Maximum Transformation Strain Research Articles

Thermomechanical response and elastocaloric effect of shape memory alloy wires

Refrigeration technologies based on the elastocaloric effect of shape memory alloys (SMAs) have attracted much interest in recent years. To seek for schemes that can improve the temperature span and efficiency of elastocaloric devices, this work explores more practical loading conditions (between adiabatic and isothermal) of SMAs. To account for the smoothness of the martensite phase transformation of SMAs, a general polynomial form of hardening-like function is adopted in the phenomenological multi-physics coupling framework. The modeling framework is further calibrated by measurements of the thermomechanical responses of pre-trained Ni–Ti wires. Due to the hardening-like function, the martensitic volume fraction cannot be explicitly expressed. Accordingly, a new numerical scheme is also presented in this work. Moreover, an empirical function of the maximum transformation strain is proposed based on the experimental observation, which improves the capability of the model to capture experimental data. This work aims to provide a paradigm from material characterization to theoretical modeling and numerical simulation, and then to elastocaloric cooling performance analysis of SMAs.

Crossover from mechanical stabilization of martensite to spanning avalanche-type reverse transformation of deformed Cu-Al-Ni shape memory crystals

A new interpretation of factors controlling the kinetics of reverse transformation of martensites stabilized by prestrain is suggested. We investigate the effect of amount of prestrain in the β1´martensite and in the β-phase on temperature and kinetics of the reverse martensitic transformation in Cu-Al-Ni shape memory alloy single crystals. Calorimetry and video recording of the jumping samples, provoked by the burst strain recovery during temperature-induced reverse transformation, are used in experiments. For crystals deformed both in the β´1 martensite and in the β-phase, we report the existence of a sharp transition (crossover) from the mechanical stabilization of martensite to the burst reverse martensitic transformation which proceeds as a single avalanche. The crossover occurs for prestrain values close to the maximum transformation strain. The specific energy of the jump during burst strain recovery depends on the maximum stress applied during prestraining the sample. The crossover from a broad transformation range to an infinite or spanning avalanche is predicted by 3D random field Ising model for disordered systems undergoing the first order phase transition. Based on this model, we explain the crossover in deformed Cu-Al-Ni crystals by a rapid decrease of structural disorder towards the critical one at the final stage of the formation of detwinned γ´1martensite. A simple solution is obtained for the critical transformation rate which produces jumping of the sample during burst reverse transformation after prestrain.

Mechanical and Metallurgical Characterization of Nickel-Titanium Wire Types for Rotary Endodontic Instrument Manufacture

This study aimed to evaluate and compare the effects of ambient temperature and post-manufacture heat-treatment on the mechanical behavior of nickel-titanium (NiTi) wires. Four types of commercial NiTi variants (Stock NiTi, heat treated "Blue", "Gold", "Superflex", all Dentsply Maillefer, Ballaigues, Switzerland) were stressed in a tensile testing machine in a temperature-controlled water bath at three different temperatures. Stress and strain values were extrapolated from the raw data, and 2-way ANOVA and Tukey's test for multiple comparisons were performed to compare the differences of the mechanical constants. Differential scanning calorimetry (DSC) tests established the martensitic transformation starting (Ms), finishing (Mf) and austenitic (reverse-martensitic) starting (As) and finishing (Af) points. Austenitic modulus of elasticity and transformation stress values increased with temperature for all NiTi groups. The martensitic modulus of elasticity, maximum transformation strain and ultimate tensile stress were not significantly affected by temperature changes. Stock NiTi and Gold wire samples presented with clearly delineated austenitic and martensitic transformations in the DSC experiments. Differences in manufacturing/heat treatment conditions and ambient temperature affect the mechanical behavior of nickel-titanium and may have clinical implications. Further improvements to the experimental setup could be considered to provide more accurate measurements of strain.

Constitutive model for nanocrystalline NiTi shape memory alloys considering grain size effects and tensile–compressive asymmetry

Mechanical properties of nanocrystalline NiTi shape memory alloys (SMAs) change drastically with grain size. The present contribution develops a constitutive model to reproduce the grain size dependent superelastic behavior and tensile–compressive asymmetry observed in the experiments of nanocrystalline NiTi SMAs. Effects of grain size are incorporated in the developed model by introducing the intrinsic length scale accounting for the transformation hardening as well as the grain-core and grain-boundary phase. In this work, nanocrystalline NiTi SMA is regarded as a two-phase composite material made of inclusions of the grain-core phase dispersed in the grain-boundary phase acting as a matrix. A transformation function allowing for the description of fine-grain strengthening mechanism and tensile–compressive asymmetry is proposed. In the grain-core phase, the evolution law for transformation strain during the forward and reverse transformation is determined. Besides, the constitutive relation of the grain-boundary phase is assumed to be linearly elastic. Based on the equivalent secant bulk and shear modulus of the grain-core and grain-boundary phase, the stress–strain relationship of nanocrystalline NiTi SMAs is derived by using the extended Mori–Tanaka method. Comparisons between experimental and predicted results demonstrate that the proposed model has the ability to reproduce the grain size dependent deformation and asymmetric stress–strain behavior under tension and compression of nanocrystalline NiTi SMAs. In detail, it is found that critical transformation stresses for forward and reverse transformations, dissipation energy density, transformation strain hardening, and maximum transformation strain are sensitive to the grain size and stress states.

A multi-featured shape memory alloy constitutive model incorporating tension–compression asymmetric interpolation

The mechanical response of shape memory alloys is heavily governed by phase transformation and plasticity. These inelastic mechanisms present added complexities in the form of asymmetries with respect to the stress state (tension–compression asymmetry) and the direction (forward or reverse) of transformation, leading to the formation of internal loops. With this in mind, a constitutive model is developed incorporating phase transformation and yield plasticity. The model represents the tension–compression asymmetry through a novel approach by interpolating the maximum transformation strain, the Young’s modulus of martensite and a plasticity factor in the deviatoric plane of the transformation strain direction. Internal loops are also considered by scaling the transformation hardening and the hysteresis width based on memory points. The interaction between the processes of reorientation and phase transformation is also taken into account. The model is validated with several proportional and non-proportional loading tests with considerable success. The capability of the model to simulate complex loading scenarios is demonstrated by simulating the manufacturing and loading of a stent structure.

Martensitic phase transformation and shape memory properties of the as-cast NiCuTiHf and NiCuTiHfZr alloys

This study investigates the structure, martensitic phase transformation behavior, and shape memory properties of the quaternary Ni44.8Cu5Ti45.2Hf5 and quinary Ni44.8Cu5Ti40.2Hf5Zr5 and Ni45.5Cu5Ti39.5Hf5Zr5 shape memory alloys (SMAs) in the as-cast state. The alloys exhibited a dual-phase microstructure composed of matrix phase (austenite or martensite depending on the chemical composition) and Ti2Ni-type phase. The experimental results revealed that the alloys underwent a one-step B2↔B19′ transformation. The Ni44.8Cu5Ti45.2Hf5 alloy showed a maximum shape memory strain of 6.2% with a recovery ratio of 81% upon thermal cycling under a tensile stress of 300 MPa, while in the Ni44.8Cu5Ti40.2Hf5Zr5 alloy, a maximum shape memory strain of about 5% was obtained under 500 MPa with a recovery ratio of 86%. The as-cast Ni44.8Cu5Ti45.2Hf5 alloy showed superelastic response with 0.3% maximum transformation strain at 125℃. On the other hand, the Ni44.8Cu5Ti45.2Hf5 alloy showed the best superelastic response at 65℃ with a recoverable strain of about 1.9%. Two-way shape memory strains of 0.8% and 3.3% were obtained in the Ni44.8Cu5Ti45.2Hf5 and Ni44.8Cu5Ti40.2Hf5Zr5 alloys, respectively. The Ni45.5Cu5Ti39.5Hf5Zr5 alloy, however, did not reveal the shape memory effect. Results obtained from low-temperature X-ray diffraction (XRD) analysis indicated that the B2→B19′ transformation was considerably suppressed in this alloy and the volume fraction of B19′martensite did not exceed 8% even at an ultra-low temperature of − 150 °C.

A Low-Cost Ni-Mn-Ti-B High-Temperature Shape Memory Alloy with Extraordinary Functional Properties.

The rapid development of aerospace, automotive, and energy exploration industries urgently requires high-temperature shape memory alloys (HTSMAs) which are utilized as compact solid-state actuators, sensors, and energy conversion devices at elevated temperatures. However, the currently prevailing Ni-Ti-X (X = Pd, Pt, and Hf) HTSMAs are very expensive owing to the high cost of Pd, Pt, and Hf elements, which greatly limits their widespread applications. Here, we have developed an inexpensive (Ni50Mn35.5Ti14.5)99.8B0.2 bulk polycrystalline HTSMA with extraordinary high-temperature superelasticity and a giant two-way shape memory effect (TWSME). This alloy exhibits perfect superelasticity with a fully recoverable strain of as high as 7.1% over a wide temperature range from 150 to 280 °C. Furthermore, it shows a giant TWSME with a remarkably high recoverable strain of 6.0%. Both the recoverable strain of superelasticity and the two-way shape memory strain of the present alloy are the highest among the bulk polycrystalline HTSMAs. The theoretical maximum transformation strain was calculated with energy-minimization theory using the crystal structure information of martensite and austenite obtained from in situ synchrotron high-energy X-ray diffraction experiments to help understand the superelastic behavior of the present alloy. Combining the advantages of low cost and easy fabrication, the present bulk polycrystalline (Ni50Mn35.5Ti14.5)99.8B0.2 alloy shows great potential for high-temperature shape memory applications. This work is instructive for developing cost-effective high-performance HTSMAs.

