Reorientation Of Martensite Variants Research Articles

Application of the Preisach Model to Tension-Compression Asymmetric Deformation Behavior of Martensitic Shape Memory Alloys

The Preisach model is applied to the hysteresis of the energy required for reorientation of martensitic variants of shape memory alloys. To express tension-compression asymmetric behavior, three variants of the martensitic phase are considered—thermal-induced, tensile-stress-induced, and compressive- stress-induced martensitic phases. Residual stresses due to unconformity at interfaces between grains are also considered in the required energy. Stress-strain hysteresis loops for a bar under tension-compression cyclic loading are simulated and they are compared with the available measured data. Results show that this model can effectively capture the asymmetric stress-strain deformation behavior for tension and compression and the difference between the stress-strain relationships in the first and second loops. This indicates that the proposed model can be used for explaining the deformation behavior of shape memory alloys and for the design of structural elements containing shape memory alloys.

Modeling of the variant reorientation in magnetic shape-memory alloys under complex magnetomechanical loading

This work is concerned with the modeling of the stress- and magnetic field-induced reorientation of martensitic variants in magnetic shape-memory alloys. Of special concern is the loading path dependence of the associated nonlinear reorientation strain and magnetization response. A loading case of variable magnetic field in the direction of a constant uniaxial stress with a constant perpendicular magnetic field is analyzed.

High-temperature shape memory alloys based on the RuNb system

Many applications of shape memory alloys (SMAs) require the development of alloys with high martensitic transformation (MT) temperatures. Among the different systems for high temperature SMAs, equiatomic RuNb alloys demonstrate both shape memory effect (SME) and MT temperatures above 800 °C. This work investigates Ru 50− x Nb 50+ x (at.%) alloys and shows that Nb content significantly affects the MT behavior. Alloys near the equiatomic composition ( x = 0, 2, 4) undergo two displacive transformations on cooling: β (B2) → β′ (body centered tetragonal) → β′′ (monoclinic). The Ru 45Nb 55 alloy exhibits a single transition from cubic to tetragonal on cooling. This MT gives rise to a highly twinned microstructure with a (0 1 1) compound-twinning mode and is considered to be responsible for the SME in both types of alloys. The reorientation of martensite variants during deformation has been confirmed through scanning electron microscopy of compression specimens. A promising shape memory behavior is obtained through three-point bend tests performed both in the β′ and β′′ phases.

The nano- and mesoscopic cooperative collective mechanisms of inhomogenous elastic-plastic transitions in polycrystalline TiNi shape memory alloys

The cooperative collective effects of strain-induced martensitic variant accommodation in nano- and micrograined polycrystalline TiNi shape memory alloys were discovered to form macroscopic strain-induced shearing bands—the Lüders-like deformation bands. We use the in situ electron backscattered diffraction technique and the single surface trace analysis method to unambiguously elucidate the formation and propagation of shearing bands derived from the chain effect of intergrain selective martensite habit plane variants. The macroscopic characteristics of shearing bands can be well interpreted by mesoscale crystallographic features using phenomenological crystallographic theory and Schmid’s law with a strong correlation to texture. It was also discovered that the nonlinear elastic feature in the stress-strain curve prior to the stress-strain plateau correlates to lattice/grain rotations other than martensitic variant reorientation.

Energy harvesting using martensite variant reorientation mechanism in a NiMnGa magnetic shape memory alloy

Magnetic shape memory alloys demonstrate significant potential for harvesting waste mechanical energy utilizing the Villari effect. In this study, a few milliwatts of power output are achieved taking advantage of martensite variant reorientation mechanism in Ni51.1Mn24Ga24.9 single crystals under slowly fluctuating loads (10Hz) without optimization in the power conversion unit. Effects of applied strain range, bias magnetic field, and loading frequency on the voltage output are revealed. Anticipated power outputs under moderate frequencies are predicted showing that the power outputs higher than 1W are feasible.

Hysteretic Behavior of Ferroelasticity of NiTi in Shear

In the present work, the hysteretic behavior of ferroelastic deformation via martensite variant reorientation in a Ti–50.15 at.% Ni alloy is studied with cycling in shear. The stress hysteresis and the irreversible work dissipated during a cycle are found to decrease with cycling. The stress hysteresis is found to be dependent on the strain span of the loop but to be independent of the apparent strain about which the loop is performed. The mechanical hysteresis is attributed to two contributions: frictional resistance to twin boundary movement and matrix resistance to shape change of polycrystalline matrices.

