DOI QR코드

DOI QR Code

A Phenomenological Constitutive Model for Pseudoelastic Shape Memory Alloy

의탄성 형상기억합금에 대한 현상학적 구성모델

  • 호광수 (계명대학교 기계자동차공학과)
  • Received : 2010.09.14
  • Accepted : 2010.11.11
  • Published : 2010.12.01

Abstract

Shape memory alloys (SMAs) have the ability to recover their original shape upon thermo-mechanical loading even after large inelastic deformation. The unique feature is known as pseudoelasticity and shape memory effect caused by the crystalline structural transformation between two solid-state phases called austenite and martensite. To support the engineering application, a number of constitutive models, which can be formally classified into either micromechanics-based or phenomenological model, have been developed. Most of the constitutive models include a kinetic law governing the crystallographic transformation. The present work presents a one-dimensional, phenomenological constitutive model for SMAs in the context of the unified viscoplasticity theory. The proposed model does not incorporate the complex mechanisms of phase transformation. Instead, the effects induced by the transformation are depicted through the growth law for the back stress that is an internal state variable of the model.

Keywords

References

  1. T. Duerig, A. Pelton, D. Stöckel, 1999, An overview of nitinol medical applications, Mater. Sci. Eng. A, Vol. 273-275, pp. 149-160. https://doi.org/10.1016/S0921-5093(99)00294-4
  2. J. V. Humbeeck, 1999, Non-medical applications of shape memory alloys, Mater. Sci. Eng. A, Vol. 273-275, pp. 134-148. https://doi.org/10.1016/S0921-5093(99)00293-2
  3. N. B. Morgan, 2004, Medical shape memory alloy applications-the market and its products, Mater. Sci. Eng. A, Vol. 378, pp. 16-23. https://doi.org/10.1016/j.msea.2003.10.326
  4. Q. P. Sun, K. C. Hwang, 1993, Micromechanics modeling for the constitutive behavior of polycrystalline shape memory alloys-I. Derivation of general relations, J. Mech. Phys. Solids, Vol. 41, pp. 1-17. https://doi.org/10.1016/0022-5096(93)90060-S
  5. E. Patoor, A. Eberhardt, M. Berveiller, 1988, Thermomechanical behavior of shape memory alloys, Arch. Mech., Vol. 40, pp. 775-794.
  6. X. Gao, M. Huang, L. C. Brinson, 2000, A multivariant micromechanical model for SMAs: Part I. Crystallographic issues for single crystal model, Int. J. Plasticity, Vol. 16, pp. 1345-1369. https://doi.org/10.1016/S0749-6419(00)00013-9
  7. T. J. Lim, D. L. McDowell, 1999, Mechanical behavior of an Ni-Ti shape memory alloy under axial-torsional proportional and nonproportional loading, J. Eng. Mater. Tech., Vol. 121, pp. 9-18. https://doi.org/10.1115/1.2816007
  8. X. Peng, W. Pi, J. Fan, 2008, A microstructurebased constitutive model for the pseudoelastic behavior of NiTi SMAs, Int. J. Plasticity, Vol. 24, pp. 966-990. https://doi.org/10.1016/j.ijplas.2007.08.003
  9. X. M. Wang, B. X. Xu, Z. F. Yue, 2008, Micromechanical modeling of the effect of plastic deformation on the mechanical behavior in pseudoelastic shape memory alloys, Int. J. Plasticity, Vol. 24, pp. 1307-1332. https://doi.org/10.1016/j.ijplas.2007.09.006
  10. S. Manchiraju, P. M. Anderson, 2010, Coupling between martensitic phase transformation and plasticity: A microstructure-based finite element model, in press, Int. J. Plasticity. https://doi.org/10.1016/j.ijplas.2010.01.009
  11. K. Tanaka, S. Nagaki, 1982, A thermomechanical description of materials with internal variable in the process of phase transitions, Ing. Arch., Vol. 51, pp. 287-299. https://doi.org/10.1007/BF00536655
  12. C. Liang, C. A. Rogers, 1990, One-dimensional thermomechanical constitutive relations for shape memory materials, J. Intell. Mater. Sys. Struct., Vol. 1, pp. 207-234. https://doi.org/10.1177/1045389X9000100205
  13. L. C. Brinson, 1993, One dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions, J. Intell. Mater. Sys. Struct., Vol. 4, pp. 229-242. https://doi.org/10.1177/1045389X9300400213
  14. D. C. Lagoudas, Z. Bo, 1999, Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part II: material characterization and experimental results for a stable transformation cycle, Int. J. Eng. Sci., Vol. 37, pp. 1205-1249. https://doi.org/10.1016/S0020-7225(98)00116-5
  15. W. Yan, C. H. Wang, X. P. Zhang, Y. Mai, 2003, Theoretical modeling of the effect of plasticity on reverse transformation in superelastic shape memory alloys, Mater. Sci. Eng. A, Vol. 354, pp. 146-157. https://doi.org/10.1016/S0921-5093(02)00941-3
  16. D. C. Lagoudas, P. B. Entchev, 2004, Modelling 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., Vol., 36, pp. 865-892. https://doi.org/10.1016/j.mechmat.2003.08.006
  17. Q. Kan, G. Kang, 2010, Constitutive model for uniaxial transformation ratcheting of super-elastic NiTi shape memory alloy at room temperature, Int. J. Plasticity, Vol. 26, pp. 441-465. https://doi.org/10.1016/j.ijplas.2009.08.005
  18. A. Krausz, K. Krausz, 1996, Unified constitutive laws of plastic deformation, San Diego, Academic Press.
  19. K. Ho, 2001, Modeling of nonlinear rate sensitivity by using an overstress model, Comp. Model. Eng. Sci., Vol. 2, No.3, pp. 351-364.
  20. K. Ho, 2007, The rate dependent deformation behavior of AISI Type 304 stainless steel at room temperature, Trans. Mater. Process., Vol. 16, No.2, pp. 101-106. https://doi.org/10.5228/KSPP.2007.16.2.101
  21. K. Ho, 2008, Effect of the rate dependence of nonlinear kinematic hardening rule on relaxation behavior, Int. J. Solid Struct., Vol. 45, pp. 821-839. https://doi.org/10.1016/j.ijsolstr.2007.09.003
  22. Z. Moumni, W. Zaki, Q. S. Nguyen, 2008, Theoretical and numerical modeling of solid-solid phase change: Application to the description of the thermomechanical behavior of shape memory alloys, Int. J. Plasticity., Vol. 24, pp. 614-645. https://doi.org/10.1016/j.ijplas.2007.07.007

Cited by

  1. A Constitutive Model for the Rate-dependent Deformation Behavior of a Solid Polymer vol.22, pp.4, 2013, https://doi.org/10.5228/KSTP.2013.22.4.216
  2. An Improved Constitutive Model of Shape Memory Alloy vol.20, pp.5, 2011, https://doi.org/10.5228/KSTP.2011.20.5.350
  3. Prediction of Shape Recovery for Ni-Ti SMA Wire after Drawing vol.22, pp.8, 2013, https://doi.org/10.5228/KSTP.2013.22.8.470