Model For Shape Memory Alloys Research Articles

A new constitutive model of shape memory alloy and its seismic mitigation capacity compared with existing models

The existing constitutive models of shape memory alloy (SMA) cannot accurately describe the mechanical behavior in martensitic strengthening segment since their loading and unloading paths in strengthening segment completely overlap. This study proposes a multi-segment linear mathematical model for SMA, which realizes the separation of loading path and unloading path in strengthening segment. A four-story steel frame structure and corresponding braced structures with various SMA constitutive models are designed, and seismic control effects of SMA braces with these models are analyzed and compared through time history analysis. The results show that the sub-cycle unloading mode of SMA constitutive model affects the seismic mitigation capacity of SMA brace in a certain extent. The position of the inflection point of unloading path has very little influence on the structural control ability of SMA braces. The SMA brace using the SMA constitutive model with a single linear sub-cyclic unloading path has the minimal seismic response and the highest seismic reduction ratio. For most evaluation indexes, the seismic mitigation ability calculated by the proposed path separation constitutive model is in the middle of the results calculated by the existing models. SMA models without considering the mechanical behavior of strengthening segment may lead to an erroneous estimation of the energy consumption of SMA brace and the structural damage. The difference of simulation results among various SMA constitutive models is almost independent with ground motion.

Simulation of SMA-based engineering applications considering large displacement and rotation, thermomechanical coupling and partial phase transformation

Shape memory alloys (SMAs) undergo large recoverable deformation due to their inherent diffusionless martensitic phase transformation. Two factors need to be taken into account to incisively emulate the behaviour of SMA based structures: (i) consideration of large displacement and rotation (LDR) effect, and (ii) capturing the consequence of transformation induced material level coupling. In this study, both these effects are apprehended by extending the infinitesimal strain-based constitutive model of SMA as proposed by Lagoudas et al. (2012), assuming small elastic strain but with finite inelastic strain. To preclude any spurious stress generation out of large rotation, the Jaumann stress rate is used, and incremental objectivity for finite rotation between two successive time instants is conserved by rotating the strain increment and spin tensor to the rotation-independent mid-point configuration following Hughes–Winget (Hughes and Winget, 1980) algorithm. In addition, the contribution of thermoelastic and latent heat evolved during transformation is taken into consideration in the thermal equilibrium equation. Moreover, the effect of partial phase transformation yielding minor hysteresis loop has also been captured. The equilibrium equation is expressed in the current configuration following the Updated Lagrangian formulation. The mechanical and thermal equilibrium equations are solved concurrently in block matrix form using the Newton–Raphson (NR) iterative technique, considering the coupling terms resulting from the phase transformation. The efficacy and robustness of the developed finite element model are corroborated through various practical applications of SMA-based members, e.g., SMA ring, SMA-actuated beam, morphing of corrugated airfoil, orthodontic palatal expander, compliant gripper, undergoing LDR while subjected to different thermomechanical loading conditions. The combined effects of LDR along with thermomechanical coupling yield a stiffening behaviour during loading and sluggish response at the time of thermal recovery.

Quantification of material modeling uncertainty on seismic performance of SMA-based self-centering concentrically braced frames

Shape memory alloys (SMAs) combine super-elasticity and energy dissipation capacity therefore is favored in seismic hazard mitigation. Simplifications are necessary to incorporate acquired material properties through material testing for dynamic analysis. This study presents a methodology to integrate SMA material testing, model inference, and probabilistic seismic analysis for uncertainty quantification of SMA model uncertainty on SMA based structures. The proposed methodology is applied to a SMA-based self-centering concentrically braced frame (SC-CBF). The posterior distribution of SMA modeling parameters is first obtained through the MCMC algorithm. Considering computational cost of MCMC algorithm, linear moments method is introduced to sample SMA modeling parameters. Extensive time-history analysis is then performed to quantify the effect of SMA modelling uncertainty and ground motions on the performance of SC-CBF. Significant response changes can be observed in SC-CBF due to the effect of uncertainty, which inevitably affect the reliability assessment of the structure. These analysis results also show that modeling uncertainty will affect seismic performance of SMA-based SC-CBF but its influence is less significant than that caused by ground motion uncertainty for the braced frame investigated in this study.

