形状记忆合金的一种基于经典塑性理论的两相混合本构模型

形状记忆合金由马氏体相和奥氏体相动态组成,其行为实质上是两相各自行为的动态组合,根据实验现象,假设在一定的变形范围内,马氏体相为弹塑性而奥氏体相为线弹性,基于经典塑性理论和混合物理论,结合Tanaka的相变描述,得到了形状记忆合金的一种本构描述,对不同温度下形状记忆合金Au-47．5at．％Cd的铁弹性、拟弹性和形状记忆特性进行了分析,取得了与实验相吻合的结果。     

形状记忆合金单晶细观本构关系的一种相变动力学模型及算法

形状记忆合金是由马氏体相和奥氏体相组成的非均质材料,热力载荷及相变不可避免地在材料中引起残余微应力场,它与外界驱动力的叠加可能导致低应力水平下发生马氏体相变或逆相变.论文假设马氏体相变及逆相变的驱动力是马氏体体积分数的连续函数,发展了形状记忆合金伪弹性的本构描述及相应的数值分析方法.分析表明,所发展的方法与理想相变模型间的误差远小于已有工作中引入的容许误差.对形状记忆合金单晶伪弹性响应的计算结果与试验结果或已有模型计算结果的比较表明所发展的方法具有较高的精度.此外,所发展的方法具有明晰的物理背景,且无需对每个变体的相变发生与否及其方向进行判断,简化了计算过程,提高了计算效率和收敛性.     

NiTi形状记忆合金动态压缩力学行为的实验研究

采用材料试验机和SHPB实验技术,对在不同初始温度(298～873K)和应变率(5×10-4、～2.3×103s-1)下的NiTi形状记忆合金的压缩力学行为进行了实验研究。结果表明:马氏体状态下的NiTi合金的力学行为对应变率的变化敏感,位错屈服段的硬化模量、相屈服段的硬化模量及马氏体重取向前的弹性模量对应变率的变化不敏感,而位错塑性变形前的弹性模量随应变率的提高迅速增大;奥氏体状态下的NiTi合金随着实验温度升高,无论是应力诱发马氏体相变应力还是奥氏体相屈服应力都逐渐下降,材料表现出温度软化效应。从超弹性温度范围内的卸载曲线中观察到了应力诱发马氏体到奥氏体的逆转变。     

应力作用下NiTi形状记忆合金微结构演化的相场模拟及其本征应变率敏感性

基于Ginzburg-Landau动力学控制方程建立了NiTi形状记忆合金非等温相场模型,实现了对NiTi合金内应力诱导马氏体相变的数值模拟。同时将晶界能密度引入系统局部自由能密度,从而考虑多晶系统中晶界的重要作用。数值计算了单晶和多晶NiTi形状记忆合金在单轴机械载荷作用下微结构的动态演化过程和宏观力学行为,并重点研究了晶粒尺寸为60 nm的NiTi纳米多晶在低应变率下（0.0005～15 s?1）力学行为的本征应变率敏感性。研究结果表明,单晶NiTi合金系统高温拉伸-卸载过程中马氏体相变均匀发生,未形成奥氏体-马氏体界面。而纳米多晶系统在加载阶段出现了马氏体带的形成-扩展现象,在卸载阶段出现了马氏体带的收缩-消失现象。相同外载作用过程中,NiTi单晶系统的宏观应力-应变曲线具有更大的滞回环面积,拥有更优的超弹性变形能力。计算结果显示,在中低应变率下纳米晶NiTi形状记忆合金应力-应变关系表现出较明显的应变率相关性,应变率升高导致材料相变应力提升。这一应变率相关性主要源于相场模型中外加载荷速率与马氏体空间演化速度的相互竞争关系。     

热弹性马氏体相变连续介质热力学研究

介绍形状记忆合金热弹性马氏体相变连续介质热力学研究方法和最新进展, 着重分析了在推广的非线性弹性力学的框架下, 应用变分方法研究热弹性马氏体相变的理论和方法、存在的问题及发展趋势. 首先介绍如何计算马氏体相变24种变体的变形梯度, 然后拓展非线性弹性力学, 引入描述相变的多阱非凸弹性势能, 进而讨论了界面能和非局部能对相变微结构和相变过程的影响的相关研究理论方法和进展.      

