Polycrystalline Shape Memory Alloys Research Articles

A half a decade timeline of shape memory alloys in modeling and applications

To unlock the lock of futuristic developments, nowadays shape memory alloys (SMAs) are acting as key by outnumbering the existing smart materials in view of new design competence, innovative techniques, enhanced technologies, and meeting the dire need according to the demand of ongoing scientific and industrial progress. Undoubtedly, it can be worthy to associate SMAs with the term polymorphism, as they possess unique capability to encapsulate multitudinous inherent characteristics under their name. Shape memory effect, superelasticity, and damping are there to name a few among many others, as prime indicators. The exhibition of these characteristics of SMAs is due to the transformation that takes place between austenite phase and martensite phase which is achieved either by temperature or stress variation. The fascinating characteristics they possess enable them to attract researchers and designers toward their potential applications in diverse domain as smart and multi-functional materials. The present work focuses on the review of research works accomplished in the recent 5 years pertaining to modeling and applications of shape memory alloys in distinct domains. Under the topic of modeling, a look into the research carried out on a variety of SMA structures—like functionally graded SMAs, SMA springs, porous SMAs, novel SMA actuators—is presented. In addition to this, the work carried out to represent SMAs with large strains and large rotations and to model polycrystalline SMAs is also covered. This is supplemented by application-oriented domains, each of which disseminates the attributes of SMAs that are self-sufficient to express what factors make SMAs more prominent. It is believed that the foregoing works comprehensively detailed in this review article will certainly lay a solid platform for the future investigations that are going to take place in time to come.

Stochastic multiscale modeling of the thermomechanical behavior of polycrystalline shape memory alloys

A multi-scale model simulating hysteretic thermomechanical behavior of polycrystalline shape memory alloys (SMA) is presented. Using a kinetic Monte-Carlo approach, the energy-based model estimates the stochastic average in terms of volume fraction for a phase or phase variant deriving from the Gibbs free energy density as a selection inside a given population. Indeed pseudo-elastic behavior for example is well-known to be associated with the nucleation of martensite plates inside the austenite parent phase. Associated variants are similar to sub-domains inside a thermodynamic system following the statistical definition of Sommerfeld et al. (1964). The germination process of a variant is on the other hand dictated by a germination potential barrier identified from a differential scanning calorimetry (DSC) measurement. The stochastic average for each type of variants inside a grain leads then to the numerical simulation of hysteresis phenomena at the single crystal scale. Homogenization operations allow finally macroscopic quantities (phases fraction, deformation and temperature) to be calculated at the polycrystalline scale. This procedure is applied to model the whole thermomechanical behavior of an equiatomic Ni-Ti SMA polycrystalline alloy considering the phase transformation between austenite, R-phase and martensite.

An investigation on the properties of boron modified Cu–Al–Be polycrystalline shape memory alloys

Effect of microalloying of boron (B) i.e., 0.02–0.15 wt% and the variation of composition of Al and Be from 11.3 to 11.9 wt% and 0.41–0.44 wt% respectively, has been investigated on the grain refinement and shape memory properties of polycrystalline Cu–Al–Be shape memory alloy. The tests have been carried out for microstructure, morphology, phases, crystal structure, phase transformation temperatures and shape recovery ratio. The investigation results in boron has strong impact on grain refinement with minimal addition, followed by Al and Be. AlB2 acts as heterogeneous nucleation site in grain refinement and it increases with increase in B and Al. Transformation temperatures increases with boron up to 0.08 wt% and then decreases, whereas increase in Al and Be decreases the temperatures. Doping and increasing of boron up to 0.15 wt% exhibits complete shape recovery, whereas Be < 0.42 wt% and Al < 11.8 wt% exhibits poor recovery ratio.