Mechanical properties and constitutive models of shape memory alloy for structural engineering: A review

Shape Memory Alloys (SMAs) are an innovative material with the unique features of superelasticity and energy dissipation capabilities under extreme loads. Due to their unique features, they have a great potential to be employed in structural engineering applications under different conditions. However, in order to effectively use SMAs in civil engineering structures and model their behaviors accurately in Finite Element (FE) packages, it is crucial for structural engineers to comprehend the mechanical properties and cyclic behavior of different SMA compositions under varying loading conditions. While previous studies have focused mainly on the cyclic behavior of SMAs under tensile loading, it is important to evaluate their fatigue behavior under cyclic tension-compression loading for seismic applications. This literature review aims to discuss the current gaps in the existing literature on the behavior of SMA rebars under low-cycle fatigue (LCF). The review provides a comprehensive overview of the primary characteristics of SMAs, summarizes the mechanical properties of SMAs presented in the literature and the parameters that affect them, and critically evaluates the effects of cyclic loading and LCF on SMAs. The review also provides a summary of the different constitutive models of SMAs and compares their advantages and limitations, which helps structural engineers to employ an appropriate constitutive model for predicting the accurate behavior of SMAs in FE software.

Shakedown theorems for shape memory alloys structures with functional fatigue — Application to nitinol stents

Shape memory alloys (SMAs) offer interesting perspectives in various fields such as aeronautics, robotics, biomedical sciences, or structural engineering. The distinctive properties of those materials stem from a solid/solid phase transformation occurring at a microscopic level. Modeling the rather complex behavior of SMAs is a topic of active research. Lately, SMA models coupling phase-transformation with permanent inelasticity have been proposed to capture degradation effects which are frequently observed experimentally for cyclic loadings — a phenomenon referred to as functional fatigue. In this paper, the classical static and kinematic shakedown of plasticity theory are extended to such material models. Those results give conditions for the energy dissipation to remain bounded, which is beneficial for the fatigue life. Analytical shakedown limits are obtained for a 3-bar truss example and compared with numerical results from step-by-step simulations. We consider the problem of a nitinol stent submitted to cyclic pressure and mixed pressure–bending as an application, showing how the approach presented can be combined with finite-element analysis to study shakedown of complex 3D structures.

A novel energetic approach for predicting fatigue crack growth in pseudoelastic NiTi alloys

A novel strain energy-based method for analyzing fatigue crack growth (FCG) in pseudoelastic Nickel-Titanium (NiTi) -based shape memory alloys (SMAs) is proposed. It uses the dissipated energy to predict the FCG. This parameter can be computed either by volume integration of near-crack-tip strain energy or by the force–displacement hysteresis measured at the loading pins of the sample. Eccentrically-loaded single Edge Crack tension samples (ESE(T)) were used for FCG tests. High resolution Digital Image Correlation (DIC) was used to capture near-crack-tip displacement and strain fields. DIC data were also used to estimate the effective stress intensity range by regressing the William’s expansion series. Furthermore, a constitutive model for SMAs was used for FE simulations of ESE(T) samples, and the evolution of the dissipated energy during FCG tests was computed. Experimental FCG rate, plotted against the cyclic dissipated energy, are well fitted by a power law equation (R2 = 0.99). This result would open new perspectives to develop predictive models for FCG in SMAs considering intricate thermomechanical coupling mechanisms and material non-linearities.

