Acta Mechanica Solida Sinica

, Volume 31, Issue 4, pp 445–458 | Cite as

A Multi-mechanism Model Describing Reorientation and Reorientation-Induced Plasticity of NiTi Shape Memory Alloy

  • Xiang Xu
  • Bo Xu
  • Han M. Jiang
  • Guo-zheng Kang
  • Qian-hua Kan


The recovery force or recovery strain is an important indicator of NiTi-based shape memory alloy devices. However, the restoring force or recoverable strain is partially restrained due to an interaction between reorientation and reorientation-induced plasticity. Therefore, a macroscopic multi-mechanism constitutive model was constructed to describe the degeneration of shape memory effect based on the phase diagram. The residual strain after cooling consists of reorientation strain and reorientation-induced plastic strain. An internal variable, i.e., the detwinned stress, and its evolution equation were introduced into the transformation kinetics equation to describe the nonlinear hardening characteristics induced by the combined reorientation and detwinning mechanisms during mechanical loading. Finally, the proposed model was numerically implemented to simulate the experiments of shape memory effect at different peak strains. Comparisons between the experimental and simulated results show that the proposed model can reasonably describe the degeneration of shape memory effect.


Shape memory alloy Shape memory effect Residual strain Constitutive model Plastic strain 



Financial supports by the National Natural Science Foundation of China (Nos. 11572265, 11532010), the Excellent Youth Found of Sichuan Province (No. 2017JQ0019), the Open Project of Traction Power State Key Laboratory (TPL1606) and the Exploration Project of Traction Power State Key Laboratory (2017TPL T04) are acknowledged.


