,17,18] freckle development,[19] macrosegregation,[20,21,22] microsegregation,[23,24,25] hot-tearing prediction,[26,27] influence of the permeability on the grain refinement,[28] thermomechanical formulations to describe the casting and mold material responses during the solidification and cooling stages including the modeling of variable thermomechanical contact conditions caused by gap formation that takes place at the casting-mold interface,[29–32] plastic or viscoplastic effects together with microstructural phase-change strains in the constitutive laws,[33,34] simulations including fluid-thermomechanical interactions,[35] and the analysis of other specific casting processes.[36–39] In particular, the description of the microstructure evolution that occurs during the gray cast-iron solidification has also been an active area of research. In this context, a thermalmicrostructural model including primary-austenite (proeutectic austenite) formation together with nucleation and growth laws for the gray (graphite) and white (cementite) eutectics has been developed and used in the analysis of different problems.[9,40,41] Although this model can only provide averaged results for the microstructural variables involved in it, its predictions reasonably capture two important aspects DIEGO J. CELENTANO and MARCELA A. CRUCHAGA, Professors, are with the Departamento de Ingeniería Mecánica, and BERND J. SCHULZ, Professor, is with the Departamento de Ingeniería Metalúrgica, are with the Universidad de Santiago de Chile, Av. Bdo. O’Higgins 3363, Santiago, Chile. Contact e-mail: [email protected] Manuscript submitted December 9, 2004. METALLURGICAL AND MATERIALS TRANSACTIONS B
observed in the experiments: the strongly dependent kinetics on both cooling rate (i.e., higher cooling rates cause a greater number of nuclei with consequently smaller radii) and chemical composition of the alloy (e.g., greater silicon contents promote the formation of gray eutectic). Thus, the solidification path (which is given by the liquid fraction–temperature relationship) is, in general, not unique. Moreover, this model has been extended to account for natural convection in the liquid and mushy zones,[10] which led, in tu
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