Shape Memory Alloy Helical Springs Research Articles

Functional fatigue of superelasticity and elastocaloric effect for NiTi springs

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.

Solid-state cooling with high elastocaloric strength and low driving force via NiTi shape memory alloy helical springs: Experiment and theoretical model

High efficiency and environment-friendly elastocaloric solid-state cooling has emerged as a promising alternative to traditional vapor-compression refrigeration. Owing to the high entropy change during martensite transformation, NiTi shape memory alloy (SMA) is a competitive candidate for the core components of solid-state refrigeration systems. However, main bottlenecks for the development of NiTi SMA based refrigeration systems are their relatively low elastocaloric strength and the requirement of high driving force. In this work, the elastocaloric effect of NiTi SMA helical springs with three geometrical configurations are investigated experimentally at first. It is found that the elastocaloric performance can be tailored by changing the spring geometrical parameters and the magnitude of applied load. Giant cooling temperature of 12.5K and elastocaloric strength of 0.31K/MPa are observed for the helical spring with a spring index of 7.7 under an ultra-low tensile driving force of 71 N. The elastocaloric strength reported in this work is ten times larger than that observed in the NiTi wires, rods, tubes, sheets and films subjected to a tensile or compressive loading, and twice larger than that in the NiTi wires under a bending deformation mode. Then, a three-dimensional (3D) thermodynamic-consistent constitutive model within the finite strain framework and considering the thermo-mechanical coupling effect is developed. The proposed model is further implemented into the finite element program ABAQUS by writing a user-defined material subroutine (UMAT). Finally, simplified analytical relations among the cooling temperature, maximum driving force, geometrical parameters of the springs and applied displacement are derived. Comparing the predictions with the experimental data, it is found that the influences of geometrical parameters and loading level on the elastocaloric strength of NiTi SMA helical spring can be well captured by both the finite element analysis and proposed analytical relation. This work shows a potential for developing the cooling technology with high elastocaloric strength and low driving force, and provides a theoretical guidance to design and assess the cooling device manufactured by SMA spring.

Thermo-mechanically coupled deformation of pseudoelastic NiTi SMA helical spring

Based on the cyclic tension-unloading tests with various displacements (40, 60 and 80 mm) and at different loading rates (0.3 mm/s, 1 mm/s and 5 mm/s), the thermo-mechanically coupled deformation and temperature evolution of pseudoelastic NiTi shape memory alloy (SMA) helical spring are investigated. Experimental results reveal that the phase transition between austenite (A) and martensite (M) phases undergoes a two-step process involving an intermediate phase, that is, rhombohedral (R) phase; the force-displacement responses of the spring depend on the loading rate strongly, which originates from Clausius-Clapeyron relation between the critical stresses of phase transitions (including R and M transformations), and the competition between the internal heat generation and heat exchange. Then, a three-dimensional phenomenological constitutive model is developed by addressing three possible phase transition processes (that is, A→R→M, A→mixed A + R→M and A→M) and thermo-mechanical coupling effect. Generalized thermodynamic forces for the phase transitions and the evolution equation of temperature are derived based on the second and first laws of thermodynamics, respectively. To accurately describe the loading amplitude-dependent dissipation and hardening behavior of MT, new dissipation and hardening laws are proposed. Furthermore, a new analytical model of helical spring is developed by simultaneously considering the torsion and bending deformation modes, curvature effect and the coupling effect between the deformation and temperature evolution. Finally, the developed model is validated by comparing the simulated results with the experimental data, and the influences of geometrical parameters and ambient temperature on the thermo-mechanical responses of the spring are also predicted and discussed.

