功能梯度形状记忆合金纳米梁力学性能研究

功能梯度形状记忆合金(Functionally Graded Shape Memory Alloys, FG-SMA)兼具功能梯度材料和形状记忆合金的双重特性,故在航空航天、生物医疗、微机电系统(Micro Electro Mechanical System, MEMS)中得到了广泛的应用。当微结构尺度达到纳米尺度,表面效应对微结构力学性能的影响是十分显著的。为了探究表面效应对功能梯度形状记忆合金纳米梁力学性能的影响规律,基于梁弯曲理论及Gurtin-Murdoch表面弹性理论,考虑拉压不对称、温度对FG-SMA纳米梁的影响,建立了考虑表面效应的FG-SMA纳米梁相变力学模型。分析了梯度指数、载荷、温度及拉压不对称系数对FG-SMA纳米梁力学性能的影响规律。研究表明,弯矩、梯度指数对截面响应影响显著,而温度和拉压不对称系数对其影响较小;忽略表面效应的影响会低估FG-SMA纳米梁的抗弯性;在弯矩达到一定程度后,表面效应对FG-SMA纳米梁中性轴偏移趋势影响不大。研究结果对FG-SMA纳米梁在微机电领域的设计及应用提供了一定的基础与依据。     

含形状记忆合金(SMA)层柔性梁的振动频响特性

主要研究具有形状记忆合金（shape memory alloy,SMA）层的梁结构的动力响应特性，重点分析了应力诱发马氏体相变的影响。首先采用SMA超弹性分段线性的应力－应变模型表示SMA的超弹性本构特征；其次借助有关粘弹性材料结构动力学分析的复模量方法，推出简谐激励作用下SMA层的面内变形和应力之间的关系，提出具有SMA表层的简支梁横向稳态频率响应求解的数学模型。SMA超弹性非线性的影响使得结构产生复杂的动力学特征，如存在多值稳态解、跳跃性、周期3响应等。上述现象的发生与激振力幅值、温度的变化密切相关。     

计及不同剪切变形的功能梯度材料梁的弯曲分析

研究矩形截面功能梯度材料(Functionally graded materials,FGM)梁在不同剪切变形理论下的静力弯曲问题。假设FGM梁由金属和陶瓷两种材料构成,其等效物性参数沿厚度方向连续变化,且遵从简单幂率变化规律。基于最小势能原理,建立以轴向位移、横向位移及转角为未知函数的FGM梁的运动微分方程组。对简支FGM梁,采用Fourier级数法获得5种剪切变形理论下FGM梁的挠度、轴向位移及转角曲线,分析梁的长高比、梯度指标对弯曲变形的影响,分析不同剪切变形理论下FGM梁的切应力和正应力的分布特性,并与均质材料梁的静力弯曲特性进行比较。给出FGM梁的中性轴位置随梯度指标的变化曲线并进行分析。     

热-机载荷下形状记忆合金梁的力学模型及其求解

在现有的形状记忆合金(Shape memory alloy,SMA)简化模型的基础上,结合温度与相变临界应力的关系,从应变角度出发,提出一种形式简单、物理意义更加明确且能反应SMA在热-机载荷下力学行为的分段线性模型。基于Bernoulli-Euler梁理论,利用SMA分段线性模型,建立SMA梁非线性弯曲过程中弯矩与曲率关系的力学模型。结合SMA梁力学模型,设计一套简便易行的求解流程,分别对纯弯曲和受均布载荷的简支梁进行数值求解,分析梁截面上应力分布、弯矩与挠度关系、记忆因子的变化等。结果显示建立的SMA分段线性模型能有效描述热-机载荷下SMA的力学行为,可建立简单有效的SMA结构的力学模型,更便于工程应用和理论分析。     

形状记忆合金超弹性缆索力学行为的有限单元法

由于涉及材料和接触双重非线性问题,很难建立描述形状记忆合金(Shape memory alloy,SMA)超弹性缆索力学行为的理论模型,为了克服试验成本高和易受环境因素影响的缺点,基于形状记忆因子概念和SMA本构模型,推导了适于有限单元法的增量型SMA本构模型。利用ABAQUS二次开发功能,考虑相变过程中SMA弹性模量的变化,编写了SMA用户材料子程序,实现了SMA超弹性缆索力学行为的有限元单元法。利用建立的有限单元法对SMA超弹性缆索的相变和力学行为进行数值模拟,并将数值结果与文献中试验结果进行了对比验证,在此基础上,分析了SMA超弹性缆索外线股螺距对缆索整体力学行为的影响。计算结果及其与试验结果的对比表明,提出的有限单元法能有效描述和预测SMA超弹性缆索在拉伸过程中的相变和力学行为,SMA超弹性缆索外线股轴线螺距对缆索整体相变和力学行为有明显影响,研究工作可为SMA超弹性缆索设计及工程应用提供计算方法与技术指导。     

形状记忆合金梁的非线性弯曲变形

形状记忆合金(Shape memory alloy,SMA)梁作为一种新型智能元件,在工程领域的应用日益广泛。基于实测的形状记忆合金材料应力-应变关系曲线及梁的大变形理论,同时考虑SMA材料拉压力学性能的不对称性及简支端移动等因素,建立形状记忆合金梁非线性弯曲变形的控制方程,并采用打靶法、辛普森数值积分等方法对方程进行数值求解。通过梁在不同载荷条件下的挠曲线以及最大挠度—弯矩曲线,分析材料非线性、几何非线性及简支端移动3个因素对SMA超弹性梁弯曲变形的影响规律。结果表明:梁中性层位置随弯矩变化;弯矩较小时,材料性能是线性的,几何非线性及简支端移动对梁的弯曲变形几乎不产生影响;弯矩较大时,材料性能是非线性的,几何非线性及简支端移动对梁的弯曲变形产生明显影响。     

NiTiNb记忆合金热力学性能的试验及其唯象本构模型

现有形状记忆合金(Shape memory alloy, SMA)管接头数值分析中没有考虑塑性变形及其影响,基于不可逆热力学框架,考虑塑性变形对逆向马氏体相变的影响,构建相变和塑性耦合的NiTiNb SMA唯象学本构模型,基于有限元软件ABAQUS二次开发功能,编译用户自定义子程序,对SMA热机耦合作用过程进行数值模拟,并与NiTiNb合金低温下的拉伸和约束升温性能试验研究结果对比。结果表明,数值分析结果能够很好地描述试验所得的应力应变曲线和升温过程的应力温度曲线特征,能够描述材料预变形提高逆向马氏体相变温度的规律,得到低温变形及升温恢复过程中材料内部Mises应力、等效相变应变和等效塑性应变的演化规律。结果表明数值仿真与试验取得了较好的一致性,为进一步的SMA管接头装配性能模拟及设计优化奠定基础。     

形状记忆合金线性驱动器的设计及位移特性分析

为克服传统带有偏置装置形状记忆合金驱动器结构复杂、响应速度慢的缺点,利用形状记忆合金(Shape memory alloy,SMA)的单程形状记忆效应,设计并制造一种不带偏置装置且可实现双程运动的线性驱动器,该驱动器由两根形状记忆合金丝、滑轮、部件、导轨、支座及固定螺钉组成。接着基于Brinson一维本构方程及转换方程,推导出两根SMA丝在不同条件下的应变表达式;提出将马氏体相变应力看作体力,分析温度变化与驱动器位移的关系及外载荷变化对驱动器最大位移的影响。对计算结果进行试验验证,结果表明,所设计驱动器可实现往复双程运动;随着SMA丝温度的升高所获得的位移呈非线性增大,当温度超过奥氏体转变结束温度Af,位移达到最大,而初始化过程获得的最大位移为正常运动的一半;增大载荷,驱动器的最大位移逐渐减小,当载荷达到51.0 N时,驱动器停止运动,即位移减小为零。     

形状记忆合金三维鼓包结构热变形的有限元模拟

基于Lagoudas唯象本构关系模型,利用ABAQUS软件二次开发功能,编写出可用于描述形状记忆合金(SMA)特性的UMAT材料子程序,并对SMA三维鼓包结构的热力学特性进行了有限元分析。结果表明:该子程序能够较好地描述SMA的超弹性和形状记忆效应特性;SMA三维鼓包结构能够产生较大的竖向挠度变形,并且鼓包大部分区域完成了马氏体逆相变,只在边界附近残留有部分马氏体相。     

基于三维本构模型的形状记忆合金弹簧力-位移关系研究

基于已有的研究成果,针对形状记忆合金(SMA)弹簧力-位移关系进行研究,提出了能够描述SMA滞回环宽度随应变幅值变化的三维本构模型,再结合弹簧基本力学性能,考虑弹簧丝截面上弯矩的影响,给出了超弹性SMA弹簧力-位移关系的数值仿真方法。此外,将本构模型编写成Abaqus用户材料子程序(UMAT),对SMA弹簧进行有限元分析。通过SMA弹簧的不同位移幅值加卸载试验,对模型进行了验证。结果表明,基于三维本构模型建立的超弹性SMA弹簧力-位移关系模型能较为准确地模拟不同幅值加载工况下弹簧的力学行为,为SMA弹簧的工程应用提供指导意义。     

