Abstract
In this chapter, the crystal plasticity-based constitutive models are proposed to describe the cyclic deformation of NiTi SMAs and its rate-dependence. The proposed models are firstly constructed for single crystals by considering different inelastic deformation mechanisms. Meanwhile, the thermo-mechanical coupling nature of rate-dependent cyclic deformation is addressed by considering the competition between the internal heat production and heat transfer to the ambient media. By employing an explicit scale transition rule, the proposed single crystal model is extended into the polycrystalline version, and then the rate-dependent cyclic deformation of NiTi SMAs are reasonably described by the proposed polycrystalline model.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
K. Gall, H. Sehitoglu, The role of texture in tension–compression asymmetry in polycrystalline NiTi. Int. J. Plast. 15(1), 69–92 (1999)
K. Gall, T.J. Lim, D.L. McDowell, H. Sehitoglu, Y.I. Chumlyakov, The role of intergranular constraint on the stress-induced martensitic transformation in textured polycrystalline NiTi. Int. J. Plast. 16(10–11), 1189–1214 (2000)
L. Anand, M.E. Gurtin, Thermal effects in the superelasticity of crystalline shape-memory materials. J. Mech. Phys. Solids 51(6), 1015–1058 (2003)
E. Patoor, D.C. Lagoudas, P.B. Entchev, L.C. Brinson, X. Gao, Shape memory alloys, part I: general properties and modeling of single crystals. Mech. Mater. 38(5), 391–429 (2006)
P. Thamburaja, H. Pan, F.S. Chau, Martensitic reorientation and shape-memory effect in initially textured polycrystalline Ti–Ni sheet. Acta Mater. 53(14), 3821–3831 (2005)
P. Thamburaja, H. Pan, F.S. Chau, The evolution of microstructure during twinning: constitutive equations, finite-element simulations and experimental verification. Int. J. Plast. 25(11), 2141–2168 (2009)
G.Z. Kang, Q.H. Kan, Cyclic Plasticity of Engineering Materials: Experiments and Models (Wiley, New York, 2017)
C. Yu, G. Kang, D. Song, Q. Kan, Micromechanical constitutive model considering plasticity for super-elastic NiTi shape memory alloy. Comput. Mater. Sci. 56, 1–5 (2012)
C. Yu, G. Kang, Q. Kan, Crystal plasticity based constitutive model of NiTi shape memory alloy considering different mechanisms of inelastic deformation. Int. J. Plast. 54, 132–162 (2014)
C. Yu, G. Kang, D. Song, Q. Kan, Effect of martensite reorientation and reorientation-induced plasticity on multiaxial transformation ratchetting of super-elastic NiTi shape memory alloy: new consideration in constitutive model. Int. J. Plast. 67, 69–101 (2015)
L. Qian, Q. Sun, X. Xiao, Role of phase transition in the unusual microwear behavior of superelastic NiTi shape memory alloy. Wear 260(4–5), 509–522 (2006)
X.M. Wang, B.X. Xu, Z.F. Yue, Micromechanical modelling of the effect of plastic deformation on the mechanical behaviour in pseudoelastic shape memory alloys. Int. J. Plast. 24, 1307–1332 (2008)
R. Hill, A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13, 213–222 (1965)
G. Cailletaud, P. Pilvin, Utilisation de modèles polycristallins pour le calcul par éléments finis. Rev. Eur. Élém. Fin. 3(4), 515–541 (1994)
B.K.D. Gairola, E. Kröner, A simple formula for calculating the bounds and the self-consistent value of the shear modulus of a polycrystalline aggregate of cubic crystals. Int. J. Eng. Sci. 19(6), 865–869 (1981)
P. Thamburaja, Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys. J. Mech. Phys. Solids 53(4), 825–856 (2015)
K. Otsuka, X. Ren, Physical metallurgy of Ti–Ni-based shape memory alloys. Prog. Mater. Sci. 50(5), 511–678 (2005)
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)
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)
Y. Liu, Z. Xie, J.V. Humbeeck, L. Delaey, Asymmetry of stress-strain curves under tension and compression for NiTi shape memory alloys. Acta Mater. 46(12), 4325–4338 (1998)
Z. Xie, Y. Liu, J.V. Humbeeck, Microstructure of NiTi shape memory alloy due to tension-compression cyclic deformation. Acta Mater. 46(6), 1989–2000 (1998)
D. Song, G. Kang, Q. Kan, C. Yu, C. Zhang, Non-proportional multiaxial transformation ratchetting of super-elastic NiTi shape memory alloy: experimental observations. Mech. Mater. 70, 94–105 (2014)
C. Yu, G. Kang, Q. Kan, Study on the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy based on a new crystal plasticity constitutive model. Int. J. Solids Struct. 51(25–26), 4386–4405 (2014)
C. Morin, Z. Moumni, W. Zaki, Thermomechanical coupling in shape memory alloys under cyclic loadings: experimental analysis and constitutive modeling. Int. J. Plast. 27(12), 1959–1980 (2011)
G.Z. Kang, Q.H. Kan, C. Yu, D. Song, Y.J. Liu, Whole-life transformation ratchetting and fatigue of super-elastic NiTi alloy under uniaxial stress-controlled cyclic loading. Mater. Sci. Eng. A. 535, 228–234 (2012)
F.A. Nae, Y. Matsuzaki, T. Ikeda, Micromechanical modeling of polycrystalline shape-memory alloys including thermo-mechanical coupling. Smart Mater. Struct. 12(1), 6 (2002)
S. Zhu, Y. Zhang, A thermomechanical constitutive model for superelastic SMA wire with strain-rate dependence. Smart Mater. Struct. 16(5), 1696 (2007)
Y.J. He, Q.P. Sun, Frequency-dependent temperature evolution in NiTi shape memory alloy under cyclic loading. Smart Mater. Struct. 19(11), 115014 (2010)
Y.J. He, Q.P. Sun, On non-monotonic rate dependence of stress hysteresis of superelastic shape memory alloy bars. Int. J. Solids Struct. 48(11), 1688–1695 (2011)
H. Yin, Q. Sun, Temperature variation in NiTi shape memory alloy during cyclic phase transition. J. Mater. Eng. Perform. 21(12), 2505–2508 (2012)
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)
J.A. Shaw, S. Kyriakides, Thermomechanical aspects of NiTi. J. Mech. Phys. Solids 43(8), 1243–1281 (1995)
Q.P. Sun, Z. Li, Phase transformation in superelastic NiTi polycrystalline micro-tubes under tension and torsion––from localization to homogeneous deformation. Int. J. Solids Struct. 39(13–14), 3797–3809 (2002)
X. Zhang, P. Feng, Y. He, T. Yu, Q.P. Sun, Experimental study on rate dependence of macroscopic domain and stress hysteresis in NiTi shape memory alloy strips. Int. J. Mech. Sci. 52(12), 1660–1670 (2010)
W. Zaki, Z. Moumni, A three-dimensional model of the thermomechanical behavior of shape memory alloys. J. Mech. Phys. Solids 55(11), 2455–2490 (2007)
Q.P. Sun, H. Zhao, R. Zhou, D. Saletti, H. Yin, Recent advances in spatiotemporal evolution of thermomechanical fields during the solid–solid phase transition. C.R. Mecanique 340(4), 349–358 (2012)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Kang, G., Yu, C., Kan, Q. (2023). Crystal Plasticity-Based 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_6
Download citation
DOI: https://doi.org/10.1007/978-981-99-2752-4_6
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-99-2751-7
Online ISBN: 978-981-99-2752-4
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)