Constitutive Model For Shape Memory Alloys Research Articles

Numerical Study on Localization of Phase Transformation in NiTi Shape Memory Wires

Martensitic phase transformation in NiTi shape memory alloys (SMA) can spread either homogenously or in localized martensitic transformation bands. Transformation band propagation is usually observed in particular loading modes (tension) and geometries of specimen (wires, thin ribbons). In this work, a well established NiTi SMA constitutive model is enhanced so that strain softening of the material response during stress induced phase transition is covered. A nonlocal integral averaging technique is adopted and the model is implemented into a finite element (FE) software. A simple validating simulation of a NiTi superelastic wire loaded in tension is performed.

Characterization and modeling of three-dimensional self-healing shape memory alloy-reinforced metal-matrix composites

In this work, three-dimensional metal-matrix composites (MMCs) reinforced by shape memory alloy (SMA) wires are modeled and simulated, by adopting an SMA constitutive model accounting for elastic deformation, phase transformation and plastic behavior. A modeling method to create composites with pre-strained SMA wires is also proposed to improve the self-healing ability. Experimental validation is provided with a composite under three-point bending. This modeling method is applied in a series of finite element simulations to investigate the self-healing effects in pre-cracked composites, especially the role of the SMA reinforcement, the softening property of the matrix, and the effect of pre-strain in the SMA. The results demonstrate that SMA reinforcements provide stronger shape recovery ability than other, non-transforming materials. The softening property of the metallic matrix and the pre-strain in SMA are also beneficial to help crack closure and healing. This modeling approach can serve as an efficient tool to design SMA-reinforced MMCs with optimal self-healing properties that have potential applications in components needing a high level of reliability.

A shape memory alloy rod element based on the co-rotational formulation for nonlinear static analysis of tensegrity structures

In this article, a shape memory alloy rod element is derived based on the co-rotational formulation. In the co-rotational approach, the rigid body modes are removed from the total deformations by employing a local coordinate system at element level, and hence, the major part of geometric nonlinearity is isolated. The linear shape memory alloy rod element is developed using a shape memory alloy constitutive model together with the small strain framework employed by the co-rotational approach. The one-dimensional shape memory alloy model is adopted to calculate both the pseudo-elastic response and the shape memory effects. The new formulation is exploited to perform static analysis of tensegrity structures in order to study the accuracy and robustness of the proposed element and its capability to describe the structural response of shape memory alloy devices.

Detailed design of an SMA-actuated self-locking device for rotary feed structure

This paper presents a detailed design of a locking device which is used to lock the rotary feed structure of a space-borne microwave radiometer during the launching stage. This locking device employs two redundant shape memory alloy (SMA) wires as the actuating elements, uses a self-locking structure to achieve the locking function and a step structure to ensure a safety clearance after release. Based on the design concept, preliminary design of the locking/release unit and the clamp unit are performed. Then, a more accurate simulation of the release process and the cyclic property of the device is carried out by using an improved Brinson’s SMA constitutive model and a heat transfer equation. After the design and simulation, four prototypes are fabricated and their performance tests are carried out to evaluate the self-locking property, lifetime and thermal tolerance.

A micromechanics-inspired constitutive model for shape-memory alloys that accounts for initiation and saturation of phase transformation

A constitutive model to describe macroscopic elastic and transformation behaviors of polycrystalline shape-memory alloys is formulated using an internal variable thermodynamic framework. In a departure from prior phenomenological models, the proposed model treats initiation, growth kinetics, and saturation of transformation distinctly, consistent with physics revealed by recent multi-scale experiments and theoretical studies. Specifically, the proposed approach captures the macroscopic manifestations of three micromechanial facts, even though microstructures are not explicitly modeled: (1) Individual grains with favorable orientations and stresses for transformation are the first to nucleate martensite, and the local nucleation strain is relatively large. (2) Then, transformation interfaces propagate according to growth kinetics to traverse networks of grains, while previously formed martensite may reorient. (3) Ultimately, transformation saturates prior to 100% completion as some unfavorably-oriented grains do not transform; thus the total transformation strain of a polycrystal is modest relative to the initial, local nucleation strain. The proposed formulation also accounts for tension–compression asymmetry, processing anisotropy, and the distinction between stress-induced and temperature-induced transformations. Consequently, the model describes thermoelastic responses of shape-memory alloys subject to complex, multi-axial thermo-mechanical loadings. These abilities are demonstrated through detailed comparisons of simulations with experiments.

