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Characterization of Martensite Orientation Relationships in Steels and Ferrous Alloys from EBSD Data Using Bayesian Inference

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Abstract

Detailed analysis of the characteristics a martensite structure inherits from the parent austenite phase requires knowledge of the crystallographic orientation relationship between austenite and martensite, which varies with composition for steel alloys. The orientation relationship is typically observed to exhibit a significant degree of variability, such that measurements from each variant occupy a range of orientations within the transformed pole figure, complicating characterization of the orientation relationship. Here, we present a Bayesian methodology to measure the orientation relationship on martensite EBSD data from four different steels and a binary Fe-Ni alloy. The number of variants that must be exhibited for an accurate measurement as well as robustness to noisy data for this approach are investigated. The Bayesian approach is found to produce results which compare favorably to those from prior work while being more easily automatable.

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Notes

  1. Strictly speaking, this results in an ODF that is proportional to, but identically equal to, the ODF. The ODF is not formally a probability distribution as it is scaled by multiples of the uniform random distribution, making it easy to interpret relative probability in terms of “times random.” This results in a proportionality factor equal to the volume of the fundamental zone for cubic orientations. However, this can be neglected as it is a constant term which can be divided out and incorporated into the proportionality factor in Eq. [6].

References

  1. S. Morito and Y. Adachi and T. Ohba: Mater. Trans., 2009, vol. 50, pp. 1919–23.

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  3. S. Morito, H. Tanaka, R. Konishi and T. Maki: Acta Mater., 2003, vol. 51, pp. 1789-99.

    CAS  Google Scholar 

  4. V.A. Yardley, E.J. Payton, T. Matsuzaki, R. Sugiura, A.T. Yokobori Jr., S. Tsurekawa and Y. Hasegawa: Creep and Fracture of Engineering Materials and Structures, Proc. 12th Int. Conf. Creep and Fracture of Eng. Mater. and Struct. (JIMIS 11), held at Kyoto TERRSA, Kyoto, Japan, May 27–31, 2012, Edited by: K.Maruyama, F.Abe, M.Igarashi, K.Kishida, M.Suzuki, K.Yoshimi, The Jap. Ins. of Met, Sendai, 2012, paper C14.

  5. K. Kimura, N. Ohi, K. Shimazu and T. Matsuo: Scripta Mater., 1987, vol. 21, pp. 19-22.

    CAS  Google Scholar 

  6. V.A. Yardley, S. Fahimi and E.J. Payton: Mater. Sci. Technol, 2015, vol. 31, pp. 547-53.

    CAS  Google Scholar 

  7. S.H. Hong and J. Yu: Scripta Mater. 1989, vol. 23, pp. 1057-62.

    CAS  Google Scholar 

  8. S.K. Banerji, C.J. McMahon Jr. and H.C. Feng: Metall. Trans. A, 1978, vol. 9A, pp. 237-47.

    CAS  Google Scholar 

  9. R.M. Horn and R.O. Ritchie: Metall. Trans. A, 1978, vol. 9A, pp.1039-53.

    CAS  Google Scholar 

  10. G. Kurdjumow and G. Sachs: Über der Mechanismus der Stahlhärtung (On the Mechanism of Hardening of Steel). Z. Physik, 1930, vol. 64, pp. 325-43.

    Google Scholar 

  11. Z. Nishiyama: X-ray Investigation of the mechanism of the tranformation from face-centered cubic to body-centered cubic. Sci. Rep., 1934, vol. 23, pp. 637-64.

    CAS  Google Scholar 

  12. G. Wassermann: Über den Mechanismus der \(\alpha ->\gamma \) Umwandlung des Eisens (On the Mechanism of the \(\alpha -> \gamma \) Transformation of Iron). Mitteilungen aus dem Kaiser Wilhelm Institut für Eisenforschung, 1935, vol. 17, pp. 149–55.