相变温度对NiTi形状记忆合金耐磨性的影响

利用WMW-1型摩擦磨损试验机研究了在相同条件下相变温度对6种NiTi形状记忆合金耐磨性的影响,并分析其磨损机制.结果表明:超弹状态NiTi合金具有热弹性马氏体相变、高阻尼效应、应力诱发马氏体和超弹性等特性而使得其耐磨性较好,合金的耐磨性主要取决于相变温度、Ni原子的析出情况和合金硬度.     

超弹性形状记忆合金管单向拉伸试验的数值模拟

NiTi形状记忆合金具有很强的超弹性行为，这种超弹性行为是由于材料在应力作用下发生可逆的马氏体相变所引起。最近Sun和Lee^[4]在NiTi形状记忆合金管单向拉伸试验中观测到，应力诱导马氏体相变具有螺旋带状的形貌特征，本文对此作了数值模拟研究。采用包含应变软化效应的三线性本构关系，建立了NiTi形状记忆合金管的三维有限元模型。通过迭代计算，成功地再现了试验中所观察到的螺旋状相变带从形成到长大的全过程。数值计算结果表明，产生这一独特现象的力学机制，在于NiTi形状记忆合金管在拉伸状态下出现的局部变形失稳极其传播。     

一种描述形状记忆合金拟弹性变形行为的本构关系

本文给出一种描述形状记忆合金拟弹性变形现象的本构关系,可用于多晶材料在一般应力状态下及单晶材料在单轴应力下的变形情况。该本构关系采用弹性应变与相变应变迭加形式,物理意义明显,形式简洁。对 Cu-Zn-Sn 合金及 Ti-Ni 合金材料的变形行为进行了模拟计算,结果与实验值有较好的吻合。     

一种描述形状记忆合金拟弹性变形行为的本构关系

本文给出一种描述形状记忆合金拟弹性变形现象的本构关系,可用于多晶材料在一般应力状态下及单晶材料在单轴应力下的变形情况。该本构关系采用弹性应变与相变应变迭加形式,物理意义明显,形式简洁。对 Cu-Zn-Sn 合金及 Ti-Ni 合金材料的变形行为进行了模拟计算,结果与实验值有较好的吻合。     

形状记忆合金椭圆孔口问题的有限单元法

基于Lagoudas形状记忆合金(SMA)三维本构模型,假设材料为各向同性,推导了SMA平面应力状态的增量型本构方程,继而编写了ABAQUS用户自定义材料(UMAT)子程序,研究了在双向拉伸情况下,外载荷、温度、椭圆孔口长短轴之比对超弹性SMA椭圆孔口板中应力诱发马氏体相变区的影响。数值结果表明:应力诱发马氏体相变首先发生在椭圆孔口长轴端点部位,在外加载荷作用下逐渐扩展到板内,并由内向外形成马氏体相区、相变混合区和奥氏体相区;SMA板内应力诱发马氏体完全相变区面积与施加外载荷成正相关,与温度成负相关;随着椭圆孔口长短轴之比增大,SMA板内应力诱发马氏体完全相变区面积呈现出先减小后增大的趋势;拉应力差值相同时,相较于拉应力沿椭圆孔口长轴方向较大的情况,当拉应力沿椭圆孔口短轴方向较大时,SMA板内完全相变区面积较大,椭圆孔口周边应力集中现象更明显。     

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.     

