梯度纳米晶NiTi形状记忆合金的超弹性和形状记忆效应相场模拟

通过建立考虑两个马氏体变体的二维相场模型,对梯度纳米晶镍钛(NiTi)合金系统的超弹性、单程和应力辅助双程形状记忆过程进行了模拟和预测.模拟结果显示:在梯度纳米晶NiTi合金的超弹性过程中,较粗晶粒的区域保留了传统粗晶的马氏体相变和逆相变特征,即局部马氏体带的形核?扩展和缩减?消失,而随着晶粒尺寸的减小,细晶粒区域表现...     

Constitutive model for uniaxial transformation ratchetting of super-elastic NiTi shape memory alloy at room temperature

The transformation ratchetting of super-elastic NiTi shape memory alloy was observed by the uniaxial stress-controlled cyclic tests [Kang, G.Z., Kan, Q.H., Qian, L.M., Liu, Y.J, 2009a. Ratchetting deformation of super-elastic and shape memory NiTi Alloys. Mech. Mater. 41, 139–153]. It is concluded that the NiTi alloy presents apparent ratchetting behaviour, and the ratchetting is collectively caused by the cyclic accumulation of residual induced-martensite and the transformation-induced plastic deformation (i.e., namely transformation ratchetting). Based on the experimental results, a cyclic constitutive model was constructed in the framework of generalized plasticity [Lubliner, J., Auricchio, F., 1996. Generalized plasticity and shape memory alloys. Int. J. Solids Struct. 33, 991–1003] to describe the transformation ratchetting of super-elastic NiTi alloy. The proposed model simultaneously accounts for the evolutions of residual induced-martensite and transformation-induced plastic strain during the stress-controlled cyclic loading by introducing an internal variable z_c, i.e., cumulated induced-martensite volume fraction. The dependence of transformation ratchetting on the applied stress levels and the phase transformation hardening behaviour of the NiTi alloy are also considered in the developed model. The anisotropic phase transformation behaviours of the alloy presented in the tension and compression cases are described by employing a Drucker–Prager-typed transformation surface. It is shown that the simulated results of transformation ratchetting obtained by the proposed model are in good agreement with the corresponding experiments, since the typical features of transformation ratchetting are reasonably captured by the proposed model.     

超弹性镍钛形状记忆合金单轴相变棘轮行为的宏观唯象本构模型

超弹性镍钛形状记忆合金因其良好的力学性能以及独特的超弹性和形状记忆效应已广泛应用于土木工程、航空航天和生物医疗等多个领域,在实际服役环境中超弹性镍钛合金元件不可避免地会承受不同应力水平的循环载荷作用,亟待建立描述相变棘轮行为(即峰值应变和谷值应变随着正相变和逆相变循环的进行不断累积)的循环本构模型.为此,基于已有的超弹性镍钛形状记忆合金在不同峰值应力下的单轴相变棘轮行为实验研究结果,在广义黏塑性框架下,对Graesser等提出的通过背应力非线性演化方程反映超弹性镍钛形状记忆合金超弹性行为的一维宏观唯像本构模型进行了拓展,考虑了正相变和逆相变过程中特征变量的差异及其随循环的演化,以非弹性应变的累积量为内变量引入了正相变开始应力、逆相变开始应力、相变应变和残余应变的演化方程,同时通过峰值应力与正相变完成应力的比值来确定演化方程中的相关系数,建立了描述超弹性镍钛合金单轴相变棘轮行为的本构模型.将模拟结果与对应的实验结果进行对比发现,建立的宏观唯像本构模型能够合理地描述超弹性镍钛形状记忆合金的单轴相变棘轮行为及其峰值应力依赖性,模型的预测结果和实验结果吻合得很好.     

Study on the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy based on a new crystal plasticity constitutive model

In this paper, a crystal plasticity based constitutive model (Yu et al., 2013) is extended to describe the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy by considering the internal heat production. Two sources of internal heat productions are included in the proposed model, i.e., the mechanical dissipations of inelastic deformation and the transformation latent heat in the NiTi shape memory alloy. With an assumption of uniform temperature field in the alloy specimen, a simplified evolution law of temperature field is obtained by the first law of thermodynamics and the heat boundary conditions. An explicit scale-transition rule is adopted to extend the proposed single crystal model to the polycrystalline version. The capability of the extended polycrystalline model to describe the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy is verified by comparing the predictions with the corresponding experimental ones. The comparison demonstrates that the proposed constitutive model considering the internal heat production predicts the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy fairly well.     

