Smart Structures and Systems

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A simple and efficient 1-D macroscopic model for shape memory alloys considering ferro-elasticity effect

  • Damanpack, A.R. (Smart Materials and Structures Laboratory, Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong) ;
  • Bodaghi, M. (Smart Materials and Structures Laboratory, Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong) ;
  • Liao, W.H. (Smart Materials and Structures Laboratory, Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong) ;
  • Aghdam, M.M. (Thermo-elasticity Center of Excellence, Department of Mechanical Engineering, Amirkabir University of Technology) ;
  • Shakeri, M. (Thermo-elasticity Center of Excellence, Department of Mechanical Engineering, Amirkabir University of Technology)
  • Received : 2014.07.18
  • Accepted : 2015.02.10
  • Published : 2015.10.25
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Abstract

In this paper, a simple and efficient phenomenological macroscopic one-dimensional model is proposed which is able to simulate main features of shape memory alloys (SMAs) particularly ferro-elasticity effect. The constitutive model is developed within the framework of thermodynamics of irreversible processes to simulate the one-dimensional behavior of SMAs under uniaxial simple tension-compression as well as pure torsion+/- loadings. Various functions including linear, cosine and exponential functions are introduced in a unified framework for the martensite transformation kinetics and an analytical description of constitutive equations is presented. The presented model can be used to reproduce primary aspects of SMAs including transformation/orientation of martensite phase, shape memory effect, pseudo-elasticity and in particular ferro-elasticity. Experimental results available in the open literature for uniaxial tension, torsion and bending tests are simulated to validate the present SMA model in capturing the main mechanical characteristics. Due to simplicity and accuracy, it is expected the present SMA model will be instrumental toward an accurate analysis of SMA components in various engineering structures particularly when the ferro-elasticity is obvious.