Analysis of interfacial debonding in shape memory alloy wire-reinforced composites

One of the common types of failure in shape memory alloy (SMA) wire-reinforced composites is interfacial debonding between the fiber and the matrix. In this paper, a three dimensional finite element model for an SMA wire-reinforced composite is developed based on cohesive zone modeling to predict interfacial debonding between the SMA wire and the surrounding matrix. The interfacial debonding is also experimentally investigated by conducting a number of pull-out tests on steel as well as Nitinol wires embedded in an epoxy matrix. To evaluate the presented method, the developed finite element analysis is employed to simulate a single wire pull-out test for ordinary (e.g. steel) wires. In order to simulate SMA wire pull-out, a 3D SMA constitutive model is implemented into the commercial finite element software ABAQUS using a user material subroutine (UMAT). An acceptable agreement is shown to exist between the theoretical results and the experimental data, indicating the efficiency of the proposed approach to model interfacial debonding in SMA wire-reinforced composites.

Implementation of Microplane Model Into Three-Dimensional Beam Element for Shape Memory Alloys

In this study, a three-dimensional (3D) beam element based on Timoshenko beam theory is introduced for shape memory alloys (SMAs). Employing the microplane approach, we use a 3D SMA constitutive model extended from a 1D model proposed by Brinson. The SMA model is implemented into a user-defined subroutine (UMAT) in the nonlinear finite element software ABAQUS/Standard. Results of numerical examples show reasonable agreement with experimental data in proportional and non-proportional loadings. Furthermore, several applications (staple, spring, structure) are simulated and the results are compared with those of continuum elements. According to the results, the 3D SMA beam element can be used in the design and analysis of various SMA applications.

Numerical Simulation of the Shape Memory Alloy Pipe Joint

Based on the existing constitutive model of shape memory alloys (SMA), as well as on the state of stress distribution between the pipe and pipe joint, a simplified constitutive model for SMA can indeed fit the SMA pipe coupling structure. Using this constitutive model to simulate the stress distribution during the process of heating up, we can use the system to discuss the relationship between the radial compressive stress and various influencing factors. KeywordsShape Memory Alloys; Constitutive Model; Radial Compressive Stress; Pipe Joint; Wall Thickness

Modeling and analysis of reversible shape memory adaptive panels

The aim of this article is to model and analyze reversible shape adaptive panels integrated with one-way shape memory alloy actuators and to examine the effects of martensite variants reorientation. A robust three-dimensional macroscopic model is implemented to simulate shape memory effect, pseudo-elasticity, and ferro-elasticity features of shape memory alloys. The shape memory alloy constitutive model provides analytical closed-form solutions for self-accommodation and martensite reorientation mechanisms while proposing an iterative solution scheme for martensite transformation or orientation assuming an exponential form for transformation kinetics. The finite element formulations are derived based on the first-order shear deformation theory considering the modified Sanders shell assumptions and including geometrical nonlinearity in the von Kármán sense. An iterative incremental procedure on the basis of the elastic-predictor inelastic-corrector return mapping algorithm is introduced to solve the coupled governing equations of equilibrium with both material and geometrical nonlinearities. The numerical illustrations emphasize the feasibility of reversible shape adaptive panels integrated with thermally activated pre-strained one-way shape memory alloy ribbons or layers. Effects of martensite reorientation, pre-strain, temperature, arrangement, and dimension of shape memory alloys as well as of thermal cycles are investigated, and their implications on the performances of reversible shape adaptive spherical panels are highlighted, and pertinent conclusions are outlined.

