Polycrystalline Shape Memory Alloys Research Articles

Analysis of uniaxial stress-strain-temperature hysteresis in an Fe-based shape memory alloy under thermomechanical loading

The uniaxial thermomechanical behavior in an Fe-based polycrystalline shape memory alloy is analyzed from the phenomenological point of view by means of the rate-type constitutive equation and the newly developed transformation kinetics. The forward and reverse transformations among the martensite phase produced in tension or in compression and the parent phase are shown to be depicted by the transformation zones bounded by the transformation start/finish lines on the stress-temperature plane. The shift of the lines, depending on the extent of prior transformation, is determined from the experimental data by the same authors. The stress-strain-temperature hysteresis loops and the recovery stress during heating are well simulated.

A stochastic thermodynamic model for the gradual thermal transformation of SMA polycrystals

The martensitic - austenitic phase transformation of a polycrystalline shape memory alloys (SMA) occurs gradually over a range of temperatures even though the monocrystal undergoes a first-order transition (at a single temperature). Factors such as material inhomogeneities and internal stresses in a polycrystal are believed to cause the spread in transformation temperatures. In this work, we assume that the local regions of a polycrystal transform at a single temperature, characteristic of a first-order transition; this temperature is taken to vary from one region to another. The first-order transition of a generic local region is modeled with the Boyd - Lagoudas thermodynamic theory and a simple averaging process is used to derive the overall response of the polycrystal. The concept of a statistical distribution in the first-order transition temperatures is then introduced. By reducing the proposed stochastic thermodynamic theory to the special case of a pure thermal transformation in a polycrystal, it becomes possible to obtain the parameters of the statistical distribution from calorimetric data. This new approach renders unnecessary the customary practice in the SMA literature to artificially assign `start' and `finish' transformation temperatures to a SMA polycrystal. The statistical distribution is also used as a basis to correlate strain recovery against temperature measurements from repetitive cycles of a thermally induced transformation in untrained polycrystalline SMA wires.

HYSTERETIC BEHAVIOR IN AN Fe-BASED SHAPE MEMORY ALLOY UNDER TENSILE/COMPRESSIVE CYCLIC THERMOMECHANICAL LOADING

The thermomechanical hysteretic behavior in an Fe-9%Cr-5%Ni-14%Mn-6%Si polycrystalline shape memory alloy is experimentally investigated under tensile and compressive cyclic thermomechanical loading. Similar to the other shape memory alloys, such as Ti-Ni and Cu-based alloys, the Fe-based shape memory alloy also exhibits the cyclic effect which appears macroscopically as the change in the hysteresis loop with cycling. The convergence to a limit loop is, however, not observed in the present alloy. The cyclic effect on the residual strain, the transformation strain and the martensite start stress is explained by the two metallurgical processes; the accumulation of the perfect dislocations and the shape irreversibility in the reverse transformation.

Modeling the transformation stress of constrained shape memory alloy single crystals

Shape memory alloys (SMA) are a unique class of engineering materials that can be further exploited with accurate polycrystal constitutive models. Previous investigators have modeled stress-induced martensite formation in unconstrained single crystals. Understanding stress-induced martensite formation in constrained single crystals is the next step towards the development of a constitutive model for textured polycrystalline SMA. Such models have been previously developed for imposition of axisymmetric strain on a polycrystal with random crystal orientation; the present paper expands the constrained single crystal SMA model to encompass arbitrary imposed strains. To evaluate the model, axisymmetric tension and compression strains and pure shear strain are imposed on three SMA: NiTi, CuAlNi (β1→γ′1) and NiAl. Model results are then used to understand the anisotropy and asymmetry of transformation stress in the three SMA considered. Finally, the impact of the present results on polycrystal behavior is addressed.

