Shape Memory Alloy Rods Research Articles

Dynamic loading of polycrystalline shape memory alloy rods

Shape memory alloys (SMAs) have recently been considered for dynamic loading applications for energy absorbing and vibration damping devices. An SMA body subjected to external dynamic loading will experience large inelastic deformations that will propagate through the body as phase transformation and/or detwinning shock waves. The wave propagation problem in a cylindrical polycrystalline SMA rod induced by an impact loading is considered in this paper. Numerical solutions for various boundary conditions are presented for stress induced martensite and detwinning of martensite. The numerical simulations utilize an adaptive finite element method (FEM) based on the Zienkiewicz–Zhu error estimator. Selected results are compared to known analytical solutions to verify the adaptive FEM approach. The energy dissipation in an SMA rod is evaluated for a square pulse stress input applied at various temperatures involving both stress induced martensite and detwinning of martensite. The dynamic response of a NiTi SMA rod is also studied experimentally in a split Hopkinson bar apparatus under detwinning conditions. Strain history records obtained by strain gauges placed at different locations along the SMA rod are compared with numerical simulations for a square pulse stress input. The quasi-static and dynamic stress–strain hysteretic response of the SMA, both due to detwinning, are found to be nearly identical. The quasi-static tests are used to calibrate the rate independent constitutive model used for the numerical simulations, which are found to match the experimental observations reasonably well.

Simulation of the Damping of a Shape Memory Alloy Rod by Using the Likhachev Model

In this paper vibration damping of a shape memory alloy rod is studied. The mathematical model includes the heat conduction equation, the stress wave equation, a kinetic law and a constitutive law. As kinetic law the Likhachev model is used, which describes the one-way effect, pseudoelasticity properties and thermal loading cycles. It is observed that the vibration amplitude of the rod decreases in this model very quickly. Results are in good agreement with earlier investigations, where other kinetic laws have been used.

Impact induced propagation of phase transformation in a shape memory alloy rod

Abstract In this work we study the propagation of a phase-transformation front induced by an impact loading. Our main goals in this paper are to demonstrate the wave structure of the solution to the impact loading and to estimate the velocity of phase front propagation using a thermodynamically based constitutive model for SMAs with internal variables. First, we study the impact problem in an isothermal setting; this study provides an important insight into the wave structure of the solution. The non-uniqueness issue inherent to such problems due to nonconvex SMA constitutive models is thoroughly discussed. Then we develop the solution for an adiabatic approximation for a simplified SMA model. Several numerical examples based on a first order Lax-Friedrichs finite difference scheme are presented.

Bending Stiffness of Rod in Pedicle Screw Systems

Purpose : To measure bending stiffness of rod in pedicle screw systems and identify the optimal rod for surgical correction of spinal deformities. Materials and Methods : Bending stiffness of six different rods 7 mm stainless steel, 6 mm titanium alloy, 6.35 mm titanium, 5.5 mm titanium, 6 mm Shape Memory Alloy after martensite temperature, 7 mm Shape Memory Alloy after martensite temperature-were measured by MTS 858 Bionix test system according to the ASTM standards. The specimen number was 8 for each rod. Young’s modulus of elasticity was calculated from load-displacement data. Results : Seven-mm stainless steel rod was stiffer than any other rods with bending stiffness of 143.7±3.8 N/mm, and also showed largest Young’s modulus of elasticity of 135.1±3.0 GPa. Six-mm Shape Memory Alloy rod after martensite temperature was most flexible with bending stiffness of 58.1±2.8 N/mm, and showed smallest Young ’s modulus of elasticity of 68.0± 2.1 GPa. Seven-mm Shape Memory Alloy rod after martensite temperature was similar to the 6.35 mm titanium and 6 mm titanium alloy rod in bending stiffness and Young’s modulus of elasticity. Conclusion : Seven-mm stainless steel rod was the stiffest rod tested, which is necessary to improve correction rate and maintain achieved correction. However, the rod selection should be individulized since stiffer rod might increase the chance of acute failure. Seven-mm Shape Memory Alloy could be more useful in deformity correction than 6 mm Shape Memory Alloy since it was not only similar to other rods in stiffness but also had shape memory function which would be necessary to establish the desired position of the spine.