Study on loss mechanism of SMA tracheal stent subjected to cough excitation.

A kind of Ti-Ni shape memory alloy (SMA) hysteretic nonlinear model is developed, and the loss mechanism of a SMA tracheal stent subjected to cough excitation is studied in this paper. Nonlinear differential items are introduced to express the hysteretic phenomena of Ti-Ni SMA, and the fitting effect of the SMA constitutive model on the experimental data is proved by the partial least-square regression method. The nonlinear dynamic model of a Ti-Ni SMA tracheal stent subjected to cough excitation is developed, and the system's dynamic response is obtained. The numerical results show that the system's vibration is little in weak excitation, becomes large with the increase of the stochastic excitation, and finally becomes little again with the further increase of the stochastic excitation; the stochastic resonance phenomenon occurs in the process, which may cause stent fracture or loss.

An incremental energy minimization state update algorithm for 3D phenomenological internal‐variable SMA constitutive models based on isotropic flow potentials

SummaryAn incremental energy minimization approach for the solution of the constitutive equations of 3D phenomenological models for shape memory alloys (SMA) is presented. A robust algorithm for the solution of the resulting nonsmooth constrained minimization problem is devised, without introducing any regularization in the dissipation or chemical terms. The proposed algorithm is based on a thorough detection of the singularities relevant to the incremental energy formulation, in conjunction with a Newton–Raphson method equipped with a Wolfe line search dealing with regular solutions. The saturation constraint on the transformation strain is treated by means of an active set strategy, thus avoiding any need for a two‐stage return‐mapping algorithm. A parametrization of the saturation constraint manifold is introduced, thus reducing the problem dimensionality, with improved computational performance. Finally, an efficient algorithm for the computation of the dissipation function in terms of Haigh–Westergaard invariants is presented, allowing for a quite general choice of deviatoric transformation functions. Numerical results confirm the robustness and consistency of the proposed state update algorithm. Copyright © 2015 John Wiley & Sons, Ltd.

Modeling Permanent Deformations of Superelastic and Shape Memory Materials.

In this paper we propose a modification of the polycrystalline shape memory alloy constitutive model originally proposed by Souza. By introducing a transformation strain energy with two different hardening coefficients, we are able to take into account the effect of the martensitic transformation of unfavorably oriented grains occurring after the main plateau. By choosing a proper second hardening coefficient, it is possible to reproduce the correct stress strain behavior of the material after the plateau without the need of introducing a much smaller Young modulus for martensite. The proposed modification is introduced in the model comprising permanent deformation effects. Model results for uniaxial stress tests are compared to experimental results showing good agreement.

On the modeling of the thermo-mechanical responses of four different classes of NiTi-based shape memory materials using a general multi-mechanism framework

The properties of a shape memory alloy (SMA) have been shown to be highly dependent on the chemical composition and thermo-mechanical processing applied to the material. These differences dictate the degree of superelasticity, pseudoplasticity, shape memory effect, and evolution under mechanical/thermal loading cycles, that is observed in the material. Understanding and utilizing these unique phenomena has become essential in many engineering applications. It is, therefore, important to provide two key ingredients in any SMA constitutive model; (i) a sufficiently comprehensive scope in the mathematical formulation to handle different classes of SMA materials; and (ii) a general model parameterization derived from fundamental tests that can be used for a specific SMA as intended for use in a given application. The present work is aimed at a detailed investigation of the interaction aspects between the above items (i) and (ii) in the context of using a recent three-dimensional, multimechanism-based SMA framework to model the experimentally measured responses of four different classes of SMA materials: (a) a commercial superelastic NiTi, (b) a powder metallurgically-processed NiTi-based SMA material, (c) a commercial Ni49.9Ti50.1 actuation material, and (d) a high-temperature Ni50.3Ti29.7Hf20 alloy. To facilitate the parameterization task, the model parameters are classified into two groups, i.e., (1) fixed parameters that are designed to capture the non-linear, hysteretic response under any thermo-mechanical loading condition, and (2) a set of functionally dependent material parameters which account for a number of refinements including asymmetry in tension and compression responses, temperature- and stress-state dependencies, etc. The results of the work showed that the complexity of the characterization is dependent on the SMA feature exploited by the specific application intended, which in turn dictates the amount and type of test data required to accurately predict a given application response.

