Effect of structural transformation and deformation nonlinearity on the stability of a shape memory alloy rod

Within the framework of a model of nonlinear deformations of shape memory alloys (SMA) under phase and structural transformations and for different statements of the problem, an analytical solution of the problem of stability of an SMA rod undergoing a direct martensitic phase transformation under the action of a compressive load is obtained. It is shown that taking account of the nonlinearity of the deformation process and structural transformation in the transition into the adjacent form of equilibrium significantly changes the solution for sufficiently flexible rods. At the same time, taking into account the strains developed in a phase transition is topical for thick-walled SMA elements.     

Taking account of the martensite inelasticity in the reverse phase transformation in shape memory alloys

The model of nonlinear deformation of shape memory alloys (SMA) is generalized to the case in which the possible structural transition in the reverse martensitic transformation is taken into account. The statement of active thermomechanical processes of proportional variation in the stress deviatoric components is justified. The problem of buckling on an SMA bar due to the reverse martensitic transformation is solved. It is shown that taking account of the structural transition under buckling in the process of reverse transformation significantly changes the solution of this problem.     

A CONSTITUTIVE MODEL FOR TRANSFORMATION, REORIENTATION AND PLASTIC DEFORMATION OF SHAPE MEMORY ALLOYS

A constitutive model is developed for the transformation, reorientation and plastic deformation of shape memory alloys (SMAs). It is based on the concept that an SMA is a mixture composed of austenite and martensite, the volume fraction of each phase is transformable with the change of applied thermal-mechanical loading, and the constitutive behavior of the SMA is the combination of the individual behavior of its two phases. The deformation of the martensite is separated into elastic, thermal, reorientation and plastic parts, and that of the austenite is separated into elastic, thermal and plastic parts. Making use of the Tanaka’s transformation rule modified by taking into account the effect of plastic deformation, the constitutive model of the SMA is obtained. The ferroelasticity, pseudoelasticity and shape memory effect of SMA Au-47.5 at.%Cd, and the pseudoelasticity and shape memory effect as well as plastic deformation and its effect of an NiTi SMA, are analyzed and compared with experimental results.     

Thermomechanical modeling of nonlinear internal hysteresis due to incomplete phase transformation in pseudoelastic shape memory alloys

This paper presents a thermomechanical model for pseudoelastic shape memory alloys (SMAs) accounting for internal hysteresis effect due to incomplete phase transformation. The model is developed within the finite-strain framework, wherein the deformation gradient is multiplicatively decomposed into thermal dilation, rigid body rotation, elastic and transformation parts. Helmholtz free energy density comprises three components: the reversible thermodynamic process , the irreversible thermodynamic process and the physical constraints of both. In order to capture the multiple internal hysteresis loops in SMA, two internal variables representing the transition points of the forward and reverse phase transformation, \(\phi _s^f\) and \(\phi _s^r\), are introduced to describe the incomplete phase transformation process. Evolution equations of the internal variables are derived and linked to the phase transformation. Numerical implementation of the model features an Euler discretization and a cutting-plane algorithm. After validation of the model against the experimental data, numerical examples are presented, involving a SMA-based vibration system and a crack SMA specimen subjected to partial loading–unloading case. Simulation results well demonstrate the internal hysteresis and free vibration behavior of SMA.

     

Shakedown analysis of shape memory alloy structures

Phase transformational shakedown of a structure refers to a status that plastic strains cease developing after a finite number of loading cycles, and subsequently the structure undergoes only elastic deformation and alternating phase transformations with limited magnitudes. Due to the intrinsic complexity in the constitutive relations of shape memory alloys (SMA), there is as yet a lack of effective methods for modeling the mechanical responses of SMA structures, especially when they develop both phase transformation and plastic deformation. This paper is devoted to present an algorithm for analyzing shakedown of SMA structures subjected to cyclic or varying loads within specified domains. Based on the phase transformation and plastic yield criteria of von Mises-type and their associated flow rules, a simplified three-dimensional phenomenological constitutive model is first formulated accounting for different regimes of elastic–plastic deformation and phase transformation. Different responses possible for SMA bodies exposed to varying loads are discussed. The classical Melan shakedown theorem is extended to determine a lower bound of loads for transformational shakedown of SMA bodies without necessity of a step-by-step analysis along the loading history. Finally, a simple example is given to illustrate the application of the present theory as well as some basic features of shakedown of SMA structures. It is interesting to find that phase transformation may either increase or decrease the load-bearing capacity of a structure, depending upon its constitutive relations, geometries and the loading mode.     

