In this study, a three-dimensional thermomechanical constitutive model based on the microplane theory is proposed to simulate the behavior of shape memory alloy tubes. The three-dimensional model is implemented in ABAQUS by employing a user material subroutine. In order to validate the model, the numerical results of this approach are compared with new experimental findings for a NiTi superelastic torque tube under tension, pure torsion, and proportional tension–torsion performed in stress- and strain-controlled manners. The numerical and experimental results are in agreement indicating the capability of the proposed microplane model in capturing the behavior of shape memory alloy tubes. This model is capable of predicting both superelasticity and shape memory effect by providing closed-form relationships for calculating the strain components in terms of the stress components.
ArghavaniJAuricchioFNaghdabadiR. (2010) A 3-D phenomenological constitutive model for shape memory alloys under multiaxial loadings. International Journal of Plasticity26: 976–991.
3.
BazantZP (1984) Chapter 3: Microplane model for strain controlled inelastic behavior. In: DesaiCSGallagherRH (eds) Mechanics of Engineering Materials. New York: John Wiley & Sons, pp. 45–59.
4.
BazantZPOhBH (1986) Efficient numerical integration on the surface of a sphere. Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)66: 37–49.
5.
BazantZPPratPC (1988a) Microplane model for brittle plastic material: I. Theory. Journal of Engineering Mechanics: ASCE114(10): 1672–1688.
6.
BazantZPPratPC (1988b) Microplane model for brittle plastic material: II. Verification. Journal of Engineering Mechanics: ASCE114(10): 1689–1699.
7.
BoydJGLagoudasDC (1996) A thermodynamic constitutive model for the shape memory alloy materials. Part I. The monolithic shape memory alloy. International Journal of Plasticity12: 805–842.
8.
BrinsonLC (1993) One dimensional constitutive behavior of memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable. Journal of Intelligent Material Systems and Structures4: 229–242.
9.
BrinsonLCHuangMS (1996) Simplifications and comparisons of shape memory alloy constitutive models. Journal of Intelligent Material Systems and Structures7: 108–114.
10.
BroccaMBrinsonLCBazantZP (2002) Three-dimensional constitutive model for shape memory alloys based on microplane model. Journal of the Mechanics and Physics of Solids50: 1051–1077.
11.
CarolIBazantZP (1997) Damage and plasticity in microplane theory. International Journal of Solids and Structures34(29): 3807–3835.
12.
CarolIJirasekMBazantZP (2001) A thermodynamically consistent approach to microplane theory. Part I. Free energy and consistent microplane stresses. International Journal of Solids and Structures38: 2921–2931.
13.
GrabeCBruhnsOT (2008) Tension/torsion tests of pseudoelastic, polycrystalline NiTi shape memory alloys under temperature control. Materials Science and Engineering A481–482: 109–113.
14.
GrabeCBruhnsOT (2009) Path dependence and multiaxial behavior of a polycrystalline NiTi alloy within the pseudoelastic and pseudoplastic temperature regimes. International Journal of Plasticity25: 513–545.
15.
HartlDJLagoudasDC (2007) Aerospace applications of shape memory alloys. Journal of Aerospace Engineering221(4): 535–552.
KadkhodaeiMSalimiMRajapakseRKND. (2008) Modeling of shape memory alloys based on microplane theory. Journal of Intelligent Material Systems and Structures19: 541–550.
18.
KeefeAC (1994) Thermo-mechanical characterization of shape memory alloy torque tube actuators. Master’s Thesis, University of California, Los Angeles, CA.
19.
KeefeACCarmanGP (1997) Thermo-mechanical characterization of shape memory alloy torque tubes. Smart Materials and Structures9: 665–672.
20.
LagoudasDCHartlDChemiskyY. (2012) Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys. International Journal of Plasticity32–33: 155–183.
21.
LimTJMcDowellDL (1995) Path dependence of shape memory alloys during cyclic loading. Journal of Intelligent Material Systems and Structures6: 817–847.
22.
MehrabiRKadkhodaeiMTaheriMElahiniaM (2012, September) Shape Memory Effect Behavior of NiTi Torque Tubes in Torsion. In ASME 2012 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, American Society of Mechanical Engineers 571–575.
23.
MehrabiRKadkhodaeiM (2013) 3D phenomenological constitutive modeling of shape memory alloys based on microplane theory. Smart Materials and Structures22(2): 025017.
24.
MehrabiRKadkhodaeiMGhaeiA (2012) Numerical implementation of a thermomechanical constitutive model for shape memory alloys using return mapping algorithm and microplane theory. Advanced Materials Research516: 351–354.
25.
NespoliABesseghiniSPittaccioS. (2010) The high potential of shape memory alloys in developing miniature mechanical devices: a review on shape memory alloy mini-actuators. Sensors and Actuators A: Physical158(1): 149–160.
26.
OliveiraSASaviMAKalamkarovAL (2010) A three-dimensional constitutive model for shape memory alloys. Archive of Applied Mechanics80: 1163–1175.
27.
PanHThamburajaPChauFS (2007) Multi-axial behavior of shape-memory alloys undergoing martensitic reorientation and detwinning. International Journal of Plasticity23: 711–732.
28.
PanicoMBrinsonLC (2007) A three-dimensional phenomenological model for martensite reorientation in shape memory alloys. Journal of the Mechanics and Physics of Solids55: 2491–2511.
29.
PrahladHChopraI (2007) Modeling and experimental characterization of SMA torsional actuators. Journal of Intelligent Material Systems and Structures18: 29–38.
30.
SaadatSSalichsJNooriM. (2002) An overview of vibration and seismic applications of NiTi shape memory alloy. Smart Materials and Structures11(2): 218–229.
31.
SaleebAPadulaSIIKumarA (2011) A multi-axial, multimechanism based constitutive model for the comprehensive representation of the evolutionary response of SMAS under general thermomechanical loading conditions. International Journal of Plasticity27: 655–687.
32.
ShishkinSV (1994) On theoretical interrelations between thermomechanical diagrams in tension, compression, and torsion for alloys possessing the shape memory effect. Industrial Laboratory60(1): 32–37.
33.
SittnerPHaraYTokudaM (1995) Experimental study on the thermoelastic martensitic transformation in shape memory alloy polycrystal induced by combined external forces. Metallurgical and Materials Transactions A26: 2923–2958.
34.
SunQPLiZQ (2002) Phase transformation in superelastic NiTi polycrystalline micro-tubes under tension and torsion—from localization to homogeneous deformation. International Journal of Solids and Structures39: 3797–3809.
35.
ThamburajaP (2005) Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys. Journal of the Mechanics and Physics of Solids53: 825–856.
36.
WangXMWangYFLuZZ. (2010) An experimental study of the superelastic behavior in NiTi shape memory alloys under biaxial proportional and non-proportional cyclic loadings. Mechanics of Materials42: 365–373.
37.
ZakiW (2012) An efficient implementation for a model of martensite reorientation in martensitic shape memory alloys under multiaxial nonproportional loading. International Journal of Plasticity37: 72–94.
