Shape Memory Alloy Bars Research Articles

Coupled rate-dependent superelastic behavior of shape memory alloy bars induced by combined axial-torsional loading: a semi-analytic modeling

In this article, the coupled thermomechanical response of superelastic shape memory alloy bars and tubes in combined tension and torsion is studied both analytically and experimentally. Using the Gibbs free energy as the thermodynamic potential and choosing appropriate internal state variables, a three-dimensional phenomenological macroscopic constitutive model for shape memory alloys is derived. Taking into account the effect of latent heat during the forward and reverse martensitic phase transformation, the appropriate form of the energy balance relation is obtained. The three-dimensional coupled relations for the energy balance in the presence of the internal heat flux and the constitutive equations are reduced to a two-dimensional form for the tension-torsion case. An explicit finite difference approach is utilized to discretize the governing boundary conditions of bars. An empirical expression for the free heat convection from the surface of a shape memory alloy bar was proposed and experimentally validated. Several sets of experiments were then carried out to evaluate the mechanical and thermal responses of the model for a shape memory alloy tube subjected to uniaxial, pure torsion and non-proportional tension and torsion loading–unloading conditions. The approach could be used in the design of shape memory alloy devices undergoing combined loads with high strain rates or in the fatigue design of shape memory alloy devices subjected to cyclic loading.

Mechanical Behavior of Super-Elastic Home-Made NiTi Shape Memory Alloy Bar in Tension

An experimental study on mechanical behavior of home-made super-elastic NiTi Shape Memory Alloy (SMA) bar subjected to tension was made. The SMA bar specimen was 8mm in gage diameter and 50mm in gage length. The experimental tests were carried out by applying repeated cyclic loads. The tested tension strain amplitudes were 1%-7% and material phase was austenite. The mechanical characteristic parameters, such as phase transformation stress, deformation module, residual strain, energy loss and equivalent damping were studied. The effects of strain amplitude, loading rate and loading cycles on these parameters were analyzed. The considerable super-elasticity and stable cyclic behaviors of home-made SMA bar during the test showed its great application potential in aseismic devices.

Seismic Vulnerability Assessment of a Multi-Span Continuous Highway Bridge Fitted with Shape Memory Alloy Bars and Laminated Rubber Bearings

This study performs seismic vulnerability assessment in the longitudinal direction of a three-span continuous highway bridge, restrained by shape memory alloy (SMA) bars and isolated with laminated rubber bearings. The analytical simulation method based on incremental dynamic analyses is used in evaluating the seismic fragility functions of the bridge components (pier and isolation bearing) and the system. A two-dimensional finite element model scheme with nonlinear force-displacement relationships is used for the bridge piers and bearings. This study shows that the bridge piers with SMA bars have led to relatively higher seismic vulnerability over the bridge piers without SMA bars, which is also reflected in the bridge system. The isolation bearings with SMA bars have revealed comparatively less seismic vulnerability than those without SMA bars. From the numerical results, it is recognized that the failure probability of the bridge system is dictated by the bridge pier over the isolation bearing.

Experimental Research of Low Shear Wall with SMA Bars Concealed Bracings

Many researchers study the seismic performance of shear wall embedded with reinforced concealed bracings, but not take the shape memory alloy bars concealed bracings into account. Quasi-static tests of a low shear wall with reinforced concealed bracings and a low shear wall with SMA bars concealed bracings are performed to study the seismic performance of the shear walls. Bearing capacity, stiffness, ductility, hysteretic energy and residual deformation of two specimens are researched and analyzed. The experimental results indicate that the SMA bars concealed bracings can increase the strength and ductility of the low shear wall considerably.

Modeling and cyclic behavior of segmental bridge column connected with shape memory alloy bars

This paper examines the quasi-static cyclic behavior, lateral strength and equivalent damping capacities of a system of post-tensioned segmental bridge columns tied with large diameter martensitic Shape Memory Alloy (SMA) link-bars. Moment-curvature constitutive relationships are formulated and analysis tools are developed for the PT column, including a modified four-spring model prepared for the SMA bars. The suggested system is exemplified using a column with an aspect ratio of 7.5 and twelve 36.5 mm diameter NiTi martensitic SMA bars. A post-tensioning force of 40% to 60% of the tendon yield strength is applied in order to obtain a self re-centering system, considering the residual stress of the martensitic SMA bars. The cyclic response results show that the lateral strength remains consistently around 10% of the total vertical load and the equivalent viscous damping ratios reach 10%–12% of critical. When large diameter NiTi superelastic SMA bars are incorporated into the column system, the cyclic response varies substantially. The creep behavior of the superelastic SMA bar is accounted for since it affects the re-centering capability of the column. Two examples are presented to emphasize the modeling sensitivities for these special bars and quantify their cyclic behavior effects within the column assembly.