A mathematical model for smart functionally graded beam integrated with shape memory alloy actuators

This paper presents a theoretical study of the thermally driven behavior of a shape memory alloy (SMA)/FGM actuator under arbitrary loading and boundary conditions by developing an integrated mathematical model. The model studied is established on the geometric parameters of the three-dimensional laminated composite box beam as an actuator that consists of a functionally graded core integrated with SMA actuator layers with a uniform rectangular cross section. The constitutive equation and linear phase transformation kinetics relations of SMA layers based on Tanaka and Nagaki model are coupled with the governing equation of the actuator to predict the stress history and to model the thermo-mechanical behavior of the smart shape memory alloy/FGM beam. Based on the classical laminated beam theory, the explicit solution to the structural response of the structure, including axial and lateral deflections of the structure, is investigated. As an example, a cantilever box beam subjected to a transverse concentrated load is solved numerically. It is found that the changes in the actuator’s responses during the phase transformation due to the strain recovery are significant.     

Interface crack of two dissimilar bonded functionally graded strips with arbitrary distributed properties under plane deformations

In this paper the plane elasticity problem of two bonded dissimilar functionally graded strips containing an interface crack with material properties varying arbitrarily is studied. The governing equation in terms of Airy stress function is formulated and exact solutions are obtained for several special variations of material properties in Fourier transformation domain. A multi-layered model is employed to model arbitrary variations of material properties based on two linear-distributed material compliance parameters. The mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. Some numerical examples are given to demonstrate the accuracy, efficiency and versatility of the model. Numerical results show that fracture behavior of materials can be greatly affected by graded variation of elastic modulus and the influence of the specific form of elastic modulus on the fracture behavior of FGM is limited.     

功能梯度材料应用在齿轮上的可行性分析

为解决齿轮热处理过程中存在畸变、齿根处弯曲应力增加、齿轮的寿命降低等问题,将功能材料技术应用到齿轮工作接触面处(简称功能梯度齿轮)。首先,开展了单质齿轮性能与单质齿轮热处理后性能的对比分析;然后,建立了单质圆柱渐开线齿轮模型与功能梯度材料圆柱渐开线齿轮模型,对其进行了弯曲应力有限元计算,并对其性能进行了对比分析。将未经热处理的单质齿轮作为桥梁,建立了单质齿轮热处理后的性能与功能梯度材料齿轮性能之间的关系。功能梯度材料不仅在轮齿表面硬度与齿根弯曲应力方面比热处理后的齿轮有更好的性能,而且能避免齿轮热处理过程中产生的畸变、渗碳层不均匀等缺陷。分析结果表明:将功能梯度材料应用到齿轮上是可行的。     

Layer-wise finite element analysis of functionally graded cylindrical shell under dynamic load

In this paper, a layer-wise finite element formulation is developed for the analysis of a functionally graded material (FGM) cylindrical shell with finite length under dynamic load. For this purpose, FGM cylinder is divided into many sub-layers and then the general layerwise laminate theory is formulated by introducing piecewise continuous approximations through the thickness for each state In this model the radial displacement is approximated linearly through each “mathematical” layer. The properties are controlled by volume fraction that is an exponential function of radius. The governing equations are derived from virtual work statement and solved by finite element method. The main contribution of the present study is to develop a discrete layerwise finite element for a 2-dimensional thick FGM cylindrical shell. Results are obtained for the time history of the displacement and stress components with different exponent “n” of functionally graded material. In addition, natural frequency and mean velocity of the radial wave propagation for different exponent “n” of functionally graded material (FGM) are studied and compared with similar ones currently obtained for FGM cylindrical shell of infinite length.     

Effect of functionally graded material on frictionally excited thermoelastic instability

Thermoelastic instability (TEI) is investigated focusing on the effect of functionally graded materials (FGM) where the FGM half plane slides against a homogeneous conducting or rigid non-conducting body at speed V. Results confirm analytically that there is maximum critical speeds occurring at a certain value of non-homogeneous parameter of FGM within a range of thermal conductivity, which was reported previously in the simulation model [Y.H. Jang, S.-H. Ahn, Frictionally-excited thermoelastic instability on functionally graded material, Wear 262 (2007) 1102–1112]. The effect of non-homogeneous parameters for FGM on thermoelastic instability shows that the non-homogeneous parameters of the elastic modulus and thermal expansion coefficient are strong influential factors. It is also found that when the non-homogeneous parameters of FGM range between two positive bounded values, unconditionally stable behavior is shown for a range of thermal conductivity.     

