A simple constitutive model of shape memory alloys for analyses of tension—compression quasiplastic behavior is derived. Here, three martensitic variants are considered; namely, thermal-induced, tensile stress-induced, and compressive stress-induced martensitic variants. Reorientation from one variant to another variant is assumed to take place according to a reorientation energy criterion based on grain-based micromechanics. Stress—strain hysteresis loops for a bar under tension—compression cyclic loading are simulated and they are compared with available experimental data. Results show that this constitutive model can capture asymmetric stress—strain behavior for tension and compression and a strain rate effect on stress—strain—temperature relationship quite well.
Adachi, Y. and Unjoh, S.1999. ``Development of Shape Memory Alloy Damper for Intelligent Bridge Systems,'' Proc. SPIE Smart Struct. Mater, 3671:31-42.
2.
Bertram, A.1982. ``Thermo-mechanical Constitutive Equations for the Description of Shape Memory Effects in Alloys,'' Nuclear Engineering and Design, 74(2):173-182.
3.
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. Intell. Mater. Syst. Struct., 4(2):229-242.
4.
Falk, F.1983. ``One-dimensional Model of Shape Memory Alloys,''Arch. Mech., 35(1):63-84.
5.
Gall, K. and Sehitoglu, H.1999. ``The Role of Texture in Tension-Compression Asymmetry in Polycrystalline NiTi,''Int. J. Plasticity, 15(1):69-92.
6.
Graesser, E.J. and Cozzarelli, F.A.1991. ``Shape-memory Alloys as New Materials for a Seismic Isolation,''J. Eng. Mech., 117(11):2590-2608.
7.
Huang, M. and Brinson, L.C.1998. ``A Multivariant Model for Single Crystal Shape Memory Alloy Behavior,''J. Mech. Phys. Solids, 46(8):1379-1409.
8.
Huo, Y. and Zu, X.1998. ``On the Three Phase Mixtures in Martensitic Transformations of Shape Memory Alloys: Thermodynamical Modeling and Characteristic Temperatures,'' Continuum Mech. Thermodyn., 10(3):179-188.
9.
Ikeda, T., Nae, F.A. and Matsuzaki, Y.2003. ``Microscopic Model of Polycrystalline Shape Memory Alloys Based on Reuss Assumption,'' Proc. SPIE Smart Struct. Mater. , 5049:35-45.
10.
Ikeda, T., Nae, F.A. and Matsuzaki, Y.2004a. ``Macroscopic Constitutive Model of Shape Memory Alloys for Partial Transformation Cycles,'' Proc. SPIE Smart Struct. Mater., 5383:112-121.
11.
Ikeda, T., Nae, F.A., Naito, H. and Matsuzaki, Y.2004b. ``Constitutive Model of Shape Memory Alloys for Unidirectional Loading Considering Inner Hysteresis Loops,'' Smart Mater. Struct., 13(4):916-925.
12.
Ivshin, Y. and Pence, T.J.1994. ``A Thermomechanical Model for a One Variant Shape Memory Material,''J. Intell. Mater. Syst. Struct., 5(4):455-473.
13.
Kamita, T. and Matsuzaki, Y.1998. ``One-dimensional Pseudoelastic Theory of Shape Memory Alloys,'' Smart Mater. Struct., 7(4):489-495.
14.
Leclercq, S. and Lexcellent, C.1996. ``A General Macroscopic Description of the Thermomechanical Behavior of Shape Memory Alloys,''J. Mech. Phys. Solids, 44(6):953-980.
15.
Liang, C. and Rogers, C.A.1990. ``One-dimensional Thermomechanical Constitutive Relations for Shape Memory Materials,''J. Intell. Mater. Syst. Struct. , 1(2):207-234.
16.
Liu, Y., Xie, Z., van Humbeeck, J. and Delaey, L.1998. ``Asymmetry of Stress-Strain Curves under Tension and Compression for NiTi Shape Memory Alloys,'' Acta Metar., 46(12):4325-4338.
17.
Liu, Y. and van Humbeeck, J.1997. ``On the Damping Behaviour of NiTi Shape Memory Alloy,'' J. de Phys. IV, 7:C5-519-524.
18.
Matsuzaki, Y., Funami, K. and Naito, H.2002. ``Inner Loops of Pseudoelastic Hysteresis of Shape Memory Alloys: Preisach Approach,'' Proc. SPIE Smart Struct. Mater. , 4699:355-364.
19.
Matsuzaki, Y., Naito, H., Ikeda, T. and Funami, K.2001. ``Thermomechanical Behavior Associated with Pseudoelastic Transformation of Shape Memory Alloys,'' Smart Mater. Struct. , 10(5):884-892.
20.
Müller, I. and Xu, H.1991. ``On the Pseudo-elastic Hysteresis,'' Acta. Metall. Mater., 39(3):263-271.
21.
Nae, F.A., Matsuzaki, Y. and Ikeda, T.2003. ``Micromechanical Modeling of Polycrystalline Shape-memory Alloys Including Thermo-mechanical Coupling,'' Smart Mater. Struct., 12(1):6-17.
22.
Ortín, J.1991. ``Preisach Modeling of Hysteresis for a Pseudoelastic Cu-Zn-Al Single Crystal,''J. Appl. Phys., 71(3):1454-1461.
23.
Raniecki, B., Lexcellent, C.H. and Tanaka, K.1992. ``Thermodynamic Models of Pseudoelastic Behavior of Shape Memory Alloys,''Arch. Mech., 44(3):261-284.
24.
Seelecke, S.1996. ``Equilibrium Thermodynamics of Pseudoelasticity and Quasiplasticity,'' Continuum Mech. Thermodyn., 8(6):309-322.
Tanaka, K.1990. ``A Phenomenological Description on Thermomechanical Behavior of Shape Memory Alloys,''Trans. ASME J. Press. Vessel Tech. , 112(2):158-163.
27.
Tobushi, H., Okumura, K., Endo, E. and Takata, K.2001. ``Stress-induced Martensitic Transformation Behavior and Lateral Strain of TiNi Shape Memory Alloy,'' In: Matsuzaki, Y. Ikeda, T. and Baburaj, V. (eds), Proc. 11th Int. Conf. Adapt. Struct. Tech, Technomic Pub. , Lancaster, pp. 367-374.