Characterization and modeling of the magnetic field-induced strain and work output in [formula omitted] magnetic shape memory alloys

This paper is concerned with the experimental characterization and the constitutive modeling of magnetic shape memory alloys (MSMA), in terms of their applicability as actuator materials. The key properties that determine the actuation characteristics are the magnetic field-induced strain (MFIS) and the blocking stress. With the goal of increasing the corresponding actuation output, a material selection strategy was followed which was aimed at obtaining a higher magnetocrystalline anisotropy energy, while keeping the detwinning stress low. This was achieved by choosing a composition in which the separation of the Curie temperature and the martensitic transformation temperatures was large, and then selecting an operating temperature just below the phase transformation temperature. In the selected Ni 51.1 Mn 24.0 Ga 24.9 composition a more than 50% increase of the actuation work output was observed, compared to corresponding data reported in the literature for other off-stoichiometric compositions of the Ni 2 MnGa intermetallic compound. The second part of the paper describes a phenomenological constitutive model that predicts the MFIS hysteresis curves observed in the first part. The model is concerned with the field-induced reorientation of martensitic variants and changes in the magnetic microstructure. Dissipative effects are captured by introducing internal state variables into the free energy function. In its most general form the contributing energy terms are the elastic strain energy, the Zeeman energy, the magnetocrystalline anisotropy energy and appropriate mixing terms. Typical loading cases are considered and the accuracy of the model predictions is evaluated by comparison with the experimental data presented in the first part of this work.

Effect of pre-deformation on martensitic transformation behavior and the microstructure of a Ni–Mn–Ga alloy

The influence of pre-deformation on the martensitic transformation behavior and its microstructure has been put forward in a Ni 55Mn 20Ga 25 (at.%) ferromagnetic shape memory alloy. It is found that the reverse martensitic transformation temperatures ( A s and A f) increase linearly with increasing amount of deformation, while the martensitic transformation temperatures ( M s and M f) are not changed even when the deformation is up to 6%. However, the effect of the pre-deformation on the reverse martensitic transformation disappears in the following heating process. Transmission electron microscopy shows well-accommodated martensite variants in the undeformed specimen and interfacial boundaries are straight and well-defined. After deformation, the reorientation of martensite variants occurs at the expense of the unfavorable martensite variants, and the interfacial boundary changes from a sharp and straight morphology to a curved and irregular one. Meanwhile, some lattice defects are formed inside the variants even in slightly compressed samples. With increasing deformation, more lattice defects are generated inside the variants as well as in the interfacial boundaries between variants. Based on the analysis of the experimental results, the micromechanism of the effect of pre-deformation on martensitic transformation behavior has been clarified.

Magnetic field-induced martensitic variant reorientation in magnetic shape memory alloys†

The magnetically induced martensitic variant reorientation process under applied mechanical load in magnetic shape memory alloys (MSMAs) is considered. Of particular interest is the associated nonlinear and hysteretic macroscopic strain response under variable applied magnetic field in the presence of stress, also known as the magnetic shape memory effect (MSME). A thermodynamically consistent phenomenological constitutive model is derived which captures the magnetic shape memory effect caused by the martensitic variant reorientation process, using internal state variables, which are chosen in consideration of the crystallographic and magnetic microstructure. The magnetic contributions to the free energy function considered in this work are the Zeeman energy and the magnetocrystalline anisotropy energy. Activation functions for the onset and termination of the reorientation process are formulated and evolution equations for the internal state variables are derived. The model is applied to a two-dimensional special case in which the application of a transverse magnetic field produces axial reorientation strain in a NiMnGa single-crystal specimen under a constant compressive axial stress. It is explicitly shown how the model parameters are obtained from experimental data. Model predictions of magnetic field-reorientation strain hysteresis loops under different applied stresses are discussed. †Dedicated to Professor Gerard Maugin on the occasion of his receiving of the 2003 SES A.C. Eringen Medal.

Tensile/compressive behaviour of non-layered tetragonal Ni52.8Mn25.7Ga21.5 alloy

The stress–strain behaviour of the alloy Ni52.8Mn25.7Ga21.5 with the non-modulated tetragonal martensite (T) crystal structure was studied below Ms temperature with stresses needed for the martensite variant structure reorientation, i.e. detwinning. At ambient temperature the stress plateau of the detwinning showed a total strain of 21–22% with 18–20 MPa stress. After the first cycle, the tensile/compression cycles were repeatable. With maximum strain the single variant structure was obtained which was verified with X-ray pole figures. The tension-compression cycling decreased the stress plateau to 10–12 MPa, while the increasing testing temperature lead to a value of 6.7 MPa close to the reverse transformation temperature.

