Skip to main content

One-Dimensional Phase Transformation Model and Its Application to Damping Enhancement Analysis

  • Chapter
  • First Online:
  • 1437 Accesses

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 73))

Abstract

A simple yet reasonably accurate constitutive model of shape memory alloys (SMAs) has been developed. It can treat more than three phases or/and variants and duplicate their rate-dependent deformation behavior quantitatively. This model was applied to damping enhancement analysis. Damping oscillations of cantilever beams with various SMA foils bonded on their both surfaces were simulated numerically. It was seen that bonding SMA foils is effective for the damping enhancement in some cases. Furthermore, it was found that adequate mechanical or/and thermal treatment for SMA foils improves the damping performance.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Barbarino S, Saavedra Flores EI, Ajaj RM, Dayyani I, Friswell MI (2014) A review on shape memory alloys with applications to morphing aircraft. Smart Mater Struct 23(6):063001 (19 pp)

    Google Scholar 

  • Bertram A (1982) Thermo-mechanical constitutive equations for the description of shape memory effects in alloys. Nucl Eng Des 74(2):173–182

    Google Scholar 

  • Boller C, Konstanzer P, Matsuzaki Y, Ikeda T (2001) Damping with shape memory alloys for structural systems. In: Proceedings of eleventh international conference on adaptive structures and technologies, pp 336–343

    Google Scholar 

  • Boyd JG, Lagoudas DC (1996) A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy. Int J Plast 12(6):805–842

    Google Scholar 

  • Brinson LC (1993) One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable. J Intell Mater Syst Struct 4(2):229–242

    Google Scholar 

  • Falk F (1983) One-dimensional model of shape memory alloys. Arch Mech 35(1):63–84

    Google Scholar 

  • Gall K, Sehitoglu H (1999) The role of texture in tension-compression asymmetry in polycrystalline NiTi. Int J Plast 15(1):69–92

    Google Scholar 

  • Gandhi F, Chapuis G (2011) Passive damping augmentation of a vibrating beam using pseudoelastic shape memory alloy wires. In: Proceedings of eleventh international conference on adaptive structures and technologies, pp 319–335

    Google Scholar 

  • Graesser EJ, Cozzarelli FA (1991) Shape-memory alloys as new materials for aseismic isolation. J Eng Mech 117(11):2590–2608

    Google Scholar 

  • Ikeda T (2005) Modeling of ferroelastic behavior of shape memory alloys. Proc SPIE 5757:344–352

    Article  Google Scholar 

  • Ikeda T (2006) Application of one-dimensional phase transformation model to tensile-torsional pseudoelastic behavior of shape memory alloy tubes. Proc SPIE 6166:61660Z (8 pp)

    Google Scholar 

  • Ikeda T (2008) Constitutive model of shape memory alloys for asymmetric quasiplastic behavior. J Intell Mater Syst Struct 19(5):533–540

    Google Scholar 

  • Ikeda T, Nae FA, Naito H, Matsuzaki Y (2004a) Constitutive model of shape memory alloys for unidirectional loading considering inner hysteresis loops. Smart Mater Struct 13(4):916–925

    Google Scholar 

  • Ikeda T, Hattori H, Matsuzaki Y (2004) Numerical analysis of damping enhancement of a beam with shape memory alloy foils bonded. In: Proceedings of ICAS 2004, ICAS 2004-5.2.1 (8 pp)

    Google Scholar 

  • Ivshin Y, Pence TJ (1994) A thermomechanical model for a one variant shape memory material. J Intell Mater Syst Struct 5(4):455–473

    Google Scholar 

  • Kamita T, Matsuzaki Y (1998) One-dimensional pseudoelastic theory of shape memory alloys. Smart Mater Struct 7(4):489–495

    Google Scholar 

  • Leclercq S, Lexcellent C (1996) A general macroscopic description of the thermomechanical behavior of shape memory alloys. J Mech Phys Solids 44(6):953–980

    Google Scholar 

  • Liang C, Rogers CA (1990) One-dimensional thermomechanical constitutive relations for shape memory materials. J Intell Mater Syst Struct 1(2):207–234

    Google Scholar 

  • Machado LG, Lagoudas DC (2008) Thermomechanical constitutive modeling of SMAs, shape memory alloys—modeling and engineering applications. In: Lagoudas DC (ed) Springer Science+Business Media, LLC, New York, pp 121–187

    Google Scholar 

  • Matsuzaki Y, Naito H, Ikeda T, Funami K (2001) Thermo-mechanical behavior associated with pseudoelastic transformation of shape memory alloys. Smart Mater Struct 10(5):884–892

    Google Scholar 

  • Müller I (1989) On the size of the hysteresis in pseudoelasticity. Continuum Mech Thermodyn 1(2):125–142

    Google Scholar 

  • Nae FA, Matsuzaki Y, Ikeda T (2003) Micromechanical modeling of polycrystalline shape-memory alloys including thermo-mechanical coupling. Smart Mater Struct 12(1):6–17

    Google Scholar 

  • Ortín J (1992) Preisach modeling of hysteresis for a pseudoelastic Cu-Zn-Al single crystal. J Appl Phys 71(3):1454–1461

    Google Scholar 

  • Otsuka K, Ren X (2005) Physical metallurgy of Ti-Ni-based shape memory alloy. Prog Mater Sci 50(5):511–678

    Google Scholar 

  • Otsuka K, Wayman CM (eds) (1998) Shape memory materials. Cambridge University Press, Cambridge

    Google Scholar 

  • Patoor E, Eberhardt A, Berveiller M (1995) Micromechanical modelling of the superelastic behavior. Journal de Physique IV 5-C2, C-2-501-C2-506

    Google Scholar 

  • Raniecki B, Lexcellent CH, Tanaka K (1992) Thermodynamic models of pseudoelastic behavior of shape memory alloys. Arch Mech 44(3):261–284

    Google Scholar 

  • Seelecke S (1996) Equilibrium thermodynamics of pseudoelasticity and quasiplasticity. Continuum Mech Thermodyn 8(5):309–322

    Google Scholar 

  • Sun QP, Hwang KC (1993) Micromechanics modelling for the constitutive behavior of polycrystaline shape memory alloys—I. Derivation of general relations. J Mech Phys Solids 41(1):1–17

    Google Scholar 

  • Tanaka K (1986) A thermomechanical sketch of shape memory effect: one-dimensional tensile behavior. Res Mechanica 18(3):251–263

    Google Scholar 

  • Thomson P, Balas GJ, Leo PH (1995) The use of shape memory alloys for passive structural damping. Smart Mater Struct 4(1):36–42

    Google Scholar 

  • Tobushi H, Matsui R, Takeda K, Pieczyska EA (2013) Material properties of shape memory materials. Nova Science Publication, New York

    Google Scholar 

  • Yamauchi K, Ohkata I, Tsuchiya K, Miyazaki S (eds) (2011) Shape memory and superelastic alloys: applications and technologies. Woodhead Publishing Limited, Oxford, Cambridge, Philadelphia, New Delhi

    Google Scholar 

Download references

Acknowledgements

The author would like to thank Mr. Yoshitaka Hata and Mr. Hidetaka Hattori for their support in experiment and calculation.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tadashige Ikeda .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Ikeda, T. (2017). One-Dimensional Phase Transformation Model and Its Application to Damping Enhancement Analysis. In: Sun, Q., Matsui, R., Takeda, K., Pieczyska, E. (eds) Advances in Shape Memory Materials. Advanced Structured Materials, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-319-53306-3_2

Download citation

Publish with us

Policies and ethics