Browse > Article
http://dx.doi.org/10.12989/sss.2015.16.4.641

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)
Publication Information
Smart Structures and Systems / v.16, no.4, 2015 , pp. 641-665 More about this Journal
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
shape memory alloys; constitutive modeling; martensitic transformation; pseudo-elasticity; ferro-elasticity;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
연도 인용수 순위
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI   ScienceOn
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI