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Application of the Kelvin Approach for the Qualitative Estimation of Possibility of Phase Transitions in Shape Memory Alloys

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Abstract

It is proposed to use the concept of eigenmoduli and eigenstates from the linear theory of elasticity to estimate the possibility of phase transitions (martensitic transformations) in alloys with the shape memory effect. For alloys with cubic and hexagonal lattices, the eigenmoduli and eigenstates are given. The elastic strain energy for the cubic and hexagonal phases is written as the sum of six independent terms. It is proposed to compare the elastic strain energies in the cubic and hexagonal phases. If the deformation energy in the hexagonal phase is greater than in the cubic phase, then the alloy may tend to return to its original state with less energy. It is also possible to use the formulas of the tensors closest in Euclidean energy norm to the cubic and hexagonal tensors to compare the energies in different phases. The examples are given for some specific values of the elasticity constants.

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REFERENCES

  1. V. A. Likhachev, S. L. Kuz’min, and Z. P. Kamentseva, Shape Memory Effect (Leningr. Univ., Leningrad, 1987) [in Russian].

    Google Scholar 

  2. S. A. Muslov, A. V. Shelyakov, and V. A. Andreev, Shape Memory Alloys: Properties, Production and Application in Engineering and Medicine (Mozartika, Moscow, 2018) [in Russian].

    Google Scholar 

  3. V. A. Likhachev, Soros. Obraz. Zh., No. 3, 107 (1997).

  4. B. D. Annin and N. I. Ostrosablin, J. Appl. Mech. Tech. Phys. 49, 998 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  5. B. D. Annin, Sib. Zh. Ind. Mat. 2 (2), 3 (1999).

    Google Scholar 

  6. B. D. Annin, in Proceedings of the Conference on Hereditary Mechanics of Deformation and Fracture of Solids, Scientific Heritage of Yu.N. Rabotnov, Moscow, Feb. 24–26, 2014 (IMASh RAN, Moscow, 2014), p. 18.

  7. N. I. Ostrosablin, J. Appl. Mech. Tech. Phys. 60, 106 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  8. S. A. Muslov, A. I. Lotkov, and S. D. Arutyunov, Russ. Phys. J. 62, 1417 (2019).

    Article  Google Scholar 

  9. P. Chadwick and L. T. C. Seet, Mathematika 17, 255 (1970).

    Article  MathSciNet  Google Scholar 

  10. J. Gump, Xia. Hua, M. Chirita, R. Sooryakumar, M. A. Tomaz, and G. R. Harp, J. Appl. Phys. 86, 6005 (1999).

    Article  ADS  Google Scholar 

  11. W. F. Weston and A. V. Granato, Phys. Rev. B 12, 5355 (1975).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics SB RAS, 630090, Novosibirsk, Russia

    B. D. Annin, N. I. Ostrosablin & R. I. Ugryumov

  2. Novosibirsk State University, 630090, Novosibirsk, Russia

    B. D. Annin & R. I. Ugryumov

Authors
  1. B. D. Annin
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  2. N. I. Ostrosablin
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  3. R. I. Ugryumov
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Correspondence to B. D. Annin, N. I. Ostrosablin or R. I. Ugryumov.

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This work was carried out within the framework of the Basic Research Program of the Siberian Branch of the Russian Academy of Sciences, project III.23.3.1, and with partial support from the Russian Foundation for Basic Research, project 19-01-00511 A.

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Annin, B.D., Ostrosablin, N.I. & Ugryumov, R.I. Application of the Kelvin Approach for the Qualitative Estimation of Possibility of Phase Transitions in Shape Memory Alloys. Dokl. Phys. 66, 26–29 (2021). https://doi.org/10.1134/S1028335821010018

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  • DOI: https://doi.org/10.1134/S1028335821010018

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