A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy

doi:10.1016/S0749-6419(96)00030-7

International Journal of Plasticity

Volume 12, Issue 6, 1996, Pages 805-842

https://doi.org/10.1016/S0749-6419(96)00030-7 Get rights and content

Abstract

Pseudoelasticity and the shape memory effect (SME) due to martensitic transformation and reorientation of polycrystalline shape memory alloy (SMA) materials are modeled using a free energy function and a dissipation potential. Three different cases are considered, based on the number of internal state variables in the free energy: (1) austenite plus a variable number of martensite variants; (2) austenite plus two types of martensite; and (3) austenite and one type of martensite. Each model accounts for three-dimensional simultaneous transformation and reorientation. The single-martensite model was chosen for detailed study because of its simplicity and its ease of experimental verification. Closed form equations are derived for the damping capacity and the actuator efficiency of converting heat into work. The first law of thermodynamics is used to demonstrate that significantly more work is required to complete the adiabatic transformation than the isothermal transformation. Also, as the hardening due to the austenite/martensite misfit stresses approaches zero, the transformation approaches the isothermal, infinite specific heat conditions of a first-order transformation. In a second paper, the single-martensite model is used in a mesomechanical derivation of the constitutive equations of an active composite with an SMA phase.

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In this work, the evolutions of superelasticity (SE) and elastocaloric effect (eCE) for NiTi shape memory alloy (SMA) helical springs under cyclic deformation are investigated experimentally and theoretically. Experimental results show that the functional fatigue of SE and eCE occur simultaneously, and these phenomena aggravate significantly with the increase/decrease of the loading level/spring index. Then, a thermo-mechanically coupled constitutive model is established. Two major inelastic deformation mechanisms, martensitic transformation (MT) and transformation-induced plasticity (TRIP), are incorporated. In addition to the martensitic and austenitic phases, the martensitic influence zone is also considered in the proposed constitutive model to characterize the high local stress in the region near the austenitic-martensitic interface. To accurately describe the deformation behavior of NiTi SMA springs, an analytical model considering both the torsion and bending deformation modes is employed. Furthermore, the lumped heat transfer analysis method is adopted to derive the evolution equation for the overall temperature of the springs. Finally, to verify the rationality of the newly developed model, predicted results for the functional fatigue of SE and eCE are compared with the experimental data.
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Shape memory alloys (SMAs) undergo large recoverable deformation due to their inherent diffusionless martensitic phase transformation. Two factors need to be taken into account to incisively emulate the behaviour of SMA based structures: (i) consideration of large displacement and rotation (LDR) effect, and (ii) capturing the consequence of transformation induced material level coupling. In this study, both these effects are apprehended by extending the infinitesimal strain-based constitutive model of SMA as proposed by Lagoudas et al. (2012), assuming small elastic strain but with finite inelastic strain. To preclude any spurious stress generation out of large rotation, the Jaumann stress rate is used, and incremental objectivity for finite rotation between two successive time instants is conserved by rotating the strain increment and spin tensor to the rotation-independent mid-point configuration following Hughes–Winget (Hughes and Winget, 1980) algorithm. In addition, the contribution of thermoelastic and latent heat evolved during transformation is taken into consideration in the thermal equilibrium equation. Moreover, the effect of partial phase transformation yielding minor hysteresis loop has also been captured. The equilibrium equation is expressed in the current configuration following the Updated Lagrangian formulation. The mechanical and thermal equilibrium equations are solved concurrently in block matrix form using the Newton–Raphson (NR) iterative technique, considering the coupling terms resulting from the phase transformation. The efficacy and robustness of the developed finite element model are corroborated through various practical applications of SMA-based members, e.g., SMA ring, SMA-actuated beam, morphing of corrugated airfoil, orthodontic palatal expander, compliant gripper, undergoing LDR while subjected to different thermomechanical loading conditions. The combined effects of LDR along with thermomechanical coupling yield a stiffening behaviour during loading and sluggish response at the time of thermal recovery.
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Shape Memory Alloys (SMAs) are becoming increasingly used in actuator technologies thanks to the generation of high specific power and reliability. These features are obtained by extremely simple architecture and actuation mechanisms that exploit the thermal-induced shape recovery properties of SMAs. Thanks to the high specific power, small diameter wires can be directly used as linear actuators whose activation can be obtained by electric currents, exploiting the Joule effect. Despite the simplicity of the actuator, the complex constitutive behaviour of such material does not allow to easily model its mechanical behavior due to the interdependency of the alloy parameters, especially when electric-thermal phonemena are also involved. In this paper, a fully coupled electric-thermo-mechanical model is proposed to predict the thermal and mechanical response of Shape Memory Alloy (SMA) wires when electrically actuated with the aim to provide user guidelines for properly design/select SMA based wire actuators for engineering applications. The model takes into account the latent heats linked to phase transformations, conduction and convective heat exchanges phenomena as well as the dependency of the resistivity from the thermo-mechanical parameter of the alloy. The implementation consists in two submodels: the electric-thermal and the thermo-mechanical one. Because of the marked dependence of the volume fraction of martensite with both temperature, generated by Joule effect, and mechanical stress, the submodels were coupled. Due to the complexity of the problem, a Matlab/Simulink code was implemented to numerically solve the governing equations. Temperature evolution, generated by the electric input, was investigated during both the heating and cooling stage and its effect on the mechanical response of the SMA actuator was studied. Results were validated with experimental measurements carried out on nickel-titanium (NiTi) wires. It was shown that the proposed model is suitable in predicting the temperature evolution of the wire, even catching phase transitions, as well as the actuation response for different loading conditions. Finally, the SMA actuators performances, in terms of input current to use, actuation time and efficiency, were investigated.
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^∗: Currently at The Department of Mechanical Engineering (M/C 251), University of Illinois at Chicago. 2039 Engineering Research Facility, 842 West Taylor Street, Chicago, IL 60607-7022, U.S.A.

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A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy

Abstract

Int. J. Engng Sci.

Scripta Metall.

Acta Metall. Mater.

Acta Metall. Mater.

Acta Metall. Mater.

Mater. Sci. Engng.

J. Mech. Phys. Solids

L'affinity

Non-equilibrium Thermodynamics

Introduction to the Mechanics of a Continuous Medium

The Nucleation of Martensite

Thermodynamic Theory of Structure, Stability and Fluctuations

55-Nitinol—The Alloy with a Memory: Its Physical Metallurgy, Properties and Application

NASA-SP 5110

Thermoelasticity, Pseudoelasticity and the Memory Effects Associated with Martensitic Transformations

J. Mater. Sci.

Sur les Materiaux Standards Generalises

J. de Mech.

Irreversible Thermodynamics of Continua and Internal Variables

Irreversible Thermodynamics and Physical Interpretation of Rational Thermodynamics

J. of Non-Equil. Thermodyn.

A Course in Thermodynamics

Micromechanics of Defects in Solids

A Thermomechanical Description of Materials with Internal Variables in the Process of Phase Transformations

Ing. Arch.