Abstract
The current study analyzes the formation and evolution of microporosity during the solidification of anodic cooper. The aim of this study is to develop a thermofluid-formulation including microstructural evolution and to perform experiments to validate some measured variables with the respective numerical predictions. To this end, a set of experiments is carried out in copper testing primary and eutectic phase formation together with porosity evolution. To evaluate the formation of different microstructural phases and porosity, anodic copper (99.80 pct purity, approximately) is poured into different types of molds. The effect of heat extraction on the thermofluid-microstructural response is evaluated using graphite and steel molds to promote different cooling rates. The microporosity depends on the microstructural formation; hence the microstructure needs to be firstly described. The proposed microstructural model takes into account nucleation and grain growth laws based on thermal undercooling together with microstructural evolution. The primary phase evolution model is based on both solute diffusion at the grain scale and the dendrite tip growth kinetics, while the eutectic evolution is assumed proportional to the copper initial composition and eutectic undercooling. The microporosity model accounts for the partial pressures of gases and the solute distribution in the liquid and solid phases. The corresponding numerical formulation is solved in the framework of the finite element method. Finally, the computed temperature, solid, and liquid volumetric fractions, and pressure histories together with the final values for the radius, density, and pore volumetric fraction, are all compared and validated with the experimental measurements.
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References
R.A. Flinn: Fundamentals of Metal Casting, Addison-Wesley, Reading, 1963, p. 225.
E.G. King, A.D. Mah, and L.B. Pankratz: Thermodynamic Properties of Copper and Its Inorganic Compounds, INCRA Monograph II, Cambridge, 1973.
W.G. Davenport, M. King, M. Schlesinger, and A.K. Biswas, Extractive Metallurgy of Copper, 4th ed., Pergamon Press, Oxford, pp. 247–88, 2002.
D. Askeland: Ciencia e Ingeniería de los Materiales, 3rd ed., Ediciones Paraninfo, S.A., Madrid, pp. 574–624, 1999.
P.D. Lee, A. Chirazi, and D.J. See (2001) J. Light Met., 1, 1-15.
K. Kubo and R.D. Pehlke: Metall. Mater. Trans., 1985, vol. 16B, pp. 359–66.
M.C. Flemmings and T.S. Piwonka: AIME, Vol. 236, pp. 1157-65, 1966.
E. Niyama, T. Uchida, M. Morikawa and S. Saito: AFS Int. J. Cast. Met., 7(3), pp. 52-63, 1982.
P.D. Lee and J.D. Hunt (1997) Acta Mater., 45, 4155-69.
K.D. Li and E. Chang (2004) Acta Mater., 52, pp. 219-31.
R.C. Atwood and P.D. Lee: Acta Mater. Vol. 51, pp. 5447-66, 2003.
R.C. Atwood, S. Sridhar, W. Zhang and P.D. Lee (2000) Acta Mater., 48, pp. 405-17.
P.K. Sung, D.R. Poirier and S.D. Felicelli: Model. Simul. Mater. Sci. Eng., Vol. 10, pp. 551-68, 2002.
A.P. Boeira, I.L. Ferreira and A. García: Mater. Sci. Eng. A, Vol. 435-436, pp. 150-57, 2006.
V.R. Voller, Can. Metall. Q., Vol. 37, pp. 169–77, 1998.
Ch. Pequet, M. Gremaud and M. Rappaz: Metall. Mater. Trans. A, Vol. 33A, pp. 2095-106, 2002.
M.L.N.M. Melo, E.M.S. Rizzo and R.G. Santos: J. Mater. Sci. Vol. 40, pp. 1599–609, 2005.
J. Zhu, S. Cockcroft, and D. Maijer: Metall. Mater. Trans. A, Vol. 37A, pp. 1075-85, 2006.
L. Yao, S. Cockcroft, C. Reilly, and J.D. Zhu: Metall. Mater. Trans. A, Vol. 43A, pp. 1004-1016, 2012.
J. Guangrui, L. Yanxiang and L. Yuan: Metall. Mater. Trans. A, Vol. 41A, pp. 3405-411, 2010.
M. Flemmings: Solidification Processing, McGraw-Hill, New York, pp. 203–210, 214–262, 1974.
J.F. Wallace and R.J. Kissling: Foundry, Part 1, 1962, pp. 36–39; Part 2, 1963, pp. 64–68.
