Advertisement

Acta Mechanica Solida Sinica

, Volume 23, Issue 2, pp 95–105 | Cite as

Super-Elastic Constitutive Model Considering Plasticity and its Finite Element Implementation

  • Qianhua Kan
  • Guozheng Kang
  • Linmao Qian
Article

Abstract

Based on the experimental results of super-elastic NiTi alloy, a three-dimensional super-elastic constitutive model including both of stress-induced martensite transformation and plasticity is constructed in a framework of general inelasticity. In the proposed model, transformation hardening, reverse transformation of stress-induced martensite, elastic mismatch between the austenite and martensite phases, and temperature-dependence of transformation stress and elastic modulus of each phase are considered. The plastic yielding of martensite occurred under high stress is addressed by a bilinear isotropic hardening rule. Drucker-Prager-typed transformation surfaces are employed to describe the asymmetric behavior of NiTi alloy in tension and compression. The prediction capability of the proposed model is verified by comparing the simulated results with the correspondent experimental ones. Based on backward Euler’s integration, a new expression of consistent tangent modulus is derived. The proposed model is then implemented into a finite element package ABAQUS by user-subroutine UMAT. Finally, the validity of such implementation was verified by some numerical samples.

Key words

NiTi alloy super-elasticity plasticity finite element implementation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Yang, K. and Gu, C.L., Research and application of the shape memory alloy. Metallic Functional, 2000, 17(15): 7–12.Google Scholar
  2. [2]
    Fu, Y., Du, H., Zhang, S. and Hu, M., TiNi-based thin films in MEMS applications: a review. Sensors and Actuators A, 2004, 112: 395–408.CrossRefGoogle Scholar
  3. [3]
    Gall, K., Juntunen, K., Matier, H.J., Sehitoglu, H. and Chumlyakov, Y.I., Instrumented micro-indentation of NiTi shape-memory alloys. Acta Materialia, 2001, 49: 3205–3217.CrossRefGoogle Scholar
  4. [4]
    Zhang, L., Xie, C.Y. and Wu, J.S., Progress in research on shape memory alloy films in MEMS field. Materials Review, 2006, 2: 109–113.Google Scholar
  5. [5]
    Lubliner, J. and Auricchio, F., Generalized plasticity and shape memory alloys. International Journal of Solids and Structures, 1996, 33(7): 991–1003.CrossRefGoogle Scholar
  6. [6]
    Panico, M. and Brinson, L.C., A three-dimensional phenomenological model for martensite reorientation in shape memory alloys. Journal of the mechanics and physics of solids, 2007, 55: 2491–2511.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Popov, P. and Lagoudas, D.C., A 3-D constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of self-accommodated martensite. International Journal of Plasticity, 2007, 23: 1679–1720.CrossRefGoogle Scholar
  8. [8]
    Brinson, L.C. and Huang, M.S., Simplification and comparisons of shape memory alloy constitutive models. Journal of Intelligent Material Systems and Structures, 1996, 7: 108–114.CrossRefGoogle Scholar
  9. [9]
    Lagoudas, D.C. and Bhattacharya, A., On the correspondence between micromechanical models for isothermal pseudoelastic response of shape memory alloys and preisach model for hysteresis. Mathematics and Mechanics of Solids, 1997, 2(4): 405–440.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Lazghab,T., Modeling of Shape Memory Alloys with Plasticity. Doctor of philosophy in mechanical engineering, 2001, Florida international university.Google Scholar
  11. [11]
    Yan, W.Y., Wang, C.H., Zhang, X.P. and Mai, Y.W., Theoretical modeling of the effect of plasticity on reverse transformation in superelastic shape memory alloys. Journal of the Mechanics and Physics of Solids, 2003, 354: 146–156.Google Scholar
  12. [12]
    Bo, Z. and Lagoudas, D.C., Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part I: theoretical derivations. International Journal of Engineering Science, 1999, 37: 1089–1140.MathSciNetCrossRefGoogle Scholar
  13. [13]
    Lagoudas, D.C. and Bo, Z., Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part II: material characterization and experimental results for a stable transformation cycle. International Journal of Engineering Science, 1999, 37: 1141–1173.MathSciNetCrossRefGoogle Scholar
  14. [14]
    Bo, Z. and Lagoudas, D.C., Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part III: evolution of plastic strains and two way shape memory effect. International Journal of Engineering Science, 1999, 37: 1175–1203.MathSciNetCrossRefGoogle Scholar
  15. [15]
    Bo, Z., Lagoudas, D.C., Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part IV: modeling of minor hysteresis loops. International Journal of Engineering Science, 1999, 37: 1205–1249.MathSciNetCrossRefGoogle Scholar
  16. [16]
    Auricchio, F. and Taylor, R.L., Shape-memory alloy modeling and numerical simulations of the finite-strain superelastic behavior. Computer Methods of Application Mechanics and Engineering, 1997, 143: 175–194.CrossRefGoogle Scholar
  17. [17]
    Auricchio, F., A robust integration algorithm for a finite strain shape memory alloy superelastic model. International Journal of Plasticity, 2001, 17: 971–990.CrossRefGoogle Scholar
  18. [18]
    Rebelo, N., Hsu, M. and Foadian, H., Simulation of super-elastic alloys behavior with abaqus. In: Proceedings of the International Conference on Shape memory and Super-elastic Technologies, SMST, 2000, Pacific Grove, USA, 2001: 457–469.Google Scholar
  19. [19]
    Lubliner, J. and Auricchio, F., Generalized plasticity and shape memory alloys. International Journal of Solids and Structures, 1996, 33: 991–1003.CrossRefGoogle Scholar
  20. [20]
    Lagoudas, D.C., Bo, Z. and Qidwai, M.A., A unified thermodynamic constitutive model for SMA and finite element analysis of active metal matrix composites. Mechanics of Composite Materials and Structures, 1996, 3: 153–179.CrossRefGoogle Scholar
  21. [21]
    Rayleigh,L., The Theory of Sound. 1877.Google Scholar
  22. [22]
    Qian, L.M., Sun, Q.P. and Xiao, X.D., Role of phase transition in the unusual microwear behavior of superelastic NiTi shape memory alloy. Wear, 2006, 260: 509–522.CrossRefGoogle Scholar
  23. [23]
    Kang, G.Z., Kan, Q.H., Qian, L.M. and Liu, Y.J., Ratchetting deformation of super-elastic and shape-memory NiTi alloys. Mechanics of Materials, 2009, 41:139–153.CrossRefGoogle Scholar
  24. [24]
    ABAQUS/Standard User’s Manual. Hibbit, Karlsson& Sorensen, Inc., Pawtucket, RI. HKS, 2001.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2010

Authors and Affiliations

  1. 1.State Key Laboratory of Traction PowerSouthwest Jiaotong UniversityChengduChina

Personalised recommendations