Extension of micromechanics model and micro-macro description to shape memory effect of NiTi SMAs

In this article, we presented an important extension of the micromechanics model and the micro-macro approach proposed by Gall et al. to the prediction of the shape memory effect (SME) of polycrystalline shape memory alloys (SMAs). In the constitutive model for a single crystal, the volume fractions of the 24 martensite variants (MVs) are taken as the internal variables, and the interaction between the MVs is considered. The constitutive description for polycrystalline SMAs was obtained by assembling the single crystals with different orientations using finite element method (FEM). The constitutive description for SME was derived by introducing the volume fraction of the detwinned-martensite and assuming that the mechanism of detwinning is identical with that of the phase transformation, incorporating the refined stress-temperature phase diagram. The corresponding numerical algorithm was developed, in which a special treatment is introduced to get rid of the contribution from the MVs that might be irrationally activated during computations, which could directly reduce the dimension of the Jacobian and effectively enable the convergence and stability of the numerical implementation, especially in the cases of complex nonproportional deformation. A thin-walled cylindrical tube model was used for FE simulations of the SMEs under biaxial tensile-shear deformations, in which the texture microstructure in the materials formed during the cold drawn process could be considered. The SMEs of some typical NiTi SMAs under uniaxial and multiaxial nonproportional loadings were simulated and compared with experimental results, and the satisfactory agreement demonstrates the validity of the developed approach.

Fe-Ni-Al-Ta polycrystalline shape memory alloys showing excellent superelasticity

Fe-Ni-Co-Al-Ta polycrystalline shape memory alloys have received extensive attention due to their excellent properties such as huge superelasticity, high strength and high damping. We herein report that Fe-Ni-Al-Ta polycrystalline alloys also have excellent superelasticity, which can exhibit a large superelastic strain of more than 17% in compression at room temperature. This superelasticity has slim hysteresis and is greatly affected by the content of Ta in the alloys. In this work, Fe-Ni-Al-Ta shape memory alloys reveal some characteristics that are different from the reported Fe-Ni-Co-Al-based shape memory alloys.

A micromechanics-based model for polycrystalline Ni–Ti wires

This paper proposes a constitutive model for polycrystalline shape memory alloy (SMA) wires arising from micromechanical arguments. The texture of the polycrystal is captured through the volume fractions and the maximal transformation strain in each crystalline orientation. As a result, the model is able to reproduce texture effects such as nonlinear hardening during phase transformation. An attractive feature of the proposed model is that closed-form expressions of the material response can be obtained for typical thermomechanical loadings of interest in SMA, such as cyclic traction at high temperature or thermal cycling at a fixed stress. Those analytical solutions are notably useful for identifying the constitutive parameters of the model. A temperature-controlled testing apparatus for SMA wires was developed for performing a reliable characterization of nickel–titanium wires. All model parameters have been identified by means of three tests: differential scanning calorimetry, isothermal traction test and thermal cycling at constant stress.

A three-dimensional constitutive model for the martensitic transformation in polycrystalline shape memory alloys under large deformation

This work presents a three-dimensional constitutive model for the martensitic transformation in polycrystalline shape memory alloys (SMAs) under large deformation. By utilizing the logarithmic strain and rate, the model is able to account for large strains and rotations that SMA-based components may undertake, but also resolves the stress errors caused by the non-integrable objective rates that are widely used in current commercial finite element software. The model is developed through classical thermodynamic laws combined with the standard Coleman–Noll procedure. The scalar martensitic volume fraction and the second-order transformation strain tensor are chosen as the internal state variables to capture the material response exhibited by polycrystalline SMAs. A detailed implementation procedure of the proposed model is described through a user-defined material subroutine. Numerical experiments considering SMA components including a bar, a beam, a torque tube and a solid flexible structure under stress/thermally-induced phase transformations are investigated via the proposed model, and the results under cyclic loading are compared against the predictions provided by the Abaqus nonlinear solver. The development framework of the proposed model and its implementation procedure can be extended to incorporate other nonlinear phenomena exhibited by SMAs, such as transformation-induced plasticity, viscoplasticity, and damage under large deformation.