Thermomechanical performance analysis and experiment of electrothermal shape memory alloy helical spring actuator

In this paper, an electrothermal shape memory alloy helical spring actuator constructed from shape memory alloy with copper-cored enameled wire is presented and fabricated. Based on the shear constitutive model of a shape memory alloy, the Thermo equilibrium equation and the geometrical equation of helical spring establish the thermomechanical theoretical model of helical spring actuator with electrothermal shape memory alloys under different scenarios. The thermomechanical behaviors of the actuator were verified by numerical simulation with experimental tests, and the actuator thermomechanical properties were derived from the analysis with current, temperature, response time, restoring force, and axial displacement as parameters. The experimental results show that the actuator produces a maximum recovery force of 70.2 N and a maximum output displacement of 7.7 mm at 100°C. The actuator response time is 26 s at a current of 3A. It is also demonstrated that the theoretical model can effectively characterize the complex thermo-mechanical properties of the actuator due to the strong nonlinearity of the shape memory alloy. The experimental temperature-force response and temperature-displacement response, as well as the force-displacement response at different temperatures, provide references for the design and fabrication of electrothermal shape-memory alloy coil spring actuators.

A shape memory alloy helix model accounting for extension and torsion

In the present paper a mathematical model able to reproduce the mechanical response of a shape memory alloy (SMA) helical spring is presented. The proposed model is based on a simplified but effective theory of the helix that assumes small strains and large displacements. The kinematics of the helix and the related generalized strain measures are introduced, with stress resultants conjugated to them and the corresponding equilibrium equations of the curved beam. A specific constitutive law for this structural model is then presented for the SMA material, which accounts for the phase transformation due to the coupling of the shear and axial strains and to the effect of the temperature variation as well. Then, a numerical procedure, based on the backward Euler time integration algorithm and the prediction-correction technique for solving the nonlinear time step, is developed. Several numerical applications are presented to assess the reliability of the proposed SMA helix model and the implemented numerical procedure, and to investigate the response of the helix. Initially, the behavior of a circular SMA cross-section is studied, comparing the results obtained by the proposed modeling approach with the ones carried out by finite element analyses. Then, the helix structural element is considered and results are again compared with finite element outcomes. Finally, a sensitivity analysis is performed varying the pitch of the helix.

A new simple formulation for instantaneous coil diameter of a SMA helical spring

Helical coil tension springs made of shape memory alloy (SMA) materials generally undergo large deflection under loading during which their mean coil diameter changes noticeably. In the design of these helical coil springs, it is necessary to identify the real behaviour which may be affected by the variation in actual coil diameter. Therefore, a simple formulation is proposed in this paper for predicting instantaneous coil diameter. The predictions from present formulation match very closely with experimental measurements. The proposed formulation is relatively easy to adopt for design calculations. The effects of varying coil diameter on the spring characteristics are also discussed. This is very general and can be used for any helical spring which undergoes small or large deflections, although the proposed formulation is derived for SMA helical spring.

A new simple formulation for instantaneous coil diameter of a SMA helical spring

Helical coil tension springs made of shape memory alloy (SMA) materials generally undergo large deflection under loading during which their mean coil diameter changes noticeably. In the design of these helical coil springs, it is necessary to identify the real behaviour which may be affected by the variation in actual coil diameter. Therefore, a simple formulation is proposed in this paper for predicting instantaneous coil diameter. The predictions from present formulation match very closely with experimental measurements. The proposed formulation is relatively easy to adopt for design calculations. The effects of varying coil diameter on the spring characteristics are also discussed. This is very general and can be used for any helical spring which undergoes small or large deflections, although the proposed formulation is derived for SMA helical spring.

