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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.

Pseudoelasticity in NiTi shape memory alloy single crystals depends on the loading direction. Here, we present a comprehensive study in which molecular dynamics simulations of austenitic bulk single crystals under strain-controlled tensile and compressive loading along the 〈 1 1 0 〉 , 〈 1 1 1 〉 , and 〈 1 0 0 〉 directions are performed, and the mechanical response of the crystals are contrasted. All simulations are performed using the MEAM interatomic potential proposed by Ko et al. (2015). The transformation strains and the Young’s modulus of the initial austenitic and the final martensitic phases are compared with values obtained from the lattice deformation model and experimental results from the literature. Results show that depending on orientation the transformation occurs either through the formation of martensitic Luders bands or through the transient formation of a multivariant martensite which, upon reorientation, becomes a dominant final single variant. Simulations are also performed to assess the orientation-dependent behavior of nano-wires subjected to bending, since the flexibility of the wires is orientation dependent.

Porosity can play an important role in altering the phase transformation characteristics of NiTi shape memory alloys (SMA), thus changing its shape memory as well as its superelasticity properties. This work, based on atomistic simulations of binary NiTi SMA, documents the effects of porosity at the nanometer length scale on phase fraction evolution kinetics, transformation temperatures, and stress-strain response. Classical molecular dynamics simulations are performed using a well-examined and verified Finnis-Sinclair type embedded-atom method interatomic potential. Simulation results for the nano-porous NiTi with various porosity configurations are compared to non-porous NiTi. The martensite phase fraction and transformation temperatures increase noticeably with increasing porosity, and the stress-strain response shows noticeable variation with porosity. The residual strain and hysteretic energy dissipation capacity increase significantly with increasing porosity.

Molecular dynamics (MD) simulations Ni-Ti based on a second nearest neighbor modified embedded-atom method potential were performed to study atomic-scale mechanical behavior and microstructural evolution of Ni-Ti alloy at different temperatures. By using four calculated characteristic transformation temperatures, the optimum simulated temperature ranges were determined. At temperatures lower than Ms, a thermally induced self-accommodating martensitic phase consisting of three variants formed. Each of the two variants was twin structures. In the subsequent loading process, the most favorable variant grew with the movement of interfaces among the variants, which produced remnants of the residual strain after unloading. After heating up to over Af, the residual strain disappeared and the shape recovered to the original. The shape memory effect under austenite state was also performed, wherein the sample exhibited a typical stress–strain temperature curve and remained in a martensitic state after unloading. After heating at a high temperature, the martensite transformed back into its parent phase accompanied with the recovery of residual strain. The material exhibited superelastic behavior above Af, and the critical transformation stress increased with increased temperature. Some parts of B2 structures remained at the end of the plateau stage and continued transforming into martensites during the hardening stage for both T > Af and Ms Ms.

Shape memory alloys (SMAs) are a class of metallic smart materials which possess pseudoelasticity (PE) and shape memory effect (SME), depending on the ambient temperature. The unique thermomechanical properties of SMAs originate from the temperature-induced as well as stress-induced martensitic transformations (MTs). Former research work has shown that the thermomechanical properties of polycrystalline SMAs are grain size and rate dependent. In order to explore the physical mechanisms behind this phenomenon, a phase field (PF) model is developed in this paper to study the microstructure evolution and the thermomechanical responses of polycrystalline SMAs under dynamic loadings. The inertial effect, the latent heat release and conduction during the phase transformation are simultaneously considered. The grain boundary energy change during the phase transformation is also accounted for in the PF model. Numerical simulations are then conducted to study the temperature-induced MT as well as the stress-induced martensite reorientation of nanocrystalline SMAs with different grain sizes. The influences of the grain size, the latent heat effect and the loading rate on the microstructure evolution process and the stress–strain curves are systematically discussed.

We investigated the process of twin boundary migration to clarify the origin of pseudoelasticity by twinning in D03-type Fe3Ga using first-principles calculations. We calculated the energy profile of twin boundary migration and found that although energy barriers appear during twin boundary migration in bcc Fe and bcc Mo, there was no energy barrier for twin boundary migration in D03-type Fe3Ga. Analysis of the shear strain at each twin layer revealed that twin boundary migration in D03-type Fe3Ga proceeded not in a layer-by-layer fashion but by the sliding of more than two layers that include the twin boundary, which led to the flat energy profile in D03-type Fe3Ga. This sliding mechanism originated from shear strain introduced near the twin boundary to accommodate the lattice distortion induced by the difference in the atomic arrangement between the D03 matrix and the pseudo twin layers.

