Modeling of globular equiaxed solidification with a two-phase approach
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I. INTRODUCTION
MODELING of solidification and grain formation is a multiphase and multiscale problem. Solidification sequence, shrinkage cavity formation, macrostructure, and macrosegregation formations are governed by mass, momentum, heat, and species transport phenomena on the system scale, while modeling of the solidification morphology and microstructure requires understanding of nucleation, growth kinetics, and species redistribution on interfacial and even atomic scale. Great efforts and progress have been made to model these phenomena with multiscale coupling.[1,2] The most promising model was the multiphase volume-averaging approach developed by Beckermann’s group.[2–8] They treated the liquid and the solid as separated but highly coupled and interpenetrating continua, and they established and solved the transport equations for both liquid and solid simultaneously, thereby permitting a rigorous description of the liquid convection and the solid movement, mass transfer between solid and liquid (solidification and remelting), solute partitioning, and many other microscopic phenomena. However, this pioneering model involves many uncertainties,[9,10] for example, the lack of a realistic nucleation model, detailed volumetric heat and mass transfer coefficients (or thermal and solutal diffusion lengths), correct stereological formulations for interfacial area concentration, etc. A good deal of additional research is needed before the advantages of the model may be fully exploited.[2,6,11] Globular equiaxed solidification has an easy-to-define morphology. The solidified grains can be simplified as spheres. The grain size can be expressed with a volumeaveraged diameter, avoiding the uncertainties mentioned previously on modeling the interfacial area concentration and the complexity for handling of the interdendritic melt in dendritic solidification. Modeling globular equiaxed solidification also has wide engineering application prospects. Many high-performance materials require fine globular grains, e.g., the newly developed thixoforming process ANDREAS LUDWIG and MENGHUAI WU, Senior Scientists, are with the Foundry Institute of Aachen, Aachen University (RWTH), D-52072 Aachen, Germany. Contact e-mail: [email protected] Manuscript submitted March 5, 2002. METALLURGICAL AND MATERIALS TRANSACTIONS A
requires the prematerial being made with spherical grains.[12,13] This article presents a two-phase volume averaging model, which is particularly valid for globular solidification alloys.[14,15] The classical nucleation law and growth kinetics[1,16,17] are implemented in the model. We have simulated a benchmark ingot casting (A1-4 wt pct Cu) emphasizing microscopic modeling, i.e., the definition of different source, interaction, and exchange terms for the macroconservation equations. Although the theory and the solution procedure apply to the multiphase and multicomponent system in general, the macroconservation equations described subsequently specialize on two phases (liquid l and solid s) and two components (
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