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Permanent Strength of Metals: A Case Study on FCC Metals Processed by Severe Plastic Deformation

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Abstract

The present study emphasizes the importance of the direct evaluation of the athermal strength of structural materials, which is the time-independent material strength that corresponds to the basic capability to bear stresses caused by external forces permanently, and we call it the “permanent strength.” The present experimental study, taking FCC metals processed by severe plastic deformation (SPD), shows that the permanent strength is unexpectedly much lower than the flow stress temporally observed in a standard tensile test. More than half of the observed flow stress corresponds to the time-dependent thermal strength. Furthermore, the grain refinement associated with SPD processing never contributes to the augmentation of the permanent strength, i.e., the Hall–Petch relation is not applicable to as-SPDed materials. In contrast to aluminum, for copper, the low permanent strength produced by SPD is never revived by subsequent annealing. These observations elicit the general view that we should know the permanent strength of structural materials, not limited to SPD-processed metals, because we must confirm that the permanent strength is higher than the allowable stress in structural design to ensure the use of the structure within its elastic range in normal environments.

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taken from Koizumi and Kuroda[12] and Koizumi et al.[24]

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Notes

  1. Raw experimental data published in Koizumi et al.[24] and new additional data have been gathered in Figure 8(b). In the present data analysis, all \({\sigma }_{\text{i}}\) values were recalculated using Eq. [3].

References

  1. Seeger, J. Diehl, S. Mader, and H. Rebstock: Philos. Mag., 1957, vol. 2, pp. 323–50.

    Article  CAS  Google Scholar 

  2. K. Ogawa and T. Nojima: J. Soc. Mater. Sci. Jpn., 1988, vol. 37, pp. 1171–77.

    Article  CAS  Google Scholar 

  3. K. Ogawa, H. Kobayashi, K. Yoshida, and F. Sugiyama: Zairyo., 1994, vol. 43, pp. 304–09.

    Article  CAS  Google Scholar 

  4. J.-H. Park, Y. Tomota, S. Takagi, S. Ishikawa, and T. Shimizu: Tetsu-to-Hagane., 2001, vol. 87, pp. 657–64.

    Article  CAS  Google Scholar 

  5. N. Tsuchida, Y. Tomota, H. Moriya, O. Umezawa, and K. Nagai: Acta Mater., 2001, vol. 49, pp. 3029–38.

    Article  CAS  Google Scholar 

  6. N. Tsuchida, Y. Izaki, T. Tanaka, and K. Fukaura: Tetsu-to-Hagané., 2011, vol. 97, pp. 201–08.

    Article  CAS  Google Scholar 

  7. N. Tsuji, Y. Ito, Y. Saito, and Y. Minamino: Scripta Mater., 2002, vol. 47, pp. 893–99.

    Article  CAS  Google Scholar 

  8. X. Huang, N. Hansen, and N. Tsuji: Science., 2006, vol. 312, pp. 249–51.

    Article  CAS  Google Scholar 

  9. N. Kamikawa, X. Huang, N. Tsuji, and N. Hansen: Acta Mater., 2009, vol. 57, pp. 4198–208.

    Article  CAS  Google Scholar 

  10. S. Gao, M. Chen, S. Chen, N. Kamikawa, A. Shibata, and N. Tsuji: Mater. Trans., 2014, vol. 55, pp. 73–77.

    Article  CAS  Google Scholar 

  11. S. Goel, Y. Wang, Y.M. Zhu, Y. Liu, and J.T. Wang: Int. J. Plast., 2021, vol. 138, p. 102939.

    Article  CAS  Google Scholar 

  12. T. Koizumi and M. Kuroda: Mater. Sci. Eng. A., 2018, vol. 710, pp. 300–08.

    Article  CAS  Google Scholar 

  13. J. Gubicza, N.Q. Chinh, G. Krállics, I. Schiller, and T. Ungár: Curr. Appl. Phys., 2006, vol. 6, pp. 194–99.

    Article  Google Scholar 

  14. J. Čížek, M. Janeček, T. Krajňák, J. Stráská, P. Hruška, J. Gubicza, and H. Kim: Acta Mater., 2016, vol. 105, pp. 258–72.

