Phase Transformation In Shape Memory Alloys Research Articles

Three dimensional large deformation analysis of phase transformation in shape memory alloys

Shape memory alloys (SMAs) have been explored as smart materials and used as dampers, actuator elements, and smart sensors. An important character of SMAs is its ability to recover all of its large deformations in mechanical loading-unloading cycles without showing permanent deformation. This paper presents a stress-induced phenomenological constitutive equation for SMAs, which can be used to describe the superelastic hysteresis loops and phase transformation between Martensite and Austenite. The Martensite fraction of SMAs is assumed to be dependent on deviatoric stress tensor. Therefore, phase transformation of SMAs is volume preserving during the phase transformation. The model is implemented in large deformation finite element code and cast in the updated Lagrangian scheme. In order to use the Cauchy stress and the linear strain in constitutive laws, a frame indifferent stress objective rate has to be used. In this paper, the Jaumann stress rate is used. Results of the numerical experiments conducted in this study show that the superelastic hysteresis loops arising with the phase transformation can be effectively captured.

Thermodynamics of shape-memory alloys under electric current

Phase transformation in shape-memory alloys is known to cause electric resistivity variation that, under electric current, may conversely influence Joule heat production and thus eventually the martensitic transformation itself. A thermodynamically consistent general continuum-mechanical model at large strains is presented. In special cases, a proof of the existence of a weak solution is outlined, using a semidiscretization in time.

Optimal Control for Nonconvex Rate-Independent Evolution Processes

Energetic solutions to rate-independent systems allow for an effective modeling of many physical systems displaying hysteretic effects, e.g., phase transformations in shape-memory alloys, elastoplasticity, and ferroelectricity. For some engineering applications, optimal control of such systems is desirable. We establish existence results for these continuous-time optimal control problems by a combination of the direct method with $\Gamma$-convergence arguments. Applicability to the common situation of a controlled external loading is demonstrated and a concrete partial differential inclusion as well as an academic model of the foreign exchange market including trading costs are investigated.

On Existence and Approximation for a 3D Model of Thermally Induced Phase Transformations in Shape-Memory Alloys

This paper deals with a three-dimensional model for thermal stress-induced transformations in shape-memory materials. Microstructure, like twined martensites, is described mesoscopically by a vector of internal variables containing the volume fractions of each phase. We assume that the temperature variations are prescribed. The problem is formulated mathematically within the energetic framework of rate-independent processes. An existence result is proved and temporal regularity is obtained in the case of uniform convexity. We also study space-time discretizations and establish convergence of these approximations.

Tensile properties of shape memory alloy chiral honeycombs

AbstractThe tensile properties of hexachiral honeycomb made of shape memory alloy (SMA) material are modelled and verified experimentally at different tensile loading and ambient temperature conditions. The numerical models describe the temperature‐pseudoelastic behaviour of the shape memory alloy materials constituted by Ni48Ti46Cu6 alloy. Parametric analysis on the Poisson's ratio effects over large strain deformation and temperature conditions are performed, as well as the analysis of the dependence of the honeycomb stress‐strain behaviour under uniaxial loading with temperature varying through the shape memory alloy phase transformation. Chiral SMA honeycomb samples are manufactured and tested under similar environmental conditions. The experimental results are compared with the numerical one, showing good convergence in terms of trends and overall quantitative values. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

OS16-1-3 Subloop Deformation Behavior of TiNi Shape Memory Alloy under Stress-Controlled Condition

The main characteristics which appear in shape memory alloys (SMAs) are the shape memory effect and superelasticity. In applications of SMAs, the thermomechanical properties of SMAs are most important. Creep and stress relaxation are induced due to the phase transformation in the subloop loading under the stress-controlled conditions. In order to design the SMA elements properly, it is important to understand the thermomechanical properties. In the present paper, the conditions for the nucleation and progress of the phase transformation in SMAs subjected to the subloop loadings are investigated under the stress-controlled conditions. The transformation-induced creep and stress relaxation and the thermomechanical neutral loading condition are discussed based on the transformation kinetics of the material.