Evaluation of structural influence on performance of shape memory alloy linear actuators by sharp phase front-based constitutive models

This paper analyzes and compares the predictions of two sharp phase-front based shape memory alloy (SMA) constitutive models – proposed by Abeyaratne and Knowles (R. Abeyaratne, J. Knowles, Journal of Mechanics and Physics of Solids 41 (1993) 541) and Bruno et al. (O. Bruno, P. Leo, F. Reitich, Phys. Rev. Lett. 74 (1995) 746–749) – in the context of an SMA linear actuator (an SMA rod or a wire) actuated electrically and subjected to spring-loaded boundary conditions at its ends. Both models are then used to analyze the performance – i.e., specific energy output and energy efficiency – of the SMA actuator. The computational modeling is done using a moving boundary finite element method (MBFEM)-based numerical approach proposed by Stoilov et al. (V. Stoilov, O. Iliev, A. Bhattacharyya, Computer Methods in Applied Mechanics and Engineering, accepted). It is seen that while both models produce somewhat differing predictions of the SMA response, the difference is not dramatic enough to prefer one model to another. Predictions of the SMA actuator performance indicate that there is an optimum spring stiffness at which the energy efficiency of the SMA actuator is at its maximum. This raises the possibility that when an SMA actuator is integrated into a structure, the passive components of the structure may play a key role in determining the optimum energy efficiency of the active structural component (the SMA actuator) during the activation of the structure.

Impact induced phase transformation in shape memory alloys

A dynamic analysis is given of the impact induced phase transformation in a shape-memory alloy rod, with a special focus on the propagation of stress waves and phase transformation fronts in the rod. The material behavior of the shape-memory alloy is modelled by a thermomechanical constitutive theory developed by Lagoudas et al. (1996: A unified thermodynamic constitutive model for SMA and finite element analysis of active metal matrix composites. Mechanics of Composite Materials and Structures 3, 153–179), which is based on the formulation of Gibbs free energy that depends on, among other variables, the martensitic volume fraction and the transformation strain, along with evolution equations derived from a dissipation potential theory. Field equations and jump conditions of the fully coupled thermal-mechanical problem are derived to account for balances of linear momentum and energy. The equations are solved using the method of characteristic curves. The solutions are found to be associated with shocks, across which various field quantities suffer jump discontinuities. A typical solution involves two wave fronts which are initiated at the impact surface and propagate into the rod. One, travelling at the acoustic speed, separates the tranquil and disturbed regions. The other, travelling at a lower speed, separates the regions of the martensitic and austenitic phases. It is found that the stress and temperature jumps across the phase boundary can be significant. A numerical example is presented.

Investigation of the damping behavior of a vibrating shape memory alloy rod using a micromechanical model

A micromechanical model developed previously by the authors is adapted to investigate the damping behavior of a shape memory alloy rod. The model delivers a kinetic equation and a stress - strain temperature-transformed volume - fraction relation. These equations are coupled with the equations for the heat conduction and the (free) vibration of a rod. Phase change leads to energy dissipation and thus to damping. From the kinetic equation and the constitutive law, the dissipation rate and the dissipated energy can be derived at a given temperature. They attain a maximum at a certain fixed temperature between the martensite start and the martensite finish temperatures. Damping would be maximized when this temperature was reached everywhere in the specimen simultaneously. Since this ideal temperature cannot be realized instantaneously everywhere, a realistic configuration of sudden cooling/heating of the fixed end of a vibrating rod is simulated. Applying this model, a working temperature for global optimal damping can be found which lies between the martensite start and the martensite finish temperatures. The damping itself is represented by the ratio of the sum of the actual kinetic energy and strain energy to the strain energy of the initial prestressed rod.

Finite Element Predictions of Active Buckling Control of Stiffened Panels

Materials systems and structures that can respond "intelligently" to their environment are currently being proposed and investigated. A series of finite element analyses was performed to investigate the potential for active buckling control of two different stiffened panels by embedded shape memory alloy (SMA) rods. Changes in the predicted buckling load increased with the magni tude of the actuation level for a given structural concept. Increasing the number of actuators for a given concept yielded greater predicted increases in buckling load. Considerable control authority was generated with a small number of actuators, with greater authority demonstrated for those struc tural concepts where the activated SMA rods could develop greater forces and moments on the struc ture. Relatively simple and inexpensive analyses were performed with standard finite elements to de termine such information, indicating the viability of these types of models for design purposes.