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Quantitative Analysis of Variant Selection for Displacive Transformations Under Stress

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Abstract

The existing variant selection models for displacive transformations are mostly qualitative in nature and attempt to predict the bulk texture using several fitting parameters. Many of these models use Kurdjumov-Sach (K-S) type orientation relationships (ORs) and ignore the phenomenological theory of martensite crystallography. So far there has not been any attempt to assess variant selection in the level of individual variants within one austenite grain. In this work, new kinds of experiments and innovative mathematical models have been developed to critically assess the variant selection phenomenon during bainite transformation under externally applied stress. Volume fractions of individual variants in a austenite grain have been calculated for the first time. Patel and Cohen’s theory on variant selection has been used in a new mathematical framework. Hitherto unknown aspects of variant selection have been found, which is exciting and provides new insight into the subject.

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References

  1. J.R. Patel and M. Cohen: Acta Metall., 1953, vol. 1, pp. 531–38.

    Article  CAS  Google Scholar 

  2. J.C. Bokros and E.R. Parker: Acta Metall., 1963, vol. 11, pp. 1291–1301.

    Article  CAS  Google Scholar 

  3. T.N. Durlu and J.W. Christian: Acta Metall., 1979, vol 11, pp. 663–66.

    Google Scholar 

  4. Y. Higo, F. Leeroisey, and T. Mori: Acta Metall., 1974, vol. 22, pp. 313–23.

    Article  CAS  Google Scholar 

  5. H. Miyaji, M. Nobuki, N. Sakuma, T. Mitsui, H. Nakajima, and E. Furubayashi: Proc. Int. Conf. on “Physical Metallurgy of Thermomechanical Processing of Steels and Other Metals”, Thermec, Tokyo, Japan, 1988, vol. 2, pp. 815–22.