A 3-D constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of self-accommodated martensite

A 3-D constitutive model for polycrystalline shape memory alloys (SMAs), based on a modified phase transformation diagram, is presented. The model takes into account both direct conversion of austenite into detwinned martensite as well as the detwinning of self-accommodated martensite. This model is suitable for performing numerical simulations on SMA materials undergoing complex thermomechanical loading paths in stress–temperature space. The model is based on thermodynamic potentials and utilizes three internal variables to predict the phase transformation and detwinning of martensite in polycrystalline SMAs. Complementing the theoretical developments, experimental data are presented showing that the phase transformation temperatures for the self-accommodated martensite to austenite and detwinned martensite to austenite transformations are different. Determination of some of the SMA material parameters from such experimental data is also discussed. The paper concludes with several numerical examples of boundary value problems with complex thermomechanical loading paths which demonstrate the capabilities of the model.     

Phase proportioning in CuAlBe shape memory alloys during thermomechanical loadings using electric resistance variation

The microstructure of shape memory alloys changes with the thermomechanical history of the material. During thermomechanical loading, austenite, thermally-induced martensite or stress-induced martensite can be simultaneously present in the material. In applications integrating SMA parts, utilization conditions seriously affect the microstructure and can generate macroscopic strain or stress. Consequently, during thermomechanical loadings, it is important to be able to proportion the different phases and consequently to understand the kinetic transformation. This is very useful in the development of constitutive equations. This study shows, by a series of tests, that the proposed experimental method, based on the measurement of the variation of electric resistance of CuAlBe wires, permits to determine the volume fraction of the different phases present in the material (i.e., austenite, stress-induced martensite and thermally-induced martensite). The proposed method is applied to the most common thermomechanical behavior met in engineering applications of shape memory alloys: pseudoelasticity, pseudoplasticity, recovery-stress and stress-assisted two-way shape memory effect. The proportioning method based on a mixture law integrating the resistivity of pure phases present in the SMA is first performed on different two-phase mixture cases and then applied to a three phase mixture case.     

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.     

Micromechanics of plastic deformation and phase transformation in a three-phase TRIP-assisted advanced high strength steel: Experiments and modeling

The micromechanics of plastic deformation and phase transformation in a three-phase advanced high strength steel are analyzed both experimentally and by microstructure-based simulations. The steel examined is a three-phase (ferrite, martensite and retained austenite) quenched and partitioned sheet steel with a tensile strength of ~980 MPa. The macroscopic flow behavior and the volume fraction of martensite resulting from the austenite–martensite transformation during deformation were measured. In addition, micropillar compression specimens were extracted from the individual ferrite grains and the martensite particles, and using a flat-punch nanoindenter, stress–strain curves were obtained. Finite element simulations idealize the microstructure as a composite that contains ferrite, martensite and retained austenite. All three phases are discretely modeled using appropriate crystal plasticity based constitutive relations. Material parameters for ferrite and martensite are determined by fitting numerical predictions to the micropillar data. The constitutive relation for retained austenite takes into account contributions to the strain rate from the austenite–martensite transformation, as well as slip in both the untransformed austenite and product martensite. Parameters for the retained austenite are then determined by fitting the predicted flow stress and transformed austenite volume fraction in a 3D microstructure to experimental measurements. Simulations are used to probe the role of the retained austenite in controlling the strain hardening behavior as well as internal stress and strain distributions in the microstructure.     

Finite Element Analysis of Shape Memory Alloy Adaptive Trusses with Geometrical Nonlinearities

This contribution deals with the nonlinear analysis of shape memory alloy (SMA) adaptive trusses employing the finite element method. Geometrical nonlinearities are incorporated into the formulation together with a constitutive model that describes different thermomechanical behaviors of SMA. It has four macroscopic phases (three variants of martensite and an austenitic phase), and considers different material properties for austenitic and martensitic phases together with thermal expansion. An iterative numerical procedure based on the operator split technique is proposed in order to deal with the nonlinearities in the constitutive formulation. This procedure is introduced into ABAQUS as a user material routine. Numerical simulations are carried out illustrating the ability of the developed model to capture the general behavior of shape memory bars. After that, it is analyzed the behavior of some adaptive trusses built with SMA actuators subjected to different thermomechanical loadings.     

Processus de réorientation des variantes de martensite dans un monocristal de Cu–Al–NiReorientation process of martensite variants in a Cu–Al–Ni monocrystal

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).