压电材料椭圆切口的力学分析

在线性压电本构方程框架下，用复势函数方法对椭圆切口模型进行了精确的数值计算。完整地考虑了各向异性力电耦合效应以及切口内不同电介质的介电性质。给出了切口内部不同介电性质对压电材料内部应力的影响。指出了Sosa文章里的一些计算错误。由于现在文献中很少有关于电导通边界条件下理论解的数值结果，所以本文同时提供了不同电边界条件下理论解的数值结果，所以本文同时提供了不同电边界条件下的理论解的数值结果。最后通过最小势能原理建立了8结点有限元模型，对椭圆切口问题进行了计算并与理论解进行了仔细比较。     

PZT-4紧凑拉伸试样的断裂分析

基于线性压电材料的复势理论,通过解析分析,导出了一种分析有限压电板裂纹问题的解析数值方法. 首先,计算了含中心裂纹有限板的断裂参数,与Woo和Wang的解析数值法(Int J Fract, 1993, 62: 203$\sim$218)相比较,表明该方法具有很高的精度和很好的计算效率. 随后,采用该方法和有限元法计算了PZT-4紧凑拉伸试样在绝缘裂纹面边界条件下断裂时的断裂参数,发现各断裂参数的临界值分散性很大,不能作为压电材料的单参数断裂准则. 进而,针对试样真实的裂隙形状,采用有限元法计算了裂隙尖端的应力、电位移场,比较了裂隙内介质的介电性能对裂隙尖端场的影响,计算了带微裂纹的真实裂隙模型的断裂参数并进行了理论分析.      

压电智能梁的阻抗分析与损伤识别

压电陶瓷具有正、逆压电效应,可以用作自驱动传感器．该文对表面粘贴有单片压电陶瓷的压电智能钢梁进行了阻抗分析．讨论了单压电片驱动下钢粱的纵向振动和弯曲振动,得到了压电智能梁的机械阻抗．介绍了压电片与基梁的机电耦合作用及基于压电阻抗技术的结构损伤识别机理．以两端自由钢梁为例对压电智能梁的压电阻抗进行了数值与实验验证,结果表明数值计算结果与实验结果基本相符．利用压电阻抗技术对两端自由的裂纹钢梁进行了损伤识别实验研究,实验结果发现,裂纹的出现引起高频段压电阻抗实部和虚部曲线出现了明显的变化;随着裂纹尺寸的增大,曲线谐振频率和反谐振频率逐渐减小．由此可见,通过测量钢梁损伤前后压电陶瓷片的电阻抗变化能够识别梁中的裂纹损伤．     

SH波在压电材料条中垂直界面裂纹处的散射

研究了SH波在压电材料条中裂纹处的散射.压电材料条两侧涂有相同梯度参数的两个半无限大功能梯度材料,裂纹垂直于界面.通过Fourier变换,利用边界条件把问题转化为柯西核奇异积分方程,然后利用Chebyshev多项式对奇异积分方程进行数值求解.通过数值计算,分析讨论了压电条的几何参数和SH波频率对标准动应力强度因子的影响.     

2-3型压电复合材料有效特性及其静水压性能的研究

压电复合材料是由至少一种压电材料与非压电材料按照一定的连通方式组合在一起而构成的具有压电效应的材料。采用均匀场理论,提出了2-3型压电复合材料的代表性体积单元,通过建立串联、并联等模型预估了压电复合材料的弹性刚度常数:C11、C12、C13、C22、C23、C33,压电常数:e31e、32e、33,介电常数:3ε3。然后用有限元方法(使用了有限元分析软件ANSYS)分析了压电复合材料的材料常数,并用有限元方法验证了均匀场理论求解2-3型压电复合材料有效特性参数的准确性。根据求得的有效特性参数进一步研究了2-3型压电复合材料的静水压性能,由于求得的静水压性能值很低,又改良了2-3型压电复合材料的模型,获得了较好的静水压性能。并将改良前后2-3型压电复合材料与3-2型压电复合材料的静水压性能进行了比较。     

基于压电振动能量俘获的弯曲结构损伤监测研究

建立了含裂纹损伤的曲梁压电能量俘获系统在强迫振动下的动力学模型. 基于Prescott型压电曲梁力电耦合振动方程的解析解和裂纹截面处的连续性条件, 求解了含裂纹损伤的压电曲梁的格林函数. 根据线性叠加原理, 对含裂纹的力电耦合模型的系统方程解耦, 得到强迫振动下含裂纹损伤的曲梁压电俘能器的输出电压. 在得到模型的强迫振动解析解后, 提出逆方法检测结构中的裂纹损伤, 这一检测方法适用于处于振动状态下的结构. 在数值计算中, 令裂纹深度为零, 通过对比本文的解析解与现有文献中的解析解, 验证了本文解的有效性. 分别分析了含裂纹损伤的压电曲梁的电压响应与裂纹深度、裂纹位置、材料的几何参数以及阻尼之间的关系. 研究结果表明: 裂纹的存在对曲梁式压电俘能器的影响比直梁式更加复杂; 裂纹出现时, 损伤曲梁在健康曲梁的一阶频率值处一定会出现波动并被激励出二阶频率, 此时的二阶频率是开路中健康压电曲梁的一阶频率值; 通过对电压响应的检测可以确定的损伤裂纹的深度和在结构中出现的位置范围; 利用振动问题的解来检测压电曲梁的健康状况是可行且准确的.      