A non-isothermal phase field study of the shape memory effect and pseudoelasticity of polycrystalline shape memory alloys

In this paper, a non-isothermal phase field (PF) model is proposed to investigate the shape memory effect (SME) and pseudoelasticity (PE) of polycrystalline shape memory alloys (SMAs) with consideration of the latent heat effect. The latent heat release and absorption accompanying the phase transformation processes are explicitly considered by coupling the phase field evolution with latent heat conduction. A modified Gibbs free energy function is proposed to accommodate the continuously varying temperature. It is shown that the SME and PE of polycrystalline SMAs under different ambient temperatures can be well characterized with the proposed PF model within a unified framework. The PF simulation results are in accordance with the previously reported experimental results. The influences of various factors such as the ambient temperature, grain size, crystal orientation, and latent heat effect on the phase transformation process and mechanical responses as well as the temperature evolution of SMAs are systematically discussed by conducting PF simulations. Some important implications for the devise of elastocaloric cooling devices are provided.

Comparative Study of Two Multiscale Thermomechanical Models of Polycrystalline Shape Memory alloys: Application to a Representative volUme Element of Titanium–Niobium

This paper presents a comparative study between two micro-macro modeling approaches to simulate stress-induced martensitic transformation in shape memory alloys (SMA). One model is a crystal plasticity based model and the other describes the evolution of the microstructure with a Boltzmann-type statistical approach. Both models consider a self-consistent scheme to perform the scale transition from the local thermomechanical behavior to the global one. The way the two modeling approaches describe the local behavior is analyzed. Similarities and differences are pointed out. Numerical simulations of the thermo-mechanical behavior of an isotropic titanium-niobium SMA are performed. These alloys have known a growing interest of scientific community given their high potential for application in the biomedical field. Stress-strain curves obtained from the two simulations are compared with experimental results. Evolutions of volume fractions of martensite variants predicted by the two approaches are compared for <100>, <110> and <111> tensile directions. Due to the absence of comparative studies between multiscale models dedicated for SMA, this paper fills a gap in the state of the art in this field and provides a significant step toward the definition of an efficient numerical tool for the analysis of SMA behavior under multiaxial loadings.

Influence of quenched-in vacancies on the elastic modulus and its dependence on the temperature in β CuAlBe shape memory alloys

The influence of quenched-in vacancies on the elastic modulus and its dependence on the temperature was studied in a β CuAlBe polycrystalline shape memory alloy. Samples with different quenching temperatures were submitted to different heat treatments and the behavior of the elastic modulus, phase transformation and microstructure with the temperature was carefully analyzed to understand the processes that occur in each stage. The quenched-in vacancies retained in β phase migrate during a heating from room temperature up to 200 °C and the modulus exhibits a two stage behavior, associated with the higher mobility of the quenched-in vacancies at higher temperatures. However, those present in martensite phase would not be eliminated during the first heating or subsequent heating cycles at 200 °C or 300 °C. Part of these vacancies would also produce the hyperstabilization of some amount of martensite phase.

Atomistic study on shape memory properties of Ni\u2013Al alloys

The shape memory properties of Ni–Al alloy are investigated using molecular dynamics simulation. The phase transformation behaviors for various Ni composition ratios are studied under quasistatic cooling and heating process. Various loadings, i.e., uniaxial, shear, and biaxial, are applied on a 68% Ni–Al alloy till plasticity takes place. The atomic configurations are inspected and analyzed using a common neighbor parameter. The shape recovery capability of the plastically deformed alloy is examined after heating above the phase transformation temperature. It is found that there would be shape recovery if the twinning plane reorientation or moving was the major yielding mechanism. For those loadings in which stacking faults or dislocations nucleate, the deformed model would not restore to its original shape after heating and the corresponding maximum shear stress is noticeably higher. There is no direct dependence between the yield strain and the shape recovery capability. Our findings could provide a possible explanation for the functional fatigue of the polycrystalline shape memory alloy.

On the validity of strain energy density criterion for mixed mode I/II fracture analysis of notched shape memory alloy components

This paper investigates the fracture behavior of notched polycrystalline shape memory alloy components utilizing the strain energy density (SED) approach and considering combined tensile/shear loading for the first time. The SED approach has been widely used to explore fracture paths and the onset of fracture in notched components made of conventional ductile metals (e.g., aluminum) as well as brittle and quasi-brittle materials, but its application to shape memory alloys has heretofore not been addressed. For a notched polycrystalline shape memory alloy component subjected to thermomechanical loading, the effects of different material parameters including maximum transformation strain, Young’s modulus, and temperature on the SED distribution around notch tip and the fracture angle are explored and discussed. The validity of the theoretical formulations deployed for estimation of the transformation zones and strain fields are examined by comparing closed-form solutions with the results obtained from comparable finite element calculations. It is shown that the efficiency of the SED approach is limited as the ratio of the normalized maximum transformation strain to the normalized effective notch stress intensity factor exceeds a critical value; such conditions have not been previously reported for non-transforming metals. Finally, the effects of the notch tip radius on the fracture angle and SED distribution around the notch tip are evaluated.