Chemical and phase composition of the novel superelastic Ti-Zr-Nb alloy with a high Zr content

The novel superelastic Ti-44Zr-10Nb (at.%) alloy was obtained by the vacuum arc remelting method and subjected to homogenization (950 °C, 60 min) and thermomechanical treatment (TMT), which consisted of cold rolling (CR) with a 25% thickness reduction rate and consequent post-deformation annealing (PDA) at 550 °C for 30 min. The analysis of the chemical composition was conducted by the EDS method. It was demonstrated that the obtained chemical composition of the alloy was in good correspondence with the nominal chemical composition. The phase composition of the alloy after TMT was investigated by the XRD technique. The lattice parameters of β and α” phases were measured using XRD data to calculate the crystallographic recovery strain limit. The maximum transformation strain of 7.3% was obtained in the [011]β direction.

Stress-induced α″ martensitic phase transformation and martensitic twinning in a metastable β titanium alloy

The stress-induced martensitic (SIM) β→α″ phase transformation and SIM α″ twinning in the fully-β Ti–7Mo–3Nb–3Cr–3Al (Ti-7333) alloy was investigated as a function of strain, following a surface-to-bulk methodology assisted by electron backscatter diffraction (EBSD), focused ion beam (FIB) milling and transmission electron microscopy (TEM). The results indicate that the Ti-7333 alloy is predominantly deformed by SIM and SIM α″ twinning. At the onset of deformation, the lattice correspondent SIM α″ martensite variant that produces the maximum transformation strain along the tensile direction is activated firstly, which follows the <-110>β//<001>α″ orientation relationship. As the strain increases, the SIM α″ laths deform by twinning, predominantly through the {130}<310>α″ compound twinning and {111}α″ type Ⅰ twinning modes. Their activation can be rationalized in terms of the magnitude of the shear and the complexity of the atomic shuffle using the Bilby-Crocker deformation twinning theory. The prevalence of {130}<310>α″ compound twinning in this alloy is attributed to the comparatively small shear (0.1872) and the simple shuffle (q = 2, ΔⅠa = 0.3257) mechanism involved. During the last stages of deformation, secondary microtwinning takes place within the primary twins due to the reduced mobility of the intervariant boundaries. The evolution of such hierarchical microstructure with strain accounts for the complex microstructural features that developed with deformation, responsible for the high work hardening displayed by this alloy.

Limit state behavior and response sensitivity analysis of endplate steel connections with shape memory alloy bolts

Shape memory alloys have been used in developing self-centering steel moment connections. This article presents a numerical study aiming at evaluating the cyclic response sensitivity and limit states of extended endplate steel connections with shape memory alloy bolts. Three-dimensional finite element models are developed and validated against a recent experimental study. Using a statistical design-of-experiment method, the effects of 21 design factors and their interactions on the cyclic response of shape memory alloy connections are assessed. The sensitivity of six response parameters is studied. In addition, four limit states for shape memory alloy connections are discussed, including beam local buckling, bolt excessive axial strain, endplate yielding, and column flange yielding. Results show that endplate thickness, shape memory alloy bolt diameter, beam web slenderness ratio, and shape memory alloy maximum transformation strain are the most influential factors. Furthermore, endplate yielding is found to be the governing limit state in almost 80% of the analyzed connections, whereas shape memory alloy bolt excessive strain and column flange yielding are observed in less than 20% and 5% of the connections, respectively. Beam local buckling is not governing in the analyzed shape memory alloy connections designed as per the AISC 358-16 and AISC 341-16 seismic design requirements for extended endplate connections and highly ductile members.