Lateral reinforcement of welded SMA rings for reinforced concrete columns

This study conducts a series of compressive tests of concrete cylinders confined by shape-memory alloy (SMA) rings to provide lateral confinement for reinforced concrete columns. Ni50Ti41Nb9 (at. %) SMA bars with a diameter of 3 mm and a length of 446 mm were prepared and strained to 7% before welding. Three of the six confined cylinders were heated to 200 ◦ C to introduce recovery stress in the SMA rings, which was predicted to provide active confinement of concrete. The behavior of two welded bars with a resulting diameter of 6 mm were tested and compared with that of the continuous SMA bars without welding. The continuous SMA bars showed the typical behavior of martensitic SMAs, such as an elastic range, a transformed state, and hardening behavior due to austenite. However, the welded bars were fractured at the welding point at or just after elastic range. The concrete cylinders confined by the SMA rings showed greater peak strength and larger failure strain compared to the plain concrete cylinders. However, the stress-strain curves of the confined cylinders showed stepping behavior due to the sequential fracturing of the SMA rings. The heated SMA ring cylinders did not show greater peak strength than the unheated SMA ring cylinders, indicating that active confining was not effective. © 2012 Elsevier B.V. All rights reserved.

Coupled thermo-mechanical analysis of shape memory alloy circular bars in pure torsion

Pure torsion of shape memory alloy (SMA) bars with circular cross section is studied by considering the effect of temperature gradient in the cross sections as a result of latent heat generation and absorption during forward and reverse phase transformations. The local form of energy balance for SMAs by taking into account the heat flux effect is coupled to a closed-form solution of SMA bars subjected to pure torsion. The resulting coupled thermo-mechanical equations are solved for SMA bars with circular cross sections. Several numerical case studies are presented and the necessity of considering the coupled thermo-mechanical formulation is demonstrated by comparing the results of the proposed model with those obtained by assuming an isothermal process during loading–unloading. Pure torsion of SMA bars in various ambient conditions (free and forced convection of air, and forced convection of water flow) subjected to different loading–unloading rates are studied and it is shown that the isothermal solution is valid only for specific combinations of ambient conditions and loading rates.

Applicability of Cu-Al-Mn shape memory alloy bars to retrofitting of historical masonry constructions

This paper investigates the applicability of newly developed Cu-Al-Mn shape memory alloy (SMA) bars to retrofitting of historical masonry constructions by performing quasi-static tests of half-scale brick walls subjected to cyclic out-of-plane flexure. Problems associated with conventional steel reinforcing bars lie in pinching, or degradation of stiffness and strength under cyclic loading, and in their inability to restrain residual deformations in structures during and after intense earthquakes. This paper attempts to resolve the problems by applying newly developed Cu-Al-Mn SMA bars, characterized by large recovery strain, low material cost, and high machinability, as partial replacements for steel bars. Three types of brick wall specimens, unreinforced, steel reinforced, and SMA reinforced specimens are prepared. The specimens are subjected to quasi-static cyclic loading up to rotation angle enough to cause yielding of reinforcing bars. Corresponding nonlinear finite element models are developed to simulate the experimental observations. It was found from the experimental and numerical results that both the steel reinforced and SMA reinforced specimens showed substantial increment in strength and ductility as compared to the unreinforced specimen. The steel reinforced specimen showed pinching and significant residual elongation in reinforcing bars while the SMA reinforced specimen did not. Both the experimental and numerical observations demonstrate the superiority of Cu-Al-Mn SMA bars to conventional steel reinforcing bars in retrofitting historical masonry constructions.

Seismic Performance of RC Frame with Shape Memory Alloy Bracing Bars

In this study, high seismic performance RC frames have been proposed to have Shape Memory Alloy (SMA) bars acting as a kind of structural bracing system at both sides of a frame to increase the energy dissipation capacity of the RC frame. The type of SMA bar used in the study is the Superelastic SMA bar. The force-displacement hysteretic loops of the RC frame with SMA bars under seismic loading are presented and compared with the test results of the bare RC frame. Test results show that the SMA bars can effectively reduce the maximum story drift of the tested frame. It was found that the reduction of story drift and base shear was depending on the characteristic of the input ground motions.