Experimental investigation of micromechanical behavior of advanced materials by moiré interferometry

Several typical instances show that moiré interferometry is an effective experimental method for micromechanics study of advanced materials. By using moiré interferometry, stress-induced martensitic transformation plastic zone in ceria-stabilized tetragonal zirconia polycrystalline ceramics (Ce-TZP) is studied. The experimental results show that the stress-induced transformation at room temperature is not uniform within the transformation zone and the phenomenon of microscopic plastic flow localization for transformation is revealed. Meanwhile, the experimental investigation of the pseudoelasticity behavior of Cu-Zn-Al polycrystalline shape memory alloy and bending behavior of carbon-fiber aluminium laminates (CALL) are reported. The experiments reveal some important features of the deformation processes of the materials. Finally, the measuring ability of moiré interferometry for micromechanics study is discussed.

Pseudoelastic Hysteresis in Martensitic Reorientation of Cu-Zn-AI Polycrystalline Shape Memory Alloys

The stress-induced martensitic reorientation of two kinds of Cu-Zn-Al polycrystalline shape memory alloys were studied through experiment. Special attention was paid to the deformation behavior of these polycrystals during the reorientation. Experimental result indicates that for the two materials after reorientation the deformation is pseudoelastic as long as applied stress is smaller than the prestress that induced the reorientation. Detailed research on the pseudoelastic hysteresis was performed. The experimental phenomena are very similar to that of the pseudoelasticity of shape memory alloys due to the forward and reverse martensitic transformations at high temperature.

多軸負荷を受ける多結晶形状記憶合金

多軸負荷を受ける多結晶形状記憶合金

A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy

Pseudoelasticity and the shape memory effect (SME) due to martensitic transformation and reorientation of polycrystalline shape memory alloy (SMA) materials are modeled using a free energy function and a dissipation potential. Three different cases are considered, based on the number of internal state variables in the free energy: (1) austenite plus a variable number of martensite variants; (2) austenite plus two types of martensite; and (3) austenite and one type of martensite. Each model accounts for three-dimensional simultaneous transformation and reorientation. The single-martensite model was chosen for detailed study because of its simplicity and its ease of experimental verification. Closed form equations are derived for the damping capacity and the actuator efficiency of converting heat into work. The first law of thermodynamics is used to demonstrate that significantly more work is required to complete the adiabatic transformation than the isothermal transformation. Also, as the hardening due to the austenite/martensite misfit stresses approaches zero, the transformation approaches the isothermal, infinite specific heat conditions of a first-order transformation. In a second paper, the single-martensite model is used in a mesomechanical derivation of the constitutive equations of an active composite with an SMA phase.

Smart Behaviour in a CuZnAl Single Crystal Alloy

The Step-wise Martensite to Austenite Reversible Transformation (SMART) has been widely investigated in polycrystalline shape memory alloys and its key features are, on the whole, well established. Though some working hypothesis have been put in advance, the full understanding of this micromemory phenomenon is still open. Specifically, the most probable origin of the SMART, relies on a local relaxation of the elastic energy. In order to clarify the advanced hypothesis, a CuZnAl single crystal alloy, where the elastic energy contribution to the thermoelastic balance is typically smaller than in the case of polycrystalline specimens, has been examined. All the investigated specimens have shown, though at different extent the SMART : results have shown that the larger the elastic energy involved, the more evident the SMART phenomenology is. Thus, the present findings further support the role of the elastic energy in the SMART.

Thermomechanical Behavior of an Fe-Based Shape Memory Alloy : Transformation Conditions and Hystereses

The transformation conditions of an Fe-based polycrystalline shape memory alloy are determined experimentally under the multiaxial stress state. The martensite start condition is represented as an oval conical surface in the axial stress-shear stress-temperature space, meaning the transformation condition is not the von Mises type condition in plasticity and clearly depends on the third invariant of the stress tensor. The austenite start and finish conditions are also determined as the planes in the multiaxial stress-temperature space. The uniaxial stress-strain-temperature hysteretic behavior determined under the uniaxial thermomechanical loads is simulated by introducing the internal state variables which represent the status of the microscopic internal structures.

