High-temperature shape memory alloys have remarkably solved the limitation of conventional shape memory alloys working at low levels of temperature and stress. The focus of this study is on a semi-analytical constitutive model for high-temperature shape memory alloys to predict their mechanical behavior. The model is based on Gibbs free energy, and the equations are simplified for NiTiHf at different loading conditions. A uniaxial compression case is used to validate the model with the experimental results. Superelastic behavior and also heating and cooling at different stress levels are compared to the experimental data reported in the literature. The nonlinear equations are solved using finite difference method, which is capable to calculate the distribution of strain and phase transformation along the cross section for various loading modes. Several more case studies on pure torsion and multiaxial loading are also investigated to show the capabilities of this approach.
AbuJudoraDNThomaPEKaoMYet al. (1992) High Transformation Shape Memory Alloy. US Patent No. 5,114,504, 1992.
2.
AnandLGurtinME (2003) Thermal effects in the superelasticity of crystalline shape-memory materials. Journal of the Mechanics and Physics of Solids51: 1015–1058.
3.
AndaniMTAlipourAEshghinejadAet al. (2013) Modifying the torque–angle behavior of rotary shape memory alloy actuators through axial loading: a semi-analytical study of combined tension–torsion behavior. Journal of Intelligent Material Systems and Structures24: 1524–1535.
4.
AndaniMTElahiniaM (2013) A rate dependent tension–torsion constitutive model for superelastic nitinol under non-proportional loading: a departure from von Mises equivalency. Smart Materials and Structures23: 015012.
5.
AndaniMTElahiniaM (2014) Modeling and simulation of SMA medical devices undergoing complex thermo-mechanical loadings. Journal of Materials Engineering and Performance23: 2574–2583.
6.
AndaniMTAndersonWElahiniaM (2015) Design, modeling and experimental evaluation of a minimally invasive cage for spinal fusion surgery utilizing superelastic Nitinol hinges. Journal of Intelligent Material Systems and Structures26: 631–638.
7.
BenafanOGaydoshDJ (2017) High temperature shape memory alloy Ni50.3Ti29.7Hf20 torque tube actuators. Smart Materials and Structures26: 095002.
8.
BigelowGSGargAPadulaIIet al. (2011) Load-biased shape-memory and superelastic properties of a precipitation strengthened high-temperature Ni50.3Ti29.7Hf20 alloy. Scripta Materialia64: 725–728.
9.
BoydJGLagoudasDC (1996) A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy. International Journal of Plasticity12: 805–842.
10.
BrinsonLC (1993) One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable. Journal of Intelligent Material Systems and Structures4: 229–242.
11.
DebergLAndaniMTHosseinipourMet al. (2014) An SMA passive ankle foot orthosis: design, modeling, and experimental evaluation. Smart Materials Research2014: 572094.
12.
DenowhCMMillerDA (2012) Thermomechanical training and characterization of Ni–Ti–Hf and Ni–Ti–Hf–Cu high temperature shape memory alloys. Smart Materials and Structures21: 065020.
13.
ElahiniaMAndaniMTHaberlandC (2014) Shape memory and superelastic alloys. In: Bar-CohenY (ed.) High Temperature Materials and Mechanisms. Boca Raton, FL: CRC Press, pp. 355–380.
14.
HartlDJChatzigeorgiouGLagoudasDC (2010) Three-dimensional modeling and numerical analysis of rate-dependent irrecoverable deformation in shape memory alloys. International Journal of Plasticity26: 1485–1507.
15.
HartlDJLagoudasDCCalkinsFTet al. (2009) Use of a Ni60Ti shape memory alloy for active jet engine chevron application: I. Thermomechanical characterization. The Journal of Smart Materials and Structures19: 015021.
16.
JahadakbarAMoghaddamNSAmerinatanziAet al. (2016) Finite element simulation and additive manufacturing of stiffness-matched niti fixation hardware for mandibular reconstruction surgery. Bioengineering3: E36.