Thermo-mechanically coupled functional fatigue of NiTi shape memory alloys under multiaxial cyclic loadings

In this work, the rate-dependent and loading path-dependent cyclic deformation behaviors of super-elastic NiTi shape memory alloy (SMA) are investigated under multiaxial cyclic loadings with various loading frequencies. The evolutions of stress–strain response, temperature and dissipation energy with increasing the number of cycles are investigated systematically. It is found that the functional fatigue occurs in the process of cyclic deformation, and such a phenomenon is more significant under non-proportionally multiaxial loadings and with higher frequency. The temperature variation induced by the internal heat generation becomes more obvious with increasing the loading frequency. Moreover, it is revealed that the path-dependent functional fatigue has a positive correlation to a newly defined indicator for different loading paths, i.e., the degree of non-proportionality, and the rate-dependent functional fatigue can be attributed to the thermo-mechanically coupled nature of martensite transformation. The experimental results performed in this work and the revealing deformation mechanisms are helpful to establish a three-dimensional thermo-mechanically coupled cyclic constitutive model of NiTi SMAs.

Design, Modeling, and Evaluation of a Hybrid Driven Knee-Ankle Orthosis With Shape Memory Alloy Actuators

Abstract This paper demonstrates the mechanical design, analysis, and evaluation of a knee-ankle orthosis (KAO) for lower limb rehabilitation, including shape memory alloy (SMA) actuators and DC brushless motor actuators. First, the mechanical structure of the KAO is detailed, including the actuator system, transmission mechanism, monitoring device, and processing method of SMA actuators. Next, the dynamic model of SMA spring actuators in the phase transition process is established based on the thermal constitutive model of SMA. In addition, the dynamic output response of the knee joint under three working states is analyzed, and the rotation angle of SMA soft actuator during bending is described by pseudo rigid body model. Finally, the output of SMA actuator is preliminarily evaluated through experiments. The experimental results show that the maximum displacement of SMA spring actuator is 54.36 mm, the maximum restoring force during phase transformation is 4.14 N, and the maximum rotation angle of SMA soft actuator is 43.18 deg. The experimental results are consistent with the theoretical model.

A portable modular vaccine injection system actuated by shape memory alloy

In order to develop a vaccination system that have no contact with healthcare workers during highly transmissible epidemics, a portable modular vaccine injection system (PMVIS) composed of YT-type modules (YTM), winding modules (WM) and an active injector (AI) actuated by shape memory alloy (SMA) wires are proposed in this article. By series layout of WMs, YTMs and AI, the multi-posture requirements of PMVIS can be realized. Then, the thermodynamic model of SMA together with kinematic and dynamic models of structure for each module are established, and studied the output stroke of each module through numerical analysis and experiments. The results show that the designed YTM achieves a maximum output of 1.84 mm displacement or 1.9° angle under the given size parameters. After connecting 1-WM in series, the output displacement and rotation angle are enlarged to 12.12 mm and 10.8°, which are increased by 558.7% and 468.4%, respectively. PMVIS can realize multi-postures through different functional modules to play the role of position adjustment. It provides theoretical and technical support for future contactless injection systems.

Dynamical responses of a Gaussian colored noise-driven shape memory alloy oscillator with a periodic force

For shape memory alloy (SMA) oscillator, the stochastic transitions between low-amplitude and undesirable high-amplitude oscillations will affect the safety and normal use of the system. Therefore, the nonlinear dynamical responses of a SMA oscillator with both periodic and Gaussian colored noise excitations are investigated in this paper. Firstly, to reveal the influences of random factors, a stochastic SMA model with a Gaussian colored noise is introduced. Subsequently, the approximate analytical solution of the steady-state amplitude response under the deterministic case is given by the averaging method, and the time-averaging mean-square response of the stochastic SMA system is obtained by the stochastic averaging method. The deduced approximated analytical solutions are verified by Monte Carlo numerical results, and a good consistency is observed. Finally, the effects of the random excitation and temperature on the steady-state responses of the SMA system are explored. We uncover that the temperature influences the frequency of bifurcation points, which can disrupt the stable structure of the SMA oscillator. In addition, noise intensity and correlation time of the colored noise can induce the occurrence of stochastic transitions between low-amplitude and high-amplitude oscillations, which are visible through the steady-state probability density and time history diagrams. All these obtained results may provide theoretical guidance and valuable insights for avoiding catastrophic stochastic transitions in SMA materials.