Thermomechanical behavior of shape memory alloy under complex loading conditions

The thermo-mechanical behavior of polycrystalline shape memory alloy (SMA) under multi-axial loading with varying temperature conditions has been studied by experiments. Recently the research has been extended theoretically and a mechanical model of polycrystalline SMA and the corresponding mesoscopic constitutive equations have been developed. The model presented in this paper is constructed on the basis of the crystal plasticity and the deformation mechanism of SMA. The variants in the crystal grains and the orientations of crystal grains in the polycrystal are considered in the proposed model; the constitutive equations are derived on the basis of the proposed model. The volume fraction of the martensite variants in the transformation process and the influence of the stress state on the transformation process are also considered. Some calculated results obtained by the constitutive equations are presented and compared with the experimental results. It is found that the deformation behavior of SMA under complex loading conditions can be well reproduced by the calculation of the constitutive equations.     

Effects of matrix inelasticity on the overall hysteretic behavior of TiNi-SMA fiber composites

The effects of the inelastic deformation of the matrix on the overall hysteretic behavior of a unidirectional titanium–nickel shape-memory alloy (TiNi-SMA) fiber composite and on the local pseudoelastic response of the embedded SMA fibers are studied under the isothermal loading and unloading condition. The multiaxial phase transformation of the SMA fibers is predicted using the phenomenological constitutive equations which can describe the two-step deformation due to the rhombohedral and martensitic transformations, and the inelastic behavior of the matrix material using the standard nonlinear viscoplastic model. The average behavior of the SMA composite is evaluated with the micromechanical method of cells. It is observed that the inelastic deformation of the matrix due to prior tension results in a compressive stress in the matrix after unloading of the SMA composite and this residual stress impedes the complete recovery of the pseudoelastic strain of the SMA fibers. This explains that a closed hysteresis behavior of the SMA composite is no longer observed in contrast with the case that an elastic behavior of matrix is assumed. The predicted local stress–strain behavior indicates that the cyclic response of matrix is crucial to the design of the hysteretic performance of the SMA composite under the repeated loading conditions.     

A finite element model for shape memory alloys considering thermomechanical couplings at large strains

In the present work we propose a new thermomechanically coupled material model for shape memory alloys (SMA) which describes two important phenomena typical for the material behaviour of shape memory alloys: pseudoelasticity as well as the shape memory effect. The constitutive equations are derived in the framework of large strains since the martensitic phase transformation involves inelastic deformations up to 8%, or even up to 20% if the plastic deformation after the phase transformation is taken into account. Therefore, we apply a multiplicative split of the deformation gradient into elastic and inelastic parts, the latter concerning the martensitic phase transformation. An extended phase transformation function has been considered to include the tension–compression asymmetry particularly typical for textured SMA samples. In order to apply the concept in the simulation of complex structures, it is implemented into a finite element code. This implementation is based on an innovative integration scheme for the existing evolution equations and a monolithic solution algorithm for the coupled mechanical and thermal fields. The coupling effect is accurately investigated in several numerical examples including pseudoelasticity as well as the free and the suppressed shape memory effect. Finally, the model is used to simulate the shape memory effect in a medical foot staple which interacts with a bone segment.     

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.     

纳米多晶NiTi形状记忆合金超弹性的晶粒取向依赖性相场研究

论文基于Ginzburg-Landau理论,建立了一个反映纳米多晶NiTi形状记忆合金取向依赖性的二维多晶相场模型,研究了晶粒取向对其超弹性性能的影响.结果 表明,纳米多晶NiTi形状记忆合金的超弹性行为依赖于晶粒取向分布,即:多晶模型中在所研究的参数变化范围内,晶粒取向分布范围越广、晶粒间取向差越大(无明显织构),超...     