The effects of shape-setting on transformation temperatures of pseudoelastic shape memory alloy springs

Abstract Since shape memory alloy (SMA) wires can hardly ever be reliably employed under compressive loadings, SMA springs are developed as axial actuators with the ability of withstanding both tension and compression. In this paper, shape memory alloy helical springs are produced by shape-setting two types of wires: one with shape memory effect (SME) and the other with pseudoelasticity (PE) at the ambient temperature. Phase transformation temperatures of the produced springs are measured by differential scanning calorimetry (DSC), and the influences of effective parameters including cold work, heat treatment temperature and duration, and cooling rate are investigated on transformation temperatures of the products. The results show that phase transition temperatures of the fabricated springs can be tuned by performing cold work and by adjusting temperature and duration of the conducted heat treatment as well as the subsequent cooling rate. It is found that transformation temperatures of the springs fabricated using the SME wire increase as the heat treatment temperature increases. However, for samples manufactured using PE wire, transformation temperatures first increase and then decrease with the increase in the heat treatment temperature. An increase in the cooling rate leads to a decrease in the austenite final temperature (Af), and an increase in the extent of cold work leads to the increase in transformation temperatures especially Af.

Mathematical model for superelastic shape memory alloy springs with large spring index

A new model is proposed for the behavior of superelastic shape memory alloy (SMA) helical springs with large index. The derived governing equations consider the response of the spring to monotonic loading followed by complete unloading. In particular, the relation between axial force and axial deformation and the distribution of shear stress in a cross section of the spring wire are determined analytically for the entire loading-unloading cycle. Special attention is given to modeling the unloading stage, for which the proposed solution improves upon existing literature. The model is validated by comparison to 3D finite element simulations and the governing equations are used to investigate the influence of temperature, wire radius and mean radius on the superelastic behavior of a sample SMA spring.

Fatigue analysis of shape memory alloy helical springs

Estimating the functional as well as structural fatigue life of shape memory alloy (SMA) components has become a challenging issue for researchers. In current work, by considering the effects of large deformations, a rate-dependent energy-based model is developed to predict behavior of SMA helical springs under cyclic mechanical loadings. The effects of strain rate, convective heat transfer coefficient, and mean applied displacement to an SMA spring on its responses are investigated. SMA springs are fabricated through shape setting NiTi wires, and simple tension and fatigue tests are conducted on the fabricated specimens at different temperatures. Fatigue curves are presented in terms of variations in the amount of dissipated energy in stabilized force-displacement response with the number of cycles to failure. The amount of dissipated energy is calculated using the developed model, and the theoretically-predicted fatigue lives are shown to be in a good agreement with experimental results. Therefore, the presented approach is found to be a reliable method to predict lifetime of SMA springs in practice. The fatigue curves confirm the influence of loading frequency on the fatigue life.

R-phase shape memory alloy helical spring based actuators: Modeling and experiments

The main goal of this paper is to propose some analytical or pseudo-analytical tools facilitating the study and modeling of SMA helical spring-based actuators. Particular attention is paid to R-phase SMA helical spring-based actuators (i.e., springs made in NiTi and concerned by R-phase transformation phenomena). First, simplified models (i.e., based on beam theory framework) of R-phase SMA helical springs taking into account detwinning and assisted two-way memory effect are proposed and validated. Then, these models are used to determine the thermo-mechanical behavior of a linear bias-spring actuator. An actuator is built and used to validate the proposed models.

Thermomechanical Characterization of Superelastic Ni-Ti SMA Helical Extension Springs Manufactured by Investment Casting

Shape memory alloy (SMA) helical springs are special mechanical parts that require a previous evaluation of its behavior for application. Therefore, in this paper thermal and mechanical behaviour of superelastic Ni-Ti SMA helical extension springs manufactured by investment casting (IC) are evaluated. Phase transformation temperatures were measured by Electrical Resistance as a function of Temperature (ERT) and Differential Scanning Calorimetry (DSC). Tensile tests were carried out within strain and temperatures ranges. The pitch angle and stiffness of each spring were determined. Results demonstrated that Ni-Ti SMA helical springs produced by IC presented phase transformation corresponding to the superelastic effect (SE). The reversible deformations under tensile test were of the order of 70%. The mechanical behavior as function of temperature revealed a linear relationship between maximum force and spring temperature.