We present a second nearest-neighbor interatomic potential improved with the mechanical properties of the bulk B2 and B19’ phases in shape-memory NiTi alloys. The potential correctly predicts the phase transformations known so far in the temperature-stress-strain diagram of equiatomic NiTi. Bulk materials show the perfect reversibility between B2 and B19’ over many thermal cycles. The perfect reversibility showing superelasticity is also observed in the nanopillars under both tensile and compressive loadings. Most important, twinning naturally occurs in the nanopillars upon cooling below the transition temperature, and the subsequent tensile loading removes twinning irreversibly. We find that a potential based on accurate mechanics warrants the mechanical and thermomechanical behaviors in shape-memory NiTi necessary for a practical use.

The pre-existing twin boundaries play an important role in the mechanical behaviors of metals. In the present work, we studied the bending deformation of [100]-oriented α-Fe nanowires seeded with 〈111〉/{112} twin boundaries using atomistic simulations. Bending behaviors along two different orientations were investigated. The initially flat twin boundaries become curved with a high density of 1/6 〈111〉/{112} partial dislocations under bending when the neutral plane intersects with twin plane along [0 1 - 1] direction, whereas could transform to the nonconventional {110} interfaces under bending when the neutral plane intersects with twin plane along [111] direction. The bent α-Fe nanowires could recover to the original state upon unloading, leading to a unique pseudoelasticity. The driving force for shape recovery primarily arises from the high interfacial energy, i.e. curved {112} twin boundaries or the transformed {110} interfaces. We further characterized the recoverability by the ratio η of the nanowire size (external length scale) to twin boundary spacing (internal length scale). This η-dependent recoverability matches well with the experimental data at large length scale. The present work may help understand the unique mechanical properties associated with twin boundaries in metals.

In this paper, the asymmetric mechanical responses of tetragonal zirconia polycrystals (TZPs) under uniaxial tension and compression are investigated by phase field (PF) modelling. The previous PF model for the tetragonal to monoclinic (t-m) phase transformation (Mamivand et al., 2013) is modified to characterize the grain size effect and the influences of ambient temperature. A modified chemical free energy functional based on the fourth-order Landau polynomial is proposed to properly describe the energy barrier of the t-m phase transformation at different ambient temperatures. In addition, a thermodynamic approach is proposed to describe the suppression effect of the grain boundaries on the t-m transformation. The interfacial energy between the martensitic twins is also differentiated from that at the austenite-martensite interface. PF simulations are then carried out to relate the microstructure evolution of TZPs with the mechanical responses during a loading cycle. In particular, the asymmetric mechanical responses of TZPs under tensile and compressive loading cycles are compared and discussed. It is demonstrated that the modified PF model can well characterize the microstructural evolution process as well as the grain size and temperature dependent stress-strain responses of TZPs. For both types of loadings, TZPs exhibit shape memory effect (SME) below the equilibrium temperature and pseudoelasticity above the austenite transition temperature. The grain size effect and the influences of ambient temperature on the microstructural evolution process and the characteristics of the stress-strain responses of TZPs under uniaxial tension and compression are systematically discussed. It is revealed that the tension-compression asymmetry of TZPs is mainly attributed to the dilatational transformation strain accompanying the t-m phase transformation.

Ni–Ti shape memory alloys (SMA) have been widely used in industrial, medical and aerospace fields due to its superior mechanical properties including the shape memory effect, superelasticity and anti-corrosion. The macroscopic deformation of Ni–Ti SMA under thermal–mechanical loading typically shows intensively nonlinearity due to the martensitic phase transformation and/or the martensite variants reorientation. In this paper, we proposed a three-dimensional computational model based on energy minimization to simulate the asymmetric deformation behaviors of Ni–Ti single crystal and polycrystals under tension and compression. The volume fractions of austenite and each type of martensite variant in a specific grain (or single crystal) are obtained by minimizing the total energy using the sequential quadratic programming optimization algorithm. For polycrystals, the mechanical constraints from the neighboring grains are considered in an Eshelby inclusion manner. The proposed model is employed to simulate the superelasticity, the asymmetric deformations and the pure martensite variants reorientation of both Ni–Ti oriented single crystal and textured polycrystals under tension and compression. The simulated asymmetric deformation behaviors under tension and compression at different temperature regions accord well with the experimental results. The volume fractions of martensite variants under stress loading were also explored, reproducing the stress induced martensitic transformation. Simulation results also show that the volume fraction variations of martensite variants under tension and compression are consistent with the observed asymmetric deformation behavior.

The unique behavior of shape memory alloys derives from its ability of phase transformation instead of slip. A reason for the phase transformation is the microstructural occurrence and amount of different variants for the multi-variant- and detwinned-martensite dependent on the stress state as well as preferred directions in textured materials. The model presented in this paper enables to take into account all martensitic variants in different orientated grains. The main focus of this paper is the numerical implementation of a known, but advanced model with a projected Newton algorithm and a residual including only two vectors of unknowns. Additionally the texture of a pseudoelastic NiTi wire is measured and the orientations and their weight/size are implemented. Finally in a finite element example the superelastic behavior of a stent with different stress states at different locations is investigated.

