Skip to main content
SpringerLink
Log in

A phenomenological model for the simulation of functional fatigue in shape memory alloy wires

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

In this contribution, a modelling framework for functional fatigue in shape memory alloy wires is introduced. The approach is in particular designed to reproduce the effective response determined by experiments as published in, e.g., Eggeler et al. (Mat Sci Eng A 378:24–33, 2004). In this context, the decrease of transformation stresses, the increase of irreversible strains, and the occurrence of “characteristic points” with respect to the stress-strain relation is explicitly covered in the model formulation. The modelling approach for the phase transformations itself offers a large potential for further micromechanically well-motivated model extensions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Notes

  1. A maximum of two simultaneously occurring discontinuities as this work proceeds.

References

  1. Abeyaratne R, Knowles J (1990) On the driving traction acting on a surface of strain discontinuity in a continuum. J Mech Phys Sol 38:345–360

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Auricchio F, Petrini L (2004) A three-dimensional model describing stress-temperature induced solid phase transformations: thermomechanical coupling and hybrid composite applications. Int J Numer Meth Engrg 61:716–737

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  4. Barrera N, Biscari P, Urbano MF (2014) Macroscopic modeling of functional fatigue in shape memory alloys. Eur J Mech A/Solids 45:101–109

    Article  Google Scholar 

  5. Bartel T, Menzel A, Svendsen B (2011) Thermodynamic and relaxation-based modeling of the interaction between martensitic phase transformations and plasticity. J Mech Phys Sol 59:1004–1019

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Bertacchini OW, Lagoudas DC, Patoor E (2009) Thermomechanical transformation fatigue of TiNiCu SMA actuators under a corrosive environment-part i: Experimental results. Int J Fatigue 31:1571–1578

    Article  Google Scholar 

  7. Biot MA (1965) Mechanics of incremental deformations. Wiley, New York

    Google Scholar 

  8. Casati R, Passaretti F, Tuissi A (2011) Effect of electrical heating conditions on functional fatigue of thin NiTi wire for shape memory actuators. Proc Engrg 10:3423–3428

    Article  Google Scholar 

  9. Coleman B, Noll W (1963) The thermodynamics of elastic materials with heat conduction and viscosity. Arch Rational Mech Anal 13:167–178

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Demersa V, Brailovski V, Prokoshkinb SD, Inaekyana KE (2009) Thermomechanical fatigue of nanostructured Ti-Ni shape memory alloys. Mat Sci Engrg A 513–514:185–196

    Article  Google Scholar 

  11. Edelen DGB (1973) On the existence of symmetry relations and dissipation potentials. Arch Rat Mech Anal 51:218–227

    Article  MathSciNet  MATH  Google Scholar 

  12. Eggeler G, Hornbogen E, Yawny A, Heckmann A, Wagner M (2004) Structural and functional fatigue of NiTi shape memory alloys. Mat Sci Eng A 378:24–33

    Article  Google Scholar 

  13. Grossmann C, Schaefer A, Wagner MFX (2010) A finite element study on localized deformation and functional fatigue in pseudoelastic NiTi strips. Mat Sci Engrg A 527:1172–1178

    Article  Google Scholar 

  14. Halphen B, Nguyen QS (1975) Sur les matériaux standards généralisés. J Mécanique 14:39–63

    MathSciNet  MATH  Google Scholar 

  15. Hartl D, Lagoudas D (2007) Aerospace applications of shape memory alloys. Proc Inst Mech Eng 221:535–552

    Article  Google Scholar 

  16. Hornbogen E (2004) Thermo-mechanical fatigue of shape memory alloys. J Mat Sci 39:385–399

    Article  ADS  Google Scholar 

  17. Jäger P, Steinmann P, Kuhl E (2008) On local tracking algorithms for the simulation of three-dimensional discontinuities. Comput Mech 42:395–406

    Article  MATH  Google Scholar 

  18. Jani JM, Leary M, Subic A, Gibson MA (2014) A review of shape memory alloy research, applications and opportunities. Mat Design 2014:1078–1113

    Article  Google Scholar 

  19. Kang G, Kan Q, Yu C, Song D, Liu Y (2012) Whole-life transformation ratchetting and fatigue of super-elastic niti alloy under uniaxial stress-controlled cyclic loading. Mat Sci Engrg A 535:228–234

    Article  Google Scholar 

  20. Lagoudas DC (2008) Shape memory alloys: modeling and engineering applications. Springer, New York

  21. Li YF, Mi XJ, Tan J, Gao BD (2009) Thermo-mechanical cyclic transformation behavior of Ti-Ni shape memory alloy wire. Mat Sci Engrg A 509:8–13

    Article  Google Scholar 

  22. McCormick PG, Liu Y (1994) Thermodynamic analysis of the martensitic transformation in NiTi-II. Effect of transformation cycling. Acta Metall Mater 42(7):2407–2413