Thermosensitive transformer as temperature and output power control device

A temperature and output power control transformer that is applied to an implanted device called artificial sphincter that is composed of shape memory alloy (SMA) is examined. The artificial sphincter is using phase transformation of SMA depending on temperature. To prevent overheating, we examined temperature control utilizing thermosensitive magnetic ferrite. As the temperature rises, the power decreases that is conveyed through the transformer that uses thermosensitive ferrite as its core. If the heater attached to SMA is provided with the electric power through the transformer, it is possible to control the temperature of SMA.

Experimental determination of initial surface of phase transformation of SMA

This paper is concerned with the mechanical behavior of Shape Memory Alloys (SMA). A particular attention is paid to the behavior under multi-axial proportional and non-proportional loadings. A large experimental data-base, composed of tension-torsion tests, tension-internal pressure tests and bi-axial compressive tests is presented and reported. For each type of multi-axial tests, an emphasis is placed on the determination of the shape of the transformation outset surface and the transformation strain rate is determined for selected loading path. Finally, a generalized J 2 -J 3 criterion of transformation outset, based on experimental observations, is proposed and identified.

Micromechanical Modelling of Shape Memory Alloy Composites

AbstractAn isothermal finite element method (FEM) model has been applied to study the behavior of two kinds of shape memory alloy (SMA) composites. For SMA‐fiber reinforced normal metal composites, the FEM analysis shows that the mechanical behavior of the composites depends on the SMA volume fraction. For normal metal‐fiber reinforced SMA matrix composites, the SMA phase transformation is affected by the increasing Young’s modulus of the metal fiber. The phase transformation was also treated using a simple numerical analysis, which assumes that there are uniform stresses and strains distributions in the fiber and the matrix respectively. It is found that there is an obvious difference between the FEM analysis and the simple numerical assessment. Only FEM can provide reasonable predictions of phase transformations in SMA/normal metal composites.

Thermodynamic Driving Forces for Martensitic Phase Transformations in Shape-Memory Alloys

ABSTRACTA macroscopic constitutive model for the martensitic phase transformations in single-crystal shape-memory alloys (SMAs) is developed in the framework of irreversible thermodynamics with internal variables. Central to the model is the notion that the rate of progression of structural rearrangements on the microscale depends on the stress state through the thermodynamic forces conjugate to the rearrangements. These thermodynamic forces, i.e. the driving forces for the phase transitions, are shown to have an important contribution that arises from changes in the effective elastic response of the SMA, which in turn depend upon the state of transformation. This contribution is shown to have a significant effect on the overall macroscopic stress-strain response.

On the effect of dissipation in shape-memory alloys

After reviewing the phenomena of martensitic phase transformation in shape-memory alloys, the conventional models that take into consideration viscosity-like and capillarity-like response are investigated for vanishing “dissipative effects”. It is shown that they do approach the fully conservative case. Experimental evidence indicates that the response is rate independent and thus a model incorporating a phenomenological rate-independent plasticity-type dissipation related with an activated phase-transformation process is investigated.

Evolution model for martensitic phase transformation in shape-memory alloys

A mesoscopical-level model for the evolution of microstructure in simple-laminate martensite undergoing an isothermal phase-transformation process within the context of a uniaxial deformation is proposed using a Hamiltonian approach to a relaxed problem involving a Young-measure-valued deformation gradient and Hill's maximum-dissipation principle involving positive homogeneous dissipation potential which reflects the energy needed for (and dissipated by) a phase transformation. A regularization by adding a (modified) volume-fraction gradient, which can be understood as a limit Ericksen-Timoshenko beam-like construction, is considered to ensure existence of a weak solution for a slow-process model. A numerical algorithm and computational experiments are also presented.

A Variational Formulation of¶Rate-Independent Phase Transformations¶Using an Extremum Principle

We propose a rate-independent, mesoscopic model for the hysteretic evolution of phase transformations in shape-memory alloys. The model uses the deformation and phase-indicator function as basic unknowns and the potentials for the elastic energy and for the dissipation as constitutive laws. Using the associated functionals, admissible processes are defined to be the ones which are stable at all times and which satisfy the energy inequality.