Galerkin Weighted Residual Method for Axially Functionally Graded Shape Memory Alloy Beams

ABSTRACTThis paper focus on the mechanical and martensitic transformation behaviors of axially functionally graded shape memory alloy (AFG SMA) beams. It is taken into consideration that material properties, such as austenitic elastic modulus, martensitic elastic modulus, critical transformation stresses and maximum transformation strain vary continuously along the longitudinal direction. According to the simplified linear SMA constitutive equations and Bernoulli-Euler beam theory, the formulations of stress, strain, martensitic volume fraction and governing equations of the deflection, height and length of transformed layers are derived. Employing the Galerkin’s weighted residual method, the governing differential equation of the deflection is solved. As an example, the bending behaviors of an AFG SMA cantilever beam subjected to an end concentrated load are numerically analyzed using the developed model. Results show that the mechanical and martensitic transformation behaviors of the AFG SMA beam are complex after the martensitic transformation of SMA occurs. The influences of FG parameter on the mechanical behaviors and geometrical shape of transformed regions are obvious, and should be considered in the design and analysis of AFG SMA beams in the related regions.

Influence of texture and transformation strain on the superelastic performance of a new Ti–20Zr–3Mo–3Sn alloy

In this work, the superelastic behavior of a new metastable β Ti–20Zr–3Mo–3Sn (at.%) biomedical alloy displaying stress-induced α" martensitic transformation (SIM) was investigated by cyclic tensile tests, electron back-scattered diffraction (EBSD) and in situ synchrotron X-ray diffraction (SXRD) for 3 different solution treatment temperatures: 700 °C, 800 °C and 900 °C. The EBSD observations revealed that the Ti–20Zr–3Mo–3Sn alloy showed a strong dependence of the solution treatment temperatures on crystallographic texture. SXRD diffraction profiles acquired under cyclic loading/unloading tensile tests clearly illustrated the reversible SIM α" transformation. In addition, the lattice parameters of β and SIM α" phases were measured for each cycle in order to establish the evolution of lattice parameters during the deformation and to calculate the maximum transformation strain for any crystallographic direction. A high recovery strain of 3.5% was obtained by tensile test after a solution treatment at 700 °C for 30 min. This high recovery strain is due to the fact that the maximum transformation strain is obtained along the tensile direction displaying the favorable <011>β{100}β recrystallization texture. The performance of the Ti–20Zr–3Mo–3Sn alloy is discussed and compared with other superelastic alloys such as NiTi and (Ti–Nb)-based alloys.

Delamination analysis in bimaterials consisting of shape memory alloy and elastoplastic layers

Bimetallic shape memory alloy composites, consisting of an active layer of shape memory alloy and a metallic elastoplastic passive layer, are used for designing the sensors and actuators. Delamination analysis in SMA/elastoplastic bimaterial composites is numerically investigated in this study due to the important effects of interface cracks on failure and load bearing response of such composites. It is known that homogeneous elastoplastic material and shape memory alloy show different path-dependent behaviors for prediction of energy release rate near the crack tip. Therefore, evaluation of J-integral for an interface crack between SMA and elastoplastic layers remains a highly complex issue in fracture analysis of such bimaterials. Presuming small-scale phase transformation and yielding zones, path dependency of J-integral for this composite is investigated for a range of mixed-mode loading conditions, and the elastoplastic material properties including the Young’s modulus, hardening slope and yield stress. In addition, the maximum transformation strain within the framework of J2 plasticity for the elastoplastic material and the thermo-mechanical coupling model of Boyd and Lagoudas for the shape memory alloy are studied. Finally, the influence of mixed-mode loading rates on the crack tip fields is comprehensively assessed.

On the cracks normal to shape memory alloy/elastic material interfaces

Theoretical and numerical analyses are performed to investigate the behavior of a crack propagating perpendicularly to a perfectly bonded bi-material interface. The bi-material system is composed of a linear elastic material in which the interface crack is initially located bonded to a shape memory alloy. Utilizing a continuum thermodynamics-based constitutive model for the shape memory alloys, the effects of different material and operational parameters, such as maximum transformation strain, relative martensitic Young’s modulus, and temperature, on the crack propagation behavior and the crack tip transformation zone are explored. Novel closed-form solutions are presented to obtain both the shape of the martensitic transformation zone and the strain energy density around the crack tip. The validity of the theoretical solutions is examined and discussed by comparing to comparable finite element results. The crack propagation behavior is analyzed based on both the critical stress intensity factor and the critical strain energy density criteria. The presented results provide a primary understanding of how the failure mechanism can be controlled in smart composites including SMA components by tuning of the material and operational parameters.

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.

Limits on Transformation Strains for Non-Negative Dissipation

Abstract We consider the maximum value of the magnitude of transformation strain for an Eshelby inclusion set by the requirement of non-negative dissipation. The general formulation for a linear elastic solid shows that the dissipation associated with a strain transformation can be calculated as an integral over the transformed inclusion. Closed-form expressions are given for the maximum transformation strain magnitude in an isotropic linear elastic solid for both cylindrical and spherical inclusions that have undergone transformations corresponding to either a pure volume (or area) change or a pure shear. Most results presented are for transformations in an infinite solid and presume uniform material properties. Examples of the effect of a finite boundary and of differing material properties inside and outside the transformed inclusion are also given. The analytical results indicate that non-negative dissipation typically limits the transformation strain to being a constant of order unity times the critical stress at transformation divided by a relevant elastic modulus.

