Hysteresis In Shape Memory Alloys Research Articles

Accelerated functional fatigue leading to hysteresis widening in Ti44Ni47Nb9 shape memory alloy with multi-scale Nb-rich particles

Martensitic transformation temperatures are the most important indicators for designing shape memory alloy (SMA) components. Subjected to alternating temperatures in service, they undergo functional fatigue, which affects little the thermal hysteresis. We investigate the thermal cycling induced functional fatigue in Ti44Ni47Nb9 wide hysteresis SMA, decorated with multi-scale Nb-rich particles. We identify an accelerated functional fatigue behavior leading to the hysteresis widening from 58 to 71 K after 20 thermal cycles, in contrast to which hysteresis maintains nearly constant in Ti-Ni binary SMAs. Compared to Ti49Ni51 with similar transformation temperatures and latent heats, the hysteresis widening in Ti44Ni47Nb9 is attributed to accelerated decrease in starting temperature of martensite transformation (Ms).Microscopic characterizations reveal an inhomogeneous microstructure, consisting of (Ti,Nb)Ni B2 matrix and multi-scale Nb-rich particles and (Ti,Nb)2Ni particles. The presence of unique multi-scale Nb-rich particles has been demonstrated at the core of the underlying mechanisms of accelerated functional fatigue. Densely distributed Nb-rich nanoparticles narrow the mean matrix distance of transformation to 156.3 nm, which restricts the size and cross-over of the transformation induced dislocation leaves. Our work provides a new mechanism to widen the thermal hysteresis of SMAs, which is probably applicable to the other SMAs systems with dense nanoparticles.

Modelling Hysteresis in Shape Memory Alloys Using LSTM Recurrent Neural Network

The complex behavior of shape memory alloys (SMAs), characterized by hysteresis and nonlinear dynamics, results in complex constitutive equations. To circumvent the complexity of solving these equations, a black box neural network (NN) has been employed in this research to model a rotary actuator actuated by an SMA wire. Considering the historical dependence of the pulley’s rotational angle on the applied voltage, a recurrent neural network (RNN) is suitable for capturing past information. Specifically, a long short‐term memory (LSTM) neural network is selected due to its ability to address issues encountered in standard recurrent networks. There are major drawbacks with modelling hysteresis with NNs that do not account for historical behavior. Traditional NNs, characterized by a one‐to‐one mapping, struggle to capture hysteresis loops wherein system behavior varies during loading and unloading cycles. Therefore, a single‐tag data is used to determine the loading or unloading state, but tag signal causes discontinuity in network and omits various aspects of hysteresis in SMA, particularly within minor loops. In contrast, NNs incorporating past data to predict hysteresis behavior alleviate the need for tag data. However, such networks tend to have complex structures with a substantial number of neurons to effectively capture the inherent nonlinearity in SMAs. The long short‐term memory (LSTM) neural network employed in this research, characterized by a simpler structure, achieves high accuracy in predicting hysteresis in SMAs without the need for tag data. In the proposed LSTM model, data related to the pulley’s rotational angle and the wire’s applied voltage from the current moment and the two previous moments serve as input. The data passes through a layer comprising three LSTM cells, and the output from the last LSTM cell is fed into a fully connected layer to predict the pulley’s rotational angle for the next moment. Training data are obtained by applying voltage at various frequencies and formats to the SMA wire while simultaneously recording the pulley’s angle with an encoder. Evaluation of the LSTM model is conducted in two configurations: online prediction (one‐step ahead) and offline prediction (multistep ahead). In the online configuration where the model uses encoder data as angular inputs, the root mean square error (RMSE) of predictions for various input voltages is significantly low at about 0.1 degrees where the maximum rotational angle of pulley is 8 degrees. In the offline configuration when using the model’s predictions as angular inputs instead of encoder data, the RMSE rises to 0.3 degrees. To provide a clear demonstration of the LSTM model’s ability in this particular configuration, a comparison has been conducted between LSTM model and a rate‐dependent Prandtl‐Ishlinskii (RDPI) hysteresis model for predicting the pulley’s angle. The LSTM model outperforms the RDPI model by 70% in terms of accuracy. Overall, the LSTM model demonstrates capability in effectively modeling SMA hysteresis in both online and offline configurations.