The phase transition processes of a single Mo nanowire under uniaxial tensile strains have been studied with molecular dynamics simulation. Two phase transitions were observed during the uniaxial tensile processes. The first one is the configuration of Mo nanowire transformed from BCC structure to FCC structure and the second one is that transformed from FCC-to-BCC. The phase structures have also been demonstrated with radial distribution function (RDF) analyses. A pseudoelasticity behavior was observed under large uniaxial tensile strain. Two average atomic energy curves of BCC and FCC structures as the function of the layer-space along [0 0 1] direction were obtained with embedded-atom method potential calculations, with which the strain-driven BCC-to-FCC and FCC-to-BCC phase transition mechanisms have been clarified clearly for Mo nanowire under uniaxial tensile strain.

For shape memory alloys (SMA) to be usable in engineering applications, it must be possible to simulate the degradation of the material when subjected to cyclic loading. This paper presents an adaptation of Likhachev’s micromechanical model capable of such a degradation, concentrating on strain accumulation. The proposed model, based on a cellular automata algorithm and on the Ramberg–Osgood theory of plasticity, is easy to characterize, with the material constants reduced to a minimum. Further, a thermal model is coupled to the micromechanical formulation in order to allow the thermal exchanges with the surroundings to be taken into account. A series of numerical validations demonstrate the potential of the model to reproduce SMA-related effects: superelasticity, thermal cycling and shape-memory effect. An experimental validation is carried out using a superelastic NiTi wire and a good agreement with experimental data is found.

Molecular dynamics (MD) study of martensitic transformation (MT) in nickel and aluminum alloy is performed. The behavior focused on is transformation between crystalline structures from B2 cubic cell to body-centered tetragonal cell, which is simply realized by uniaxial tensile loading. The potential function used is Finnis–Sinclair type having only single energy minimum where B2 structure exists. The availability of this specific many-body potential for stress-induced MT phenomena under uniaxial loading is fully discussed. In MD simulations, martensite phase is induced by tensile stress or strain in the atomic system, as predicted by a potential energy map. It is understood that the characteristic of the potential energy function with regard to deformation is crucial for MT studies and investigating energy-strain or stress–strain map is worthwhile. The MT behavior in the atomic system occurs during a plateau region of stress–strain (S–S) curve of the whole specimen, that is typical for experimental superelastic or shape-memory alloys under uniaxial loading. It is found that, during each MT event, large jump of atomic strain is observed. Owing to single energy minimum, the atomic system shows almost perfect recovery in S–S curve, where the graph comes completely back to initial state after unloaded. Besides, the present paper focuses on surface effect for MT behavior. Since the surface effect is dominant in MT phenomena especially in microscopic specimens, a novel computational scheme for stabilizing condition in which uniaxial loading is always applied together with arbitrary periodic boundary condition(s) is devised. By comparing one-, two-, and three-dimensional models under uniaxial loading, it is recognized that the nucleation behavior depends strongly on the existence of free surface region (including corner edge). When there is no surface, a chaotic nucleation of martensite is observed. On the other hand, the free surface induces first martensite because of less constraint in tensile deformation of unit cells. It is confirmed that the tendency toward MT nucleation corresponds to yield stress or strain of the specimen. In order to define and detect martensite structure as for each atom, an atomic strain measure (ASM) with our own formation is introduced. It is shown that the ASM is very effective to distinguish martensite bct unit structure from others.

Shape memory alloys (SMAs) are good candidates for being used as passive dampers, strain sensors, stiffness or shape drivers. To design these structures, an implementation which takes into account the obvious asymmetry between tension–compression and the thermomechanical coupling taken into account with the introduction of the heat equation is required. We present in this paper an implementation of a phenomenological model based on the R L model (Raniecki and Lexcellent [B. Raniecki, C. Lexcellent, Eur. J. Mech. A/Solids 17 (2) (1998) 185–205]) in a finite element code called COMSOL© which allows to build automatically many loading cases in force or displacement. The results clearly show the influence of the temperature on the pseudoelastic behavior of SMA and on the asymmetry between tension and compression. This implementation could be useful to simulate complex three dimensional SMA structures as dynamical devices.