Hybrid Recentering Energy Dissipative Device for Seismic Protection

A hybrid recentering energy dissipative device that has both recentering and energy dissipation capabilities is proposed and studied in this paper. The proposed hybrid device, referred to as the hybrid shape memory alloy (SMA) recentering viscous fluid (RCVF) energy dissipation device, connects the apex of a chevron brace to an adjoining beam using two sets of SMA wires arranged in series on either side of the brace and a viscous fluid damper arranged in parallel with the SMA wires. The viscous damper is used because being a velocity-dependent device it does not exert any force that counteracts the recentering force from the SMA wires after the vibration of the frame ceases. In the numerical study, the Wilde’s SMA constitutive model is used to model the SMA wires, and the Maxwell model is used to simulate the viscous fluid damper. To demonstrate the viability and effectiveness of the proposed hybrid device, comparative studies are performed on several single-story shear frames and a series of four-story steel frames. The results show that the frames equipped with the hybrid device have noticeably smaller peak top story displacements and residual story drifts when subjected to ground motions at three different intensity levels.

A new SMA shell element based on the corotational formulation

Aim of this paper is to develop a new shape memory alloy (SMA) facet-shell finite element accounting for material and geometric nonlinearities. A corotational formulation is exploited, able to filter out large rigid-body motions from the element transformation. Accordingly, a geometrically linear core-element is employed, along with a SMA constitutive model formulated in the small strain framework. In particular, in accordance with the formulation of the classical thin shell theory, a plane-stress SMA model accounting for the pseudo-elastic as well as the shape memory effect is adopted. The time integration of the evolutive equation is performed developing a step-by-step backward-Euler numerical procedure. A highly efficient implementation of the corotational machinery is used, endowed with a fully consistent tangent stiffness. Applications are carried out for assessing the performances of the developed computational procedure and to investigate on some interesting engineering examples. The numerical results show the effectiveness of the proposed shell element, whose simplicity makes it attractive for the design of new advanced SMA-based devices undergoing significant configuration changes during their operation.

An active compression bandage based on shape memory alloys: a preliminary investigation.

BackgroundDisorders associated with excessive swelling of the lower extremities are common. They can be associated with pain, varicose veins, reduced blood pressure when standing and may cause syncope or fainting. The common physical remedy to these disorders is the use of compression stockings and pneumatic compression leg massagers, which both attempt to limit blood pooling and capillary filtration in the lower limbs. However, compression stockings provide a constant pressure, and their efficiency has been challenged according to some recent studies. Air compression leg massagers on the other hand, restricts patient mobility. In this work we therefore present an innovative active compression bandage based on the use of a smart materials technology that could produce intermittent active pressure to mitigate the symptoms of lower extremity disorders.MethodsAn active compression bandage (ACB), actuated by shape memory alloy (SMA) wires, was designed and prototyped. The ACB was wrapped around a calf model to apply an initial pressure comparable to the one exerted by commercial compression stockings. The ACB was controlled to apply different values of compression. A data acquisition board and a LabVIEW program were used to acquire both the pressure data exerted by the ACB and the electrical current required to actuate the SMA wires. An analytical model of the ACB based on a SMA constitutive model was developed. An optimizer was implemented to identify optimal parameters of the model to best estimate the performance of the ACB.ResultsThe maximum increase in pressure due to the SMA wires activation was 40.8% higher than the initially applied pressure to the calf model. The analytical model of the ACB estimated the behaviour of the ACB with less than 0.32 mmHg difference with the experimental results.ConclusionsThe prototyped ACB was able to apply an initial compression comparable to the one applied by commercial compression stockings. Activation of the ACB resulted in an increase of compression up to 9.06 mmHg. Comparison between analytical and experimental results showed the analytical model was suitable to predict the behaviour of the ACB.