  13. A. B. Greninger and A. R. Troiano: Metall. Trans., 1949, vol. 185, pp. 590-98.

    Google Scholar 

  14. G. Miyamoto, N. Iwata, N. Takayama and T. Furuhara: Acta Mater., 2010, vol. 58, pp.6393-6403.

    CAS  Google Scholar 

  15. E.J. Payton, A. Aghajani, F. Otto, G. Eggler and V.A. Yardley: Scripta Mater., 2012, vol. 66, pp. 1045-48.

    CAS  Google Scholar 

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

    Google Scholar 

  17. J.S. Bowles and J.K. Mackenzie: Acta. Metall. 1954, vol. 2, pp. 129-37.

    CAS  Google Scholar 

  18. J.K. Mackenzie and J.S. Bowles: Acta. Metall. 1954, vol. 2, pp. 138-47.

    CAS  Google Scholar 

  19. J.S. Bowles and J.K. Mackenzie: Acta. Metall. 1954, vol. 2, pp. 224-34.

    CAS  Google Scholar 

  20. J.K. Mackenzie and J.S. Bowles (1957) Acta. Metall. vol. 5, pp. 137–49.

    Google Scholar 

  21. J.S. Bowles and J.K. Mackenzie: Acta Metall. 1962, vol. 10, pp. 625-636.

    CAS  Google Scholar 

  22. Z. Nishiyama, M.E. Fine, and C.M. Wayman (1978) Martensitic Transformation, Cambridge. Academic Press

    Google Scholar 

  23. C.M. Wayman (1964) Introduction to the Crystallography of Martensitic Transformations. . London

    Google Scholar 

  24. H. Kitahara, R. Ueji, M. Ueda, N. Tsuji and Y. Minamino: Mater. Charact., 2005, vol. 54, pp. 378-386.

    CAS  Google Scholar 

  25. M. Nikravesh, M. Naderi, G.H. Akbari: Mater. Sci. Eng., 2012, vol. 540, pp. 24-29.

    CAS  Google Scholar 

  26. L. Malet and M.R. Barnett and P.J. Jacques and S. Godeta: Scripta Mater., 2009, vol. 61, pp. 520-23.

    CAS  Google Scholar 

  27. G. Miyamoto and N. Takayama and T. Furuhara: Scripta Mater., 2009, vol. 60, pp. 1113-16.

    CAS  Google Scholar 

  28. A.H. Pham and T. Ohba and S. Morito and T. Hayashi: Mater. Char., 2017, vol. 132, pp. 108-18.

    CAS  Google Scholar 

  29. V.A. Yardley and E.J. Payton: Mater. Sci. Technol., 2014, vol. 30, pp. 1125-30.

    CAS  Google Scholar 

  30. E. Gomes and L.A.I. Kerstens: IOP Conf. Series: Mater. Sci. Eng., 2015, vol. 82, pp. 1-4.

    Google Scholar 

  31. N.Y. Zolotorevsky and S.N. Panpurin and A.A. Zisman and S.N. Petrov: Mater. Char., 2015, vol. 107, pp. 278-82.

    CAS  Google Scholar 

  32. T. Nyyssönen and M. Isakov and P. Peura and V.T. Kuokkala: Met. Mater. Trans. A, 2016, vol. 47, pp. 2587-90.

    Google Scholar 

  33. F. Bachmann and R. Hielscher and H. Schaeben: J. Appl. Crystallogr., 2010, vol. 43, pp. 1338-55.

    CAS  Google Scholar 

  34. E.C. Bain: Trans. Am. Inst. Min. Met. Eng., 1924, vol. 70, pp. 25.

    Google Scholar 

  35. T. Bayes: Philos. Trans. R. Soc. Lond. 1764, vol. 53, pp. 370-428.

    Google Scholar 

  36. A.F. de Vos: Preprint, 2004.

  37. B.M. Hill: J. Am. Stat. Assoc., 1968, vol. 63, pp. 677-91.

    Google Scholar 

  38. B.A. Olshausen: Retrieved from: http://www.rctn.org/bruno/npb163/bayes.pdf, 2004.

  39. J.M. Bernardo and A.F.M Smith: Wiley, 2009.

  40. N. Metropolis and A.W. Rosenbluth and M.N. Rosenbluth and A.H. Teller and E. Teller: J. Chem. Phys., 1953, vol. 21, pp. 1087-92.