Finite Element Method on Shape Memory Alloy Structure and Its Applications

It is significant to numerically investigate thermo-mechanical behaviors of shape memory alloy(SMA) structures undergoing large and uneven deformation for they are used in many engineering fields to meet special requirements To solve the problems of convergence in the numerical simulation on thermo-mechanical behaviors of SMA structures by universal finite element software.This work suppose a finite element method to simulate the super-elasticity and shape memory effect in the SMA structure undergoing large and uneven deformation.Two scalars,named by phase-transition modulus and equivalent stiffness,are defined to make it easy to establish and implement the finite element method for a SMA structure.An incremental constitutive equation is developed to formulate the relationship of stress,strain and temperature in a SMA material based on phase-transition modulus and equivalent stiffness.A phase-transition modulus equation is derived to describe the relationship of phase-transition modulus,stress and temperature in a SMA material during the processes of martensitic phase transition and martensitic inverse phase transition.A finite element equation is established to express the incremental relationship of nodal displacement,external force and temperature change in a finite element discrete structure of SMA.The incremental constitutive equation,phase-transition modulus equation and finite element equation compose the supposed finite element method which simulate the thermo-mechanical behaviors of a SMA structure.Two SMA structures,which undergo large and uneven deformation,are numerically simulated by the supposed finite element method.Results of numerical simulation show that the supposed finite element method can effectively simulate the super-elasticity and shape memory effect of a SMA structure undergoing large and uneven deformation,and is suitable to act as an effective computational tool for the wide applications based on the SMA materials.     

Effects of gradient on stress distribution in rotating functionally graded solid disks

This paper presents the elastic analysis of a rotating sandwich solid disk composed of three-layered perfectly-bonded composites. The center and outer regions of the solid disk are two homogeneous isotropic media, and the middle region is a transition zone made of functionally graded materials (FGM). Two cases are considered. One is on FGM with power-law gradient. For this case, explicit expressions for full elastic fields are derived. The other is on FGM with any radial nonhomogeneity, for which an analytic approach is proposed to reduce the problem into a Fredholm integral equation. The validity of the latter method is ensured by comparing numerical results of the elastic fields with the exact ones for the case of power-law gradient. For a general case, the current study presents the influences of the gradient, width variation of the FGM, and rotational velocity on the distribution of the radial and hoop stresses for a rotating composite disk made of aluminum and zirconia. The method presented in this paper may help engineering designers in choosing appropriate gradients and materials to acquire the optimal state of a rotating functionally graded disk.     

Effect of the volume of a functionally graded material layer on frictionally excited thermoelastic instability

A finite element model is used to identify the effect of the volume of a functionally graded material (FGM) on thermoelastic instability (TEI). An optimal FGM volume that exhibits the highest critical speed was found to exist. Beyond the optimal FGM volume, the critical speed is much lower than that of a homogeneous steel layer. For all FGM volumes, the performance against TEI is dominant for the same nonhomogeneous parameter, which determines the compositional shape of the material property grading in the FGM. In addition, the thermal conductivity of the frictional material and the modulus of elasticity of the FGM were found to have the most significant impact on an increase in the critical speed.     

Postbuckling of shear deformable FGM cylindrical shells surrounded by an elastic medium

This paper presents a study on the postbuckling response of a shear deformable functionally graded cylindrical shell of finite length embedded in a large outer elastic medium and subjected to axial compressive loads in thermal environments. The surrounding elastic medium is modeled as a tensionless Pasternak foundation that reacts in compression only. The postbuckling analysis is based on a higher order shear deformation shell theory with von Kármán-Donnell-type of kinematic nonlinearity. The thermal effects due to heat conduction are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent. The nonlinear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the postbuckling response of the shells and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the shell and the elastic medium. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of FGM shells surrounded by an elastic medium of tensionless Pasternak foundation, from which the postbuckling results for FGM shells with conventional elastic foundations are also obtained for comparison purposes. The results reveal that the unilateral constraint has a significant effect on the postbuckling responses of shells subjected to axial compression in thermal environments when the foundation stiffness is sufficiently large.     

Thermally induced buckling of functionally graded hybrid composite plates

In this paper, thermal buckling analysis is performed on hybrid functionally graded plates (FGPs) with an arbitrary initial stress. The governing equations are derived using the average stress method, including the effect of transverse shear deformation. Then, an eigenvalue problem is formed to evaluate thermal buckling temperatures for simple supported initially stressed ceramic-FGM-metal plates. The effects of functionally graded material (FGM) layer thickness, volume fraction index, layer thickness ratio, thickness ratio, aspect ratio and initial stress on the thermal buckling temperature of hybrid FGPs are investigated. The results reveal that the volume fraction index, initial stresses and FGM layer thickness have significant influence on the thermal buckling of hybrid FGPs.