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Quantitative Characterization of Solidification Structure in Different Sections for Calculating the Permeability in Actual High-Carbon Steel Billet

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Abstract

Macrosegregation, a critical defect in metallic alloys, is mainly caused by the flow of solute-rich liquid phase in interdendritic channels. Liquid flow in the interdendritic zone can be evaluated by Darcy’s law when permeability is known. However, there is almost no effective way to calculate the permeability of actual macrostructure in industrial production. In the present work, a method for evaluating the permeability based on the actual macrostructure of continuous casting billet is proposed. First, dendrite arm spacing (DAS) of solidification structure in different sections was measured, and fractal dimension was introduced to evaluate the complexity of the dendritic outline. Then the permeability was calculated using DAS, fractal dimension (D), and segregation area ratio (Rseg). By comparing with the Santos–Melo model and solidification theory, the method proposed in the present work for calculating permeability was found to be effective. The value of permeability shows that the flow resistance in the mushy zone of a metallic alloy is different in each of the three spatial dimensions. The present results also show that flow velocity and direction of liquid in the mushy zone can be predicted using permeability of the actual metal. This may provide a new approach for delicately controlling the segregation defect.

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References

  1. D.Z. Li, X.Q. Chen, P.X. Fu, X.P. Ma, H.W. Liu, Y. Chen, Y.F. Cao, Y.K. Luan and Y.Y. Li: Nat. Commun., 2014, vol. 5, pp. 5572-5578.

    Article  CAS  Google Scholar 

  2. H.B. Chen, M.J. Long, D.F. Chen, T. Liu and H.M. Duan: Int. J. Heat Mass Transf., 2018, vol. 126, pp. 843-853.

    Article  CAS  Google Scholar 

  3. D.B. Jiang, W.L. Wang, S. Luo, C. Ji and M.Y. Zhu: Int. J. Heat Mass Transf., 2018, vol. 122, pp. 315-323.

    Article  Google Scholar 

  4. M.C. Flemings: ISIJ Int., 2000, vol. 40, pp. 838-841.

    Article  Google Scholar 

  5. H.Q. Hu: Fundamentals of metallic solidification, 2nd ed., Machinery Industry Press, Beijing, 2010, pp. 210-212.

    Google Scholar 

  6. T.S. Piwonka and M.C. Flemings: Trans. Metall. Soc. AIME, 1996, vol. 236, pp. 1157-1165.

    Google Scholar 

  7. N. Streat and F. Weinberg: Metall. Trans. B, 1976, vol. 7, pp. 417-423.

    Article  CAS  Google Scholar 

  8. R. Nasser-Rafi, R. Deshmukh and D.R. Poirier: Metall. Trans. A, 1985, vol. 16, pp. 2263-2271.

    Article  CAS  Google Scholar 

  9. D. Apelian, M.C. Flemings and R. Mehrabian: Metall. Trans., 1974, vol. 5, pp. 2533-2537.

    Article  CAS  Google Scholar 

  10. Q. Han, A.J. Duncan and S. Viswanathan: Metall. Mater. Trans. B, 2003, vol. 34B, pp. 25-28.

    Article  CAS  Google Scholar 

  11. R.G. Santos and M.L.N.M. Melo: Mater. Sci. Eng. A, 2005, vol. 391, pp. 151-158.

    Article  Google Scholar 

  12. Y. Natsume, D. Takahashi, K. Kawashima, E. Tanigawa and K. Ohsasa: ISIJ Int., 2014, vol. 54, pp. 366-373.

    Article  CAS  Google Scholar 

  13. S.G.R. Brown, J.A. Spittle, D.J. Jarvis and R. Walden-Bevan: Acta Mater., 2002, vol. 50, pp. 1559-1569.

    Article  CAS  Google Scholar 

  14. E. Khajeh and D.M. Maijer: Acta Mater., 2011, vol. 59, pp. 4511-4524.

    Article  CAS  Google Scholar 

  15. S. Ganesan, C.L. Chan and D.R. Poirier: Mater. Sci. Eng. A, 2015, vol. 151, pp. 97-105.

    Article  Google Scholar 

  16. J. Madison, J. Spowart, D. Rowenhorst, L.K. Aagesen, K. Thornton and T.M. Pollock: Acta Mater., 2010, vol. 58, pp. 2864-2875.

