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.     

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.     

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.     

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,细晶粒区域表现为均匀相变的特点, 即无局部马氏体带产生; 此外,在超弹性和形状记忆过程中,马氏体相变和重取向都首先在较粗晶粒区域开始并逐步向细晶粒区域传播,而逆相变则相反.马氏体相变和重取向的逐步扩展使梯度纳米晶NiTi合金的应力-应变和应变-温度曲线呈现出“硬化状”,其可归因于纳米多晶NiTi合金中马氏体相变对晶粒尺寸的依赖性,即随着晶粒尺寸的减小, 相变或重取向壁垒逐渐增大,马氏体相变或重取向的形核、扩展越来越困难. 可见,梯度纳米晶结构具有比传统均匀晶粒尺寸NiTi合金更宽的相变应力区间、重取向应力区间和相变温度区间,可显著提高该合金非弹性变形的可控性.      

Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel: Damage evolution and damage-coupled visco-plastic constitutive model

Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel were observed by the tests under the uniaxial stress-controlled cyclic loading with non-zero mean stress [G.Z. Kang, Y.J. Liu, Mater. Sci. Eng. A 472 (2008) 258–268]. Based on the obtained experimental results, the evolution features of whole-life ratcheting behavior and low-cycle fatigue (LCF) damage of the material were discussed first. Then, in the framework of unified visco-plasticity and continuum damage mechanics, a damage-coupled visco-plastic cyclic constitutive model was proposed to simulate the whole-life ratcheting and predict the fatigue failure life of the material presented in the uniaxial stress cycling with non-zero mean stress. In the proposed model, the damage was divided into two parts, i.e., elastic damage and plastic damage, which were described by the evolution equations with the same form but different constants, since the maximum applied stresses in most of loading cases were lower than the nominal yielding strength of the material. The ratcheting of the material was still described by employing a nonlinear kinematic hardening rule based on the Abdel-Karim–Ohno combined kinematic hardening model [M. Abdel Karim, N. Ohno, Int. J. Plast. 16 (2000) 225–240] but extended by considering the effect of damage. The maximum strain criterion combined with an elastic damage threshold was employed to determine the failure life of the material caused by two different failure modes, i.e., fatigue failure (caused by low-cycle fatigue due to plastic shakedown) and ductile failure (caused by large ratcheting strain). The simulated whole-life ratcheting behavior and predicted failure life of tempered 42CrMo steel are in a fairly good agreement with the experimental ones.     

考虑塑性应变记忆恢复的循环棘轮本构模型研究

在统一粘塑性循环本构理论框架下,以Ohno-Abdel-Karim非线性随动硬化模型为基础,建立了一个循环本构模型。模型通过引入塑性应变幅值记忆效应,并在塑性应变记忆项中加入恢复系数,提高了对循环硬化材料单轴棘轮行为的预言能力。将模型应用于316L不锈钢单轴棘轮行为的描述中,模拟不同平均应力、应力幅值下的棘轮应变,均与实验数据吻合较好,证明本文改进的本构模型能合理地描述循环硬化材料的单轴棘轮行为。     

调质42CrMo钢的棘轮-疲劳交互作用及其耦合损伤粘塑性本构模型

对调质42CrMo钢的棘轮-疲劳交互作用的实验结果进行了分析,揭示了材料在非对称应力循环下的全寿命棘轮变形特征和低周疲劳损伤演化特性.在统一粘塑性循环本构模型框架下,基于连续损伤力学理论,提出一个耦合损伤的牯塑性本构模型.该模型中将损伤分为宏观弹性损伤和塑性损伤两部分,并采用不同的损伤演化方程来描述这两类损伤.针对材料不同的失效模式,分别采用损伤变量门槛值和最大应变作为失效判据.将模型应用于调质42CrMo钢单轴应力循环下全寿命棘轮行为的描述和低周疲劳寿命预测中,模拟结果和实验结果吻合较好.     