KaracaHESaghaianSMBasaranBet al. (2011) Compressive response of nickel-rich NiTiHf high-temperature shape memory single crystals along the [1 1 1] orientation. Scripta Materialia65: 577–580.
19.
KumarPKLagoudasDC (2010) Experimental and microstructural characterization of simultaneous creep, plasticity and phase transformation in Ti50Pd40Ni10 high-temperature shape memory alloy. Acta Materialia58: 1618–1628.
20.
LagoudasDCEntchevPB (2004) Modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys. Part I: constitutive model for fully dense SMAs. Mechanics of Materials36: 865–892.
21.
LagoudasDCChatzigeorgiouGKumarPK (2009) Modeling and experimental study of simultaneous creep and transformation in polycrystalline high-temperature shape memory alloys. Journal of Intelligent Material Systems and Structures20: 2257–2267.
22.
MaJKaramanINoebeRD (2010) High temperature shape memory alloys. International Materials Reviews55: 257–315.
23.
ManchirajuSAndersonPS (2010) Coupling between martensitic phase transformations and plasticity: a microstructure-based finite element model. International Journal of Plasticity26: 1508–1526.
24.
MehrabiRKadkhodaeiMElahiniaM (2014) A thermodynamically-consistent microplane model for shape memory alloys. International Journal of Solids and Structures51: 2666–2675.
25.
MehrabiRKadkhodaeiMAndaniMTet al. (2015) Microplane modeling of shape memory alloy tubes under tension, torsion, and proportional tension–torsion loading. Journal of Intelligent Material Systems and Structures26: 144–155.
26.
MirzaeifarRDesRochesRYavariA (2011) Analysis of the rate-dependent coupled thermo-mechanical response of shape memory alloy bars and wires in tension. Continuum Mechanics and Thermodynamics23: 363–385.
27.
MoghaddamNSElahiniaMMillerMet al. (2014) Enhancement of bone implants by substituting nitinol for titanium (Ti-6Al-4V): a modeling comparison. In: ASME 2014 conference on smart materials, adaptive structures and intelligent systems, Newport, RI, 8–10 September. New York: American Society of Mechanical Engineers.
28.
MoghaddamNSSkorackiRMillerMet al. (2016) Three dimensional printing of stiffness-tuned, nitinol skeletal fixation hardware with an example of mandibular segmental defect repair. Procedia CIRP49: 45–50.
29.
MonroeJKaramanILagoudasDCet al. (2011) Determining recoverable and irrecoverable contributions to accumulated strain in a NiTiPd high-temperature shape memory alloy during thermomechanical cycling. Scripta Materialia65: 123–126.
30.
MulderJH (1995) Investigation of high temperature shape memory alloys from the Ni-Ti-Zr and Ni-Ti-Hf systems. PhD Thesis, University of Twente, Twente.
31.
PadulaIINoebeRDBigelowGet al. (2007) Development of a HTSMA-Actuated Surge Control Rod for High-Temperature Turbomachinery Applications. Honolulu, HI: AIAA.
32.
QidwaiMALagoudasDC (2000) Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms. International Journal for Numerical Methods in Engineering47: 1123–1168.
33.
QuackenbushTMcKillipJR (2012) Selected applications of aeropropulsion actuation and shape control devices using HTSMAs. Metallurgical and Materials Transactions A43: 2870–2881.
34.
RahmanianRMoghaddamNSHaberlandCet al. (2014) Load bearing and stiffness tailored niti implants produced by additive manufacturing: a simulation study. In: SPIE smart structures and materials + Nondestructive evaluation and health monitoring, San Diego, CA, 9–13 March. Bellingham, WA: International Society for Optics and Photonics.
35.
SakhaeiAHLimK (2016) Transformation-induced plasticity in high-temperature shape memory alloys: a one-dimensional continuum model. Continuum Mechanics and Thermodynamics28: 1039–1047.