Variational Modeling and Finite-Element Simulation of Functional Fatigue in Polycrystalline Shape Memory Alloys

Based on our previous works, we present the finite-element implementation of an energy-based material model that displays the effect of functional fatigue of shape memory alloys during cyclic loading. The functional degradation is included in our model by taking account of irreversible martensitic volume fractions. Three internal variables are used: reversible and irreversible volume fractions for the crystallographic phases and Euler angles for parametrization of the martensite strain orientation. The evolution of the volume fractions is modeled in a rate-independent manner, whereas a viscous approach is employed for the Euler angles, which account for the materials’ polycrystalline structure. For the case of a cyclically loaded wire, we calibrate our model using experimental data. The calibration serves as input for the simulation of two more complex boundary value problems to demonstrate the functionality of our material model for localized phase transformations.

An accurate dynamic model for polycrystalline shape memory alloy wire actuators and sensors

Thermal shape memory alloy (SMA) wires exhibit a mechanical hysteresis of which the shape depends on both temperature and loading rate. Commercially available actuator wires typically exhibit polycrystalline behavior, which also depends on training effects. Polycrystallinity may lead to complex hysteresis loops, differing substantially from standard box shapes often employed in modeling attempts. In addition, actuation often results in loading trajectories leading through the interior of the hysteresis, making accurate modeling and control of SMA systems a highly challenging task. In this paper, we present a novel dynamic model for polycrystalline SMA actuator wires based on a modified version of the Müller–Achenbach–Seelecke model. The model permits to predict time evolution of stress and resistance of a one-dimensional SMA wire under arbitrary input strain and Joule heating profiles. The constitutive equations are developed by properly exploiting the concept of a representative single-crystal, resulting in an optimal trade-off between physical interpretation and computational efficiency. After developing constitutive model equations, experimental validation is performed by means of two case studies, given by a superelastic NiTi wire and a quasi-plastic NiTi wire, respectively. The experiments are intended to illustrate the model capabilities in predicting internal hysteresis loops, loading rate effects, as well as actuation and sensing behavior at the same time. A remarkable accuracy is observed in all of the investigated experimental scenarios, making the model particularly suitable for high-precision control and self-sensing applications.

Shape Memory and Elastocaloric Effect in Au &lt;sub&gt;7&lt;/sub&gt;Cu &lt;sub&gt;5&lt;/sub&gt;Al &lt;sub&gt;4&lt;/sub&gt; Shape Memory Alloy

The shape memory and elastocaloric properties of Au7Cu5Al4 polycrystalline shape memory alloy were investigated. The alloy exhibits a reversible martensitic transformation from body-centered cubic (BCC) austenite to body-center tetragonal (BCT) martensite. During the load-biased thermal cycling test, the recoverable transformation strain increased with increasing stress and saturated at about 1.4% under 75 MPa. The entropy change and the relative cooling power under 95 MPa were determined to be 7.2 J·K-1·kg-1 and 74.4 J·kg-1, respectively. Our results suggest that the Au-Cu-Al shape memory alloy can serve as a candidate for actuator and elastocaloric application in harsh environments.

Influence of Directional Solidification on the Mechanical Properties of Cu-Al-Be-Nb-Ni Alloy

Copper-based polycrystalline shape memory alloys (SMAs) have limitations for many practical applications due to their low superelasticity and low ductility. In order to overcome this situation, in recent years, the production of copper-based SMAs by directional solidification process has attracted the interest of many researches. In this sense, the present work had as objective to evaluate, through instrumented indentation tests, the influence of the solidification direction on the elastic modulus, hardness and superelasticity of a Cu-Al-Be-Nb-Ni alloy produced by directional solidification. The results showed that the superelasticity, remnant depth, elastic modulus and hardness DHV-1 are strongly dependent on the direction of application of the load in relation to the solidification direction, that is, the alloy presented an anisotropic behavior for its mechanical properties.

