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Phenomenological Constitutive Models of NiTi SMAs

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Thermo-Mechanically Coupled Cyclic Deformation and Fatigue Failure of NiTi Shape Memory Alloys

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 335))

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Abstract

In this chapter, the phenomenological constitutive models of NiTi SMAs are proposed. Firstly, a generalized plasticity-based phenomenological model is proposed to describe the uniaxial transformation ratchetting of NiTi SMAs at room temperature. Then, by considering the interaction between the martensite transformation and dislocation slipping, a dislocation-based phenomenological constitutive model is constructed to describe the temperature-dependent transformation ratchetting of NiTi SMAs observed at different ambient temperature. Finally, in the framework of irreversible thermodynamics and further considering the internal heat production, a thermo-mechanically coupled phenomenological constitutive model is developed to describe the rate-dependent cyclic deformation of NiTi SMAs.

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References

  1. D. Lagoudas, Shape Memory Alloys: Modeling and Engineering Applications (Springer, Berlin, 2008)

    Google Scholar 

  2. G. Kang, Advances in transformation ratcheting and ratcheting-fatigue interaction of NiTi shape memory alloy. Acta Mech. Solida Sin. 26(3), 221–236 (2013)

    Article  Google Scholar 

  3. G.Z. Kang, Q.H. Kan, Cyclic Plasticity of Engineering Materials: Experiments and Models (Wiley, New York, 2017)

    Google Scholar 

  4. K. Tanaka, F. Nishimura, T. Hayashi, H. Tobushi, C. Lexcellent, Phenomenological analysis on subloops and cyclic behavior in shape memory alloys under mechanical and/or thermal loads. Mech. Mater. 19(4), 281–292 (1995)

    Article  CAS  Google Scholar 

  5. C. Lexcellent, G. Bourbon, Thermodynamical model of cyclic behaviour of Ti-Ni and Cu-Zn-Al shape memory alloys under isothermal undulated tensile tests. Mech. Mater. 24(1), 59–73 (1996)

    Article  Google Scholar 

  6. D.C. Lagoudas, Z. Bo, Thermomechanical modeling of polycrystalline SMAs under cyclic loading. Part II: material characterization and experimental results for a stable transformation cycle. Int. J. Eng. Sci. 37(9), 1141–1173 (1999)

    Google Scholar 

  7. C. Lexcellent, S. Leclercq, B. Gabry, G. Bourbon, The two way shape memory effect of shape memory alloys: an experimental study and a phenomenological model. Int. J. Plast. 16(10–11), 1155–1168 (2000)

    Article  CAS  Google Scholar 

  8. D.C. Lagoudas, P.B. Entchev, 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. 36(9), 865–892 (2004)

    Google Scholar 

  9. F. Auricchio, S. Marfia, E. Sacco, Modelling of SMA materials: training and two way memory effects. Comput. Struct. 81(24), 2301–2317 (2003)

    Article  Google Scholar 

  10. F. Auricchio, A. Reali, U. Stefanelli, A three-dimensional model describing stress-induced solid phase transformation with permanent inelasticity. Int. J. Plast. 23(2), 207–226 (2007)

    Article  CAS  Google Scholar 

  11. W. Zaki, Z. Moumni, A 3D model of the cyclic thermomechanical behavior of shape memory alloys. J. Mech. Phys. Solids 55(11), 2427–2454 (2007)

    Google Scholar 

  12. L. Saint-Sulpice, S.A. Chirani, S. Calloch, A 3D super-elastic model for shape memory alloys taking into account progressive strain under cyclic loadings. Mech. Mater. 41(1), 12–26 (2009)

    Article  Google Scholar 

  13. G. Kang, Q. Kan, L. Qian, Y. Liu, Ratchetting deformation of super-elastic and shape-memory NiTi alloys. Mech. Mater. 41(2), 139–153 (2009)

    Article  Google Scholar 

  14. Q. Kan, G. Kang, Constitutive model for uniaxial transformation ratchetting of super-elastic NiTi shape memory alloy at room temperature. Int. J. Plast. 26(3), 441–465 (2010)