    Article  CAS  Google Scholar 

  15. T. Krajňák, P. Minárik, J. Gubicza, K. Máthis, R. Kužel, and M. Janeček: Mater. Charact., 2017, vol. 123, pp. 282–93.

    Article  CAS  Google Scholar 

  16. J. May, H.W. Höppel, and M. Göken: Scripta Mater., 2005, vol. 53, pp. 189–94.

    Article  CAS  Google Scholar 

  17. A.S. Khan and C.S. Meredith: Int. J. Plast., 2010, vol. 26, pp. 189–203.

    Article  CAS  Google Scholar 

  18. C.S. Meredith and A.S. Khan: Int. J. Plast., 2012, vol. 30–31, pp. 202–17.

    Article  CAS  Google Scholar 

  19. M.S. Mohebbi, A. Akbarzadeh, B.H. Kim, and S.K. Kim: Metall. Mater. Trans. A, 2014, vol. 45A, pp. 5442–50.

    Article  CAS  Google Scholar 

  20. C.S. Meredith and A.S. Khan: J. Mater. Proc. Tech., 2015, vol. 219, pp. 257–70.

    Article  CAS  Google Scholar 

  21. D. Rodríguez-Galán, I. Sabirov, and J. Segurado: Int. J. Plast., 2015, vol. 70, pp. 191–205.

    Article  CAS  Google Scholar 

  22. J. Xu, J. Li, L. Shi, D. Shan, and B. Guo: Mater. Charact., 2015, vol. 109, pp. 181–88.

    Article  CAS  Google Scholar 

  23. F. Kabirian, A.S. Khan, and T. Gnäupel-Herlod: J. Alloys Compd., 2016, vol. 673, pp. 327–35.

    Article  CAS  Google Scholar 

  24. T. Koizumi, A. Kurumatani, and M. Kuroda: Sci. Rep., 2020, vol. 10, p. 14090.

    Article  CAS  Google Scholar 

  25. F.R. Larson and J. Miller: Trans. ASME., 1952, vol. 74, pp. 765–71.

    Google Scholar 

  26. V.M. Segal: Mater. Sci. Eng. A, 1995, vol. 197, pp. 157–64.

    Article  Google Scholar 

  27. Y. Iwahashi, Z. Horita, M. Nemoto, J. Wang, and T.G. Langdon: Scripta Mater., 1996, vol. 35, pp. 143–46.

    Article  CAS  Google Scholar 

  28. Y. Iwahashi, Z. Horita, M. Nemoto, and T.G. Langdon: Acta Mater., 1998, vol. 46, pp. 3317–31.

    Article  CAS  Google Scholar 

  29. N. Kamikawa, N. Tsuji, X. Huang, and N. Hansen: Acta Mater., 2006, vol. 54, pp. 3055–66.

    Article  CAS  Google Scholar 

  30. A. Zhilyaev, B.-K. Kim, J. Szpunar, M. Baró, and T.G. Langdon: Mater. Sci. Eng. A, 2005, vol. 391, pp. 377–89.

    Article  CAS  Google Scholar 

  31. E.A. El-Danaf: Mater. Sci. Eng. A, 2008, vol. 487, pp. 189–200.

    Article  CAS  Google Scholar 

  32. G. Williamson and W. Hall: Acta Metall., 1953, vol. 1, pp. 22–31.

    Article  CAS  Google Scholar 

  33. S. Takaki, T. Masumura, and T. Tsuchiyama: ISIJ Int., 2018, vol. 58, pp. 2354–56.

    Article  CAS  Google Scholar 

  34. G. Williamson and R. Smallman: Phil. Mag., 1956, vol. 1, pp. 34–46.

    Article  CAS  Google Scholar 

  35. K. Levenberg: Q. Appl. Math., 1944, vol. 2, pp. 164–68.

    Article  Google Scholar 

  36. D.W. Marquardt: J. Soc. Ind. Appl. Math., 1963, vol. 11, pp. 431–41.

