Numerical simulation of martensitic phase transitions in shape memory alloys using an improved integration algorithm

The numerical simulation of structures made of shape memory materials is of increasing interest in different fields. Among others, the computation of pipe connectors or medical devices like endoscopic instruments and stents is a challenge. In such practical applications the pseudoelastic effect as well as the one‐way and two‐way shape memory effects are utilized. These material properties are caused by martensitic phase transitions between austenite and martensite. In the present contribution, a recently proposed constitutive theory is numerically treated in the context of the finite element method. This constitutive theory is formulated in the framework of continuum thermomechanics for geometrically linear problems and is able to represent the occurring martensitic phase transitions in shape memory alloys. For the numerical integration of the evolution equations, the backward Euler method is applied. In spite of the complexity of the constitutive theory, it is shown that an improved integration procedure can be formulated, which merely involves the solution of three non‐linear equations for three scalar‐valued unknown variables. Numerical examples show the capability of the proposed model and the improved integration algorithm. Copyright © 2006 John Wiley & Sons, Ltd.     

形状记忆合金超弹性本构关系的神经网络模型

通过试验，研究了受过循环变形、具有稳定超弹性变形性能的形状记忆合金丝在拉伸到不同应变幅值条件下卸载的超弹性变形行为。根据试验测得的结果，提出了基于神经网络的形状记忆合金超弹性本构关系模型，并把模型计算的结果和实验数据进行了比较分析，结果表明，该模型具有很高的精度。该模型避免了已有模型在参数确定上的困难，具有一定的工程应用价值，为建立形状记忆合金本构模型提供了一个新的思路。     

超弹性形状记忆合金的神经网络连续本构模型

对超弹性形状记忆合金(SMA)丝在不同应变幅值和荷载速率下进行加卸载单轴拉伸试验,分析其滞回特性随环境因素的变化规律。将径向基函数神经网络(RBFNN)和Graesser模型结合起来,Graesser模型参数取自试验曲线,能由数学式确定的模型参数和应变幅值、荷载速率一起作为网络的输入信息,不能由数学式确定的模型参数作为输出神经元。数值计算表明,RBFNN可以精确地预测Graesser模型参数,且计算的SMA应力-应变曲线与Graesser模型结果吻合很好。     

Be、Ni元素对Cu-Al系形状记忆合金性能的影响研究

利用Bridgemen定向凝固炉制备了不同成分的Cu-Al系形状记忆合金单晶.并对其形状记忆特性进行了系统分析.结果表明,Be元素与Ni元素同时添加的Cu-Al-Ni-Be形状记忆合金单晶具有比单独添加Be元素或Ni元素的合金单晶更优越的性能.Ni与Be元素的同时加入导致固溶淬火组织的变化,对改善合金形状记忆性能起了交互加强的作用.     

基于塑性理论的形状记忆合金本构模型、试验和数值模拟

通过拉伸试验,研究了超弹性形状记忆合金（SMA）丝在不同应变幅值反复加卸载条件下的滞回变形行为。在测得试验数据的基础上,针对目前广泛使用的SMA Graesser＆Cozzarelli模型仅描述了小应变情况下SMA特性,而在大应变下SMA马氏体的硬化特性不能得到描述的问题,提出了修正的SMA本构模型,并把模型拟合结果和实验数据进行了比较分析。结果表明,模型数值拟合结果和试验数据吻合很好,可以很好地描述SMA在不同应变幅值下的应力-应变关系;且模型形式简单,概念明确,参数容易得到,具有一定的工程应用价值。     

A physical mechanism based constitutive model for temperature-dependent transformation ratchetting of NiTi shape memory alloy: One-dimensional model