A.J. Phillips: Metall. Trans. Vol. 4, pp. 1935-43, 1973.
J.P. Neumann, T. Zhong and Y.A. Chang, Bull. Alloy Phase Diagr., 5(2), pp. 141-44, 1984.
O.M. Barabash and Yu. N. Koval, Crystal Structures of Metals and Alloys, Naukova Dumka, Kiev, pp. 211-12, 1986.
D.J. Chakrabarti and D.E. Laughlin, Bull. Alloy Phase Diagr. 4, pp. 254-70, 1983.
V. Voller, A. Brent and C. Prakash: Int. J. Heat Mass Transf., Vol. 32(9), pp. 1719-31, 1989.
M.B. Bever and C.F. Floe (1946) Trans. AIME, 166, 128-41.
C. J. Smithels: “Gases in Metals”, Chapman and Hall Ltd., London, 1937.
J. Romero, D. Celentano and M. Cruchaga (2011) Metall. Mater. Trans. B, Vol. 42B, pp. 612-31.
M. Cruchaga, D. Celentano and R. Lewis: Int. J. Numer. Methods Heat Fluid Flow, 14, pp. 167-86, 2004.
P.D. Lee, J.D. Hunt (2001) Acta Mater., 49, pp. 1383-98.
J. Dantzig: Int. J. Numer. Methods Eng., Vol. 28, pp. 1769-85, 1989.
A. Brent, V. Voller and K. Reid: Numer. Heat Transf., 13, pp. 297-318, 1988.
C. Beckermann and R. Viskanta: Int. J. Heat Mass Transf., 31(1), pp. 35-46, 1988.
W. Bennon and F. Incropera: Int. J. Heat Mass Transf., Vol. 30(10), pp. 2161-70, 1987.
D. Celentano and M. Cruchaga: Metall. Mater. Trans. B, Vol. 30B, pp. 731-44, 1999.
O. Kubaschewski, E.Ll. Evans, and C.B. Alcock: Metallurgical Thermochemistry, Pergamon Press, Oxford, 1967.
E. Kato, H. Veno and T. Orimo: Trans. JIM, Vol. 11, pp. 351-58, 1970.
N.P. Allen and T. Hewitt: J. Inst. Met., Vol. 51, pp. 257-76, 1933.
K. Sano and H. Sakao: Univ. Mem. Fac. Eng. Vol. 8, pp. 137-63, 1956.
R.P. Singh and D.R. Heldman (1984) Introduction to Food Engineering. Academic Press, San Diego, p. 305.
R.P. Singh and D.R. Heldman (1993) Introduction to Food Engineering. Academic Press, San Diego, p. 499.
D. Gaskell (1981) Introduction to Metallurgical Thermodynamics, 2nd Ed., McGraw-Hill, New York, pp. 113–24.
Goodfellow: Metals, Alloys, Compounds, Ceramics, Polymers & Composites, Catalogue-1993/1994.
E. Gebhardt and K. Kostlin (1952) Z. Metallkd. 43, p. 292.
ASM Ready Reference: Thermal Properties of Metals, Product code 06702G.
Graphite Electrodes Catalogue for Electrical Furnaces IGRI, Comercial Waldecker Limitada, Santiago.
R.W. Powell, C.Y. Ho, and P.E. Liley: Thermal Conductivity of Selected Materials, National Standard Reference Data Series, National Bureau of Standards—8, Purdue University, 1966.
Empresa Nacional de Minería ENAMI-CHILE: Especifications for copper anode quality produced in HVL Copper Smelter, 2010.
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The support provided by CONICYT and FONDECYT (Project No. 1095028) is gratefully acknowledged.
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Romero, J.S., Cruchaga, M.A. & Celentano, D.J. Evaluation of Formation and Evolution of Microporosity in Anodic Copper Solidification Processes: Simulation and Experimental Validation. Metall Mater Trans B 44, 624–652 (2013). https://doi.org/10.1007/s11663-013-9815-y
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DOI: https://doi.org/10.1007/s11663-013-9815-y