旋转压电纳米梁的振动分析

本文基于非局部弹性理论，对旋转压电纳米梁模型的振动进行了分析．首先由哈密顿原理导出旋转压电纳米梁的动力学控制方程及相应的边界条件；再通过微分求积法对控制方程和两类边界条件进行离散；最后通过数值计算分析振动特性．通过改变旋转角速度、轮毂半径、非局部参数以及外部电压分析它们对压电纳米梁振动频率的影响关系．数值结果表明这些参数对压电纳米梁固有频率有不可忽略的影响，本文进一步讨论了旋转角速度对结构模态的影响．     

1-3型压电复合材料及其研究进展

1-3型压电智能复合材料是由一维连通的压电相平行排列于三维连通的聚合物中而形成的两相压电复合材料.简述了1-3型压电智能复合材料形成及其材料结构构成变化的发展历程,并从理论分析、参数辨识、数值计算和试验方法四方面阐述了宏观等效特征参数的研究状况.在此基础上对现有的制备工艺技术的优缺点进行了比较,对声学、医学、控制、航空航天等已应用和可能应用的领域的现状和发展趋势进行了回顾和展望,最后建议了1-3型压电智能复合材料今后几个较为重要的研究方向.      

压电复合材料粘接界面断裂有限元模拟

根据数字化FRMM(Fix-Ratio Mix-Mode)断裂试验,得到了压电复合材料试件的断裂韧性和位移及应变场。本文在试验的基础上,通过非线性有限元软件ABAQUS及用户子程序UMAT进行了模拟分析,采用基于损伤力学的粘聚区模型(CZM)对压电复合材料界面的起裂和脱胶扩展进行了分析,并与VCCT方法进行了比较。计算得到的荷载位移曲线更接近于试验结果,但在裂纹扩展路径上的吻合需要对粘聚区法则进一步修正。通过进一步对CZM参数进行分析,表明界面粘结强度和界面刚度对计算结果的影响很大。研究结果表明,粘聚区模型可以很好地表征压电复合材料弱粘接界面脱胶断裂问题。     

延性材料动态断裂的实验研究和数值分析

本文对延性材料纯铜和ＬＹ１２铝合金进行了层裂实验，对软回收试件进行了仔细的定量和显微金相观测，观察到了两种材料中不同微损伤的形核、增长和聚合机制，为理论分析提供了真实的实验结果。将文〔４〕提出的延性动态损伤模型编入了一维Ｌａｇｒａｎｇｅ有限差分动力学程序，对两组层裂实验进行了数值模拟，计算结果与实验吻合较好。     

Finite-part integral and boundary element method to solve three-dimensional crack problems in piezoelectric materials

Using the hypersingular integral equation method based on body force method, a planar crack in a three-dimensional transversely isotropic piezoelectric solid under mechanical and electrical loads is analyzed. This crack problem is reduced to solve a set of hypersingular integral equations. Compare with the crack problems in elastic isotropic materials, it is shown that for the impermeable crack, the intensity factors for piezoelectric materials can be obtained from those for elastic isotropic materials. Based on the exact analytical solution of the singular stresses and electrical displacements near the crack front, the numerical method of the hypersingular integral equation is proposed by the finite-part integral method and boundary element method, which the square root models of the displacement and electric potential discontinuities in elements near the crack front are applied. Finally, the numerical solutions of the stress and electric field intensity factors of some examples are given.     

Heterogeneous linearly piezoelectric patches bonded on a linearly elastic body

In [1], we studied the response of a thin homogeneous piezoelectric patch perfectly bonded to an elastic body. Here we extend this study to the case of a very thin heterogeneous patch made of a periodic distribution of piezoelectric inclusions embedded in a linearly elastic matrix and perfectly bonded to an elastic body. Through a rigorous mathematical analysis, we show that various asymptotic models arise, depending on the electromechanical loading together with the relative behavior between the thickness of the patch and the size of the piezoelectric inclusions.     

Moving eccentric crack in a piezoelectric strip bonded to elastic materials

Summary  The steady-state of a propagation eccentric crack in a piezoelectric ceramic strip bonded between two elastic materials under combined anti-plane mechanical shear and in-plane electrical loadings is considered in this paper. The analysis based on the integral transform approach is conducted on the permeable crack condition. Field intensity factors and energy release rate are obtained in terms of a Fredholm integral equation of the second kind. It is shown for this geometry that the crack propagation speed has influence on the dynamic energy release rate. The initial crack branching angle for a PZT-5H piezoceramic structure is predicted by the maximum energy release rate criterion. Received 23 January 2001; accepted for publication 18 October 2001     

Monitoring Fatigue Crack Growth in Compact Tension Specimens Using Piezoelectric Sensors

This paper aims to report the results of an experimental study on the application of piezoelectric dynamic strain sensors for crack length measurement in fracture mechanics specimens. The performance of the piezoelectric sensors was assessed through fatigue crack propagation tests in compact tension (CT) specimens. Sensors of polarized polyvinilidene fluoride polymer (PVDF) were bonded to the back face of CT specimens, in the same manner as the electrical resistance strain gages installed for crack length measurement in the back face strain technique. The results showed that, mainly due to its high sensitivity to strain, the use of piezoelectric materials as dynamic strain sensors can contribute to the experimental investigation in the field of fracture mechanics.     