A new isolation device using shape memory alloy and its application for long-span structures

The key points to consider in determining the effectiveness of using structural isolation with shape memory alloys (SMA) are the constitutive model, the SMA isolation device and the analysis method. In this paper, a simplified constitutive model based on the classic theory of plasticity is proposed to simulate the behavior of the superelasticity of the SMA, in which the martensite volume fraction is considered as one of the state variables. Comparisons between simulation results and experimental results are made and indicate that the proposed constitutive model yields stress-strain curves that are in good agreement with the experimental ones. Thus, the proposed model can correctly simulate the yield mechanism and energy dissipation capacity of the SMA. Next, in order to make full use of the superelasticity of SMA, a new SMA isolator composed of pre-tensioned SMA bars is presented. Then, a finite element analytical model is established to simulate the behavior of the SMA isolator according to its configuration and simplified constitutive model. Finally, a simplified design method for long-span structures installed with SMA isolators is proposed, which is further used to investigate the isolation effects of a space grid structure. Results show that the SMA isolator can reduce the seismic responses of the structure effectively, which indicates the effectiveness of the proposed SMA isolation method.

Seismic behaviour of repaired superelastic shape memory alloy reinforced concrete beam-column joint

Large-scale earthquakes pose serious threats to infrastructure causing substantial damage and large residual deformations. Superelastic (SE) Shape-Memory-Alloys (SMAs) are unique alloys with the ability to undergo large deformations, but can recover its original shape upon stress removal. The purpose of this research is to exploit this characteristic of SMAs such that concrete Beam-Column Joints (BCJs) reinforced with SMA bars at the plastic hinge region experience reduced residual deformation at the end of earthquakes. Another objective is to evaluate the seismic performance of SMA Reinforced Concrete BCJs repaired with flowable Structural-Repair-Concrete (SRC). A <TEX>$\frac{3}{4}$</TEX>-scale BCJ reinforced with SMA rebars in the plastic-hinge zone was tested under reversed cyclic loading, and subsequently repaired and retested. The joint was selected from an RC building located in the seismic region of western Canada. It was designed and detailed according to the NBCC 2005 and CSA A23.3-04 recommendations. The behaviour under reversed cyclic loading of the original and repaired joints, their load-storey drift, and energy dissipation ability were compared. The results demonstrate that SMA-RC BCJs are able to recover nearly all of their post-yield deformation, requiring a minimum amount of repair, even after a large earthquake, proving to be smart structural elements. It was also shown that the use of SRC to repair damaged BCJs can restore its full capacity.

Analysis of the rate-dependent coupled thermo-mechanical response of shape memory alloy bars and wires in tension

In this paper, the coupled thermo-mechanical response of shape memory alloy (SMA) bars and wires in tension is studied. By using the Gibbs free energy as the thermodynamic potential and choosing appropriate internal state variables, a three-dimensional phenomenological macroscopic constitutive model for polycrystalline SMAs is derived. Taking into account the effect of generated (absorbed) latent heat during the forward (inverse) martensitic phase transformation, the local form of the first law of thermodynamics is used to obtain the energy balance relation. The three-dimensional coupled relations for the energy balance in the presence of the internal heat flux and the constitutive equations are reduced to a one-dimensional problem. An explicit finite difference scheme is used to discretize the governing initial-boundary-value problem of bars and wires with circular cross-sections in tension. Considering several case studies for SMA wires and bars with different diameters, the effect of loading–unloading rate and different boundary conditions imposed by free and forced convections at the surface are studied. It is shown that the accuracy of assuming adiabatic or isothermal conditions in the tensile response of SMA bars strongly depends on the size and the ambient condition in addition to the rate dependency that has been known in the literature. The data of three experimental tests are used for validating the numerical results of the present formulation in predicting the stress–strain and temperature distribution for SMA bars and wires subjected to axial loading–unloading.

Study on Hysteretic Energy Dissipation of SMA Wires, Bars and Plates

Through tensile tests of shape memory alloy(SMA)wires,bars and plates, this paper analyzes hysteretic energy-dissipating capacities of thesesmartSMA materials in cyclic loading conditions. According to the test results, this article demonstrates the influence on energy dissipating capacity of SMA wires,bars and plates by different strain amplitudes, loading frequencies, cyclic numbers and pre-strains, then obtains change rules of hysteretic energy-dissipation.The test results show that the SMA wires is better than the other two SMA bars and plates, the SMA wires, bars and plates had better to be trainingbefore civil engineering application.