    Article  Google Scholar 

  37. M.A. Muñoz-Morris, C. Garcia Oca, and D.G. Morris: Scripta Mater., 2003, vol. 48, pp. 213–18.

    Article  Google Scholar 

  38. Watanabe, H. Hiraide, Z. Zhang, and R. Monzen: J. Soc. Mater. Sci. Jpn., 2005, vol. 54, pp. 717–23.

    Article  CAS  Google Scholar 

  39. E. Sato, T. Yamada, H. Tanaka, and I. Jimbo: Mater. Trans., 2006, vol. 47, pp. 1121–26.

    Article  CAS  Google Scholar 

  40. F. Nishijima, K. Nomura, C. Watanabe, and R. Monzen: J. Jpn. Inst. Met. Mater., 2008, vol. 72, pp. 427–32.

    Article  CAS  Google Scholar 

  41. R. Monzen and C. Watanabe: Mater. Sci. Eng. A., 2008, vol. 483–484, pp. 117–19.

    Article  CAS  Google Scholar 

  42. K. Hariharan, P. Dubey, and J. Jain: Mater. Sci. Eng. A., 2016, vol. 673, pp. 250–56.

    Article  CAS  Google Scholar 

  43. Y. Zhao, J. Bingert, Y. Zhu, X. Liao, R. Valiev, Z. Horita, T. Langdon, Y. Zhou, and E. Lavernia: Appl. Phys. Lett., 2008, vol. 92, p. 081903.

    Article  CAS  Google Scholar 

  44. R.Z. Valiev, M.Y. Murashkin, A. Kilmametov, B. Straumal, N.Q. Chinh, and T.G. Langdon: J. Mater. Sci., 2010, vol. 45, pp. 4718–24.

    Article  CAS  Google Scholar 

  45. A.V. Polyakov, I.P. Semenova, R.Z. Valiev, Y. Huang, and T.G. Langdon: MRS Commun., 2013, vol. 3, pp. 249–53.

    Article  CAS  Google Scholar 

  46. I.-C. Choi, Y.-J. Kim, M.-Y. Seok, B.-G. Yoo, J.-Y. Kim, Y. Wang, and J.-I. Jang: Int. J. Plast., 2013, vol. 41, pp. 53–64.

    Article  CAS  Google Scholar 

  47. L. Mishnaevsky and E. Levashov: Comput. Mater. Sci., 2015, vol. 96, pp. 365–73.

    Article  CAS  Google Scholar 

  48. P. Sun, E. Cerreta, G. Gray, and J. Bingert: Metall. Mater. Trans. A., 2006, vol. 37A, pp. 2983–94.

    Article  CAS  Google Scholar 

  49. L. Su, C. Lu, A. Tieu, L. He, Y. Zhang, and D. Wexler: Mater. Lett., 2011, vol. 65, pp. 514–16.

    Article  CAS  Google Scholar 

  50. J. Gubicza: Adv. Eng. Mater., 2020, vol. 22, p. 1900507.

    Article  CAS  Google Scholar 

  51. A. Habibi and M. Ketabchi: Mater. Des., 2012, vol. 34, pp. 483–87.

    Article  CAS  Google Scholar 

  52. E. Hall: Proc. Phys. Soc. B, 1951, vol. 64, p. 747.

    Article  Google Scholar 

  53. N. Petch: J. Iron Steel Inst., 1953, vol. 174, pp. 25–28.

    CAS  Google Scholar 

  54. D.-H. Kang and T.-W. Kim: Mater. Des., 2010, vol. 31, pp. S54–60.

    Article  CAS  Google Scholar 

  55. T. Shanmugasundaram, M. Heilmaier, B. Murty, and V.S. Sarma: Mater. Sci. Eng. A., 2010, vol. 527, pp. 7821–25.

    Article  CAS  Google Scholar 

  56. A. Loucif, R.B. Figueiredo, T. Baudin, F. Brisset, R. Chemam, and T.G. Langdon: Mater. Sci. Eng. A, 2012, vol. 532, pp. 139–45.