Optimal hysteresis of shape memory alloys for eliminating seismic pounding and unseating of movement joint systems

Bridge structures adapt to movement through the addition of joint systems that accommodate anticipated movement due to temperature variations or earthquakes, thereby relieving stress on the bridge structure. Shape memory alloys (SMAs) have been proposed to limit joint displacements because of their ability to dissipate seismic energy and restore their original shape. A parametric study is conducted in this study using computer simulations of some advanced MATLAB programs to show the effects of all hysteretic parameters of SMA retrofit devices on seismic joint openings. The results show that SMA hysteretic parameters have a huge effect on SMA efficiency as a restrainer, which is compatible with energy dissipation philosophy, but there are some reversible impacts of some hysteretic parameters in some cases due to the resonance problem and their dependence on other parameters such as natural time period, period ratio, mass ratio, and seismic records. As a result, some design charts are created in this study after more than 200 million trials, taking into account the variation of all key parameters of the structure and the SMA under a suite of historical ground motion records. Moreover, bridge designers can choose optimal SMA hysteresis for a desired opening width, a desired time period, and desired period/mass ratios between adjacent frames with the help of these charts to overcome the two bridge problems of pounding and unseating of bridge decks.

Molecular dynamics simulations of austenite-martensite interface migration in NiTi alloy

The mechanism of austenite-martensite interface migration is a key component in understanding the phase transformations in shape memory alloys. It is also intimately tied to their observed hysteresis. Molecular dynamics simulations offer a unique capability to study phase transformations in detail, however, their associated timescales prevent the observation of interface formation via nucleation and growth near the transformation temperature. To address this challenge, we present a simulation methodology in which steady-state austenite-martensite interfaces are allowed to form close to equilibrium. The resulting structures contain well-defined interfaces which can be perturbed from equilibrium to study their migration. In NiTi specifically, the austenite-martensite interfaces are semicoherent, made up of terrace planes separated by structural disconnections. The disconnections advance via kink pairs and provide an atomic-scale mechanism for interface migration. The methodology and results presented here provide a foundation toward further leveraging molecular dynamics simulations to better understand how the atomic-scale structure of austenite-martensite interfaces impacts macroscopic properties such as hysteresis in shape memory alloys.

Nb/NiTi laminate composite with high pseudoelastic energy dissipation capacity

NiTi shape memory alloys (SMAs) with marked hysteresis between the forward and reverse martensitic transformations are attractive for the applications in passive damping. However, the stress hysteresis of NiTi SMAs is usually 150–300 MPa, limiting their energy dissipation to ∼10 MJ/m3. Here, we designed a bulk Nb/NiTi laminate composite with a reversible energy dissipation capacity of ∼30 MJ/m3 and a plateau strength of ∼750 MPa, which are outstanding among the common bulk energy dissipation materials. This high performance is attributed to the strong interaction between the pseudoelastic NiTi and the non-pseudoelastic Nb lamellae within the composite. The intrinsically plastic Nb layers deform in a pseudo-super elastic manner, involving elastic lattice deformation, reversible motion of dislocations, and reversed plastic deformation. These are enabled by the unique phenomenon of lattice strain matching the martensitic transforming. This study offers a new pathway for the design of high energy dissipated bulk materials.

