A combined analytical, numerical, and experimental study of shape-memory-alloy helical springs

Abstract

a b s t r a c tIn this paper, the pseudoelastic response of shape memory alloy (SMA) helical springs under axial force is studied both analytically and numerically. In the analytical solution two different approximations are considered. In the first approximation, both the curvature and pitch effects are assumed to be negligible. This is the case for helical springs with large ratios of mean coil radius to the cross sectional radius (spring index) and small pitch angles. Using this assumption, analysis of the helical spring is reduced to that of the pure torsion of a straight bar with circular cross section. A three-dimensional phenomenological macroscopic constitutive model for polycrystalline SMAs is reduced to the one-dimensional pure shear case and a closed-form solution for torsional response of SMA bars in loading and unloading is obtained. In the next step, the curvature effect is included and the SMA helical spring is analyzed using the exact solution presented for torsion of curved SMA bars. In this refined solution, the effect of the direct shear force is also considered. In the numerical analyses, the three-dimensional constitutive equations are implemented in a finite element method and using solid elements the loading-unloading of an SMA helical spring is simulated. Analytical and numerical results are compared and it is shown that the solution based on the SMA curved bar torsion gives an accurate stress analysis in the cross section of the helical SMA spring in addition to the global load-deflection response. All the results are compared with experimental data for a Nitinol helical spring. Several case studies are presented using the proposed analytical and numerical solutions and the effect of changing different parameters such as the material properties and temperature on the loading-unloading hysteretic response of SMA helical springs is studied. Finally, some practical recommendations are given for improving the performance of SMA helical springs used as energy dissipating devices, for example for seismic applications.

A three-species model for simulating torsional response of shape memory alloy components using thermodynamic principles and discrete Preisach models

“…Although such elastoplasticitybased models have firm thermodynamic foundations, these strategies become extremely cumbersome for the identification of model parameters from experimental data as the identification is mostly heuristic and there is no automated scheme for identifying them. Incorporating temperature effects and accounting for internal loops is cumbersome as many of model parameters or hardening functions must be recomputed for simulating these effects (for example, see table 1 in [44], and also [47][48][49][50][51] for the number of parameters needed for model verification). If such models are employed to simulate a torsional response of a SMA component such as wire or spring, then one needs to simulate a full 3D model or a reduced 3D model for analyzing specific cases.…”

FEM model of middle ear prosthesis with pseudo-elastic effect

“…The pseudoelastic response of shape memory alloy (SMA) helical springs under axial force is studied both analytically and numerically in [12]. An analysis of the helical spring is classically reduced to the pure torsion of a straight bar with circular cross section.…”

Relationship between input power and power density of SMA spring

“…While the strain limit of a human skeletal muscle is only 40%, that of an SMA spring could exceed 200%. 3,14 In addition, an SMA spring fabricated from a 6-mm-radius wire is capable of generating a force in excess of 3,000 N. 15 Moreover, the generated force can be easily increased by using parallel springs in the actuator. 2,10,11 SMA springs have so far been mainly investigated in terms of the parameter relationships such as the relationships between the generated force and the displacement, between the generated force and the input power, and between the displacement and the input power.…”

“…2,10,11 SMA springs have so far been mainly investigated in terms of the parameter relationships such as the relationships between the generated force and the displacement, between the generated force and the input power, and between the displacement and the input power. 4,11,15 However, the relationship between the maximum power or power density and the input power has not been investigated. In the present study, the maximum power density of an SMA spring was evaluated with respect to the input power.…”