    Article  CAS  Google Scholar 

  57. N. Stepanov, A. Kuznetsov, G. Salishchev, G. Raab, and R. Valiev: Mater. Sci. Eng. A, 2012, vol. 554, pp. 105–15.

    Article  CAS  Google Scholar 

  58. P. Bazarnik, Y. Huang, M. Lewandowska, and T.G. Langdon: Mater. Sci. Eng. A, 2015, vol. 626, pp. 9–15.

    Article  CAS  Google Scholar 

  59. T. Koizumi and M. Kuroda: Key Eng. Mater., 2016, vol. 725, pp. 202–07.

    Article  Google Scholar 

  60. Y. Ito, K. Edalati, and Z. Horita: Mater. Sci. Eng. A, 2017, vol. 679, pp. 428–34.

    Article  CAS  Google Scholar 

  61. R. Tejedor, K. Edalati, J.A. Benito, Z. Horita, and J.M. Cabrera: Mater. Sci. Eng. A, 2019, vol. 743, pp. 597–605.

    Article  CAS  Google Scholar 

  62. D.-L. Zou, L.-F. He, D.-W. Xiao, Y.-W. Zhao, Z.-C. Qiu, L. Chao, and L. Fan: Trans. Nonferrous Met. Soc. China, 2020, vol. 30, pp. 2749–56.

    Article  CAS  Google Scholar 

  63. N. Hansen: Scripta Mater., 2004, vol. 51, pp. 801–06.

    Article  CAS  Google Scholar 

  64. T. Tabata, K. Takagi, and H. Fujita: Trans. Jpn. Inst. Met., 1975, vol. 16, pp. 569–79.

    Article  CAS  Google Scholar 

  65. M.A. Meyers and K.K. Chawla: Mechanical Behavior of Materials, 2nd ed. Cambridge University Press, London, 2008, p. 272.

    Book  Google Scholar 

  66. N. Kosarev, M. Khazin, R. Apakashev, and N. Valiev: J. Mater. Sci. Chem. Eng., 2013, vol. 01, pp. 7–10.

    CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  68. G.I. Taylor: Proc. R. Soc. Lond. A., 1934, vol. 145, pp. 362–87.

    Article  CAS  Google Scholar 

  69. M. Kassner: Acta Mater., 2014, vol. 52, pp. 1–9.

    Article  CAS  Google Scholar 

  70. Y. Tanaka, S. Takaki, T. Tsuchiyama, and R. Uemori: ISIJ Int., 2018, vol. 58, pp. 1927–33.

    Article  CAS  Google Scholar 

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Acknowledgments

The authors are grateful for the support provided by JSPS KAKENHI Grant Number 19K04066.

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On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Author notes

  1. Takayuki Koizumi

    Present address: Mechanical Engineering, National Institute of Technology, Tokyo College, Kunugida-machi 1220-2, Hachioji, Tokyo, 193-0997, Japan

Authors and Affiliations

  1. Faculty of Human Resources Development, Polytechnic University of Japan, Tokyo, 187‑0035, Japan

    Takayuki Koizumi

  2. Graduate School of Science and Engineering, Mechanical Engineering, Yamagata University, Jonan 4-3-16, Yonezawa, Yamagata, 992-8510, Japan

    Kazuki Ogoda & Mitsutoshi Kuroda

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  1. Takayuki Koizumi
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  2. Kazuki Ogoda
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Correspondence to Takayuki Koizumi.

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Koizumi, T., Ogoda, K. & Kuroda, M. Permanent Strength of Metals: A Case Study on FCC Metals Processed by Severe Plastic Deformation. Metall Mater Trans A 53, 2004–2017 (2022). https://doi.org/10.1007/s11661-022-06641-1

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