Influence of Gd on the microstructure, mechanical and shape memory properties of Cu-Al-Be polycrystalline shape memory alloy

In the present study, the influence of rare earth element gadolinium (Gd) on Cu-Al-Be polycrystalline shape memory alloy has been investigated. Cu 88.13 Al 11.42 Be 0.45 ternary alloy with addition of Gd from 0.05 to 0.15 wt% has been used for investigation. The tests have been carried out for microstructure, morphology, ductility, phases, crystal structure, phase transformation temperatures and shape recovery ratio. Refinement of the grain size resulted as gadolinium increased from 0 to 0.08 wt%, the grain size decreases from 463.45 to 81.80 µm with reduction of 82.34%. The tensile strength has increased from 398.93 to 581.42 MPa with improvement in the ductility from 10.05% to 23.72% at 0.08 wt% gadolinium. The phase transformation temperatures increases as gadolinium increases and reduction in shape recovery ratio from 97% to 65%.

The role of bimodal grain size distribution in nanocrystalline shape memory alloys

We report on a phase field simulation study of the effects of grain size and grain size distribution on martensitic transformations in shape memory alloys (SMAs). Recent experimental studies of polycrystalline SMAs revealed interesting grain size effects when grain sizes are reduced to tens of nanometers. While small grain sizes yield superior mechanical strength, the material loses its shape memory property if grain sizes are smaller than some critical size. To reintroduce shape memory properties, and at the same time retain strong mechanical properties, we propose to introduce several large grains (much larger than the critical transformation grain size) amid the nano-sized grains, which yields a grain microstructure with a bimodal grain size distribution. A phase field model is adopted to simulate the martensitic transformation in polycrystals, to which excess grain boundary energy is introduced that suppresses martensitic transformation in the grain boundaries. We observe that simulated as-quenched microstructures of the bimodal grain size distribution may in a special case equilibrate as a phase composite (austenite + martensite). The spatial distribution of these phases and alloy functionalities (shape memory) may be controlled by the design of the grain size distribution. Loading and unloading simulations of the equilibrium martensitic microstructures show that the large grains enable martensitic detwinning to occur, hence reintroducing shape memory functionality to the nanocrystalline SMA.

Microstructure, martensitic transformation and elastocaloric effect in Pd-In-Fe polycrystalline shape memory alloys

In this work, we have investigated the microstructure, martensitic transformation, and elastocaloric effect of Pd-In-Fe polycrystalline alloys. For this new magnetic shape memory alloys, both phase constitution and morphology highly depend on the Fe content. Exhibiting a single austenite phase at room temperature, Pd59.3In23.2Fe17.5 alloy has a large superelastic cooling effect of −5.4 K with a low critical stress of 80 MPa to trigger the martensitic transformation. Interestingly, the onset of superelastic stress can be drastically reduced by mechanical training. The rare-earth/Mn-free and non-toxic element constitution, good ductility and tunable transformation temperature render the Pd-In-Fe Heusler system as a promising candidate for elastocaloric cooling.

An equivalent local constitutive model for grain size dependent deformation of NiTi polycrystalline shape memory alloys

In this paper, an equivalent local constitutive model is constructed to describe the grain size dependent deformation of NiTi polycrystalline shape memory alloys (SMAs). The aim of such a model is to convert the existed microscopic nonlocal model into a macroscopic local one and ensure them to be equivalent in energy and dissipation. Firstly, based on the experimental observations, an existing nonlocal model is simplified and the analytical solution for the evolution of martensite volume fraction is derived. Then, an energy-equivalent rule is proposed and the scaling law of transformation hardening modulus is obtained. Finally, with the help of proposed scaling law, a macroscopic local model is constructed from the irreversible thermodynamics. The capability of the local model to describe the grain size dependent deformation of polycrystalline NiTi SMAs is verified by comparing the simulations with corresponding experimental results [7].