Numerical modeling of iron-based SMA confined concrete columns under axial compressive loading

This paper presents the results of a Finite Element (FE) model developed to simulate the behavior of confined concrete columns with iron-based shape memory alloys (Fe-SMA) under compressive loading. The performed simulations aimed to accurately demonstrate the combined effect of external shape memory alloy (SMA) reinforcement and internal transverse steel reinforcement under different loading conditions and presented a simplified approach to model external confinement as discrete elements near the surface of the concrete element.The primary objective of this study was to develop a FE model that can be used to predict and replicate the response of actively confined columns using Fe-SMA. The FE model was developed using the results of an experimental study conducted on circular Fe-SMA confined columns under concentric loading. The experimental study evaluated the influence of: 1) the presence of internal reinforcement, and 2) the ratio of external SMA confinement used. The simplifications and approximations considered in the numerical approach to predict the capacity and deformation responses showed to be adequate, and the results obtained were in good agreement with the compressive behavior of the actively SMA confined columns obtained from the experimental work.In addition to the concentric case, eccentric loading simulations are presented in this study to evaluate the combined confinement mechanism in terms of the structural element response to a different loading configuration. The predictions obtained in terms of load-carrying capacity and deformations can be used to expand the research work done using the SMA as a form of active confinement.

Shape Memory Alloy-Polymer Composites: Static and Fatigue Pullout Strength under Thermo-Mechanical Loading.

This work was carried out within the context of an R&D project on morphable polymer matrix composites (PMC), actuated by shape memory alloys (SMA), to be used for active aerodynamic systems in automotives. Critical issues for SMA–polymer integration are analyzed that are mostly related to the limited strength of metal–polymer interfaces. To this aim, materials with suitable thermo-mechanical properties were first selected to avoid premature activation of SMA elements during polymer setting as well as to avoid polymer damage during thermal activation of SMAs. Nonstandard samples were manufactured for both static and fatigue pullout tests under thermo-mechanical loading, which are made of SMA wires embedded in cylindrical resin blocks. Fully coupled thermo-mechanical simulations, including a special constitutive model for SMAs, were also carried out to analyze the stress and temperature distribution in the SMA–polymer samples as obtained from the application of both mechanical loads and thermal activation of the SMA wires. The results highlighted the severe effects of SMA thermal activation on adhesion strength due to the large recovery forces and to the temperature increase at the metal–polymer interface. Samples exhibit a nominal pullout stress of around 940 MPa under static mechanical load, and a marked reduction to 280 MPa was captured under simultaneous application of thermal and mechanical loads. Furthermore, fatigue run-out of 5000 cycles was achieved, under the combination of thermal activation and mechanical loads, at a nominal stress of around 200 MPa. These results represent the main design limitations of SMA/PMC systems in terms of maximum allowable stresses during both static and cyclic actuation.

A multi-posture 3D printed actuator composed of VT-type bidirectional deflection fishbone-like modules based on shape memory alloy wires

In this paper, a multi-posture actuator (MPA) composed of VT-type bidirectional deflection fishbone-like modules (VBFM) based on shape memory alloy (SMA) wires is proposed for realizing multi-posture deformation control. Through sizing of the VT-type structure and the arrangement of VBFM in series, it is possible to realize the actuator design meeting specific deformation requirements. The thermo-mechanical coupling analysis model based on kinematics, dynamics, thermodynamics and SMA models is established to study the VBFM deflection angle and multi-posture performance of the MPA. The experimental and numerical results show that the MPA can achieve the target postures and the maximum deflection angle of the single VBFM can reach about 1.8°, and the 5-VBFM MPA can deflect a maximum angle of approximately 9° in one direction. In addition, the load actuation performance of 1-VBFM and 5-VBFM MPA is investigated, and the results show that the actuated deflection angle increases with the input electrical power within its effective range and decreases with the external resistance load. When multiple modules are combined, the deflection angle can be accumulated, and they can be used in medical robotic arms, space cleaning grab mechanisms, etc.