The concept of material forces in phase transition problems within the level-set framework

The dynamics of a phase transition front in solids using the level set method is examined in this paper. Introducing an implicit representation of singular surfaces, a regularized version of the sharp interface model arises. The interface transforms into a thin transition layer of nonzero thickness where all quantities take inhomogeneous expressions within the body. It is proved that the existence of an inhomogeneous energy of the material predicts inhomogeneity forces that drive the singularity. The driving force is a material force entering the canonical momentum equation (pseudo-momentum) in a natural way. The evolution problem requires a kinetic relation that determines the velocity of the phase transition as a function of the driving force. Here, the kinetic relation is produced by invoking relations that can be considered as the regularized versions of the Rankine–Hugoniot jump conditions. The effectiveness of the method is illustrated in a shape memory alloy bar.

On non-monotonic rate dependence of stress hysteresis of superelastic shape memory alloy bars

This paper presents a simple thermo-mechanical model to explain and quantify the observed strain-rate dependence of the stress hysteresis of shape memory alloys (SMAs) bars/strips during stress-induced forward/reverse phase transition with latent heat release/absorption. By solving the convective heat transfer equation and employing the temperature dependence of the SMA’s transformation stresses, we are able to prove that the stress hysteresis depends non-monotonically on the applied strain rate with a peak appearing at an intermediate strain rate. We further showed that such a non-monotonic rate dependence is governed by the competition of phase-transition time (or latent-heat release/absorption time) and the time of heat exchange with the environment, and that the hysteresis peak is achieved when the two time scales become comparable. A bell-shaped scaling law of the rate dependence is derived, agreeing quantitatively well with the results of experiments.

Fatigue tests on SMA bars in span control

The estimation of the fatigue lifetime of copper-based shape memory alloy (SMA) specimens in the form of bars is investigated in view of their use in passive devices for structural control applications. In the envisaged application, the pre-stress value assigned to the SMA bars is selected so that it is only slightly modified when strain variations occur within an operative range. This condition requires that the fatigue cycles are performed in span control, conversely to the common practice of driving the tests in load control to study the fatigue behaviour of traditional metals such as steel. Several experiments are carried out at different temperatures for different strain ranges and the results are arranged with the aim of building suitable fatigue models.

Finite Element Analysis of Adaptive Trusses Using Shape Memory Alloys

The finite element procedure for the three-dimensional adaptive trusses using shape memory alloys is formulated in the present study, in which the extended form of Brinson's constitutive equation considering the asymmetric tensile and compressive behavior is expressed in a tangentially incremental form. The validity of the present computational modeling is demonstrated by conducting numerical studies for the superelastic, shape memory behaviors of two-bar, nine-bar and twenty eight-bar adaptive trusses subjected to load and temperature changes. The proposed computational procedure is expected to be useful for the optimum design of the adaptive trusses with shape memory alloy bars.

An Experimental Study on Mechanical Behavior of Superelastic NiTi Shape Memory Alloy Bar Subjected to Torsion

An experimental study on mechanical behavior of superelastic NiTi shape memory alloy (SMA) bar subjected to torsion was made. The SMA specimen was in round bar shape, material phase was austenite and stress mode was torsion. The test was carried out by applying repeated cyclic uniform torsional load. Strain rate, strain amplitude and number of cycles were considered as test parameters. The test was described and analyzed in terms of three fundamental mechanical quantities: secant stiffness, energy loss per unit weight and equivalent damping. The test results show that SMA bar subjected to torsion, have great potential for application in seismic devices due to their considerable superelasticity and stable cyclic behaviors.

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

In 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.

Frequency-dependent temperature evolution in NiTi shape memory alloy under cyclicloading

We present a simple analytical model to study the temperature evolution of asuperelastic NiTi shape memory alloy (SMA) bar under cyclic tensile loading. Bydividing the cycle into five characteristic stages and solving the heat transferequations for each of the stages, we obtain the analytical expressions of thetemperature evolution under the cyclic loading of different frequencies (cycle periodtp) in different convective ambients (characterized by heat transfer timeth). It is found that, due to latent-heat release/absorption, the specimen’stemperature oscillates during the cyclic loading, and the oscillation amplitude (δstable)increases with the loading frequency and reaches a saturated value in the high-frequency range (tp/th < 0.1). Moreover, due to the heat accumulated from the intrinsic mechanical dissipation(internal friction), the mean-temperature of the specimen increases with the loadingfrequency. The temperature rise becomes significant in the high-frequency range. Thesepredictions quantitatively agree well with experiments.