Mathematical Analysis of the Solidification Behavior of Plain Steel Based on Solute- and Heat-Transfer Equations in the
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NUMERICAL methods are effectively used to simulate heat transfer phenomena during solidification processes. While these methods provide reliable surface temperatures (i.e., those calibrated with the measured values), inner temperatures, especially at the solidus point, are not generally confirmed with the actual (measured) values. The main reason for these problems lies in the difficulty[1] of achieving reliable results while measuring the solidus position during the casting process with an associated solidus temperature for general carbon steels. In addition, the fraction of solid in a solid–liquid coexisting zone (i.e., mushy zone) remains partly unknown. With respect to the liquidus temperature, while it is not also generally measured during the casting process, the problems are not serious because microsegregation at the dendrite tips is so small that super-cooling is limited only a few degrees. Therefore, the liquidus temperature for FeC plain steel can be estimated from the phase diagram or from measurements which are in reasonable agreement with each other. However, with regard to the solidus
TOSHIO FUJIMURA is with the Rinko.co., Iwamoto-chou 2-1-18, Chiyoda-Ku, Tokyo, 101-0032, Japan, Contact e-mail: tomohio1000@ gmail.com KUNIMASA TAKESHITA is with the Mechanical Engineering Course, Graduate School of Engineering, University of Fukui, 9-1 Bunkyo-3, Choume, Fukui, Fukui, 910-8507, Japan. RYOSUKE O. SUZUKI is with the Division of Materials Science and Engineering, Faculty of Engineering, Hokkaido University, Kita-13 Jou, Nishi-8, Choume, Kita-Ku, Sapporo, Hokkaido, 060-8628, Japan. Manuscript submitted May 9, 2017. METALLURGICAL AND MATERIALS TRANSACTIONS B
temperature of steel, discrepancies exist between estimates of solidus temperature based on the phase diagram and models accounting for microsegregation (i.e., 40 K discrepancies).[2–5] Recently, Gryc et al.[6] thermoanalytically measured the solidus temperature for various steel grades and reported significant discrepancies between the measurements and the values obtained from reported formulas (up to 42 K) or thermodynamic calculations (up to 50 K). These discrepancies could lead to considerable errors while estimating the position at which the shell develops with a target thickness. The lack of knowledge about the fraction of solid in the mushy zone has spurred the onset of numerous methods based on heat analysis: (A) methods[7–9] assuming a linear relationship between the solid fraction and the temperature (e.g., equivalent specific heat model); (B) methods[10,11] assuming the equilibrium lever rule, the Scheil equation, and back diffusion models such as the Brody–Flemings model[12] or the Clyne–Kurz[13] model; (C) methods[14] recovering the temperature with the latent heat release after solidification. However, these methods are not always consistent with the real solidification process. For example, (C) methods assume that the primary dendrites should grow after solidification. When the (B) methods are used along the dendrite axial direction, a flat bou
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