Dynamic Response Analysis of a Frame Structure with Superelastic Nitinol SMA Helical Spring Braces for Vibration Reduction

AbstractThis paper proposes a new type of energy dissipation brace system that is composed of superelastic Nitinol shape memory alloy (SMA) helical springs to reduce seismic responses of a frame st...

A novel model-based approach for resistance estimation using rise time and sensorless position control of sub-millimetre shape memory alloy helical spring actuator

Shape memory alloy shows considerable strain during heating and cooling. This effect is due to its phase transformation with temperature. Due to this property, shape memory alloys can be deployed for physical actuation in place of conventional actuators in bio-medical and bio-mimicking robots. Sub-millimetre diameter shape memory alloy wires wound as helical springs are also used for this purpose. Due to their small size, it is difficult to use sensors for temperature or displacement measurements of shape memory alloy springs. This article attempts to demonstrate that the rise time of the current through a sub-millimetre diameter shape memory alloy helical spring is directly proportional to its displacement. To characterize the rise time–displacement hysteresis, a constant current drive with overcurrent protection is developed. The data generated are utilized to implement an open-loop sensorless control. A method to estimate the resistance from the rise time is proposed with which the temperature of the shape memory alloy during actuation can be obtained. The design avoids using an analogue-to-digital converter for the direct measurement of voltage and current for measuring the resistance variation in the shape memory alloy under actuation. This helps in the development of a new sensorless control using only the digital Input/Output pins of a microcontroller/microprocessor.

Aeroelastic behavior of a typical section with shape memory alloy springs: Modeling nonhomogeneous distribution of state variables

In this paper, a two-degree-of-freedom (namely, plunge and pitch) aeroelastic typical section with shape memory alloy helical springs in the pitch degree-of-freedom is modeled. A linear aerodynamic model is employed to predict the unsteady loads. The shape memory springs model is based on classical models modified by the von Mises pure shear assumption. Nonhomogeneous distributions of shear strain, shear stress and martensitic fraction in the wire cross-section are represented by axi-symmetric annular regions. The numerical predictions of the effects of pseudoelastic hysteresis of shape memory alloy springs on the aeroelastic behavior of the typical section when both the homogeneous and nonhomogeneous cross-sectional distributions are considered in the simulations are compared with experimental data obtained in wind tunnel tests. The nonhomogeneous assumption results in good agreement between numerical predictions and experiments. Both the numerical and experimental results show that the pseudoelastic hysteresis of SMAs can be employed as a passive alternative to modify the behavior of aeroelastic systems.

Experimental study on the aeroelastic behavior of a typical airfoil section with superelastic shape memory alloy springs

An experimental study on the aeroelastic behavior of a 2-degree-of-freedom typical airfoil section with superelastic shape memory alloy springs is reported. Shape memory alloy helical springs are included in the pitch degree-of-freedom of the typical section so that the effects of pseudoelastic hysteresis on the aeroelastic behavior of the system can be investigated. The experimental identification of the aeroelastic parameters is described. Wind tunnel tests are conducted for different shape memory alloy springs’ preload levels, airflow speeds, and initial conditions. It is shown that the linear unstable post-flutter behavior is transformed into stable limit cycle oscillations of acceptable amplitudes over a range of airflow speeds due to pseudoelastic hysteresis. Therefore, shape memory alloy springs can be effectively exploited to passively enhance the aeroelastic behavior of a typical section.

A thermomechanically coupled finite deformation constitutive model for shape memory alloys based on Hencky strain

