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A thermomechanical model accounting for the behavior of shape memory alloys in finite deformations

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Abstract

Shape memory alloys (SMA) comport an interesting behavior. They can undertake large strains and then recover their undeformed shape by heating. In this context, one of the aspects that challenged many researchers was the development of a mathematical model to predict the behavior of a known SMA under real-life conditions, or finite strain. This paper is aimed at working out a finite strain mathematical model for a Ni–Ti SMA, under the superelastic experiment conditions and under uniaxial mechanical loading, based on the Zaki–Moumni 3D mathematical model developed under the small perturbations assumption. Within the current article, a comparison between experimental findings and calculated results is also investigated. The proposed finite strain mathematical model shows good agreement with experimental data.

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References

  1. Lagoudas D.: Shape Memory Alloys. Springer, Berlin (2008)

    MATH  Google Scholar 

  2. Bujoreanu, L.Gh., Dia, V., Mărginean, S.: Tehnologie şi utilaje de obţinere a unor aliaje cu memoria formei (vol. I). Editura Ştiinţifică “Fundaţia Metalurgia Română” (1998)

  3. Bujoreanu, L.Gh.: Materiale inteligente. Editura Junimea (2000)

  4. Jani J.M., Leary M., Subic A., Gibson M.: A review of shape memory alloys research, applications and opportunities. Mater. Des. 56, 1078–1113 (2014)

    Article  Google Scholar 

  5. Auricchio, F.: Shape-memory alloys: applications, micromechanics, macromodelling and numerical simulations. Ph.D. thesis, University of California at Berkeley (1995)

  6. Nespoli A., Rigamonti D., Villa E., Passaretti F.: Design, characterization and perspectives of shape memory alloy elements in miniature sensor proof of concept. Sens. Actuators A Phys. 218, 142–153 (2014)

    Article  Google Scholar 

  7. Gao X., Brinson L.: A simplified multivariant SMA model based on invariant plane nature of martensitic transformation. J. Intell. Mater. Syst. Struct. 13, 795–810 (2002)

    Article  Google Scholar 

  8. Li Z., Sun Q.: The initiation and growth of macroscopic martensite band in nano-grained NiTi microtube under tension. Int. J. Plast. 18, 1481–1498 (2002)

    Article  Google Scholar 

  9. Sun Q., Li Z.: Phase transformation in superelastic NiTi polycrystalline micro-tubes under tension and torsion—from localization to homogeneous deformation. Int. J. Solids Struct. 39, 3797–3809 (2002)

    Article  Google Scholar 

  10. Lexcellent C., Boubakar M., Bouvet C., Calloch S.: About modelling the shape memory alloy behavior based on the phase transformation surface identification under proportional and anisothermal conditions. Int. J. Solids Struct. 43, 613–626 (2006)

    Article  MATH  Google Scholar 

  11. Shaw J.: A thermomechanical model for a 1-D shape memory alloy wire with propagating instabilities. Int. J. Solids Struct. 39, 1275–1305 (2002)

    Article  MATH  Google Scholar 

  12. Bekker A., Brinson L.: Temperature-induced phase transformation in a shape memory alloy: phase diagram based kinetics approach. J. Mech. Phys. Solids 45(6), 949–988 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Bekker A., Brinson L.: Phase diagram based description of the hysteresis behavior of shape memory alloys. Acta Mater. 46, 3649–3665 (1999)

    Article  Google Scholar 

  14. Zaki W., Moumni Z.: A three-dimensional model of the thermomechanical behavior of shape memory alloys. J. Mech. Phys. Solids 55, 2455–2490 (2007)

    Article  ADS  MATH  Google Scholar 

  15. Halphen B., Nguyen Q.: Plastic and visco-plastic materials with generalized potential. Mech. Res. Commun. 1, 43–47 (1974)

    Article  MATH  Google Scholar 

  16. Holzapfel G.A.: Nonlinear Solid Mechanics. Wiley, London (2000)

    MATH  Google Scholar 

  17. Ranieki B., Lexcellent C., Tanaka K.: Thermodynamic model of pseudoelastic behaviour of shape memory alloys. Arch. Mech. 44(3), 261–288 (1992)

    MathSciNet  MATH  Google Scholar 

  18. Ranieki B., Rejzner J., Lexcellent C.: Anatomization of hysteresis loops in pure bending of ideal pseudoelastic SMA beams. Int. J. Mech. Sci. 43, 1339–1368 (2001)

    Article  MATH  Google Scholar 

  19. Bekker A., Brinson L.: Phase diagram based description of the hysteresis behavior of shape memory alloys. Acta Mater. 46, 3649–3665 (1998)

    Article  Google Scholar 

  20. Müller C., Bruhns O.: A thermodynamic finite-strain model for pseudoelastic shape memory alloys. Int. J. Plast. 22, 1658–1682 (2006)

    Article  MATH  Google Scholar 

  21. Lagoudas D., Entchev P., Popov P., Patoor E., Brinson L., Gao X.: Shape memory alloys. Part II. Modeling of polycrystals. Mech. Mater. 38, 430–462 (2006)

    Article  Google Scholar 

  22. Auricchio F., Reali A., Stefanelli U.: A three-dimensional model describing stress-induced solid phase transformation with permanent inelasticity. Int. J. Plast. 23, 207–226 (2007)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Military Technical Academy, 39-49 G. Coşbuc Blvd., Bucharest, Romania

    Laviniu Haller, Ioan Vedinaş & Eugen Trană

  2. ENSTA ParisTech, 839 Blvd. des Marechaux, Palaiseau, Essonne, France

    Boumedienne Nedjar & Ziad Moumni

Authors
  1. Laviniu Haller
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  2. Boumedienne Nedjar
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  3. Ziad Moumni
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  4. Ioan Vedinaş
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  5. Eugen Trană
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Corresponding author

Correspondence to Laviniu Haller.

Additional information

Communicated by Andreas Öchsner.

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Haller, L., Nedjar, B., Moumni, Z. et al. A thermomechanical model accounting for the behavior of shape memory alloys in finite deformations. Continuum Mech. Thermodyn. 28, 957–975 (2016). https://doi.org/10.1007/s00161-015-0431-8

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  • DOI: https://doi.org/10.1007/s00161-015-0431-8

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