Direct Simulation of a Solidification Benchmark Experiment
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MACROSEGREGATION is defined by composition heterogeneities of alloying elements in cast parts, measured over a volume larger than the microstructure. It forms during solidification processing and remains a major concern for the casting industry. As reported in a dedicated review,[1] the origin of macrosegregation is multifold: (1) solute transport in the free liquid and in the mushy zone due to fluid flow, (2) grain transport because of gravity and convection, (3) liquid flow driven by shrinkage and deformation, and (4) diffusion of solute in the liquid and solid phases. Because these mechanisms most often overlap, great difficulty is found in assessing the magnitude of each mechanism on a measured macrosegregation map. The studies of macrosegregation were first conducted at the end of the 1960s and the beginning of the 1970s.[2–8] The role of the density variation between the solid and the liquid phases, known as shrinkage, was named inverse segregation. The effect of gravity-driven buoyancies was identified as the main cause for natural convection of the melt because of the presence of temperature and composition variations. Finally, the role of the deformation of the solid phase in the presence of a mushy zone was also presented. A discussion based TOMMY CAROZZANI, Ph.D. Student, CHARLES-ANDRE´ GANDIN, CNRS Research Fellow, HUGUES DIGONNET, Research Fellow, and MICHEL BELLET, Professor, are with the Mines ParisTech CEMEF UMR 7635, 06904 Sophia Antipolis, France. Contact e:mail: [email protected] KADER ZAIDAT, Research Fellow, and YVES FAUTRELLE, Professor, are with the Institut National Polytechnique de Grenoble SIMAP UMR 5266, 38402 Saint Martin d’He`res, France. Manuscript submitted May 20, 2012. Article published online October 25, 2012 METALLURGICAL AND MATERIALS TRANSACTIONS A
on mathematical modeling, which summarizes all mechanisms, was proposed by Lesoult et al.[9] The experiment developed by Hebditch and Hunt in Pb-Sn alloys serves as a reference for the current study.[8] It was presented in details in Hebditch’s Ph. D. work.[10] A similar experiment was recently redeveloped with enhanced data acquisition and metallurgical inspection.[11,12] The objective was to provide quantitative measurements for comparison with numerical simulation of solidification. An attempt was already done to simulate the experiment for a Sn-10 wt pct Pb alloy.[13] However, it suffered from its two-dimensional (2D) approximation as well as measurement uncertainties. In this contribution, we propose quantitative comparison of solidification simulations with a selected macrosegregation benchmark experiment in a Sn-3 wt pct Pb alloy.[12] The experimental procedure is first briefly presented. It is followed by a description of the model developed to solve volume average conservation equations, first without and then with the grain structure. The coupling methodology with thermodynamic data and solidification paths is also explained in detail. Finally, simulation results are shown and compared with the measurements of the macrose
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