Data-driven shape memory alloy discovery using Artificial Intelligence Materials Selection (AIMS) framework

One of the obstacles to the deployment of shape memory alloys (SMAs) in solid-state actuation is the low efficiency and functional instability due to the transformation thermal hysteresis and large temperature ranges during martensitic phase transformation. Numerous studies have been conducted in an effort to minimize the thermal hysteresis and transformation temperature range of SMAs through ternary and quaternary alloying of known binary alloy systems, such as NiTi, and considerable success has been achieved. However, and crucially, the alloys discovered so far have failed to maintain a narrow hysteresis under applied stress. In the present study, an AI-enabled materials discovery framework was successfully used to identify both SMA chemistries and the associated thermo-mechanical processing steps that result in narrow transformation hysteresis and transformation range under an applied stress. The major elements of the proposed workflow are described in detail and its materials-agnostic character makes it widely applicable to other alloy discovery challenges. Using this framework, and without relying on subsequent experimental exploratory analysis, an SMA composition, i.e. Ni32Ti47Cu21 (at. %), was predicted and confirmed to have the narrowest thermal hysteresis and transformation range under stress achieved thus far for a NiTi-based SMA. Furthermore, the alloy was shown to exhibit excellent cyclic stability and actuation strain. The methodology and the dataset introduced here can be extended to design novel SMAs with other target functions.

Nonlinear dynamic characteristics and stability analysis of energy storage flywheel rotor with shape memory alloy damper

In this paper, the nonlinear dynamic characteristics and stability of an energy storage flywheel rotor with shape memory alloys (SMA) damper are studied. A new type of SMA constitutive model is proposed to express SMA's hysteresis properties, and the nonlinear dynamic model of an energy storage flywheel rotor with SMA damper is established. A developed multi-scale method is proposed to obtain the natural frequency of the system with high accuracy in strong nonlinear condition, and the nonlinear dynamic characteristics of the system are analyzed. To a cracked flywheel rotor, a time-varying function is proposed to express the effect of the crack depth on the system's stiffness, and the variation of the system's area with different parameters is discussed. Simulation results show that the nonlinearity and crack will both affect the stable area of the system. To a flywheel rotor subjected to stochastic excitation, a developed analysis method for the stability is proposed to obtain the global stability of the system. Finally, the conditions on stochastic bifurcation are determined. Simulation results show that the stochastic system's motion will change from balance point to periodic orbit, and will also jump from one orbit to another in special cases. The results of this paper are helpful for the design of energy storage flywheel rotor.

The mechanism of thermal transformation hysteresis in ZrO2-CeO2 shape-memory ceramics

Hysteresis is an important phase transformation property to understand and control in shape-memory materials. While a detailed understanding of hysteresis has been developed in shape-memory alloys (SMAs), it is far less understood in emerging shape-memory ceramics (SMCs). Here, we systematically study thermal hysteresis of the tetragonal-monoclinic martensitic transformation in ZrO2-CeO2 SMCs. We present calorimetry measurements of thermal hysteresis, which reveal a non-monotonic trend with CeO2 content as well as significant rate dependence, and correlate these findings with the transformation crystallography measured by in situ X-ray diffraction. We quantitatively analyze these results in the framework of martensite nucleation theory and conclude that the initial decrease in hysteresis with CeO2 content can be attributed to improving interface compatibility (λ2) for coherent nucleation whereas the sharp increase in hysteresis at higher CeO2 contents (below temperatures of ~773 K) is a result of interface friction consistent with thermally-activated interactions with the Peierls barrier of the crystal. Our analysis gives an activation energy of ~136 kJ/mol, which is consistent with previously reported activation energies of isothermal transformation in these materials. These findings clarify contradicting reports in the ZrO2 literature and confirm that the same controlling factors of hysteresis in SMAs, namely λ2 and thermal friction, are also operative in SMCs.