In this paper, the effect of test temperature on the transformation ratchetting of super-elastic NiTi shape memory alloy was first investigated in the cyclic tension-unloading tests. It is shown that all the residual strain, dissipation energy, the start stress of martensite transformation and their evolutions during the cyclic loading depend greatly upon the test temperature. Based on the experimental observations, a new one-dimensional constitutive model is constructed by considering two different inelastic deformation mechanisms (i.e., martensite transformation and transformation-induced plasticity). The proposed model employs a new evolution rule of transformation-induced plasticity which considers the physical mechanism of the plastic deformation, i.e., the dislocation slipping in the austenite phase near the austenite–martensite interfaces. Furthermore, the interaction between dislocation and martensite transformation is also taken into account in the proposed model. The capability of the proposed model to predict the uniaxial temperature-dependent transformation ratchetting of NiTi shape memory alloy is verified by comparing the predictions with the experimental data.     

Trust‐region based return mapping algorithm for implicit integration of elastic‐plastic constitutive models

A new method for the solution of the non‐linear equations forming the core of constitutive model integration is proposed. Specifically, the trust‐region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic‐plastic models. Although attention here is restricted to these rate‐independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non‐quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared with other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared with existing algorithms. Through these efforts, it is shown that the utilization of a trust‐region approach leads to superior performance versus a traditional closest‐point projection Newton–Raphson method and comparable speed and robustness to a line search augmented scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

形状记忆合金-玻璃纤维/环氧树脂复合材料在振动边界条件下的低速冲击数值模拟

采用有限元方法（FEM）研究了振动边界条件对形状记忆合金（SMA）-玻璃纤维/环氧树脂复合材料的抗低速冲击性能的影响。在数值模拟过程中,将改进的三维Hashin失效准则和Brinson模型分别应用于玻璃纤维/环氧树脂复合材料层合板和SMA,以表征其本构关系。首先通过与固定边界条件下的SMA-玻璃纤维/环氧树脂复合材料板低速冲击实验进行比较,验证了数值模拟过程中所用模型及材料参数的准确性。其次,在模拟过程中,应用了包含不同振幅的一系列振动边界条件,对其进行模拟,揭示了振动边界条件对其抗低速冲击性能的影响。数值模拟结果表明,在大振幅条件下,无SMA复合材料的抗冲击性能比小振幅条件下弱;在相同振动边界条件下,SMA-玻璃纤维/环氧树脂复合材料与无SMA复合材料相比,其抗低速冲击性能提高。      

Tensile properties of a Fe-32Mn-6Si shape memory alloy

The tensile properties of a Fe-32Mn-6Si shape memory alloy were investigated. It was found that tensile properties depend on temperature, heat treatment and material structure. The relationships of martensitic transformation, tensile properties, and shape memory effect are discussed. Finally, we propose a macroscopic one-dimensional constitutive law describing the thermomechanical behavior in tensile loading. Numerically obtained results are close to the experimental ones. __________ Translated from Problemy Prochnosti, No. 2, pp. 55–65, March–April, 2008.     

形状记忆合金超弹性分段线性模型及其阻尼特性

建立简单有效的本构关系模型是形状记忆合金（SMA）工程应用和理论分析的一个必要条件。考虑相变过程中马氏体含量的影响,对SMA非线性本构关系进行简化,建立了SMA超弹性应力应变关系的分段线性模型。以此为基础,给出了损耗因子等特性参数计算表达式,并探讨了特性参数随应变幅值、温度等变化的规律,最后应用于一种常见的振动模型,考察了影响其隔振性能的因素。结果表明：应变幅值是影响SMA耗能能力的主要因素;并联弹簧的刚度会对SMA的作用效果产生影响。     

Theoretical analysis of a functionally graded shape memory alloy plate under graded temperature loading

As a new kind of functional material, functionally graded shape memory alloy (FG-SMA) possesses the excellent properties of both shape memory alloy (SMA) and functionally graded material (FGM). By combining the heat conduction theory with the theory of the mechanics of composite materials, a macro constitutive model, which can be used to describe the mechanical behavior of FG-SMA under graded temperature loading, is established. With this macro constitutive model, the thermo-mechanical properties of an FG-SMA plate, which is composed by ceramic and SMA and subjected to different surface temperature loads, are investigated. The theoretical results show good agreement with the existing data, which indicates that the macro constitutive model provided here is valid. The obtained results show that the martensite transformation does not always happen first at the top or bottom of the plate, and it is dependent on the surface temperatures. It can also be found that the stress decreases markedly due to the martensite transformation. This research can provide a basis for the design and in-depth investigation of FG-SMA material.     

