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Piecewise Model with Two Overlapped Stages for Structure Formation and Hardening upon High-Pressure Torsion

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Abstract

The evolution of micro/nanostructure in metals subjected to high-pressure torsion (HPT) still need to be explained theoretically although experimental datasets are growing persistently. A major problem associated with the understanding of HPT is the synergetic effect of several competing processes that alter the material structure. In this study, we propose a piecewise model to analyze material hardness and true strain data during the HPT procedure. The model is built on two postulates: (a) the hardness vs true strain dependence is a sum of two piecewise power-law functions (each of these functions describes an unique micro/nanostructural stage of the deformation) and (b) each piecewise function has free-fitting strain breakpoints, which limit the strain range in which one mechanism predominantly determines the micro/nanostructure. The model was applied to analyze the HPT data for pure polycrystalline iron, AISI 1020 steel, and AISI 13B20 steel to reveal the distinctive strain breakpoints and power-law exponents. In the result, we found that deduced power-law exponents for AISI 1020 and AISI 13B20 steels are remarkably close to each other within full strain range.

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References

  1. G. Langford and M. Cohen: Trans. ASM., 1969, vol. 62, pp. 623–38. .

    CAS  Google Scholar 

  2. A.P. Gusenkov, V.V. Zatsarinnyi, and R.M. Shneiderovich: Ind. Lab., 1971, vol. 37, pp. 596–601. .

    Google Scholar 

  3. A. Azushima, R. Kopp, A. Korhonen, D.Y. Yang, F. Micari, G.D. Lahoti, P. Groche, J. Yanagimoto, N. Tsuji, A. Rosochowski, and A. Yanagid: CIRP Ann. Manuf. Technol., 2008, vol. 57, pp. 716–35. .

    Article  Google Scholar 

  4. T.P. Krinitsina, E.I. Kuznetsova, Y.V. Blinova, and M.V. Degtyarev: J. Phys. Conf. Ser., 2019, vol. 1389, p. 12068. .

    Article  CAS  Google Scholar 

  5. J. Karch, R. Birringer, and H. Gleiter: Nature., 1987, vol. 330, pp. 556–8. .

    Article  CAS  Google Scholar 

  6. R.Z. Valiev, Y. Estrin, Z. Horita, T.G. Langdon, M.J. Zehetbauer, and Y.T. Zhu: Mater. Res. Lett., 2016, vol. 4, pp. 1–21. .