Macro versus micro-scale constitutive models in simulating proportional and nonproportional cyclic and ratcheting responses of stainless steel 304

A recent study by Hassan et al. [Hassan, T., Taleb, L., Krishna, S., 2008. Influences of nonproportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plasticity, 24, 1863–1889.] demonstrated that some of the nonproportional ratcheting responses under stress-controlled loading histories cannot be simulated reasonably by two recent cyclic plasticity models. Two major drawbacks of the models identified were: (i) the stainless steel 304 demonstrated cyclic hardening under strain-controlled loading whereas cyclic softening under stress-controlled loading, which depends on the strain-range and which the existing models cannot describe; (ii) the change in biaxial ratcheting responses due to the change in the degree of nonproportionality were not simulated well by the models. Motivated by these findings, two modified cyclic plasticity models are evaluated in predicting a broad set of cyclic and ratcheting response of stainless steel 304. The experimental responses used in evaluating the modified models included both proportional (uniaxial) and nonproportional (biaxial) loading responses from Hassan and Kyriakides [Hassan, T., Kyriakides, S., 1994a. Ratcheting of cyclically hardening and softening materials. Part I: uniaxial behavior. Int. J. Plasticity, 10, 149–184; Hassan, T., Kyriakides, S., 1994b. Ratcheting of cyclically hardening and softening materials. Part II: multiaxial behavior. Int. J. Plasticity, 10, 185–212.] and Hassan et al. [Hassan, T., Taleb, L., Krishna, S., 2008. Influences of nonproportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plasticity, 24, 1863–1889.] The first model studied is a macro-scale, phenomenological, constitutive model originally proposed by Chaboche et al. [Chaboche, J.L., Dang-Van, K., Cordier, G., 1979. Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. In: Proceedings of the Fifth International Conference on SMiRT, Div. L, Berlin, Germany, L11/3.]. This model was systematically modified for incorporating strain-range dependent cyclic hardening–softening, and proportional and nonproportional loading memory parameters. The second model evaluated is a polycrystalline model originally proposed by Cailletaud [Cailletaud, G., 1992. A micromechanical approach to inelastic behavior of metals. Int. J. Plasticity, 8, 55–73.] based on crystalline slip mechanisms. These two models are scrutinized against simulating hysteresis loop shape, cyclic hardening–softening, cross-effect, cyclic relaxation, subsequent cyclic softening and finally a broad set of ratcheting responses under uniaxial and biaxial loading histories. The modeling features which improved simulations for these responses are elaborated in the paper. In addition, a novel technique for simulating both the monotonic and cyclic responses with one set of model parameters is developed and validated.     

SUPER-ELASTIC CONSTITUTIVE MODEL CONSIDERING PLASTICITY AND ITS FINITE ELEMENT IMPLEMENTATION

Based on the experimental results of super-elastic NiTi alloy, a three-dimensional super-elastic constitutive model including both of stress-induced martensite transformation and plasticity is constructed in a framework of general inelasticity. In the proposed model, transformation hardening, reverse transformation of stress-induced martensite, elastic mismatch between the austenite and martensite phases, and temperature-dependence of transformation stress and elastic modulus of each phase are considered. The plastic yielding of martensite occurred under high stress is addressed by a bilinear isotropic hardening rule. Drucker-Prager-typed transformation surfaces are employed to describe the asymmetric behavior of NiTi alloy in tension and compression. The prediction capability of the proposed model is verified by comparing the simulated results with the correspondent experimental ones. Based on backward Euler＇s integration, a new expression of consistent tangent modulus is derived. The proposed model is then implemented into a finite element package ABAQUS by user-subroutine UMAT. Finally, the validity of such implementation was verified by some numerical samples.     

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

本文基于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）,超弹性性能越差;而晶粒取向分布范围越窄、晶粒间取向差越小（织构越强）,超弹性性能越好。该晶粒取向依赖性可解释为：由于晶粒取向的不同,马氏体相变过程中相邻晶粒间的变形不匹配程度不同,因此,多晶模型中在所研究的参数变化范围内,晶粒间取向差异越大,晶界处的变形失配越严重,由此而产生的局部内应力将阻碍其附近马氏体相变的扩展,进而导致纳米多晶NiTi形状记忆合金超弹性性能下降。     

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。     

Study on cyclic deformation and fatigue of thermal and magnetic shape memory alloys

形状记忆合金(包括热致和磁致形状记忆合金)由于其特有的超弹性和形状记忆效应, 一直以来受到学者和工程界人士广泛关注, 且已有诸多成功的工程应用案例.为了进一步拓展该类合金的工程应用范围, 对其热--力和磁--力耦合循环变形和疲劳失效行为的宏微观实验观察和理论模型研究成果进行了综述. 总结了NiTi和NiTiX两类合金材料的温度诱发(即热致)的热--力耦合循环变形和疲劳失效行为研究的最新成果; 对以NiMnGa合金为代表的磁场诱发(即磁致)的磁--力耦合循环变形和疲劳失效行为的研究现状进行了评述; 提出并预测了未来的研究方向及发展趋势.     