Development of Ni44Ti35Zr15Cu6 Quaternary Shape Memory Alloy: Experimental and Density Functional Theory Studies

The effect of Zr and Cu additions on the phase stability, microstructure and martensitic transformation temperature of binary NiTi alloys has been investigated with a combined approach of experimental measurements and first principle density functional theory calculations. In this work, multilayer Ni/Ti/Zr/Cu films have been deposited using the magnetron sputtering on Si substrates at room temperature and subsequently annealed at 350 °C for complete inter-diffusion of multilayers to create amorphous phase followed by high temperature annealing at 600 °C for 5 min to achieve Ni44Ti35Zr15Cu6 shape memory alloys. The high temperature annealing is required for the formation of crystalline phases. The x-ray diffraction pattern of the film annealed at 600 °C indicated the presence of martensite phase. The surface and interface studies were performed focusing on morphology and interlayer diffusion over the nano-level structure at 600 °C. The elemental mapping showed near-uniform distribution of constituent elements after annealing. Atomic force microscopy results showed the increase in surface roughness at annealing temperature of 600 °C due to grain growth. The formation energy results indicate that the Zr and Cu additions to NiTi favor the formation of monoclinic B19’ phase. The differential scanning calorimetry results show that the martensitic transformation temperature increases with Zr and Cu additions. Nanoindentation studies for Ni44Ti35Zr15Cu6 films showed an increase in depth recovery for the crystalline film. A theoretical model has been used, to determine the hysteresis of shape memory alloys as predicted by the geometric nonlinear theory of martensite.

Effect of stress on the thermal hysteresis of martensitic transformations - A continuum based particle dynamics model

The hysteretic behavior of shape memory alloys (SMA) is technologically important and advantageous in some applications but detrimental in others. In this paper, the effect of stress on the thermal hysteresis of SMA during the martensite transformation is studied. A recently developed discrete particle approach referred to as the continuum based particle dynamics (CPD) is used for this study. The CPD model uses a multibody interactions among the discrete particles which is directly derived from poly-convex free energy pertinent to such material behaviors. In the analysis, temperature of the domain is considered as the control parameter and is varied uniformly through out the domain above and below the transformation temperature. The hysteresis response resulting from this thermal cycle is observed in specific heat-temperature plot (DSC curve) and strain-temperature plot. The effect of prestress on thermal hysteresis along with the corresponding martensite microstructure is modeled. The results show a decrease in hysteresis with increased stress. This effect is attributed to the force required to propagate the ledges along the twin or phase boundary, which is smaller for the stressed material as compared to the stress–free material.

Stochastic recruitment control of shape memory alloy cellular actuators based on multi-state Markov chain model

A new broadcast stochastic recruitment approach to the control of shape memory alloy (SMA) cellular actuators is proposed. The control design is based on a Markov chain model of multi-state cells, which is able to better characterize the inherent hysteresis of SMA in phase transition. The closed-loop and open-loop control laws are derived from random Lyapunov stability analysis and the stability conditions are analyzed. Simulation experiments demonstrate the effectiveness of the proposed method.

The Mechanism of Thermal Transformation Hysteresis in Zro 2-Ceo 2 Shape-Memory Ceramics

Hysteresis is an important phase transformation property to understand and control in shape-memory materials. While a detailed understanding of hysteresis has been developed in shape-memory alloys (SMAs), it is far less understood in emerging shape-memory ceramics (SMCs). Here, we systematically study thermal hysteresis of the tetragonal-monoclinic martensitic transformation in ZrO2-CeO2 SMCs. We present calorimetry measurements of thermal hysteresis, which reveal a non-monotonic trend with CeO2 content as well as significant rate dependence, and correlate these findings with the transformation crystallography measured by in situ X-ray diffraction. We quantitatively analyze these results in the framework of martensite nucleation theory and conclude that the initial decrease in hysteresis with CeO2 content can be attributed to improving interface compatibility (λ2) for coherent nucleation whereas the sharp increase in hysteresis at higher CeO2 contents (below temperatures of ~773 K) is a result of interface friction consistent with thermally-activated interactions with the Peierls barrier of the crystal. Our analysis gives an activation energy of ~136 kJ/mol, which is consistent with previously reported activation energies of isothermal transformation in these materials. These findings clarify contradicting reports in the ZrO2 literature and confirm that the same controlling factors of hysteresis in SMAs, namely λ2 and thermal friction, are also operative in SMCs.