    Article  CAS  Google Scholar 

  17. H. Ishida, Y. Natsume and K. Ohsasa: ISIJ Int., 2009, vol. 49, pp. 37-43.

    Article  CAS  Google Scholar 

  18. J.H. Cao, Z.B Hou, D.W. Guo, Z.A. Guo and P. Tang: J. Mater. Sci., 2019, vol. 54, pp. 12851-12862.

    Article  CAS  Google Scholar 

  19. A.L. Genau, A.C. Freedman and L. Ratke: J. Cryst. Growth, 2013, vol. 363, pp. 49-54.

    Article  CAS  Google Scholar 

  20. C. Cicutti and R. Boeri: Scr. Mater., 2001, vol. 45, pp. 1455-1460.

    Article  CAS  Google Scholar 

  21. A.F. Ferreira, E.G.D. Melo and L.D.O. Ferreira: Steel Res. Int., 2015, vol. 86, pp. 58-64.

    Article  CAS  Google Scholar 

  22. Y.M. Won and B.G. Thomas: Metall. Mater. Trans. A, 2001, vol. 32, pp. 1755-1767.

    Article  CAS  Google Scholar 

  23. S. Chakraborty and P. Dutta: Mater. Sci. Technol., 2001, vol. 17, pp. 1531-1538.

    Article  CAS  Google Scholar 

  24. M.A. Tschopp, J.D. Miller, A.L. Oppedal and K.N. Solanki: Metall. Mater. Trans. A, 2013, vol. 45, pp. 426-437.

    Google Scholar 

  25. Y.M. Wang, S.M. Li, H. Zhong and H.Z. Fu: Acta Metall. Sin., 2015, vol. 51, pp. 1038-1048.

    CAS  Google Scholar 

  26. D.R. Poirier: Metall. Trans. B, 2013, vol. 18B, pp. 245-255.

    Google Scholar 

  27. S.K. Choudhary, S. Ganguly, A. Sengupta and V. Sharma: J. Mater. Process. Technol., 2017, vol. 243, pp. 312-321.

    Article  CAS  Google Scholar 

  28. B.B. Mandelbrot: The Fractal Geometry of Nature. Freeman Press, New York, pp. 131-135 (1982)

    Google Scholar 

  29. B.B. Mandelbrot: Science, 1967, vol. 155, pp. 636-638.

    Article  Google Scholar 

  30. M. Zaiser, K. Bay and P. HaHner: Acta Mater., 1999, vol. 47, pp. 2463-2476.

    Article  CAS  Google Scholar 

  31. Q. Chang, D.L. Chen, H.Q. Ru, X.Y. Yue, L. Yu and C.P. Zhang: J. Mater. Sci., 2011, vol. 46, pp. 6118-6123.

    Article  CAS  Google Scholar 

  32. S. Kobayashi, T. Maruyama, S. Tsurekawa and T. Watanabe: Acta Mater., 2012, vol. 60, pp. 6200-6212.

    Article  CAS  Google Scholar 

  33. V.V. Usov, M.D. Rabkona, N.M. Shkatulyak and T.S. Cherneva: Mater. Sci., 2015, vol. 50, pp. 612-620.

    Article  Google Scholar 

  34. B. Christian, M.D. Jules, C.E. Krill and R. Birringer: Sci Rep, 2018, vol. 8, pp. 1592-1597.

    Article  Google Scholar 

  35. Q.Y. Long, Y.H. Wen, Z. Zhu, X.M. Zhang, Z.Q. Mu and C.W. Lung: Philos. Mag. A, 1993, vol. 68, pp. 885-890.

    Article  CAS  Google Scholar 

  36. Z.B. Hou, J.H. Cao, Y. Chang, W. Wang and H Chen: Acta Metall. Sin., 2017, vol. 53, pp. 769-777.

    CAS  Google Scholar 

  37. Z.B. Hou, D.W. Guo, J.H. Cao and Y. Chang: J. Alloy. Compd., 2018, vol. 762, pp. 508-519.

    Article  CAS  Google Scholar 

  38. T. Takaki, S. Sakane, M. Ohno, Y. Shibuta and T. Aoki: Acta Mater., 2019, vol. 164, pp. 237-249.

    Article  CAS  Google Scholar 

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Acknowledgments

The authors are very grateful for support from United Funds between National Natural Science Foundation and Baowu Steel Group Corporation Limited from China (Grant No. U1860101).

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Authors and Affiliations

  1. College of Materials Science and Engineering, Chongqing University, Chongqing, 400044, P.R. China

    Jianghai Cao, Zibing Hou, Qian Liu, Zhongao Guo & Dongwei Guo

  2. Chongqing Key Laboratory of Vanadium-Titanium Metallurgy and Advanced Materials, Chongqing University, Chongqing, 400044, P.R. China

    Jianghai Cao, Zibing Hou, Qian Liu, Zhongao Guo & Dongwei Guo

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  1. Jianghai Cao
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  2. Zibing Hou
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Correspondence to Zibing Hou.

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Manuscript submitted July 9, 2020, accepted January 15, 2021.

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Cao, J., Hou, Z., Liu, Q. et al. Quantitative Characterization of Solidification Structure in Different Sections for Calculating the Permeability in Actual High-Carbon Steel Billet. Metall Mater Trans B 52, 1132–1141 (2021). https://doi.org/10.1007/s11663-021-02087-9

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