    Article  CAS  Google Scholar 

  15. C. Yu, G.Z. Kang, Q.H. Kan, A physical mechanism based constitutive model for temperature-dependent transformation ratchetting of NiTi shape memory alloy: one-dimensional model. Mech. Mater. 78, 1–10 (2014)

    Google Scholar 

  16. C. Yu, G.Z. Kang, Q.H. Kan, Y.L. Zhu, Rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy: thermo-mechanical coupled and physical mechanism-based constitutive model. Int. J. Plast. 72, 60–90 (2015)

    Article  CAS  Google Scholar 

  17. J. Lubliner, F. Auricchio, Generalized plasticity and shape-memory alloys. Int. J. Solids Struct. 33(7), 991–1003 (1996)

    Article  Google Scholar 

  18. V.P. Panoskaltsis, S. Bahuguna, D. Soldatos, On the thermomechanical modeling of shape memory alloys. Int. J. Non-Linear Mech. 39(5), 709–722 (2004)

    Article  Google Scholar 

  19. F. Auricchio, J. Lubliner, A uniaxial model for shape-memory alloys. Int. J. Solids Struct. 34(27), 3601–3618 (1997)

    Article  Google Scholar 

  20. C. Bouvet, S. Calloch, C. Lexcellent, A phenomenological model for pseudoelasticity of shape memory alloys under multiaxial proportional and nonproportional loadings. Eur. J. Mech. A Solid 23(1), 37–61 (2004)

    Article  Google Scholar 

  21. J.G. Boyd, D.C. Lagoudas, A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy. Int. J. Plast. 12(6), 805–842 (1996)

    Google Scholar 

  22. D.J. Hartl, G. Chatzigeorgiou, D.C. Lagoudas, Three-dimensional modeling and numerical analysis of rate-dependent irrecoverable deformation in shape memory alloys. Int. J. Plast. 26(10), 1485–1507 (2010)

    Article  CAS  Google Scholar 

  23. D. Lagoudas, D. Hartl, Y. Chemisky, L. Machadv, P. Popov, Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys. Int. J. Plast. 32, 155–183 (2012)

    Article  Google Scholar 

  24. K. Gall, H.J. Maier, Cyclic deformation mechanisms in precipitated NiTi shape memory alloys. Acta Mater. 50(18), 4643–4657 (2002)

    Article  CAS  Google Scholar 

  25. T. Simon, A. Kröger, C. Somsen, A. Dlouly, G. Eggeler, On the multiplication of dislocations during martensitic transformations in NiTi shape memory alloys. Acta Mater. 58(5), 1850–1860 (2010)

    Article  CAS  Google Scholar 

  26. R. Delville, B. Malard, J. Pilch, P. Sittner, D. Schryvers, Transmission electron microscopy investigation of dislocation slip during superelastic cycling of Ni–Ti wires. Int. J. Plast. 27(2), 282–297 (2011)

    Article  CAS  Google Scholar 

  27. C. Grabe, O.T. Bruhns, On the viscous and strain rate dependent behavior of polycrystalline NiTi. Int. J. Solids Struct. 45(7), 1876–1895 (2008)

    Article  CAS  Google Scholar 

  28. H. Mecking, U.F. Kocks, Kinetics of flow and strain-hardening. Acta Metall. 29(11), 1865–1875 (1981)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  30. Q. Kan, C. Yu, G. Kang, J. Li, W. Yan, Experimental observations on rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy. Mech. Mater. 97, 48–58 (2016)

    Article  Google Scholar 

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Authors and Affiliations

  1. Southwest Jiaotong University, Chengdu, Sichuan, China

    Guozheng Kang, Chao Yu & Qianhua Kan

Authors
  1. Guozheng Kang
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  2. Chao Yu
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  3. Qianhua Kan
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Corresponding author

Correspondence to Guozheng Kang .

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Kang, G., Yu, C., Kan, Q. (2023). Phenomenological Constitutive Models of NiTi SMAs. In: Thermo-Mechanically Coupled Cyclic Deformation and Fatigue Failure of NiTi Shape Memory Alloys. Springer Series in Materials Science, vol 335. Springer, Singapore. https://doi.org/10.1007/978-981-99-2752-4_5

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