Thermomechanical modeling of nonlinear internal hysteresis due to incomplete phase transformation in pseudoelastic shape memory alloys

This paper presents a thermomechanical model for pseudoelastic shape memory alloys (SMAs) accounting for internal hysteresis effect due to incomplete phase transformation. The model is developed within the finite-strain framework, wherein the deformation gradient is multiplicatively decomposed into thermal dilation, rigid body rotation, elastic and transformation parts. Helmholtz free energy density comprises three components: the reversible thermodynamic process , the irreversible thermodynamic process and the physical constraints of both. In order to capture the multiple internal hysteresis loops in SMA, two internal variables representing the transition points of the forward and reverse phase transformation, $$\phi _s^f$$ and $$\phi _s^r$$ , are introduced to describe the incomplete phase transformation process. Evolution equations of the internal variables are derived and linked to the phase transformation. Numerical implementation of the model features an Euler discretization and a cutting-plane algorithm. After validation of the model against the experimental data, numerical examples are presented, involving a SMA-based vibration system and a crack SMA specimen subjected to partial loading–unloading case. Simulation results well demonstrate the internal hysteresis and free vibration behavior of SMA.

Physics-informed machine learning for composition – process – property design: Shape memory alloy demonstration

Machine learning (ML) is shown to predict new alloys and their performances in a high dimensional, multiple-target-property design space that considers chemistry, multi-step processing routes, and characterization methodology variations. A physics-informed featured engineering approach is shown to enable otherwise poorly performing ML models to perform well with the same data. Specifically, previously engineered elemental features based on alloy chemistries are combined with newly engineered heat treatment process features. The new features result from first transforming the heat treatment parameter data as it was previously recorded using nonlinear mathematical relationships known to describe the thermodynamics and kinetics of phase transformations in alloys. The ability of the ML model to be used for predictive design is validated using blind predictions. Composition - process - property relationships for thermal hysteresis of shape memory alloys (SMAs) with complex microstructures created via multiple melting-homogenization-solutionization-precipitation processing stage variations are captured, in addition to the mean transformation temperatures of the SMAs. The quantitative models of hysteresis exhibited by such highly processed alloys demonstrate the ability for ML models to design for physical complexities that have challenged physics-based modeling approaches for decades.

Development of a frequency-dependent constitutive model for hysteresis of shape memory alloys

In this study, a constitutive model based on Liang-Rogers’s relations is developed to characterize the effect of the excitation frequency in the hysteresis of shape memory alloys. Shape memory alloys are good candidates as smart actuators because of their high strain and power density, although the complex hysteresis behavior barricades their usage. Although constitutive models are one of the most potent methods to predict the shape memory alloys behavior, they cannot consider the effect of excitation frequency in active applications. In this paper, the Liang-Rogers model is modified to consider this effect using a linear relation between the excitation frequency and martensite transformation temperatures. A shape memory alloy-driven actuator as a morphing wing is employed to characterize the frequency effect on shape memory alloy hysteresis. Experimental results show that the hysteresis is widened when the excitation frequency increases. The modeling results show that the original model significantly fails to predict the correct behavior when the frequency increases, whereas the proposed model can adequately handle the frequency effect on the behavior of the shape memory alloy-driven actuator.

Tuning the hysteresis of a metal-insulator transition via lattice compatibility

Structural phase transitions serve as the basis for many functional applications including shape memory alloys (SMAs), switches based on metal-insulator transitions (MITs), etc. In such materials, lattice incompatibility between transformed and parent phases often results in a thermal hysteresis, which is intimately tied to degradation of reversibility of the transformation. The non-linear theory of martensite suggests that the hysteresis of a martensitic phase transformation is solely determined by the lattice constants, and the conditions proposed for geometrical compatibility have been successfully applied to minimizing the hysteresis in SMAs. Here, we apply the non-linear theory to a correlated oxide system (V1−xWxO2), and show that the hysteresis of the MIT in the system can be directly tuned by adjusting the lattice constants of the phases. The results underscore the profound influence structural compatibility has on intrinsic electronic properties, and indicate that the theory provides a universal guidance for optimizing phase transforming materials.