ADVANCES IN TRANSFORMATION RATCHETING AND RATCHETING-FATIGUE INTERACTION OF NITI SHAPE MEMORY ALLOY

The accumulation of inelastic deformation occurring in NiTi shape memory alloy under the stress-controlled cyclic loading condition is named transformation ratcheting, since it is mainly caused by the solid-solid transformation from austenite to martensite phase and vice versa. The transformation ratcheting and its effect on the fatigue life (i.e., transformation-fatigue interaction) are key issues that should be addressed in order to assess the fatigue of NiTi shape memory alloy more accurately. In this paper, the advances in the studies on the transformation ratcheting and ratcheting-fatigue interaction of super-elastic NiTi shape memory alloy in recent years are reviewed: First, experimental observation of the uniaxial transformation ratcheting and ratcheting-fatigue interaction of super-elastic NiTi alloy under the stress-controlled cyclic loading conditions is treated, and the detrimental effect of transformation ratcheting on the fatigue life is addressed; Secondly, two types of cyclic constitutive models (i.e., a macroscopic phenomenological model and a micromechanical one based on crystal plasticity) constructed to describe the transformation ratcheting of super-elastic NiTi alloy are discussed; Furthermore, an energy-based failure model is provided and dealt with by comparing its predicted fatigue lives with experimental ones; Finally, some suggestions about future work are made.     

An inclusion theory for the propagation of martensite band in NiTi shape memory alloy wires under tension

In this paper, we present analytical modelling for the pure mechanical response of uniaxial tensioned NiTi wire that experiences stress-induced martensitic transformation via a propagating martensite band at the superelastic temperature regime. The model aims to predict the overall behavior of the SMA wire as a structural response containing propagating instabilities. Based on the systematic experimental investigation of Shaw and Kyriakides (Shaw, J.A., Kyriakides, S., 1995. Thermomechemical aspects of NiTi. J. Mech. Phys. Solids 43, T243–1281 and Shaw, J.A., Kyriakides, S., 1997. On the nucleation and propogation of phase transformation fronts in a NiTi alloy. Acta Mater. 45(2), 638–700), the wire is modeled as an elastic rod containing a single cylindrical transformation inclusion with a uniform axisymmetric eigenstrain. The analytical expression of the free energy of this special matrix-inclusion system is formulated and the length of the martensite band is identified as the key variable describing the transformation process of the system. Theoretical predictions on the peak stress and the subsequent steady-state propagation stress of the wire during forward and reverse transformations are provided and compared with the available experimental data. Specimen size effect on the nominal stress-strain curves and general deformation features of the wire are discussed.     

纳米单晶NiTi合金单程形状记忆效应的分子动力学模拟

采用基于第二近邻修正型嵌入原子势的分子动力学方法研究了纳米单晶NiTi合金的单程形状记忆效应,详细阐明了温度诱发马氏体相变和应力诱发马氏体重定向过程中纳米单晶的变形行为和微结构演化,进一步分析了加/卸载速率对NiTi合金单程形状记忆效应的影响。结果表明,NiTi纳米单晶在应力加载过程中发生马氏体重定向,卸载后存在残余应变;当加热到奥氏体转变结束温度以上时,马氏体逆相变为奥氏体相,残余应变逐渐减小,但未完全回复;随着应力加载速率的增加,重定向临界应力和模量逐渐增加;再次降温过程中不同加载速率下的原子结构演化各不相同。     

纳米单晶NiTi合金单程形状记忆效应的分子动力学模拟

采用基于第二近邻修正型嵌入原子势的分子动力学方法研究了纳米单晶NiTi合金的单程形状记忆效应,详细阐明了温度诱发马氏体相变和应力诱发马氏体重定向过程中纳米单晶的变形行为和微结构演化,进一步分析了加/卸载速率对NiTi合金单程形状记忆效应的影响。结果表明,NiTi纳米单晶在应力加载过程中发生马氏体重定向,卸载后存在残余应变;当加热到奥氏体转变结束温度以上时,马氏体逆相变为奥氏体相,残余应变逐渐减小,但未完全回复;随着应力加载速率的增加,重定向临界应力和模量逐渐增加;再次降温过程中不同加载速率下的原子结构演化各不相同。     