Study on behaviors of functionally graded shape memory alloy cylinder

For better controllability in actuations,it is desirable to create Functionally Graded Shape Memory Alloys(FG-SMAs)in the actuation direction.It can be achieved by applying different heat treatment processes to create the gradient along the radius of a SMA cylinder.Analytical solutions are derived to predict the macroscopic behaviors of such a functionally graded SMA cylinder.The Tresca yield criterion and linear hardening are used to describe the different phase transformations with different gradient parameters.The numerical results for an example of the model exhibit different pseudo-elastic behaviors from the non-gradient case,as well as a variational hysteresis loop for the transformation,providing a mechanism for easy actuation control.When the gradient disappears,the model can degenerate to the non-gradient case.     

Anisotropy of martensitic transformations in modeling of shape memory alloy polycrystals

Based on the knowledge of the anisotropy associated with the martensitic transformations obtained from tension/compression experiments with oriented CuAlNi single crystals, a simple constant stress averaging approach is employed to model the SMA polycrystal deformation behaviors. Only elastic and inelastic strains due to the martensitic transformation, variant reorientations in the martensite phase and martensite to martensite transformations in thermomechanical loads are considered. The model starts from theoretical calculation of the stress-temperature transformation conditions and their orientation dependence from basic crystallographic and material attributes of the martensitic transformations. Results of the simulations of the NiTi, NiAl, and Cu-based SMA polycrystals in stress–strain tests are shown. It follows that SMA polycrystals, even with randomly oriented grains, typically exhibit tension/compression asymmetry of the shape of the pseudoelastic σ−ε curves in transformation strain, transformation stress, hysteresis widths, character of the pseudoelastic flow and in the slope of temperature dependence of the transformation stresses. It is concluded that some macroscopic features of the SMA polycrystal behaviors originate directly from the crystallography of the undergoing MT's. The model shows clearly the crystallographic origin of these phenomena by providing a link from the crystallographic and material attributes of martensitic transformations towards the macroscopic σ−ε−T behaviors of SMA polycrystals.     

Large Deformation of Nitinol Under Shear Dominant Loading

Full-field quantitative strain maps of phase transformation and plasticity in Nitinol under large shear-dominated deformation are presented. To achieve a shear-dominated deformation mode with relatively uniform stresses and strains, a shear compression specimen (SCS) geometry was utilized. Shear deformation appears to impede the development of the strain localization during phase transformation that is seen in uniaxial testing. The shear-dominant deformation of Nitinol in the plastic regime exhibits low hardening and results in the development of significant strain inhomogeneity.     

Force-displacement characteristics of simply supported beam laminated with shape memory alloys

As a preliminary step in the nonlinear design of shape memory alloy(SMA) composite structures,the force-displacement characteristics of the SMA layer are studied.The bilinear hysteretic model is adopted to describe the constitutive relationship of SMA material.Under the assumption that there is no point of SMA layer finishing martensitic phase transformation during the loading and unloading process,the generalized restoring force generated by SMA layer is deduced for the case that the simply supported beam vibrates in its first mode.The generalized force is expressed as piecewise-nonlinear hysteretic function of the beam transverse displacement.Furthermore the energy dissipated by SMA layer during one period is obtained by integration,then its dependencies are discussed on the vibration amplitude and the SMA’s strain(Ms-Strain) value at the beginning of martensitic phase transformation.It is shown that SMA’s energy dissipating capacity is proportional to the stiffness difference of bilinear model and nonlinearly dependent on Ms-Strain.The increasing rate of the dissipating capacity gradually reduces with the amplitude increasing.The condition corresponding to the maximum dissipating capacity is deduced for given value of the vibration amplitude.The obtained results are helpful for designing beams laminated with shape memory alloys.     