This paper presents a new thermomechanically coupled constitutive model for polycrystalline shape memory alloys (SMAs) undergoing finite deformation. Three important characteristics of SMA behavior are considered in the development of the model, namely the effect of coexistence between austenite and two martensite variants, the variation of hysteresis size with temperature, and the smooth material response at initiation and completion of phase transformation. The formulation of the model is based on a multi-tier decomposition of the deformation kinematics comprising, a multiplicative decomposition of the deformation gradient into thermal, elastic and transformation parts, an additive decomposition of the Hencky strain into spherical and deviatoric parts, and an additive decomposition of the transformation stretching tensor into phase transformation and martensite reorientation parts. A thermodynamically consistent framework is developed, and a Helmholtz free energy function consisting of elastic, thermal, interaction and constraint components is introduced. Constitutive and heat equations are then derived from this energy in compliance with thermodynamic principles. Time-discrete formulations of the constitutive equations and a Hencky-strain return-mapping integration algorithm are presented. The algorithm is then implemented in Abaqus/Explicit by means of a user-defined material subroutine (VUMAT). Numerical results are validated against experimental data obtained under various thermomechanical loading conditions. The robustness and efficiency of the proposed framework are illustrated by simulating a SMA helical spring actuator.

Fabrication and modeling of shape memory alloy springs

In this paper, shape memory alloy (SMA) helical springs are produced by shape setting two sets of NiTi (Ti-55.87 at% Ni) wires, one of which showing shape memory effect and another one showing pseudoelasticity at the ambient temperature. Different pitches as well as annealing temperatures are tried to investigate the effect of such parameters on the thermomechanical characteristics of the fabricated springs. Phase transformation temperatures of the products are measured by differential scanning calorimetry and are compared with those of the original wires. Compression tests are also carried out, and stiffness of each spring is determined. The desired pitches are so that a group of springs experiences phase transition during loading while the other does not. The former shows a varying stiffness upon the application of compression, but the latter acts as passive springs with a predetermined stiffness. Based on the von-Mises effective stress and strain, an enhanced one-dimensional constitutive model is further proposed to describe the shear stress–strain response within the coils of an SMA spring. The theoretically predicted force–displacement responses of the produced springs are shown to be in a reasonable agreement with the experimental results. Finally, effects of variations in geometric parameters on the axial force–displacement response of an SMA spring are investigated.

Modelling, characterisation and uncertainties of stabilised pseudoelastic shape memory alloy helical springs

The thermo-mechanical behaviour of pseudoelastic shape memory alloy helical springs is of concern discussing stabilised and cyclic responses. Constitutive description of the shape memory alloy is based on the framework developed by Lagoudas and co-workers incorporating two modifications related to hardening and sub-loop functions designated by Bézier curves. The spring model takes into account both bending and torsion of the spring wire, thus representing geometrical non-linearities. Simplified models are explored showing that a single point in the wire cross section is enough to represent the global spring behaviour in spite of complex stress–strain distributions. The experiments are carried out considering different deflection amplitudes, frequencies and ambient temperatures, which influence the spring behaviour to different extents. The model is fitted against a calibration data set resulting in 1.3% residual standard deviation relative to the full range force. Compared to the validation data set, the errors are below 10% relative to the full range of the complex modulus. Uncertainty analysis of the model parameters using a Markov chain Monte Carlo technique shows low to high parameter correlation, and the relative uncertainties are less than ±12%. Both the heat capacity and the convection coefficient are clearly identifiable from the performed experiments.

Modeling of mechanical response of NiTi shape memory alloy subjected to combined thermal and non-proportional mechanical loading: a case study on helical spring actuator

Textured polycrystals of NiTi-based shape memory alloys (SMA) exhibit pronounced anisotropic properties which significantly influence their response to mechanical and thermal loading. In this work, a constitutive model tailored for non-proportional multi-axial loading of NiTi SMA exhibiting two-stage phase transformation via R-phase is enhanced so that the anisotropy of martensitic structure is captured. Numerical simulations of the mechanical response of a NiTi SMA helical spring subjected to thermal cycling at a constant applied force are performed and compared with experimental data. Quantitative correspondence between experiments and simulations demonstrates the predictive potential of the model. Simulations also provide detailed information on the evolution of distributions of phase fractions and stress within a cross-section of the wire forming the spring. Because the loading is non-proportional, the evolution is rather complex and intriguing.