应变幅值对循环载荷下NiTi合金力学性质的影响

实验研究了应变幅值对循环载荷下NiTi合金伪弹性退化特征的影响规律,结果表明:当卸载发生在NiTi合金应力诱发马氏体相变阶段时,应变幅值对马氏体相变开始应力的退化规律影响较小,但此时应变幅值的增加会显著增大奥氏体弹性模量的退化程度,而其大变形可回复能力和阻尼特性在应变幅值大于6%时才有大幅度降低。对各参数退化程度进行定量分析,得到了NiTi合金具有较强可回复能力和阻尼性能的应变幅值范围。该研究可为NiTi合金阻尼器的设计提供参考。     

CONSTITUTIVE MODELING OF ROLLED SHAPE MEMORY ALLOY SHEETS TAKING INTO ACCOUNT PRE-TEXTURE AND ANISOTROPIC HARDENING

The drawing or rolling process endows polycrystal shape memory alloy with a crys- tallographic texture, which can result in macroscopic anisotropy. The main purpose of this work is to develop a constitutive model to predict the thermomechanical behavior of shape memory alloy sheets, which accounts for the crystallographic texture. The total macroscopic strain is decom- posed into elastic strain and macro-transformation strain under isothermal condition. Considering the transformation strain in local grains and the orientation distribution function of crystallo- graphic texture, the macro-transformation strain and the effective elastic modulus of textured polycrystal shape memory alloy are developed by using tensor expressions. The kinetic equation is established to calculate the volume fraction of the martensite transformation under given stress. Furthermore, the Hill＇s quadratic model is developed for anisotropic transformation hardening of textured SMA sheets. All the calculation results are in good agreement with experimental data, which show that the present model can accurately describe the macro-anisotropic behaviors of textured shape memory alloy sheets.     

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...     

具有层状微观结构的NiTi单晶本构模型

建立了应力诱发的具有层状微观结构的NiTi单晶本构模型. 模型考虑母相和马氏体相弹性各向异性性质的差异, 以NiTi单晶相变过程中可能出现的24个马氏体变体为基础, 利用相变驱动力和理想界面的连续条件推导了马氏体相变的发生及发展过程, 以及单晶相变过程中宏微观应力应变的演化, 数值模拟了在不同加载方向材料的应力应变响应.结果表明, 对于不同的加载方向, NiTi单晶既存在强化也存在软化现象.      

Oliver–Pharr indentation method in determining elastic moduli of shape memory alloys—A phase transformable material

Instrumented indentation test has been extensively applied to study the mechanical properties such as elastic modulus of different materials. The Oliver–Pharr method to measure the elastic modulus from an indentation test was originally developed for single phase materials. During a spherical indentation test on shape memory alloys (SMAs), both austenite and martensite phases exist and evolve in the specimen due to stress-induced phase transformation. The question, “What is the measured indentation modulus by using the Oliver–Pharr method from a spherical indentation test on SMAs?” is answered in this paper. The finite element method, combined with dimensional analysis, was applied to simulate a series of spherical indentation tests on SMAs. Our numerical results indicate that the measured indentation modulus strongly depends on the elastic moduli of the two phases, the indentation depth, the forward transformation stress, the transformation hardening coefficient and the maximum transformation strain. Furthermore, a method based on theoretical analysis and numerical simulation was established to determine the elastic moduli of austenite and martensite by using the spherical indentation test and the Oliver–Pharr method. Our numerical experiments confirmed that the proposed method can be applied in practice with satisfactory accuracy. The research approach and findings can also be applied to the indentation of other types of phase transformable materials.     

NiTi合金伪弹性退化规律及尺度效应的试验研究

以NiTi合金在结构振动控制中的应用为背景,试验研究了加卸载循环次数和直径尺度对NiTi合金丝伪弹性特征的影响规律。研究结果表明,NiTi合金丝的残余应变随循环次数的增加呈指数关系增加,而其马氏体相变开始应力、奥氏体弹性模量、相变应变和等效阻尼比随循环次数的增加呈指数关系降低;随着直径尺度增加,循环加卸载后,NiTi合金丝的伪弹性退化程度显著增加。此外,残余应变与残余内应力、奥氏体弹性模量以及相变应变之间的线性关系揭示了NiTi合金伪弹性退化的内在机理。     

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.     