    Article  CAS  Google Scholar 

  7. K. Edalati and Z. Horita: Mater. Sci. Eng. A., 2016, vol. 652, pp. 325–52. .

    Article  CAS  Google Scholar 

  8. Y. Cao, S. Ni, X. Liao, M. Song, and Y. Zhu: Mater. Sci. Eng. R., 2018, vol. 133, pp. 1–59. .

    Article  Google Scholar 

  9. M. Kawasaki: J. Mater. Sci., 2014, vol. 49, pp. 18–34. .

    Article  CAS  Google Scholar 

  10. X.H. An, S.D. Wu, Z.G. Wang, and Z.F. Zhang: Prog. Mater. Sci., 2019, vol. 101, pp. 1–45. .

    Article  CAS  Google Scholar 

  11. R. Birringer, H. Gleiter, H.-P. Klein, and P. Marquardt: Phys. Lett. A., 1984, vol. 102, pp. 365–9. .

    Article  Google Scholar 

  12. W.A. Fietz and W.W. Webb: Phys. Rev., 1969, vol. 178, pp. 657–67. .

    Article  CAS  Google Scholar 

  13. E. Anderson, D.W.W. King, and J. Spreadborough: Trans. TMS-AIME., 1968, vol. 242, pp. 115–9. .

    CAS  Google Scholar 

  14. A.W. Thompson: Acta Metall., 1975, vol. 23, pp. 1337–42. .

    Article  CAS  Google Scholar 

  15. A.H. Chokshi, A. Rosen, J. Karch, and H. Gleiter: Scripta Metall., 1989, vol. 23, pp. 1679–84. .

    Article  CAS  Google Scholar 

  16. Z.C. Cordero, B.E. Knight, and C.A. Schuh: Int. Mater. Rev., 2016, vol. 61, pp. 495–512. .

    Article  CAS  Google Scholar 

  17. A.P. Zhilyaev and T.G. Langdon: Prog. Mater. Sci., 2008, vol. 53, pp. 893–979. .

    Article  CAS  Google Scholar 

  18. K. Edalati, K. Imamura, T. Kiss, and Z. Horita: Mater. Trans., 2012, vol. 53, pp. 123–7. .

    Article  CAS  Google Scholar 

  19. M.V. Degtyarev, T.I. Chashchukhina, L.M. Voronova, A.M. Patselov, and V.P. Pilyugin: Acta Mater., 2007, vol. 55, pp. 6039–50. .

    Article  CAS  Google Scholar 

  20. M.V. Degtyarev, T.I. Chashchukhina, L.M. Voronova, L.S. Davydova, and V.P. Pilyugin: Phys. Met. Metallogr., 2000, vol. 90, pp. 604–11. .

    Google Scholar 

  21. M.V. Degtyarev, L.M. Voronova, T.I. Chashchukhina, V.B. Vykhodets, L.S. Davydova, T.E. Kurennykh, A.M. Patselov, and V.P. Pilyugin: Phys. Met. Metallogr., 2003, vol. 96, pp. 642–50. .

    Google Scholar 

  22. R.Z. Valiev, Yu.V. Ivanisenko, E.F. Rauch, and B. Baudelet: Acta Mater., 1996, vol. 44, pp. 4705–12. .

    Article  CAS  Google Scholar 

  23. V.P. Pilyugin, L.M. Voronova, T.M. Gapontseva, T.I. Chashchukhina, and M.V. Degtyarev: Int. J. Refract. Met. Hard Mater., 2014, vol. 43, pp. 59–63. .

    Article  CAS  Google Scholar 

  24. T.M. Gapontseva, M.V. Degtyarev, V.P. Pilyugin, T.I. Chashchukhina, L.M. Voronova, and A.M. Patselov: Phys. Met. Metall., 2016, vol. 117, pp. 349–61. .

    Article  CAS  Google Scholar 

  25. L.M. Voronova, M.V. Degtyarev, T.I. Chashchukhina, Yu.G. Krasnoperova, and N.N. Resnina: Mater. Sci. Eng. A., 2015, vol. 635, pp. 155–64. .

    Article  CAS  Google Scholar 

  26. M.K. Riahi, I.A. Qattan, J. Hassan, and D. Homouz: AIP Adv., 2019, vol. 9, p. 055112. .

    Article  CAS  Google Scholar 

  27. K. Yamafuji and T. Kiss: Physica C., 1996, vol. 258, pp. 197–212. .

    Article  CAS  Google Scholar 

  28. J.W. Ekin: Supercond. Sci. Technol., 2010, vol. 23.

    Article  CAS  Google Scholar 

  29. J. Hänisch, K. Iida, F. Kurth, E. Reich, C. Tarantini, J. Jaroszynski, T. Förster, G. Fuchs, R. Hühne, V. Grinenko, L. Schultz, and B. Holzapfel: Sci. Rep., 2015, vol. 5, p. 17363. .

    Article  CAS  Google Scholar 

  30. P.P. Poole, H.A. Farach, R.J. Creswick, and R. Prozorov: Superconductivity. 2nd ed. Academic, London, 2007.

    Google Scholar 

  31. T. Baumgartner, M. Eisterer, H.W. Weber, R. Flükiger, C. Scheuerlein, and L. Bottura: Supercond. Sci. Technol., 2014, vol. 27.

    Article  CAS  Google Scholar 

  32. X. Li, J. Sun, P. Shahi, M. Gao, A.H. MacDonald, Y. Uwatoko, T. Xiang, J.B. Goodenough, J. Cheng, and J. Zhou: Proc. Natl Acad. Sci. USA., 2018, vol. 115, pp. 9935–40. .