Keywords

References

  1. Brinson, L.C. (1993), "One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variable", J. Intel. Mat. Syst. Struct., 4(2), 229-242. https://doi.org/10.1177/1045389X9300400213
  2. Boyd, J.G. and Lagoudas, D.C. (1996), "A thermodynamical constitutive model for shape memory materials Part I: The monolithic shape memory alloy", Int. J. Plast., 12, 805-842. https://doi.org/10.1016/S0749-6419(96)00030-7
  3. Bekker, A. and Brinson, L.C. (1998), "Phase diagram based description of the hysteresis behavior of shape memory alloys", Acta Mater., 46, 3649-3665. https://doi.org/10.1016/S1359-6454(97)00490-4
  4. BenMekki, O. and Auricchio, F. (2011), "Performance evaluation of shape-memory-alloy superelastic behavior to control a stay cable in cable-stayed bridges", Int. J. Nonlinear Mech., 46, 470-477. https://doi.org/10.1016/j.ijnonlinmec.2010.12.002
  5. Bodaghi, M., Damanpack, A.R., Aghdam, M.M. and Shakeri, M. (2013), "A phenomenological SMA model for combined axial-torsional proportional/non-proportional loading conditions", Mater. Sci. Eng. A., 587, 12-26. https://doi.org/10.1016/j.msea.2013.08.037
  6. Casciati, S. and Hamdaoui, K. (2008), "Experimental and numerical studies toward the implementation of shape memory alloy ties in masonry structures", Smart Struct. Syst., 4(2), 153-169. https://doi.org/10.12989/sss.2008.4.2.153
  7. Chung, J.H., Heo, J.S. and Lee, J.J. (2007), "Implementation strategy for the dual transformation region in the Brinson SMA constitutive model", Smart Mater. Struct., 16, 1-5. https://doi.org/10.1088/0964-1726/16/1/001
  8. Carreras, G., Casciati, F., Casciati, S., Isalgue, A., Marzi, A. and Torra, V. (2011), "Fatigue laboratory tests toward the design of SMA portico-braces", Smart Struct. Syst., 7(1), 41-57. https://doi.org/10.12989/sss.2011.7.1.041
  9. Daghia, F., Inman, D.J., Ubertini, F. and Viola, E. (2010), "Active shape change of an SMA hybrid composite plate", Smart Struct. Syst., 6(2), 91-100. https://doi.org/10.12989/sss.2010.6.2.091
  10. Flor, S.D., Urbina, C. and Ferrando, F. (2006), "Constitutive model of shape memory alloys: theoretical formulation and experimental validation", Mater Sci. Eng. A., 427, 112-122. https://doi.org/10.1016/j.msea.2006.04.008
  11. Liang, C. and Rogers, C.A. (1990) "One-dimensional thermomechanical constitutive relations for shape memory materials", J. Intel. Mat. Syst. Str., 1(2), 207-234. https://doi.org/10.1177/1045389X9000100205
  12. Lagoudas, D.C., Bo, Z. and Qidwai, M.A. (1996) "A unified thermodynamic constitutive model for SMA and finite element analysis of active metal matrix composites", Mech. Compos. Mater. Struct., 3, 153- 179. https://doi.org/10.1080/10759419608945861
  13. Lexcellent, C., Boubakar, M.L., Bouvet, C. and Calloch, S. (2006), "About modelling the shape memory alloy behaviour based on the phase transformation surface identification under proportional loading and anisothermal conditions", Int. J. Solids Struct., 43(3-4), 613-626. https://doi.org/10.1016/j.ijsolstr.2005.07.004
  14. Lagoudas, D.C. (2008), Shape Memory Alloys: modeling and engineering applications, Springer, New York, USA.
  15. Mirzaeifar, R.,.DesRoches, R. and Yavari, A. (2011), "Analysis of the rate-dependent coupled thermo-mechanical response of shape memory alloy bars and wires in tension", Continuum Mech. Therm., 23, 363-385. https://doi.org/10.1007/s00161-011-0187-8
  16. Patoor, E., Lagoudas, D.C., Entchev, P.B., Brinson, L.C. and Gao, X. (2006), "Shape memory alloys, Part I: General properties and modeling of single crystals", Mech. Mater., 38, 391-429. https://doi.org/10.1016/j.mechmat.2005.05.027
  17. Panico, M. and Brinson, L.C. (2007), "A three-dimensional phenomenological model for martensite reorientation in shape memory alloys", J. Mech. Phys. Solids., 55, 2491-2511. https://doi.org/10.1016/j.jmps.2007.03.010
  18. Roh, J.H., Oh, I.K., Yang, S.M., Han, J.H. and Lee, I. (2004), "Thermal post-buckling analysis of shape memory alloy hybrid composite shell panels", Smart Mater. Struct., 13, 1337-1344. https://doi.org/10.1088/0964-1726/13/6/006
  19. Simo, J.C. and Hughes, T.J.R. (1998), Computational Inelasticity, Springer, New York, USA.
  20. Sittner, P., Pilch, J. and Heller, L. (2009) .
  21. Seelecke, S. and Muller, I. (2004), "Shape memory alloy actuators in smart structures: Modeling and simulation", Appl. Mech. Rev., 57, 23-46. https://doi.org/10.1115/1.1584064
  22. Shahria Alam, M., Nehdi, M. and Youssef, M.A. (2009), "Seismic performance of concrete frame structures reinforced with superelastic shape memory alloys", Smart Struct. Syst., 5(5), 565-585. https://doi.org/10.12989/sss.2009.5.5.565
  23. Saleeb, A.F., Kumar, A., Padula, S.A. and Dhakal, B. (2013), "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., 63, 21-47. https://doi.org/10.1016/j.mechmat.2013.04.003
  24. Sedlak, P., Frost, M., Benesova, B., Ben Zineb, T. and Sittner, P. (2012), "Thermomechanical model for NiTi-based shape memory alloys including R-phase and material anisotropy under multi-axial loadings", Int. J. Plast., 39, 132-151. https://doi.org/10.1016/j.ijplas.2012.06.008
  25. Tanaka, K. (1986), "A thermomechanical sketch of shape memory effect: One-dimensional tensile behavior", Res. Mechanica., 18, 251-263.
  26. Thamburaja, P. and Anand, L. (2002), "Superelastic behavior in tension-torsion of an initially-textured Ti-Ni shape-memory alloy", Int. J. Plast., 18(11), 1607-1617. https://doi.org/10.1016/S0749-6419(02)00031-1
  27. Torra, V., Auguet, C., Isalgue, A., Carreras, G., Terriault, P. and Lovey, F.C. (2013), "Built in dampers for stayed cables in bridges via SMA. The SMARTeR-ESF project: A mesoscopic and macroscopic experimental analysis with numerical simulations", Eng. Struct., 49, 43-57. https://doi.org/10.1016/j.engstruct.2012.11.011
  28. Youssef, M.A. and Elfeki, M.A. (2012), "Seismic performance of concrete frames reinforced with superelastic shape memory alloys", Smart Struct. Syst., 9(4), 313-333. https://doi.org/10.12989/sss.2012.9.4.313
  29. Zhang, Y. and Zhao, Y.P. (2007), "A study of composite beam with shape memory alloy arbitrarily embedded under thermal and mechanical loadings", Mater. Design, 28(4), 1096-1115. https://doi.org/10.1016/j.matdes.2006.02.001