Experimental characterization and micromechanical modeling of superelastic response of a porous NiTi shape-memory alloy

Porous shape-memory alloys are usually brittle due to the presence of various nickel-titanium intermetallic compounds that are produced in the course of most commonly used synthesizing techniques. We consider here a porous NiTi shape-memory alloy (SMA), synthesized by spark-plasma sintering, that is ductile and displays full shape-memory effects over the entire appropriate range of strains. The porosity however is only 12% but the basic synthesizing technique has potential for producing shape-memory alloys with greater porosity that still are expected to display superelasticity and shape-memory effects. The current material has been characterized experimentally using quasi-static and dynamic tests at various initial temperatures, mostly within the superelastic strain range, but also into the plastic deformation regime of the stress-induced martensite phase. To obtain a relatively constant strain rate in the high strain-rate tests, a novel pulse-shaping technique is introduced. The results of the quasi-static experiments are compared with the predictions by a model that can be used to calculate the stress-strain response of porous NiTi shape-memory alloys during the austenite-to-martensite and reverse phase transformations in uniaxial quasi-static loading and unloading at constant temperatures. In the austenite-to-martensite transformation, the porous shape-memory alloy is modeled as a three-phase composite with the parent phase (austenite) as the matrix and the product phase (martensite) and the voids as the embedded inclusions, reversing the roles of austenite and martensite during the reverse transformation from fully martensite to fully austenite phase. The criterion of the stress-induced martensitic transformation and its reversal is based on equilibrium thermodynamics, balancing the thermodynamic driving force for the phase transformation, associated with the reduction of Gibbs’ free energy, with the resistive force corresponding to the required energy to create new interface surfaces and to overcome the energy barriers posed by various microstructural obstacles. The change in Gibbs’ free energy that produces the driving thermodynamic force for phase transformation is assumed to be due to the reduction of mechanical potential energy corresponding to the applied stress, and the reduction of the chemical energy corresponding to the imposed temperature. The energy required to overcome the resistance imposed by various nano- and subnano-scale defects and like barriers, is modeled empirically, involving three constitutive constants that are then fixed based on the experimental data. Reasonably good correlation is obtained between the experimental and model predictions.     

Micromechanical modelling of the effect of plastic deformation on the mechanical behaviour in pseudoelastic shape memory alloys

Except for the recoverable strain induced by phase transformation, NiTi alloys are very ductile even in the martensite phase. The purpose of the present paper is to study the influence of permanent deformation, which results from plastic deformation of martensite, on the mechanical behaviour of pseudoelastic NiTi alloys. Based on phenomenological theory of martensitic transformation and crystal plasticity, a new three dimensional micromechanical model is proposed by coupling both the slip and twinning deformation mechanisms. The present model is implemented as User MATerial subroutine (UMAT) into ABAQUS/Standard to study the influences of plastic deformation on the stress and strain fields, and on the evolution of martensite transformation. Results show that with the increasing of plastic deformation the residual strain increases and the phase transformation stress–strain curves from the martensite to austenite become steeper and less obvious. Both characteristics, stabilisation of martensite and impedance of the reverse transformation, due to plastic deformation are captured.     

NiTi形状记忆合金裂纹尖端热力耦合行为研究

本文对NiTi形状记忆合金I型裂纹尖端热力耦合行为进行了数值仿真分析和实验验证。建立了包含相变和热力耦合的本构模型,通过有限元计算得到了裂纹尖端附近的纵向应变、马氏体体积分数和温度场分布,依据马氏体相变情况对裂纹尖端有效应力强度因子进行了修正,揭示了加载速率对形状记忆合金裂纹尖端有效应力强度影子的影响规律。参数研究表明,随着加载频率的增加,裂纹尖端附近温度逐渐升高,马氏体相变区域逐渐缩小,有效应力强度因子呈下降趋势,形状记忆合金表现出增韧效应,有助于减缓裂纹扩展。本研究结果对于揭示热力耦合作用下超弹性形状记忆合金疲劳裂纹扩展规律具有重要参考意义。     

Analysis of phase transformation from austenite to martensite in NiTi alloy strips under uniaxial tension

Phase transformation from austenite to martensite in NiTi alloy strips under the uniaxial tension has been observed in experiments and numerically simulated as a localized deformation.This work presents an analysis using the theory of phase transfor- mation.The jump of deformation gradient across the interface between two phases and the Maxwell relation are considered.Governing equations for the phase transformation are derived.The analysis is reduced to finding the minimum value of the loading at which the governing equations have a unique,real and physically acceptable solution.The equa- tions are solved numerically and it is verified that the unique solution exists definitely. The Maxwell stress,the stresses and strains inside both anstenite and martensite phases, and the transformation-front orientation angle are determined to be in reasonably good agreement with experimental observations.     

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（0.000 5～15 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。