Effects of microstructure and composition on constitutive response of high temperature shape memory alloys: Micromechanical modeling using 3-D reconstructions with experimental validation

NiTiHf alloys are high temperature Shape Memory Alloys (SMAs) suitable for actuation applications in a wide range of temperatures. Aging heat treatments in NiTiHf SMAs cause the formation of nano-sized, non-transforming and elastic precipitates, which modify phase transformation behavior. Experimental observations of the aged alloys showed a counterintuitive trend of increasing phase transformation strain with precipitation. In order to predict such microstructure effects on constitutive response of precipitated NiTiHf SMAs, in this work a finite element based micromechanical modeling framework is developed. Two types of representative volume elements are considered: (i) exact 3-D reconstructions of precipitates using transmission electron microscopy, and (ii) less expensive ellipsoidal representation of precipitates. The composition changes in the material are modeled, and their effects are incorporated by considering composition dependency of phase transformation properties in the matrix. The resulting model is used to predict the constitutive responses for different aging conditions in Ni50.3Ti29.7Hf20 and Ni50.3Ti34.7Hf15 SMAs. The model predictions are in good agreement with the experimental measurements, and experimental and modeling results are presented with confidence intervals from sample-to-sample variations. The present work constitutes the first micromechanical modeling of high temperature SMAs with consideration of real microstructures.

Effect of Pore Shape on Mechanical Properties of Porous Shape Memory Alloy

Porous shape memory alloys (SMAs) have been widely used in the aerospace, military, medical, and health fields due to its unique mechanical properties such as superelasticity, biocompatibility, and shape memory effect. In this work, the pore shape was considered in the constitutive model of the porous SMAs by respectively introducing the parameter of aspect ratio and for different pore shapes including oblate, sphere, and prolate shapes, so the expression of Young’s modulus for the porous SMA can be derived. Then, the constitutive model for such a porous shape memory alloy was established. When the porosity was zero, the model can be degenerated to the dense case. The stress–strain curves for the porous SMA with a porosity of 13% with different aspect ratio are then given. Numerical results showed good agreement with the published experimental data that proved the validation of the model. Based on the proven constitutive model, the properties of porous SMA with different porosity and pore shapes are discussed. The results showed that the pore shapes and the porosities had a big effect on the stress–strain curves for the porous shape memory, while with the increasing porosities, the Young’s modulus and the hysteresis both decreased. With the same porosities, the Young’s modulus and hysteresis loop of SMA with round pores were the largest, while the Young’s modulus and hysteresis loop were the smallest when , and they were greater when than when . It can be seen that the closer to the circle, the better the performance of the material.

Numerical Simulation of Ultrasonic Spot Welding of Superelastic NiTi Alloys: Temperature Distribution and Deformation Behavior

Abstract Ultrasonic spot welding (USW) has attracted increasing attention due to its high-throughput solid-state bonding mechanism, which shows great potential in the semiconductor and automotive industries for joining of metal sheets. However, the short welding cycle makes it challenging to effectively monitor the temperature history and deformation of the workpieces during the process. In this study, a three-dimensional (3D) finite element analysis model for USW of superelastic NiTi shape memory alloy (SMA) with Cu interlayer was developed using ansysworkbench. The thermal-stress coupled phenomena including the heat generation and stress distribution during the welding process were simulated and analyzed. First, a superelastic constitutive model for NiTi SMAs was constructed. The distribution of temperature and stress fields was then obtained by thermal-stress analysis using the direct coupling method, and the superelasticity of SMAs was observed. The simulation results showed that the highest temperature occurred in the center of the welding area during USW, which is proportional to the welding time and inversely proportional to the clamping pressure. In addition, the maximum stress occurred at the center of the contact surface between upper NiTi and Cu interlayer. After that, the validity of the simulation results was verified by setting up a thermocouple temperature measurement platform to collect the temperature data, which exhibited a good agreement with the simulated results. The simulation procedure demonstrates its potential to predict temperature and stress distributions during the USW process.