Interfacial cracks between piezoelectric and elastic materials under in-plane electric loading

A new experimental technique for accelerated fatigue crack growth tests was recently developed (Du et al., 2001). The technique, which uses piezoelectric actuators, enables application of cyclic loading at frequencies several orders higher than that by mechanical loading. However, the validity of this technique relies on the equivalence between piezoelectric and mechanical loading. In this paper, the behavior of an interfacial crack between a piezoelectric material and an elastic material under in-plane electric loading is studied. The displacement mismatch along a bonded interface due to electric potential loading on the piezoelectric material is modeled by inserting an array of uniformly distributed dislocations along the interface. By means of Fourier transformation methods, the governing equations are converted to an integral equation, which is then converted to a standard Hilbert problem. A closed form solution for stresses, electric field, and electric displacements along the bonded interface is obtained. The results agree very well with those obtained from numerical simulations. The results show that the closed form solution is accurate not only for far field distributions of stresses and electric variables, but also for the asymptotic distributions near the crack tip. The solution also suggests the likelihood of domain switching in the piezoelectric material near the crack tip, a process that may influence the interfacial fracture resistance.     

压电材料中的Bueckner功共轭积分及和J积分M积分的关系

研究横观各向同性压电材料中裂纹问题,提出了Bueckner功共轭积分在这类材料中的表达式：并通过引出两类辅助的应力-位移-电位移-电势场,证明功共轭积分和这类材料中的J积分和M积分仍然存在简单的两倍关系由此,各类在脆性材料断裂问题中已广泛应用的权函数方法可顺理成章地推广到压电材料的研究中来．这对独立地确定电位移强度因子和经典的I、II型应力强度因子提供了有力的数学上的工具．进而通过计算机械应变能释放率对压电材料中裂纹的稳定做出判断．     

压电圆柱形夹杂对邻近裂纹三维应力场的影响

研究了压电复合材料薄板中压电圆柱形夹杂与邻近宏观钝裂纹间的相互作用。重点分析了外加电场，裂尖与压电圆柱形夹杂间韧带长度对裂尖三维应力场的影响。计算结果表明：在不同的外加电场作用下，压电体不仅能改变裂尖张开应力的大小，还能改变其分布。所得结果对进一步探讨线弹性介质中裂纹的启裂控制有参考价值。     

Dynamic interfacial crack propagation in elastic–piezoelectric bi-materials subjected to uniformly distributed loading

In transversely isotropic elastic solids, there is no surface wave for anti-plane deformation. However, for certain orientations of piezoelectric materials, a surface wave propagating along the free surface (interface) will occur and is called the Bleustein–Gulyaev (Maerfeld–Tournois) wave. The existence of the surface wave strongly influences the crack propagation event. The nature of anti-plane dynamic fracture in piezoelectric materials is fundamentally different from that in purely elastic solids. Piezoelectric surface wave phenomena are clearly seen to be critical to the behavior of the moving crack. In this paper, the problem of dynamic interfacial crack propagation in elastic–piezoelectric bi-materials subjected to uniformly distributed dynamic anti-plane loadings on crack faces is studied. Four situations for different combination of shear wave velocity and the existence of MT surface wave are discussed to completely analyze this problem. The mixed boundary value problem is solved by transform methods together with the Wiener–Hopf and Cagniard–de Hoop techniques. The analytical results of the transient full-field solutions and the dynamic stress intensity factor for the interfacial crack propagation problem are obtained in explicit forms. The numerical results based on analytical solutions are evaluated and are discussed in detail.     

Reduction of applied electric potential controlling thermoelastic displacement in a piezoelectric actuator

Summary The present paper discusses how to reduce the applied electric potential which controls a distribution of the elastic displacement, when temperature change induces elastic deformation in a piezoelectric-based solid state actuator. The actuator consists of an isotropic structural plate, onto which multiple piezoelectric ceramic plates of crystal class 6mm are perfectly bonded. The analysis of this thermoelastic problem leads to electric potential applied to piezoelectric ceramic plates. Numerical calculations are carried out for an isotropic steel plate, onto which multiple cadmium-selenide plates are perfectly bonded. Finally, it is shown that the maximum applied electric potential in the case of ten cadmium selenide plates can be reduced to 11% of that derived from the previous study of a similar problem of one cadmium selenide plate bonded onto an isotropic steel plate. Received 10 September 1998; accepted for publication 23 March 1999