    CAS  Google Scholar 

  41. W.K. Hastings: Biometrika, 1970, vol. 57, pp. 97-109.

    Google Scholar 

  42. C.J. Geyer: Stat. Sci., 1992, vol. 7, pp. 473-511.

    Google Scholar 

  43. D. Gamerman and H. Lopes: Chapman and Hall/CRC, 2006.

  44. A.F. Brust and S.R. Niezgoda and V.A. Yardley and E.J. Payton: Met. Trans. Mater. A, 2018, vol. 50, pp. 837-55.

    Google Scholar 

  45. M. Natori, Y. Futamura, T. Tsuchiyama, S. Takaki: Scripta Mater., 2005, vol. 53, pp. 603–08.

    CAS  Google Scholar 

  46. A.F. Brust and T.J. Hobbs and E.J. Payton and S.R. Niezgoda: Microsc. Microanal., 2019, vol. 25, pp. 924-41.

    CAS  Google Scholar 

  47. R. Abrahams: Unit. Sts. Pat. Appl. Pub., US 2016/0369362 A1.

  48. V. Sinha, E.J. Payton, M. Gonzales, R. A. Abrahams, B.S. Song: Metallogr. Microstruct. Anal. 2017, vol. 6(6), pp. 610-18.

    CAS  Google Scholar 

  49. Y. He and Q. Rao and Y. Tan: J. Cent. South Univ. Technol., 1996, vol. 3, pp. 122-34.

    CAS  Google Scholar 

  50. G. Krauss: ASM International, 1990.

  51. S. Matsuda, T. Inoue, H. Mimura and Y. Okamura: Climax Molybdenum Development Company, Ltd., Japan, 1971, pp. 45–66.

  52. Z. Guo, C.S. Lee and J.W. Morris: Acta. Mater., 2004, vol. 52(19), pp. 5511-18.

    CAS  Google Scholar 

  53. S. Morito, H. Yoshida, T. Maki and X. Huang: J. Mat. Sci. Eng. A, 2006, 438-440, pp. 237-40.

    Google Scholar 

  54. M. Ueda and H. Yasuda and Y. Umakoshi: Sci. Technol. Adv. Mater., 2001, vol. 3, pp. 171-79.

    Google Scholar 

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Acknowledgments

AFB and SRN received support from the Air Force Office of Scientific Research (AFOSR) Summer Faculty Fellowship Program (SFFP) for the portion of this work performed at the Materials and Manufacturing Directorate of the Air Force Research Laboratory (AFRL/RX) and from the Defense Associated Graduate Student Innovators (DAGSI) for the portion of the work performed at The Ohio State University.

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Authors and Affiliations

  1. Department of Materials Science and Engineering, The Ohio State University, Columbus, OH, 43210, USA

    A. F. Brust & S. R. Niezgoda

  2. Air Force Research Laboratory, Materials and Manufacturing Directorate, Dayton, OH, 45433, USA

    E. J. Payton & V. Sinha

  3. UES, Inc., Dayton, OH, 45433, USA

    V. Sinha

  4. Impression Technologies, Ltd., Coventry, CV5 9PT, UK

    V. A. Yardley

  5. Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH, 43210, USA

    S. R. Niezgoda

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  1. A. F. Brust
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Correspondence to S. R. Niezgoda.

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Manuscript submitted April 14, 2019.

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Brust, A.F., Payton, E.J., Sinha, V. et al. Characterization of Martensite Orientation Relationships in Steels and Ferrous Alloys from EBSD Data Using Bayesian Inference. Metall Mater Trans A 51, 142–153 (2020). https://doi.org/10.1007/s11661-019-05514-4

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