Enhanced Work-Hardening and Toughening Via Contiguous Stress-Induced Martensitic Transformation and Mechanical Twinning in Ti-Zr-Hf-Nb-Al High Entropy Alloys

Refractory high entropy alloys (HEAs) have been considered as candidate alloys for next-generation high-temperature applications, but encounter the strength-ductility trade-off dilemma. In this article, we proposed a strategy of strengthening and toughening for Ti-rich refractory HEAs by the initiation of martensitic transformation and mechanical twinning successively. Three Ti-Zr-Hf-Al-Nb HEAs with the tensile strength and elongation up to 1167 MPa and 34%, respectively, which are superb among most of the reported BCC HEAs, have been successfully prepared. By using the SEM, TEM, HE-XRD and EBSD setups, the as-cast and fully recrystallized microstructures for these HEAs were characterized. And the mechanisms for the martensitic transformation and mechanical twinning in these HEAs are deeply explored. It has been clarified that under the as-cast and fully recrystallized state, these HEAs are mainly composed of β phase and a little of α′′ martensite phase. Stress-induced martensitic transformation took place in favor of special variants with the [110]β//LD, which has the maximum transformation strain of 7.8%. At the later stage, mechanical twinning α′′ phase have formed between the α′′ laths and the β matrix with the preferential orientation relationship of [111]β//[101]α′′M//[-10-1]α′′T.

Giant rubber-like behavior induced by martensite aging in Ni51Fe18Ga27Co4 single crystals

Stress-induced martensite aging along the [110]B2||[100]L10-direction in compression was employed to enhance the functional properties of Ni51Fe18Ga27Co4 single crystals. Stress-induced martensite aging induces two effects. Firstly, a two-way shape memory effect with a reversible compressive strain of −4.3% along the [110]В2 direction and a reversible tensile strain of +9.0% along the normal [001]B2-direction. Secondly, rubber-like behavior with giant reversible compression strain up to −15.0% along the [100]B2-direction caused by L10-martensite variant reorientation was observed. This exceeds the maximum compressive transformation strain (−6.3%) during the B2-L10 martensitic transformation by a factor of two.

In situ, 3D characterization of the deformation mechanics of a superelastic NiTi shape memory alloy single crystal under multiscale constraint

Microstructural elements in NiTi shape memory alloys (SMAs) – precipitates, phase boundaries, inclusions, grain boundaries – can be viewed as sources of multiscale constraint that influence their deformation response. We characterized in situ, and in 3D, the deformation and the evolution of microstructure during a tension test in a superelastic NiTi specimen containing some of these sources of constraint. The method used was far-field high-energy X-ray diffraction microscopy (ff-HEDM), complemented by electron microscopy. We simulated the local stress state in the specimen using a microstructural model informed by the experimental data. Using these combined microstructure, deformation, and stress data, we report three phenomena, and relate them to specific sources of constraint. During initial elastic loading, axial lattice strain in austenite increased monotonically. On partial stress-induced phase transformation to martensite, the stress redistributed to both phases leading to a stress relaxation in austenite. The specimen contained a dense distribution of inclusions, which led to the activation of martensite habit plane variants that produce less than theoretical maximum transformation strain. Large Ni4Ti3 precipitates potentially contributed to the poor transformation response. Under load, proportional gradients in local rotation and elastic stretch developed in the martensite phase, because of the constraint at phase interfaces. This combined ff-HEDM, electron microscopy, microstructural simulation toolbox provides a versatile method to understand the effect of constraint on inelastic deformation in other alloys with hierarchical microstructure.

Shape memory and transformation behavior of high strength 60NiTi in compression

This study investigates the transformation behavior of highly Ni-rich 60NiTi alloys after aging at 600 °C for 3 h. After 600 °C-3h aging, R-phase disappeared and alloy transformed in one step. The latent heats of austenite to martensite and martensite to austenite transformations were 13 Jg−1 and 16.4 Jg−1, respectively, for 600 °C-3h aged alloy. The elastic strain energy of 0.75 Jg−1 was obtained in aged alloy. The maximum recoverable transformation strain of 1.7% is obtained under 500 MPa in compression. The superelastic behavior was observed accompanied with a recoverable strain of 1.4%, even high stress level of 1000 MPa is applied.