Beam balancing ball driven by shape memory alloy: prospective actuator for stabilised control

An alternative actuation mechanism is applied to the most sought after control laboratory system - the ball on beam. The system is driven by antagonistic shape memory alloy (SMA) wires which are engaged to play the role of both sensing and actuation in closed loop. The control objective is to govern the position of the ball on the beam. The angular altitude of the beam is varied by shifting the lateral position of the beam, through control of the smart actuator's angular acceleration. The focus is to study the use of SMA for systems with complex dynamics. A discrete sliding mode controller is implemented which requires no detailed information about the constitutive model of SMA. The differential resistance of the antagonistic SMA wires measured during actuation is utilized as the sensing signal. The innovation in this work is direct feedback of the measured signal which is facilitated by a specially designed signal processing electronics. The performance of the self-sensing under actuated system is illustrated through real time position control.

On the vibration control capability of shape memory alloy composite beams

In this paper, the vibration control capability of shape memory alloy (SMA) composite beams subjected to impulsive loads is examined. In order to simulate the SMA response, a one-dimensional constitutive model is introduced which is able to reproduce pseudo-elasticity, martensite transformation/orientation and in particular ferro-elasticity effects. A numerical algorithm is presented to solve non-linear SMA constitutive model by means of an elastic-predictor inelastic-corrector return map procedure. The equivalent single layer theory of Rayleigh–Euler–Bernoulli is used to describe displacement field of SMA laminated composite beams. Geometrical non-linearity is also considered in the von Karman sense. Considering rotary inertia effects, finite element equations of motion are developed using the Hamilton principle. Newmark and Newton–Raphson methods are utilized to obtain an incremental solution of the problem. Extensive numerical results are presented to provide an insight into the influence of pre-strain, temperature, location and thickness of SMA layers on the vibration control of SMA composite beams subjected to various blast pulses. Considering ferro-elasticity effect, results reveal the fact that SMA layers with high pre-strain have a passive vibration control capability in low temperatures and yield a better efficiency in comparison with pseudo-elastic SMA layers.

An improvement on the Brinson model for shape memory alloys with application to two-dimensional beam element

In this article, the one-dimensional phenomenological constitutive model originally proposed by Brinson for shape memory alloys is improved to predict asymmetric behavior in tension and compression. We propose an approach that decomposes stress-induced martensite volume fraction into two parts, one in tension and one in compression. Results of numerical examples show reasonable agreement with experimental data. Moreover, we implement the proposed model in a user-defined material subroutine in the nonlinear finite element software ABAQUS/Standard as a two-dimensional Euler–Bernoulli beam element. We simulate several beam problems and a shape memory alloy staple. Regarding the results, the proposed shape memory alloys constitutive model, employed in a two-dimensional beam element, can be used to simulate various shape memory alloys applications in the design and analysis.

Tensile Test of Shape Memory Alloys and Numerical Simulation

Shape memory alloy (SMA) as an effective alternative to steel has received much attention. The constitutive model of SMA has raped developed for nearly 10 years, such as Boyd and Lagoudas model, Auricchio model, etc. However, a number of constitutive models were more complex, and not easily applied to engineering. In order to study SMA concrete pullout test using numerical simulation software, the tensile property of superelastic SMA was studied in this paper, different units (SOLID185 and LINK8) were simulated at the same time. Through the comparative analysis of results of different constitutive models, an easier used constitutive model of SMA was obtained. Combining with the numerical case, it shows that link8 is more convenient and accurate to simulates SMA.