Effect of microstructure on the hardening and softening behavIors of polycrystalline shape memory alloys Part I: Micromechanics constitutive modeling

The effects of microstructure and its evolution on the macroscopic superelastic stress-strain response of polycrystalline Shape Memory Alloy (SMA) are studied by a microstructure-based constitutive model developed in this paper. The model is established on the following basis: (1) the transformation conditions of the unconstrained single crystal SMA microdomain (to be distinguished from the bulk single crystal), which serve as the local criterion for the derivation of overall transformation yield conditions of the polycrystal; (2) the micro- to macro-transition scheme by which the connection between the polycrystal aggregates and the single crystal microdomain is established and the macroscopic transformation conditions of the polycrystal SMA are derived; (3) the quantitative incorporation of three microstructure factors (i.e., nucleation, growth and orientation distribution of martensite) into the modeling. These microstructural factors are intrinsic of specific polycrystal SMA systems and the role of each factor in the macroscopic constitutive response is quantitatively modeled. It is demonstrated that the interplay of these factors will result in different macroscopic transformation kinematics and kinetics which are responsible for the observed macroscopic stress-strain hardening or softening response, the latter will lead to the localization and propagation of transformation bands in TiNi SMA. The project supported by the Research Grant Committee (RGC) of Hong Kong SAR, the National Natural Science Foundation of China and the Provincial Natural Foundation of Jiangxi Province of China     

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基于形状记忆合金Brinson一维热力学本构关系和von K\'{a}rm\'{a}n几何非线性薄板理论,研究了径向嵌入SMA丝复合材料加热圆板在横向均布 机械载荷作用下的弯曲响应, 获得了周边不可移简支和夹紧圆板的中心最大挠度与升温之间的关系曲线. 结果表明,形状 记忆合金丝在从马氏体向奥氏体的逆相变过程中所产生的相变回复力对板的弯曲变形具有明 显的调整作用. 通过嵌入SMA纤维丝和施加升温载荷可以主动而有效地调节受机 械载荷作用圆板的弯曲变形.     

Numerical simulation and experimental investigation of the elastocaloric cooling effect in sputter-deposited TiNiCuCo thin films

The exploitation of the elastocaloric effect in superelastic shape memory alloys (SMA) for cooling applications shows a promising energy efficiency potential but requires a better understanding of the non-homogeneous martensitic phase transformation. Temperature profiles on sputter-deposited superelastic \({\mathrm {Ti_{55.2}Ni_{29.3}Cu_{12.7}Co_{2.8}}}\) shape memory alloy thin films show localized release and absorption of heat during phase transformation induced by tensile deformation with a strong rate dependence. In this paper, a model for the simulation of the thermo-mechanically coupled transformation behavior of superelastic SMA is proposed and its capability to reproduce the mechanical and thermal responses observed during experiments is shown. The procedure for experiment and simulation is designed such that a significant temperature change from the initial temperature is obtained to allow potential cooling applications. The simulation of non-local effects is enabled by the use of a model based on the one-dimensional Müller–Achenbach–Seelecke model, extended by 3D mechanisms such as lateral contraction and by non-local interaction, leading to localization effects. It is implemented into the finite element software COMSOL Multiphysics, and comparisons of numerical and experimental results show that the model is capable of reproducing the localized transformation behavior with the same strain rate dependency. Additionally to the thermal and the mechanical behavior, the quantitative prediction of cooling performance with the presented model is shown.     

应力引起的镍钛单晶形状记忆合金相变的实验研究

在单晶形状记忆合金试样中,由于没有晶粒之间的约束,它的马氏体相界面移动比多晶容易,用实验方法研究其相变的特点,对建立新的理论模型有意义,因而对它的实验分析显得重要。本文利用高分辨率的CCD系统监测到NiTi单晶形状记忆合金在拉伸时的相变伪弹性的过程;利用X射线衍射法得到了NiTi单晶试样在拉伸方向的晶向;运用高分辨率的云纹干涉技术,获得了应力引起的NiTi单晶形状记忆合金相变时的变形场;利用高分辨率、高灵敏度的红外相机记录了NiTi单晶在拉伸状态下的温度变化规律;对低温下NiTi单晶的拉伸性能做了初步的研究,得到一些有意义的现象。