Thermal Modal Performance of Composite Laminates Embedded with Anti-Symmetric Oblique Coupling Gradient Pre-Strained SMA Wires for Suppressing Resonance

As an extension of conventional gradient, anti-symmetric oblique coupling gradient has a superior modal modification ability on composite laminates embedded with pre-strained shape memory alloys (SMA) wires, which is beneficial to suppress modal resonance of composite laminates in the thermal environment. This paper presents an anti-symmetric oblique coupling gradient model of SMA along the thickness direction. That is, the gradient model of SMA wires’ orientation and the positive and negative gradient model of SMA volume fraction. Considering the internal force of composite laminates composed of the pre-strain recovery force of SMA and the thermal expansion force of the substrate, the free vibration equation of composite laminates with additional internal forces energy is derived from first-order shear plate theory and Hamilton principle. The influence of coupling gradient parameters on the thermal modal performance of SMA composite laminates is analyzed and verified by experiments. The proposed anti-symmetric oblique coupling gradient SMA wires’ distribution form effectively exerts the recovery stress generated by SMA tensile pre-strain, i.e., effectively improves the stiffness and critical buckling temperature. Coupling gradient distribution broadens the frequency modulation range, which makes the fine regulation of the natural frequency and critical buckling temperature feasible.

Modeling and Position Control Simulation Research on Shape Memory Alloy Spring Actuator.

The shape memory alloy (SMA) actuator is widely used in aerospace, medical and robot fields because of its advantages of low driving voltage, large driving force, no noise and high-power–weight ratio. Therefore, it is of great significance to establish the theoretical model of the SMA actuator and analyze the driving characteristics of the SMA actuator. On the basis of summarizing the constitutive model of the shape memory alloy spring, the phase transformation dynamics model of SMA including the minor hysteresis loop is established using the Duhem model in this paper, and the theoretical models of the bias and differential SMA spring actuator are established. At the same time, a PID position controller including anti-saturation and anti-overheating functions is proposed to control the position of the SMA actuator. Finally, the position control simulation model of the SMA spring actuator is established and simulated. Simulation results show that the position of the SMA actuator can be well controlled by using the model and control method established in this paper.

Modelling fatigue crack growth in shape memory alloys

AbstractWe present a phase field‐based framework for modelling fatigue damage in Shape Memory Alloys (SMAs). The model combines, for the first time: (i) a generalized phase field description of fracture, incorporating multiple phase field formulations, (ii) a constitutive model for SMAs, based on a Drucker–Prager form of the transformation surface, and (iii) a fatigue degradation function, with damage driven by both elastic and transformation strains. The theoretical framework is numerically implemented, and the resulting linearized system is solved using a robust monolithic scheme, based on quasi‐Newton methods. Several paradigmatic boundary value problems are addressed to gain insight into the role of transformation stresses, stress‐strain hysteresis, and temperature. Namely, we compute Δε − N curves, quantify Paris law parameters, and predict fatigue crack growth rates in several geometries. In addition, the potential of the model for solving large‐scale problems is demonstrated by simulating the fatigue failure of a 3D lattice structure.

Parametric Random Vibration Analysis of an Axially Moving Laminated Shape Memory Alloy Beam Based on Monte Carlo Simulation.

The study of the bifurcation, random vibration, chaotic dynamics, and control of laminated composite beams are research hotspots. In this paper, the parametric random vibration of an axially moving laminated shape memory alloy (SMA) beam was investigated. In light of the Timoshenko beam theory and taking into consideration axial motion effects and axial forces, a random dynamic equation of laminated SMA beams was deduced. The Falk’s polynomial constitutive model of SMA was used to simulate the nonlinear random dynamic behavior of the laminated beam. Additionally, the numerical of the probability density function and power spectral density curves was obtained through the Monte Carlo simulation. The results indicated that the large amplitude vibration character of the beam can be caused by random perturbation on axial velocity.