  6. P. Bate and B. Hutchinson: Acta Mater., 2000, vol. 48, pp. 3183–92.

    Article  CAS  Google Scholar 

  7. V. Pancholi, M. Krishnan, I.S. Samajdar, V. Yadav, and N.B. Ballal: Acta Mater., 2008, vol. 56, pp. 2037–50.

    Article  CAS  Google Scholar 

  8. N.J. Wittridge, J.J. Jonas, and J.H. Root: Metall. Mater. Trans. A, 2001, vol. 32A, pp. 889–901.

    Article  CAS  Google Scholar 

  9. S. Kundu and H.K.D.H. Bhadeshia: Scripta Mater., 2006, vol. 55, pp. 779–81.

  10. S. Kundu and H.K.D.H. Bhadeshia: Scripta Mater., 2007, vol. 57, pp. 869–72.

  11. N. Gey, B. Petit, and M. Humbert: Metall. Mater. Trans. A, 2005, vol. 36A, pp. 3291–99.

    Article  CAS  Google Scholar 

  12. M.P. Butron-Guillen, C.S. Da Costa Viana, and J.J. Jonas: Metall. Mater. Trans. A, 1997, vol. 28A, pp. 1755–68.

    Article  CAS  Google Scholar 

  13. L. Kestens, R. Petrov, and Y. Houbeart: ISIJ Int., 2003, vol. 43, pp. 1444–52.

    Article  CAS  Google Scholar 

  14. L. Kestens, R. Docker, and R. Petrov: Mater. Sci. Forum, 2002, vols. 408–412, pp. 1173–78.

    Article  Google Scholar 

  15. S. Kundu: Scripta Mater., 2008, vol. 58, pp. 934–36.

  16. S. Kundu, K. Hase, and H.K.D.H. Bhadeshia: Proc. R. Soc. Lond. A, 2007, vol. 463, pp. 2309–28.

  17. S. Kundu: Ph.D. Thesis, University of Cambridge, Cambridge, United Kingdom, 2007.

  18. J.S. Bowles and J.K. MacKenzie: Acta Metall., 1954, vol. 2, pp. 129–37.

    Article  CAS  Google Scholar 

  19. J.K. MacKenzie and J.S. Bowles: Acta Metall., 1954, vol. 2, pp. 138–47.

    Article  CAS  Google Scholar 

  20. M.S. Wechsler, D.S. Lieberman, and T.A. Read: Trans. AIME, 1953, vol. 197, pp. 1503–15.

    Google Scholar 

  21. G. Kurdjumov and G. Sachs: Z. Physik., 1930, vol. 64, pp. 325–43.

    Article  Google Scholar 

  22. Z. Nishiyama: Technical Report No. 23, Science Report, Tohoku Imperial University, Tokyo, 1934, pp. 637–61.

  23. G. Wassermannn: Mitt. K.-With.-Inst. Eisenforsch, 1935, vol. 17, pp. 149–55.

    Google Scholar 

  24. G. Nolze: Cryst. Res. Technol., 2008, vol. 43, pp. 61–73.

    Article  CAS  Google Scholar 

  25. H. Kitahara, R. Ueji, N. Tsuji, and Y. Minamino: Acta Mater., 2006, vol. 54, pp. 1279–88.

    Article  CAS  Google Scholar 

  26. N. Stanford and P.S. Bate: Acta Mater., 2005, vol. 53, pp. 859–67.

    Article  CAS  Google Scholar 

  27. N. Stanford and P.S. Bate: Acta Mater., 2004, vol. 52, pp. 5215–24.

    Article  CAS  Google Scholar 

  28. M. Humbert and N. Gey: Acta Mater., 2003, vol. 51, pp. 4783–90.

    Article  CAS  Google Scholar 

  29. J. Romero, M. Preuss, and J.Q. Fonseca: Acta Mater., 2009, vol. 57, pp. 5501–11.

    Article  CAS  Google Scholar 

  30. N.R. Barton, D.J. Benson, and R. Becker: Model. Simul. Mater. Sci. Eng., 2005, vol. 13, pp. 707–31.

    Article  CAS  Google Scholar 

  31. K. Hase, C.G. Mateo, and H.K.D.H. Bhadeshia: Mater. Sci. Technol., 2004, vol. 20, pp. 1499–1505.

    Article  CAS  Google Scholar 

  32. J.H. Cho, A.D. Rollett, and K.H. Oh: Metall. Mater. Trans. A, 2005, vol. 36A, pp. 3427–38.

    Article  CAS  Google Scholar 

  33. H.K.D.H. Bhadeshia: Bainite in Steel, 2nd ed., Institute of Materials, London, 2001.

    Google Scholar 

  34. H.J. Stone, M.J. Peet, and H.K.D.H. Bhadeshia: Proc. Roy. Soc. London A, 2008, vol. 436, pp. 1009–27.

    Google Scholar 

  35. S.P. Timoshenko and J.N. Goodier: Theory of Elasticity, McGraw-Hill International Book Company, London, 1982.

    Google Scholar 

  36. H.K.D.H. Bhadeshia: Geometry of Crystals, 2nd ed., Institute of Materials, London, 2001.

    Google Scholar 

  37. Z. Guo, C.S. Lee, and J.W. Morris, Jr.: Acta Mater., 2004, vol. 52, pp. 5511–18.

    Article  CAS  Google Scholar 

  38. Y. He, S. Godet, P.J. Jacques, and J.J. Jonas: Acta Mater., 2006, vol. 54, pp. 1323–34.

  39. M.M. Desu and D. Raghavarao: Nonparametric Statistical Methods for Complete and Censored Data, Chapman & Hall/CRC Press, Boca Raton, FL, 2004.

    Google Scholar 

  40. J.W. Christian: Proc. Int. Conf. on Martensitic Transformations ICOMAT, 1979, pp. 220–34.

  41. A. Lambert-Perlade, A.F. Gourgues, and A. Pineau: Acta Mater., 2004, vol. 52, pp. 2337–48.

    Article  CAS  Google Scholar 

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Acknowledgements

The authors express their sincere gratitude to Professor H.K.D.H. Bhadeshia, Tata Chair Professor, University of Cambridge, for many helpful discussions. He has also kindly given us permission to use the super bainitic steel for this work. The authors would also like to thank Dr. Mathew Peet, University of Cambridge, and Ms. Ankita Mangal, Tata Steel, for their help with this work.

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Correspondence to Saurabh Kundu.

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Manuscript submitted January 22, 2011.

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Kundu, S., Verma, A.K. & Sharma, V. Quantitative Analysis of Variant Selection for Displacive Transformations Under Stress. Metall Mater Trans A 43, 2552–2565 (2012). https://doi.org/10.1007/s11661-011-0971-x

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