A robust model of pseudoelasticity in shape memory alloys

A model of pseudoelasticity in shape memory alloys is developed within the incremental energy minimization framework. Three constitutive functions are involved: the Helmholtz free energy and rate‐independent dissipation that enter incrementally the minimized energy function, and the constraint function that defines the limit transformation strains. The proposed implementation is based on a unified augmented Lagrangian treatment of both the constitutive constraints and nonsmooth dissipation function. A methodology for easy reformulation of the model from the small‐strain to finite‐deformation regime is presented. Finite element computations demonstrate robustness of the finite‐strain version of the model and illustrate the effects of tension–compression asymmetry and transversal isotropy of the surface of limit transformation strains. Copyright © 2012 John Wiley & Sons, Ltd.     

功能梯度形状记忆合金复合梁的力学行为

功能梯度形状记忆合金（Functionally graded shape memory alloy,FGSMA）兼具功能梯度材料和形状记忆合金材料的双重特性,广泛应用于微机电、航空航天等工程领域。为研究FGSMA复合梁的弯曲行为,本文对形状记忆合金（SMA）力学本构方程进行简化处理,并根据复合材料层合板理论建立了FGSMA复合梁的力学模型,据此研究了SMA体积分数沿厚度方向呈线性变化的FGSMA悬臂梁内SMA纤维铺设角度对悬臂梁横截面应变、中面轴向位移、中性面高度和相变层高度的影响以及悬臂梁中面应变、曲率、SMA马氏体相变临界层高度和中性面高度随弯矩载荷的变化规律。研究结果表明:在弯矩载荷作用下,悬臂梁中性面位置与中面位置不重合,且悬臂梁上下层SMA马氏体相变临界层位置不对称;截面轴向应变绝对值随铺设角度增大而增大,截面纵向应变绝对值随铺设角度增大先增大后减小,中面轴向位移随铺设角度增大先增大后减小;随着铺设角度增大,悬臂梁中性面高度逐渐增大,拉伸状态下相变结束临界层高度先减小后增大,压缩状态的趋势相反;随着弯矩载荷绝对值逐渐增大,中性面位置高度表现出先稳定后减小然后逐渐增大的趋势,相变临界层逐渐向中性面位置靠拢;中面正应变和挠曲率随着弯矩载荷绝对值逐渐增大而发生变化,且变化率先增大后减缓。      

Structural evolution of magnetron sputtered shape memory alloy Ni-Ti films

Near equiatomic and Ti-rich Ni-Ti polycrystalline films have been deposited by magnetron co-sputtering using a chamber installed at a synchrotron radiation beamline. The in situ X-ray diffraction studies enabled the identification of different steps of the structural evolution during film processing.The depositions on a 140 nm amorphous SiO₂ buffer layer heated at 520 °C (without applying bias voltage, V_b, to the substrate) led to a preferential growth of <100> oriented grains of the Ni-Ti B2 phase from the beginning of film growth until the end of the deposition. Films exhibiting a preferential growth of <110> oriented grains of the Ni-Ti B2 phase from the beginning of the deposition were obtained (without and with a V_b of −45 V) by using a TiN coating with a topmost layer formed by <111> oriented grains. Those trends have been observed for the growth of near equiatomic (≈50.0 at.% Ti-Ni) and Ti-rich (≈50.8 at.% Ti-Ni) Ni-Ti films.Additionally, an ion gun had been commissioned, which allows ion bombardment during sputter deposition or post-deposition ion irradiation. In this first series of experiments, a Ni-Ti film was irradiated with He ions after deposition (without exposing the film to the atmosphere, i.e., avoiding surface oxide formation), thus modifying deliberately the microstructure of the film locally.     