Tensile/compressive behaviour of non-layered tetragonal Ni52.8Mn25.7Ga21.5 alloy

The stress–strain behaviour of the alloy Ni 52.8 Mn 25.7 Ga 21.5 with the non-modulated tetragonal martensite (T) crystal structure was studied below M s temperature with stresses needed for the martensite variant structure reorientation, i.e. detwinning. At ambient temperature the stress plateau of the detwinning showed a total strain of 21–22% with 18–20 MPa stress. After the first cycle, the tensile/compression cycles were repeatable. With maximum strain the single variant structure was obtained which was verified with X-ray pole figures. The tension-compression cycling decreased the stress plateau to 10–12 MPa, while the increasing testing temperature lead to a value of 6.7 MPa close to the reverse transformation temperature.

Coupled stress-strain and electrical resistivity measurements on copper based shape memory single crystals

Recently, electrical resistivity (ER) measurements have been done during some thermomechanical tests in copper based shape memory alloys (SMA's). In this work, single crystals of Cu-based SMA's have been studied at different temperatures to analyse the relationship between stress (s) and ER changes as a function of the strain (e). A good consistency between ER change values is observed in different experiments: thermal martensitic transformation, stress induced martensitic transformation and stress induced reorientation of martensite variants. During stress induced martensitic transformation (superelastic behaviour) and stress induced reorientation of martensite variants, a linear relationship is obtained between ER and strain as well as the absence of hys teresis. In conclusion, the present results show a direct evidence of martensite electrical resistivity anisotropy.

Microstructural evolution in an Ni-Mn-Ga alloy during compression

Microstructural aspects and interfacial characteristics of deformed martensite variants in a compressed Ni55Mn20Ga25 (at.-%) alloy have been investigated using transmission electron microscopy. It is shown that the undeformed specimen exhibits a well accommodated morphology and a straight and well defined interfacial boundary. After deformation, reorientation of martensite variants occurs at the expense of unfavourable martensite variants, and the interfacial boundary changes from sharp and straight to curved and irregular. Meanwhile, lattice defects are formed inside the variants even in slightly compressed samples. With increasing deformation, high density lattice defects are generated and rearranged inside the variants as well as in the interfacial boundaries between variants.

Martensitic transformation and magnetic-field-induced strain in Ni-Mn-Ga magnetic shape memory alloys

The present paper deals with the thermal- and stress-induced martensitic transformations, effects of bias magnetic field and external compressive stress on transformation- and magnetic-field-induced strain in Ni-Mn-Ga alloys. The effect of the external magnetic field and compressive stress on the reorientation of martensitic variants is discussed. It is found that the stress-induced spear-like martensitic crystal forms at the beginning of loading, at the temperature a little higher than Ms. The interfaces between the parent phase and the stress-induced martensite migrate reversibly under the increasing/decreasing stress, showing the characteristics of thermoelastic martensitic transformation. When the Ni 52 Mn 24 Ga 24 single crystal is cooled down to 200K, an intermartensitic transformation occurs, however there is no appearance of this case for the powder sample of the same alloy with average particle size of about 50 μm. About 1.8% magnetic-field-induced strain is obtained in the [100] direction of Ni 2 MnGa single crystal when a 1.5T pulse magnetic field is applied at the Ms temperature.

Deformation behaviors at various temperatures and corresponding microscturcures of Ti36Ni49Hf15alloy

The deformation behaviors at various temperatures and corresponding microstructures of Ti 36 Ni 45 Hf 15 high temperature shape memory alloy had been studied. The tensile behavior of the Ti 36 Ni 49 Hf 15 alloy is characterized by continuous yielding and high work hardening in the temperature range from 293K to 673K. The critical stress for martensite variant reorientation is relatively high and a maximum elongation of about 30% is observed at about 510K. No superelasticity is observed. The substructure of SIM and deformed SIM in the present alloy is (001) compound twin. Martensite variants are (011) type I twin related. Further increasing the deformation temperature and strain, the preferential oriented SIM gradually develop to martensite variants with variant-crack/ variant-intersect morphologies.

Processus de réorientation des variantes de martensite dans un monocristal de Cu–Al–Ni

On the one hand, Chu (Thesis, Minnesota, 1993), Abeyaratne et al. (Philos. Mag. A 73 (2) (1996) 457–497) performed biaxial tensile tests on a single crystal Cu–Al–Ni plate, in order to analyze the reorientation process of martensite variants. On the other hand, use is made of a constitutive model with n+1 internal variables (the volume fractions of austenite and of the n martensite variants) specific to the thermomechanical behavior of SMA single crystals in order to simulate the martensite variant reorientation. The comparison between experimental results and model prediction is fairly good. To cite this article: P. Blanc, C. Lexcellent, C. R. Mecanique 331 (2003).