    Article  CAS  Google Scholar 

  33. C. Cai, B. Holzapfel, J. Hänisch, L. Fernández, and L. Schultz: Phys. Rev. B., 2004, vol. 69, p. 104531. .

    Article  CAS  Google Scholar 

  34. L.N. Oveshnikov, A.B. Davydov, A.V. Suslov, A.I. Ril’, S.F. Marenkin, A.L. Vasiliev, and B.A. Aronzon: Sci. Rep., 2020, vol. 10, p. 4601. .

    Article  CAS  Google Scholar 

  35. Y.J. Kim, T.S. Shin, H.D. Choi, J.H. Kwon, Y.-C. Chung, and H.G. Yoon: Carbon., 2005, vol. 43, pp. 23–30. .

    Article  CAS  Google Scholar 

  36. Y. Zare and K.Y. Rhee: Results Phys., 2020, vol. 16, p. 102945. .

    Article  Google Scholar 

  37. Y. Tsuchiya, S. Miura, S. Awaji, Y. Ichino, K. Matsumoto, T. Izumi, K. Watanabe, and Y. Yoshida: Supercond. Sci. Technol., 2017, vol. 30, p. 104004. .

    Article  CAS  Google Scholar 

  38. K.A. Bukreeva, A.M. Iskandarov, S.V. Dmitriev, R.R. Mulyukov, and Y. Umeno: Phys. Solid State., 2014, vol. 56, pp. 423–8. .

    Article  CAS  Google Scholar 

  39. V.I. Trefilov, V.F. Moiseev, and E.P. Pechkovskii: Deformational Strengthening and Fracture of Metals. Naukova Dumka, Kiev, 1987. (in Russian).

    Google Scholar 

  40. Yu.V. Mil’man and V.I. Trefilov: Powder Metall. Met. Ceram., 2010, vol. 49, pp. 374–85. .

    Article  CAS  Google Scholar 

  41. D.M.M. Cardona, J. Wongsa-Ngam, H. Jimeneza, and T.G. Langdon: J. Mater. Res. Technol., 2014, vol. 7, pp. 355–60. .

    Google Scholar 

  42. Y.Z. Tian, S.D. Wu, Z.F. Zhang, R.B. Figueiredo, N. Gao, and T.G. Langdon: Acta Mater., 2011, vol. 59, pp. 2783–96. .

    Article  CAS  Google Scholar 

  43. O.A. Zambrano: J. Eng. Mater. Technol., 2016, vol. 138, p. 041010. .

    Article  CAS  Google Scholar 

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Acknowledgments

Authors thank Dr. T. M. Gapontseva (M. N. Mikheev Institute of Metal Physics) for fruitful discussion and valuable help, and Justin Brooks (Robinson Research Institute, Victoria University of Wellington) for proofreading the manuscript. Authors also thank financial support provided by the Ministry of Ministry of Science and Higher Education of the Russian Federation (theme “Pressure” No. AAAA-A18-118020190104-3).

Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflict of interest

The authors declare no conflict of interest.

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Authors and Affiliations

  1. M. N. Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, 18, S. Kovalevskoy St., Ekaterinburg, 620108, Russia

    E. F. Talantsev, M. V. Degtyarev, T. I. Chashchukhina, L. M. Voronova & V. P. Pilyugin

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  1. E. F. Talantsev
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  2. M. V. Degtyarev
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  3. T. I. Chashchukhina
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  4. L. M. Voronova
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  5. V. P. Pilyugin
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Correspondence to E. F. Talantsev.

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Manuscript submitted December 16, 2020; accepted July 13, 2021.

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Talantsev, E.F., Degtyarev, M.V., Chashchukhina, T.I. et al. Piecewise Model with Two Overlapped Stages for Structure Formation and Hardening upon High-Pressure Torsion. Metall Mater Trans A 52, 4510–4517 (2021). https://doi.org/10.1007/s11661-021-06403-5

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