考虑加/卸载速率影响的Ti-Ni形状记忆合金简化本构模型

系统研究了Ti-Ni形状记忆合金丝(SMA)应力-应变曲线、特征点应力、耗能能力、等效阻尼比随材料直径、应变幅值、加载速率、加载循环次数的变化规律;针对SMA唯象Brinson本构模型无法描述SMA动态力学性能的缺点,结合前述试验结果,提出了一种可考虑加/卸载速率影响的SMA简化本构模型。应用该模型对试验用SMA丝进行模拟,所得应力-应变曲线各特征点平均误差仅为3%,结果表明:所建立的速率相关SMA简化本构模型可较为精确地描述SMA在应力诱发相变过程中的超弹性力学行为,同时可反映加/卸载速率和应变幅值等主要因素对其动力本构模型的影响;该模型结构形式简单,具有较好的工程应用前景。     

An analytical model for the vibration of a composite plate containing an embedded periodic shape memory alloy structure

This paper explores the integration of a periodic repeating arrangement of shape memory alloy (SMAs) within a composite plate, with a view to active control of the vibrations of the plate by means of a controllable activation strategy for the SMA elements. The benefits of this configuration are that ‘antagonistic’ operation of SMAs on the plate allows the significantly longer cooling time constant of previously activated elements to be shortened by means of active elements working against them during that phase. This concept dramatically shortens the cooling time constant and brings it into the same order of magnitude of the heating phase. The paper examines the mathematical modelling of such a plate, and offers an approximate analytical solution by means of a hybrid WKB–Galerkin method. The antagonistic operation of the system is represented mathematically by terms in which the stiffness and damping are both time dependent. Therefore the equation of motion contains terms with time variant coefficients and is impossible to solve without recourse to specialised methods. Comparisons with numerical methods are given and it is shown that good similarity can be obtained for judicious choice of practical values for the time variant stiffness and damping functions.     

NiTiHf高温形状记忆合金的相变行为和形状记忆效应

利用透射电镜、X射线衍射仪和示差热分析仪系统分析了Ni49Ti36Hf15合金的相变行为及其形状记忆效应。结果表明，Ni49Ti36Hf15合金的热马氏体变体间构成典型的自协作组态，主要呈矛头状、镶嵌块状和楔状3种形态，亚结构主要为（001）复合孪晶。随着热循环次数的增加，相变温度降低，经50次热循环后，相变温度随热循环次数增加变化趋势不明显。固溶处理Ni49Ti36Hf15合金在20－184℃范围内弯曲变形时，呈现良好的形状记忆效应，其最大可恢复应变可达3％。形状恢复率随着弯曲变形温度的增加而下降，当弯曲变形温度大于317℃时，形状恢复率下降为0。     

Optimal design of a variable-twist proprotor incorporating shape memory alloy hybrid composites

The tiltrotor blades, or proprotor, act as a rotor in the helicopter mode and a propeller in the airplane mode. The helicopter mode generally requires relatively a low built-in twist angle, whereas in the airplane mode, a high built-in twist is desired. Meeting these rather conflicting requirements make the tiltrotor design a challenging task. This paper explores an optimal design of a variable-twist proprotor that changes the built-in twist in an adaptive manner by using the shape memory alloy hybrid composite (SMAHC). The optimum design problem attempts to find the cross-section internal layout that maximizes the twist actuation of the variable-twist proprotor while satisfying a series of design constraints. An optimum design framework is constructed in the current work by combining various analysis and design tools, such as an active composite cross-sectional analysis, a nonlinear flexible multibody dynamics analysis, a 3-D strain analysis, and a gradient-based optimizer. The MATLAB is used to integrate and synthesize the individual tools. A static tip twist is chosen as an objective function that should be maximized for the best performance. The optimum results exhibit that the twist actuation of the variable-twist proprotor can be maximized while satisfying all the prescribed design constraints.