An explicit simulation of arbitrarily-shaped pseudo-elastic hysteresis loops in shape-memory alloys

A new and explicit approach is proposed for accurately simulating pseudo-elastic hysteresis loops of any shape in shape-memory alloys (SMAs). For this purpose, new finite strain elastoplastic J2-flow equations are established for modeling finite strain behavior of SMAs. A stress-strain loop of any given shape in each uniaxial loading-unloading cycle is derived exactly from these equations. Then, a new technique is further introduced toward integrating usual piecewise linear splines into a single smooth interpolating function in a unified form. With the proposed equations and technique, test data for SMA hysteresis loops of any shape may be automatically fitted with high accuracy based on a single-parameter identification.

Uncertainty quantification of the parameters and predictions of a phenomenological constitutive model for thermally induced phase transformation in Ni–Ti shape memory alloys

In this work, a probabilistic calibration approach has been adopted to quantify the uncertainties of the parameters and predictions of a phenomenological shape memory alloys (SMAs) constitutive model which has been used to predict the thermally induced phase transformation of Ni–Ti SMAs. Furthermore, the impact of the adopted calibration method, which enables the determination of the uncertainty bounds of the model predictions, on the design of robust engineering applications has been discussed. To this end prior to the probabilistic model calibration, a design of experiments has been performed in order to identify the most influential parameters on the response of the system and thus reduce the dimensionality of the problem. Subsequently, uncertainty quantification (UQ) of the influential parameters has been carried out through Bayesian Markov Chain Monte Carlo (MCMC). The assessed uncertainties in the model parameters has been then propagated to the model predictions using an approximate approach based on the variance–covariance matrix of the MCMC-calibrated model parameters and then an explicit propagation of uncertainty through MCMC-based sampling. The determined 95% Bayesian confidence intervals of the model predictions, by the latter methods, have been demonstrated and compared. Additionally, good agreement between the experimentally measured and model predicted SMA hysteresis loops has been observed where the experimental data are situated within the predicted 95% Bayesian confidence intervals. Finally, the application of the MCMC-based UQ/UP approach in decision making for experimental design has also been shown by comparing the information that can be gained by performing multiple repetitive experiments under identical thermo-mechanical conditions versus experiments under different conditions.

Phase engineering and supercompatibility of shape memory alloys

Abstract In recent years examples of unprecedented functional and structural fatigue resistance and lowered hysteresis in shape memory alloys have been achieved by combining conditions of supercompatibility between phases with suitable grain size and a favorable array of fine precipitates. We collect, review and compare these examples to elucidate the relative roles of these factors, especially in the case of the more demanding stress-induced phase transformations, and we pose key open questions. The control of these factors lends itself to systematic alloy development. Taken together, these results point to significant opportunities to discover improved shape memory alloys as well has new reversible transforming multiferroics.

Thermally modulated shape memory alloy friction pendulum (tmSMA-FP) for substantial near-fault earthquake structure protection

Vibration control of structures under near-fault earthquakes by employing a friction pendulum supplemented with thermally modulated shape memory alloy (SMA) springs as damper system is studied. Temperature modulation of the SMA spring during the earthquake effectively alters its hysteretic energy dissipation capacity and thereby the control efficiency of the isolation system. The response of a structure with the isolation system is evaluated through nonlinear dynamic time-history analysis under a set of recorded near-fault ground motions. Through temperature modulation that effectively yields a large SMA hysteretic energy dissipation, the hybrid friction pendulum system with SMA temperature modulation shows enormous control efficiency. A parametric study reveals that under a wide range of conditions, the thermally modulated SMA friction pendulum isolation system shows improved control efficiency over conventional friction pendulum and SMA friction pendulum isolation systems. Further, the temperature-tuned SMA hysteresis loops substantially suppress the high frequency components of earthquake motions, thus reducing the possibility of damage to the structure.