Experimental study on the thermoelastic martensitic transformation in shape memory alloy polycrystal induced by combined external forces

Combined tension and torsion experiments with thin wall specimens of Cu-Al-Zn-Mn polycrystalline shape memory alloy (SMA) were performed at temperatureT =A f + 25 K. The general stress-strain behaviors due to the thermoelastic martensitic transformation, induced by a combination of external forces of axial load and torque, were studied. It is shown that the progress of martensitic transformation (MT) at general stress conditions can be well considered as triggered and controlled by the supplied mechanical work (a kind of equivalent stress) in the first approximation. Pseudoelastic strains in proportional as well as nonproportional combined tension-torsion loadings were found fully reversible, provided that uniaxial strains were reversible. The axial strain can be controlled by the change of torque andvice versa due to the coupling among tension and torsion under stress, not only in forward transformation, but also in reverse transformation on unloading. The pseudoelastic strains of SMA polycrystal are path dependent but well reproducible along the same stress path. The evolution of macroscopic strain response of SMA polycrystal, subjected to the nonproportional pseudoelastic loading cycles with imposed stress path, was systematically investigated. The results bring qualitatively new information about the progress of the MT in SMA polycrystal, subjected to the general variations of external stress.

Effect of Prior Transformation on Transformation Start Stress and Temperature in an Fe-based Shape Memory Alloy

Transformation start conditions in an Fe-Cr-Ni-Mn-Si polycrystalline shape memory alloy are found to be determined by the martensite start stresses in the stress-strain plane and the austenite start temperatures in the temperature-strain plane. The martensite start stress changes nonlinearly with the extent of prior reverse transformation, and the austenite start temperature with the extent of prior martensitic transformation. In both cases the prior transformation is shown to be characterized by means of the two parameters. The alloy performance is similar to that in some Cu- and Fe-based alloys but quite different from the data in TiNi alloys and the thermodynamic prediction, suggesting a generalization of the theory, especially of the form of the driving force

Quasistatic dynamics and pseudoelasticity in polycrystalline shape memory wires

A number of related but somewhat conflicting theories have been proposed to explain the pseudoelastic hysteresis exhibited by shape memory alloys (SMAs). Some recent experimental results motivated the author to introduce yet another model of thermoelasticity. Attempts to justify this model from a microthermomechanical perspective have led to the theoretical considerations presented in this paper. These discussions provide support for the model and give new perspectives on previous approaches. Based on these ideas, the author proposes that a realistic microscopic model of polycrystalline SMAs should be based on homogenization of a system of non-linear crystallites and dislocations. He also indicates a route of attack for this new problem in homogenization theory.

Transformation start lines in TiNi and Fe-based shape memory alloys after incomplete transformations induced by mechanical and/or thermal loads

Abstract The transformation start condition in the stress-strain or strain-temperature planes is examined in a TiNi polycrystalline shape memory alloy and an Fe-based polycrystalline shape memory alloy under mechanical and/or thermal loads. The martensite start and austenite start stresses in the TiNi alloy are revealed to be almost constant during isothermal loading at the pseudoelastic temperature range, being independent of the extent of prior transformations. In the Fe-based alloy, however, both the martensite start stress and the austenite start temperature are strongly dependent on the extent of prior transformations. The alloy performance is fully contrary to the prediction of the thermodynamic theory of 1. Miller and co-workers (I. Mu¨ller, 1989, Cont. Mech. Thermodyn. 1, 125; I. Mu¨ller and H.B. Xu, 1991, Acta Metall. Mater. 36, 263) and B. Raniecki et al. (1992, Arch. Mech. 44, 261)

複合負荷条件下の熱弾性マルテンサイト変態特性に関する実験的研究

Combined tension-torsion experiments with hollow bar specimens of Cu-Al-Zn-Mn polycrystalline shape memory alloy (SMA) were performed at temperature T=Af+25K. Pseudoelastic strain in non-proportional loading-unloading along various simple stress (strain) paths in stress (strain)-controlled tests were found fully reversible. The experimental data of non-proportional tests, particularly the recorded transformation pathways, provide the first experimental informations about the progress of the general stress induced thermoelastic martensitic transformation in SMA polycrystal under general stress conditions whose forward and reverse transformation pathways are not identical.