    Article  Google Scholar 

  23. Miyazaki S, Igo Y, Otsuka K (1986) Effect of thermal cycling on the transformation temperatures of Ti-Ni alloys. Acta Metal 34(10):2045–2051

    Article  Google Scholar 

  24. Müller I, Seelecke S (2001) Thermodynamic aspects of shape memory alloys. Math Comp Modell 34:1307–1355

    Article  MathSciNet  MATH  Google Scholar 

  25. Nayan N, Buravalla V, Ramamurty U (2009) Effect of mechanical cycling on the stress-strain response of a martensitic Nitinol shape memory alloy. Mat Sci Engrg A 525:60–67

    Article  Google Scholar 

  26. Olbricht J, Yawny A, Cond’o AM, Lovey FC, Eggeler G (2008) The influence of temperature on the evolution of functional properties during pseudoelastic cycling of ultra fine grained NiTi. Mat Sci Engrg A 481–482:142–145

    Article  Google Scholar 

  27. Ostwald R, Bartel T, Menzel A (2012) Phase-transformations interacting with plasticity—a micro-sphere model applied to trip steel. Comput Mat Sci 64:12–16

    Article  Google Scholar 

  28. Ostwald R, Bartel T, Menzel A (2015) An energy-barrier-based computational micro-sphere model for phase-transformations interacting with plasticity. Comput Methods Appl Mech Engrg 293:232–265

    Article  ADS  MathSciNet  Google Scholar 

  29. Petrini L, Migliavacca F (2011)Biomedical applications of shape memory alloys. J Metall. doi:10.1155/2011/501483

  30. Robertson SW, Pelton AR, Ritchie RO (2012) Mechanical fatigue and fracture of nitinol. Int Mat Rev 57(1):1–37

    Article  Google Scholar 

  31. Shaw JA, Kyriakides S (1998) Initiation and propagation of localized deformation in elasto-plastic strips under uniaxial tension. Int J Plast 13(10):837–871

    Article  Google Scholar 

  32. Souza AC, Mamiya EN, Zouain N (1998) Three-dimensional model for solids undergoing stress-induced phase transformations. Eur J Mech A/Solids 17:789–806

    Article  MATH  Google Scholar 

  33. Merzouki T, Duval TZ (2012) Finite element analysis of a shape memory alloy actuator for a micropump. Sim Mod Pract Theory 27:112–126

  34. Wagner M (2005) Ein Beitrag zur strukturellen und funktionalen Ermüdung von Drähten und Federn aus NiTi-Formgedächtnislegierungen

  35. Waimann J, Junker P, Hackl K (2016) A coupled dissipation functional for modeling the functional fatigue in polycrystalline shape memory alloys. Eur J Mech A 55:110–121

    Article  MathSciNet  Google Scholar 

  36. Weighardt SC, Maier HJ, Chumlyakov YI (2013) Dependence of functional degradation on crystallographic orientation in NiTi shape memory alloys aged under stress. J Alloys Comp 577:219–221

    Article  Google Scholar 

  37. Wolfram S (2016) NMinimize—Wolfram language documentation. https://reference.wolfram.com/language/ref/NMinimize.html

  38. Yawny A, Olbricht J, Sade M, Eggeler G (2008) Pseudoelastic cycling and ageing effects at ambient temperatures in nanocrystalline Ni-rich NiTi wire. Mat Sci Engrg A 481–482:86–90

    Article  Google Scholar 

  39. Yin H, He Y, Sun Q (2014) Effect of deformation frequency on temperature and stress oscillations in cyclic phase transition of NiTi shape memory alloy. J Mech Phys Sol 67:100–128

    Article  ADS  Google Scholar 

  40. Zaki W, Moumni Z (2007) A 3d model of the cyclic thermomechanical behavior of shape memory alloys. J Mech Phys Sol 55:2427–2454

    Article  ADS  MATH  Google Scholar 

  41. Ziegler H (1963) Some extremum principles in irreversible thermodynamics with application to continuum mechanics. North-Holland, No. IV in Progress in Solid Mechanics

Download references

Acknowledgments

The financial support by the Mercator Research Centre Ruhr (MERCUR) through project PR-2013-0048 is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Institute of Mechanics, TU Dortmund, Leonhard-Euler-Str. 5, 44227, Dortmund, Germany

    T. Bartel, M. Osman & A. Menzel

  2. Division of Solid Mechanics, Lund University, P.O. Box 118, 22100, Lund, Sweden

    A. Menzel

Authors
  1. T. Bartel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Osman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Menzel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Bartel.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bartel, T., Osman, M. & Menzel, A. A phenomenological model for the simulation of functional fatigue in shape memory alloy wires. Meccanica 52, 973–988 (2017). https://doi.org/10.1007/s11012-016-0419-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-016-0419-x

Keywords

Search

Navigation