Amicromechanical theory for the thermally induced phasetransformation in shape memory alloys

The micromechanical theory that we recently developed (Lu Z K andWeng G J 1997 J. Mech. Phys. Solids 45 1905-28) forthe stress-induced martensitic transformation is extended to studythe thermally induced phase transformation of shape memory alloys. This further development makes use of two martensitemorphologies: one with aligned plates and the other with randomlyoriented plates, intended respectively for the presence of asuperimposed applied stress and for a pure thermally inducedprocess. Inherent in the adoption of these two simple morphologiesis the assumption of scale-invariant transition from the singlecrystal to the homogenized polycrystal level without going throughthe calculation of the individual contributions of the constituentgrains. In the presence of an applied stress the orientation of thealigned martensite plates is chosen to maximize the transformationwork, while for a pure thermally induced setting the randomlyoriented plates are used to reflect the variously oriented variantsin the constituent grains. The theory developed is found to havetwo important characteristics: (i) the rate of transformation tendsto decrease during the cooling process and increase upon heating;and (ii) in the presence of an applied stress the hysteresis loopduring cooling and heating in the martensiteconcentration-temperature (cM-T) space translatesrigidly to the right, with a magnitude given by the transformationwork divided by the entropy change. The uncovered autoretardednature of the A→M transformation and theautocatalytic nature of the M→A transformation arefound to be in good quantitative accord with the experimental datafor a Ni-Ti system under a superimposed tension and of a Cu-Al-Nisystem undergoing a pure thermally induced process.

519 形状記憶合金を用いた人工括約筋の開発(バイオエンジニアリング)

This paper describes a work on the development of an artificial sphincter actuator for the treatment of the functional disorder on bowel movement. The prototype acuator is composed of two shape memory alloy (SMA) plates with all-round shape memory effect (ARSME) ; the shapes of those plates are transformed from straight to arc in the heating process and reversed in the cooling process. This actuator is expected to work as a valve of a digestive canal. Its thermo-mechanical properties including the deformation and force generated during the phase transformation of SMA have been measured. The experiments on an living body show that this actuator has good self-bowel movement function.

Micromechanics modeling of composite with ductile matrix and shape memory alloy reinforcement

A quantitative micromechanics-based analysis on the role of microstructure and constituent properties in the overall behavior of shape memory alloy (SMA) composite is carried out in the present work. The composite consists of ductile matrix and SMA second phase inclusions. The macroscopic constitutive relations of the composite are established by using self-consistent approach where the micro–macro correlation is realized by volume averaging and by introducing the concept of stress and strain concentration tensors. In this micromechanics modeling, the internal stress and strain in both matrix and SMA and their evolution are derived as function of externally applied thermomechanical loading as well as the degree of phase transformation in SMA. As an application of the present theory in the microstructural design of this novel composite, the constitutive response of composites with spherical SMA particulate embedded in two different elastoplastic matrixes under uniaxial tension is calculated. The obtained results demonstrate several interesting deformation features of the new composite, which are expected to have potential applications in the future.

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.

Characterization of the phase transformations in shape-memory alloys by modulated differential scanning calorimetry

Abstract Modulated differential scanning calorimetry (MDSC) is a recently developed calorimetric technique, which has demonstrated some significant advantages over the conventional differential scanning calorimetry (DSC). By separating the reversing quantity from the non-reversing component in the total thermal events, it provides some new information that can not be obtained from the conventional DSC. The technique has been applied to various polycrystalline and single crystalline shape-memory alloys, including Cu-Zn-Al, Cu-Al-Ni, Ti-Ni(Cu), Ni-Mn-Ga and Fe-Mn-Si, to characterize the martensitic transformations, bainitic transformation, chemical and magnetic ordering transitions, atomic reordering and other kinetic relaxation processes in the alloys. The preliminary results of the MDSC measurements are summarized and the interpretation of the MDSC results and some factors affecting the results are discussed.

Three-dimensional Landau theory describing the martensitic phase transformation of shape-memory alloys

In shape-memory alloys a first-order martensitic phase transition is responsible for pseudo-elastic and for ferro-elastic stress-strain relations. To describe this behaviour a modified Landau theory is proposed in which the free energy of the crystal depends on the temperature and on the full strain tensor. The energy is invariant with respect to the cubic point group Oh of the high-temperature phase. To predict the cubic-to-monoclinic phase transition of beta -phase shape-memory alloys an expansion up to sixth order in strain is necessary for which, for the class of alloys considered, odd terms may be neglected. For a CuAlNi alloy the expansion coefficients are determined by comparison with experimental results. In contrast to classical Landau theory of second-order phase transitions, not only a single second-order but also a fourth-order expansion coefficient depend on temperature.