Study of reorientation of martensite variants under stress in Ti-Ni-Cu by resistivity and by thermoelectric power techniques

It is well known that the martensitic phase of shape memory alloys presents a self- accommodation of variants when it is obtained by simple cooling. Theses variants can be reoriented in a new configuration by applying a stress on the material. Macroscopic properties like, electrical and mechanical ones, are very sensitive to this phenomenon. Moreover, it has been proved that thermoelectric power (TEP) is a powerful technique to characterize isotropic properties. In this work, thermoelectric power under stress has been used to study the evolution of the reorientation of variants in a shape memory alloy. The obtained results are compared with those of mechanical and electrical tests.

Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms

Previous studies by the authors and their co-workers show that the structure of equations representing shape Memory Alloy (SMA) constitutive behaviour can be very similar to those of rate-independent plasticity models. For example, the Boyd–Lagoudas polynomial hardening model has a stress-elastic strain constitutive relation that includes the transformation strain as an internal state variable, a transformation function determining the onset of phase transformation, and an evolution equation for the transformation strain. Such a structure allows techniques used in rate-independent elastoplastic behaviour to be directly applicable to SMAs. In this paper, a comprehensive study on the numerical implementation of SMA thermomechanical constitutive response using return mapping (elastic predictor-transformation corrector) algorithms is presented. The closest point projection return mapping algorithm which is an implicit scheme is given special attention together with the convex cutting plane return mapping algorithm, an explicit scheme already presented in an earlier work. The closest point algorithm involves relatively large number of tensorial operations than the cutting plane algorithm besides the evaluation of the gradient of the transformation tensor in the flow rule and the inversion of the algorithmic tangent tensor. A unified thermomechanical constitutive model, which does not take into account reorientation of martensitic variants but unifies several of the existing SMA constitutive models, is used for implementation. Remarks on numerical accuracy of both algorithms are given, and it is concluded that both algorithms are applicable for this class of SMA constitutive models and preference can only be given based on the computational cost. Copyright © 2000 John Wiley & Sons, Ltd.

Shape Memory Alloys: Micromechanical Modeling and Numerical Analysis of Stuctures

Multiscale modeling of structures made from shape memory alloys (SMA) is presented. Starting with consideration of a single transformation event at the micro-level and averaging over the representative volume, micromechanically-based macroscopic constitutive equations are derived, which are used in Finite Element Method (FEM) code to model the behaviour of structures. Using the thermodynamic theory of phase transformations (PT) in elastic materials on the micro-level, the macroscopic associated transformation flow rule, the corresponding extremum principle and the nonconcavity of the transformation surface are derived for transformational micromechanisms of inelastic deformation due to phase transformation, twinning and reorientation of martensitic variants. A simple three-dimensional micromechanically-based model for thermoelastic martensitic PT is presented. The model is transformed to the fashion similar to that for J2-plasticity theory. It allows one to modify the FEM for elastoplasticity (including the radial return algorithm for numerical integration of the constitutive equations and calculation of the consistent tangent moduli) in order to model PT in SMA. Some axisymmetric problems for PT in SMA tubes are solved. In particular, PT regularities of a tube assembly with a SMA cylinder element are investigated at different external conditions.

Lüders-like deformation associated with martensite reorientation in NiTi

It is known that near-equiatomic NiTi shape memory alloys may exhibit a Lueders-like deformation behavior under a variety of testing conditions. These conditions include the tensile deformation associated with the stress-induced martensitic transformation from the austenite, the reverse transformation of the stress-induced martensite to austenite in pseudoelasticity, and the deformation in martensitic state via a martensite variant reorientation process. The Lueders-like deformation behavior is characterized by a stress plateau and a stress-drop at the beginning of the process for the forward transformation upon loading and a stress minimum for the reverse transformation on unloading. Based largely on this observation in pseudoelasticity, it has been suggested that the stress peaks at the beginning of the stress plateau are associated with the nucleation of the product phase for the corresponding transformations and that the stress plateau corresponds to the process of the transformations. This common belief, however, is challenged by a number of experimental observations. This seems to suggest that the occurrence of the stress plateau on a stress-strain curve is mechanical in nature instead of being determined by the transformation. This uncertainty, however, needs to be clarified.