A 3D thermo-mechanical constitutive model for the polycrystalline shape memory alloy (SMA) has been used to predict the superelastic response of the textured thin-walled NiTi tubes under combined tension–torsion loading. This model is based on the work of Lim et al. and Wang. Considering the difference of Young’s modulus between austenite and martensite phase, some formulas have been modified. The new developed model has been implemented into ABAQUS as UMAT. In order to validate the model, thin-walled tube has been tested under biaxial loading. From the comparison between the simulated and experimental results, it is found that the model is quite good in predicting the overall loading–unloading process of the SMA. Both the experimental and simulated results demonstrate the significant differences in the superelastic responses under different biaxial loading paths. For both biaxial loading paths, at relatively low level of tensile strain, the overall behaviour of the tubes is smooth. But with the increase of the tensile strain level, the equivalent stress–strain curves fluctuate. For torsion–tension loading program, corresponding to about 4% strain, stress decrease upon tensile loading and stress increase upon tensile unloading are observed due to the change of shear stresses. For Type II loading program (tension followed by torsion, unload in reverse order), a stress decrease upon loading and a stress increase upon unloading are observed but the corresponding strains become big with the increase of the tensile strain level. In addition, according to the simulated results, the rate of martensite formation under tensile loading is higher than that under shearing loading.

In this paper, a finite element method (FEM) has been applied to predict the pseudoelastic behavior of NiTi shape memory alloys at different temperatures with only one temperature testing results. A three-dimensional micromechanical model has been developed based on Gall and Lim’s expression for Gibbs free energy. The difference of elastic properties between austenite and martensite are taken into consideration. The formulations for the evolution of volume fraction of the 24 martensite variants are derived. The time-discrete evolutionary equations are presented with the expression of the mechanical Jacobian matrix. This model has been implemented as UMAT into ABAQUS, which is used to simulate the pseudoelastic behavior by aggregate grains. The grain number in the aggregate is big enough to have little influence of the grain number on the simulated behavior. Tensile experiments are performed at 28, 35 and 50 °C. The experimental results at 35 °C are used to validate the pseudoelastic model and derive the model parameters, which are used to predict the pseudoelastic behavior at 28 and 50 °C. Two kinds of predictions are presented. One considers different elastic modulus at different temperatures. And the other uses the same elastic modulus at different temperatures. Both show satisfactory agreement with the experimental results.

To obtain an unified treatment of the phase transformation materials pseudoelasticity, a model based on the two independent normal dissipative processes assumption has been developed, one for forward transformation and the other one for reverse transformation. Within the context of building a numerical tool for the optimal design of adaptive structures embedding shape memory alloys (sma), the use of these materials as command components needs the implementation of a specific homogenization method into a structural computation to take into account anelastic constituents. The transformation field analysis is used to predict the pseudoelastic behavior of shape memory alloys reinforced composite materials. The sma composite behavior evaluated by this approach was compared to the response using a two-level micromechanical theory developed by Lu. His prediction considers an inactive elastomeric matrix and volume concentration effects of sma fibers periodically aligned are examined. Both results point to the advantage of using fibrous composites for actuators or sensors under a tensile loading.

Many applications involve actuated devices made of shape memory alloys, but the lack of efficient numerical tools hinders the development of such technologies. Software using a finite element method like ANSYS allows the user to predict complex responses of a system without extensive programming. In this paper, a homemade phenomenological 1D bilinear model is programmed through the USERMAT procedure in ANSYS. The model allows the representation of both mechanical and thermal hystereses. The martensitic transformation is controlled by transformation criteria similar to those used in conventional plasticity, and subcycles are modeled by a simple elastic return through the hysteresis. The model is validated through isothermal tensile testing, assisted two-way shape memory testing and stress generation testing, and a good agreement with experimental results is shown. Finally, thermomechanical response of a single-degree-of-freedom actuator is simulated as a typical application and a case study involving the shape change of a radio controlled aircraft wing shows the potential of the numerical simulations.

Due to the thermoelastic nature of the austenite–martensite phase transformation in the pseudoelastic temperature range the mechanical response of a polycrystalline NiTi specimen strongly depends on the thermal boundary conditions of the experimental setup. In uniaxial tensile tests the transformation is inhomogeneous and localised in bands with moving transformation fronts. The latent heat of the transformation leads to a local increase of the temperature near the moving front. Analytical solutions for the moving heat source problem will be derived for adiabatic conditions as well as for the case of heat transfer at the surface of the specimen.

In this paper, a new type of the seismic resisting members with the shape memory alloys (SMA) wire, such as brace and exposed-type column base, were proposed as a hysteretic damper for building structures. Pulsating tension loading tests were performed with constant, increasing and decreasing strain amplitude to investigate restoring force characteristics of the wire. Then, the metallo-thermomechanics model with internal variable was introduced. Using the numerical model, the restoring force characteristics of the wire under high speed loading, such as a seismic loading, were predicted. The results showed that the phenomena should be treated in the numerical model with transformation. Furthermore, these results are used to discuss the applicability and availability of the SMA wire for the seismic resisting members.