Transformation Conditions and Subloops In an Fe-Based Shape Memory Alloy Under Thermomechanical Loading

The martensite/austenite start and finish conditions, the transformation lines in the stress-temperature plane, are determined in an Fe-Cr-Ni-Mn-Si polycrystalline shape memory alloy under the mechanical and/or thermal loads. The transformation lines are show to be almost linear with nearly the same slope. The martensitic transformation zone and the reverse transformation zone are apart to each other, and the latter is very wide; T Af -T As 180 K. Both the martensite start stress and the austenite start temperature are strongly dependent on the extent of prior transformations, the amount of preload and residual strain. The alloy performance is, therefore, fully contrary to the prediction of the thermodynamic theory and to the experimental result by Paskal and Monasevich in TiNi alloy. The effect of hold stress and temperature is measured to compare the transformation start condition with the yield condition in plasticity

OVERALL THERMOMECHANICAL BEHAVIOR OF SHAPE MEMORY ALLOYS

Overall thermomechanical behavior of the polycrystalline shape memory alloys is described from the micromechanical point of view by modeling the alloys as a matrix-inclusions material system. The martensite inclusions are assumed to be born in the austenite matrix at the moment when a transformation condition is satisfied there during thermomechanical loading. The macroscopic constitutive equation is derived in rate form by means of Eshelby's inhomogeneous theory. The Mori-Tanaka theory is employed to take into account the interaction of the martensite inclusions. The formula of the overall thermomechanical material parameters, which exhibits the effect of transformation, is derived explicitly.

Thermodynamic Modelling of Shape Memory Behaviour : Some Examples

This paper gives a general view of a recently developed thermodynamic model of the thermoelastic martensitic transformation. Unlike existing empirical, mathematical or thermodynamic models, this generalised thermodynamic model can be used to understand and describe quantitatively the overall thermomechanical behaviour of polycrystalline shape memory alloys. Important points of difference between this and previous thermodynamic models are that the contributions of the stored elastic energy and of the crystal defects are also included. In addition, the mathematical approach and the assumptions in this model are selected in such a way that the calculations yield close approximations of the real behaviour and that the final mathematical equations are relatively simple. Several illustrations indicate that this model, in contrast to other models, can be used to understand the shape memory behaviour of complex cases. As an example of quantitative calculations, it is shown that this modelling can be an effective tool in the design of multifunctional materials consisting of shape memory lements embedded in matrix materials.

EXPERIMENTAL STUDY ON PERFORMANCES IN Cu-BASED SHAPE MEMORY ALLOY UNDER MULTI-AXIAL LOADING CONDITIONS

This paper reports several interesting features in the shape memory alloy observed experimentally under multi-axial complex loading conditions including some temperature changes (the general loading condition). The experiments were performed systematically by applying the combined loads of axial force and torque to thin-walled tubular specimen made of a Cu-based polycrystalline shape memory alloy. In these systematic experiments, the strong path dependency of pseudo-elastic phenomenon was observed, and moreover this dependency was disappeared completely only when the materirals went back to the stress free state. This kind of unique behaviour of shape memory alloy may be quite interesting from a view point of new engineering applications of shape memory alloy.

Hysteretic behavior in an Fe-Cr-Ni-Mn-Si polycrystalline shape memory alloy during thermomechanical cyclic loading

Stress-strain-temperature hysteretic behavior is examined in an Fe-Cr-Ni-Mn-Si polycrystalline shape memory alloy during thermomechanical cyclic loading, each cycle of which consists of isothermal loading/unloading followed by isostatic heating/cooling. Transformation start and finish lines are first determined in the stress-temperature plane, which are revealed to be less cycle dependent. Hysteretic behavior is, on the contrary, shown to be highly cycle dependent. Its strong dependence on hold stress as well as on temperature range is also examined. The martensite start line is clearly determined above the yield stress of the parent phase.