  1. 1.
    Jani JM, Leary M, Subic A, Gibson MA. A review of shape memory alloy research, applications and opportunities (1980–20151). Mater Des. 2014;56:1078–113.CrossRefGoogle Scholar
  2. 2.
    Miyazaki S, Imai T, Igo Y, Otsuka K. Effect of cyclic deformation on the pseudoelasticity characteristics of Ti–Ni alloys. Metall Trans A. 1986;17(1):115–20.CrossRefGoogle Scholar
  3. 3.
    Liu Y, Xie ZL, Van Humbeeck J. Cyclic deformation of NiTi shape memory alloys. Mater Sci Eng A. 1999;273–275(3):673–8.CrossRefGoogle Scholar
  4. 4.
    Bo Z, Lagoudas DC. Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part III: evolution of plastic strains and two-way shape memory effect. Int J Eng Sci. 1999;37(9):1175–203.CrossRefzbMATHGoogle Scholar
  5. 5.
    Auricchio F, Reali A, Stefanelli U. A three-dimensional model describing stress-induced solid phase transformation with permanent inelasticity. Int J Plast. 2007;23(2):207–26.CrossRefzbMATHGoogle Scholar
  6. 6.
    Kang GZ, Kan QH, Qian LM, Liu YJ. Ratchetting deformation of super-elastic and shape-memory NiTi alloys. Mech Mater. 2009;41(2):139–53.CrossRefGoogle Scholar
  7. 7.
    Song D, Kang GZ, Kan QH, Yu C, Zhang CZ. Non-proportional multiaxial transformation ratchetting of super-elastic NiTi shape memory alloy: experimental observations. Mech Mater. 2014;70(1):94–105.CrossRefGoogle Scholar
  8. 8.
    Kan QH, Yu C, Kang GZ, Li J, Yan WY. Experimental observations on rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy. Mech Mater. 2016;97:48–58.CrossRefGoogle Scholar
  9. 9.
    Delville R, Malard B, Pilch J, Sittner P, Schryvers D. Transmission electron microscopy investigation of dislocation slip during superelastic cycling of Ni–Ti wires. Int J Plast. 2011;27(2):282–97.CrossRefGoogle Scholar
  10. 10.
    Miyazaki S, Oshiba M, Nadai T. Precaution on use of hydrochloride salts in pharmaceutical formulation. J Pharm Sci. 1981;70(6):594.CrossRefGoogle Scholar
  11. 11.
    Liu YN, McCormick PG. Factors influencing the development of two-way shape memory in NiTi. Acta Mater. 1990;38(7):1321–6.CrossRefGoogle Scholar
  12. 12.
    Lim TJ, Mcdowell DL. Mechanical behavior of an Ni–Ti shape memory alloy under axial-torsional proportional and nonproportional loading. J Eng Mater Technol. 1999;121(1):9–18.CrossRefGoogle Scholar
  13. 13.
    Saleeb AF, Kumar A, Ii SAP, Dhakal B. The cyclic and evolutionary response to approach the attraction loops under stress controlled isothermal conditions for a multi-mechanism based multi-axial SMA model. Mech Mater. 2013;63(1):21–47.CrossRefGoogle Scholar
  14. 14.
    Benafan O, Noebe RD, Ii SAP, Brown DW, Vogel S, Vaidyanathan R. Thermomechanical cycling of a NiTi shape memory alloy-macroscopic response and microstructural evolution. Int J Plast. 2014;56(3):99–118.CrossRefGoogle Scholar
  15. 15.
    Miller DA, Lagoudas DC. Thermomechanical characterization of NiTiCu and NiTi SMA actuators: influence of plastic strains. Smart Mater Struct. 2000;9(5):640.CrossRefGoogle Scholar
  16. 16.
    Yu C, Kang GZ, Kan QH. A macroscopic multi-mechanism based constitutive model for the thermo-mechanical cyclic degeneration of shape memory effect of NiTi shape memory alloy. Acta Mech Sin. 2017;33(3):1–16.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Auricchio F, Marfia S, Sacco E. Modelling of SMA materials: training and two way memory effects. Comput Struct. 2003;81(24–25):2301–17.CrossRefGoogle Scholar
  18. 18.
    Lagoudas DC, Entchev PB. Modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys. Part I: constitutive model for fully dense SMAs. Mech Mater. 2004;36(9):865–92.CrossRefGoogle Scholar
  19. 19.
    Saleeb AF, Padula SA, Kumar A. A multi-axial, multimechanism based constitutive model for the comprehensive representation of the evolutionary response of SMAs under general thermomechanical loading conditions. Int J Plast. 2011;27(5):655–87.CrossRefzbMATHGoogle Scholar
  20. 20.
    Song ZL, Dai HH. Closed-form solutions for inhomogeneous states of a slender 3-D SMA cylinder undergoing stress-induced phase transitions. Int J Eng Sci. 2015;88:40–63.MathSciNetCrossRefGoogle Scholar
  21. 21.
    Zhu PP, Feng P, Sun QP, Wang J, Dai HH. Determining the up–down–up response through tension tests of a pre-twisted shape memory alloy tube. Int J Plast. 2016;85:52–76.CrossRefGoogle Scholar
  22. 22.
    Brinson LC. 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. 1993;4(2):729–42.CrossRefGoogle Scholar
  23. 23.
    Leclercq S, Lexcellent C. A general macroscopic description of the thermomechanical behavior of shape memory alloys. J Mech Phys Solids. 1996;44(6):953–7.CrossRefGoogle Scholar
  24. 24.
    Juhász L, Schnack E, Hesebeck O, Andrä H. Macroscopic modeling of shape memory alloys under non-proportional thermomechanical loadings. J Intell Mater Syst Struct. 2002;13(12):825–36.CrossRefGoogle Scholar
  25. 25.
    Lagoudas DC, Shu SG. Residual deformation of active structures with SMA actuators. Int J Mech Sci. 1999;41(6):595–619.CrossRefzbMATHGoogle Scholar
  26. 26.
    Thamburaja P. Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys. J Mech Phys Solids. 2005;53(4):825–56.MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Liu Y, Xie Z, Humbeeck JV, Delaey L. Asymmetry of stress–strain curves under tension and compression for NiTi shape memory alloys. Acta Mater. 1998;46(12):4325–38.CrossRefGoogle Scholar
  28. 28.
    Yu C, Kang GZ, Kan QH, Zhu YL. Rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy: thermo-mechanical coupled and physical mechanism-based constitutive model. Int J Plast. 2015;72:60–90.CrossRefGoogle Scholar
  29. 29.
    Simon T, Kröger A, Somsen C, Dlouhy A, Eggeler G. On the multiplication of dislocations during martensitic transformations in NiTi shape memory alloys. Acta Mater. 2010;58(5):1850–60.CrossRefGoogle Scholar
  30. 30.
    Wagner MF, Nayan N, Ramamurty U. Healing of fatigue damage in NiTi shape memory alloys. J Phys D Appl Phys. 2008;41(18):185408.CrossRefGoogle Scholar
  31. 31.
    Tan G, Liu YN. Comparative study of deformation-induced martensite stabilisation via martensite reorientation and stress-induced martensitic transformation in NiTi. Intermetallics. 2004;12(4):373–81.CrossRefGoogle Scholar
  32. 32.
    Liu YN, Liu Y, Humbeeck JV. Two-way shape memory effect developed by martensite deformation in NiTi. Acta Mater. 1998;47(1):199–209.CrossRefGoogle Scholar
  33. 33.
    Liang C, Rogers CA. One-dimensional thermomechanical constitutive relations for shape memory materials. J Intell Mater Syst Struct. 1997;1(2):207–34.CrossRefGoogle Scholar
  34. 34.
    Gerhard W, Boyer RR, Collings EW. Materials properties handbook: titanium alloy. Geauga: ASM International; 1994.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2018

Authors and Affiliations

  • Xiang Xu
    • 1
  • Bo Xu
    • 1
  • Han M. Jiang
    • 1
  • Guo-zheng Kang
    • 1
    • 2
  • Qian-hua Kan
    • 1
    • 2
  1. 1.State Key Laboratory of Traction PowerSouthwest Jiaotong UniversityChengduChina
  2. 2.Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and EngineeringSouthwest Jiaotong UniversityChengduChina

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