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。     

Stress-induced transformation behavior of a polycrystalline NiTi shape memory alloy: micro and macromechanical investigations via in situ optical microscopy

An experimental investigation of the micro and macromechanical transformation behavior of polycrystalline NiTi shape memory alloys was undertaken. Special attention was paid to macroscopic banding, variant microstructure, effects of cyclic loading, strain rate and temperature effects. Use of an interference filter on the microscope enabled observation of grain boundaries and martensitic plate formation and growth without recourse to etching or other chemical surface preparation. Key results of the experiments on the NiTi include observation of localized plastic deformation after only a few cycles, excellent temperature and stress relaxation correlation, a refined definition of “full transformation” for polycrystalline materials, and strain rate dependent effects. Several of these findings have critical implications for understanding and modeling of shape memory alloy behavior.     

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。     

热致和磁致形状记忆合金循环变形和疲劳行为研究

形状记忆合金(包括热致和磁致形状记忆合金)由于其特有的超弹性和形状记忆效应, 一直以来受到学者和工程界人士广泛关注, 且已有诸多成功的工程应用案例.为了进一步拓展该类合金的工程应用范围, 对其热--力和磁--力耦合循环变形和疲劳失效行为的宏微观实验观察和理论模型研究成果进行了综述. 总结了NiTi和NiTiX两类合金材料的温度诱发(即热致)的热--力耦合循环变形和疲劳失效行为研究的最新成果; 对以NiMnGa合金为代表的磁场诱发(即磁致)的磁--力耦合循环变形和疲劳失效行为的研究现状进行了评述; 提出并预测了未来的研究方向及发展趋势.      

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。     

316L不锈钢随动强化模型改进研究

本文对316L不锈钢进行了单轴与多轴非比例路径下的应力控制棘轮试验,考察了应力幅值、平均应力和加载历程对棘轮特性的影响。同时进行了应变控制循环试验以研究材料的应力松弛特性。试验结果表明轴向棘轮效应在对称剪切荷载下效果明显,同时棘轮应变随应力幅值和平均应力的增加而增加。研究了Chen-Jiao随动强化模型与Jiang-Sehitoglu随动强化模型采用的单轴与多轴参数对背应力分量增量方向的影响,将Chen-Jiao模型中的多轴系数替换为界面饱和率,并在此基础上引入新的参数对塑性模量系数进行修正,计算结果表明修正后的模型能提升应力控制下多轴棘轮的预测精度,并能很好的预测应力松弛现象,表明了新模型的正确性与有效性。     

Cyclic viscoelastoplasticity and low-cycle fatigue of polymer composites

Observations are reported on a polymer composite (polyamide-6 reinforced with short glass fibers) in tensile relaxation tests with various strains, tensile creep tests with various stresses, and cyclic tests with a stress-controlled program (ratcheting with a fixed maximum stress and various minimum stresses). Constitutive equations are developed in cyclic viscoelastoplasticity of polymer composites. Adjustable parameters in the stress–strain relations are found by fitting observations in relaxation tests and cyclic tests (16 cycles of loading–unloading). It is demonstrated that the model correctly predicts experimental data in creep tests and dependencies of maximum and minimum strains per cycle on number of cycles up to fatigue fracture of specimens. The influence of strain rate and minimum stress on number of cycles to failure is studied numerically.     

Uniaxial ratcheting of SS304 stainless steel at high temperatures: visco-plastic constitutive model

The uniaxial ratcheting of SS304 stainless steel at high temperatures (300, 600 and 700 °C) were analyzed experimentally, and described by a cyclic constitutive visco-plasticity model. The rate dependence of the material was accounted for by introducing a viscous term. The cyclic hardening and cyclic flow behavior of the material under asymmetrical stress-controlled cycling were described by the evolution rules of kinematic hardening back stress and isotropic deforming resistance. Under the isothermal condition, temperature effect was included by terms involving temperature in the evolution equations of isotropic deforming resistance. The effect of load history on ratcheting was also considered by introducing a fading memory function of the maximum inelastic strain amplitude and isotropic deformation resistance. After the material constants were determined from the experimental data, the uniaxial ratcheting of SS304 stainless steel was numerically simulated and compared with the corresponding experimental results at high temperatures. The predicted results agree well with the experimental ones.