Stress intensity factors for an interface crack with impermeable surfaces between dissimilar electrostrictive materials

The asymptotic problem of a semi-infinite interface crack between dissimilar electrostrictive materials that are subjected to electric loading is numerically analyzed by using the finite element method. Numerical results of electric displacement fields are obtained on the basis of the mathematical equivalence of the mode III problem and an electrostatic problem. The shape and the size of saturation zones are explored as a function of the ratio of the saturated electric displacements of dissimilar electrostrictive materials. In contrast with conventional wisdom, the ratio of the permittivities is shown to exert a negligibly small influence on electric displacement fields. For various combinations of the material properties of dissimilar electrostrictive materials, stress fields and stress intensity factors are systemically calculated by using the numerical results of electric displacement fields. The effects of the electric, elastic, and electrostrictive properties on stress intensity factors are demonstrated.     

Modified boundary layer analysis of an electrode in an electrostrictive material

A thin electrode embedded in an electrostrictive material under electric loading is investigated. In order to obtain an asymptotic form of electric fields and elastic fields near the electrode edge, we consider a modified boundary layer problem of an electrode in an electrostrictive material under the small scale saturation condition. The exact electric solution for the electrode is obtained by using the complex function theory. It is found that the shape of the electric displacement saturation zone is sensitive to the transverse electric displacement. A perturbation solution of stress fields induced by incompatible electrostrictive strains for the small value of the transverse electric displacement is obtained. The influence of transverse electric displacement on a microcrack initiation from the electrode edge is also discussed.     

Asymptotic analysis of an impermeable crack in an electrostrictive material subjected to electric loading

The simple asymptotic problem of an impermeable crack in an electrostrictive ceramic under electric loading is analyzed. Closed form solutions of elastic fields are obtained by using the complex function theory. It is found that the K_I-dominant region is very small compared to the electric saturation zone. A fracture parameter for an electrostrictive material subjected to electric loading is discussed. In order to investigate the influence of the transverse electric displacement on fracture behavior under the small-scale conditions, we also consider the modified boundary layer problem of a crack in an electrostrictive material. Analytic solutions of electric displacement fields for the asymptotic problem are obtained based on the nonlinear dielectric theory from a modified boundary layer analysis. The shape of the electric displacement saturation zone is shown to depend on the transverse electric displacement. Stress intensity factors induced by the electrostrictive strains are evaluated using the nonlinear solution of the electric displacements. It is found that the transverse electric displacement affects strongly the variation of the mode mixity.     

A Crack with an Electric Displacement Saturation Zone in an Electrostrictive Material

A crack with an electric displacement saturation zone in an electrostrictive material under purely electric loading is analyzed. A strip saturation model is here employed to investigate the effect of the electrical polarization saturation on electric fields and elastic fields. A closed form solution of electric fields and elastic fields for the crack with the strip saturation zone is obtained by using the complex function theory. It is found that the K _I -dominant region is very small compared to the strip saturation zone. The generalized Dugdale zone model is also employed in order to investigate the effect of the saturation zone shape on the stress intensity factor. Using the body force analogy, the stress intensity factor for the asymptotic problem of a crack with an elliptical saturation zone is evaluated numerically.     

Mode-III interface edge crack between two bonded quarter-planes of dissimilar piezoelectric materials

Summary  The problem of an interface edge crack between two bonded quarter-planes of dissimilar piezoelectric materials is considered under the conditions of anti-plane shear and in-plane electric loading. The crack surfaces are assumed to be impermeable to the electric field. An integral transform technique is employed to reduce the problem under consideration to dual integral equations. By solving the resulting dual integral equations, the intensity factors of the stress and the electric displacement and the energy release rate as well as the crack sliding displacement and the electric voltage across the crack surfaces are obtained in explicit form for the case of concentrated forces and free charges at the crack surfaces and at the boundary. The derived results can be taken as fundamental solutions which can be superposed to model more realistic problems. Received 10 November 2000; accepted for publication 28 March 2001     

Solution of a flat elliptical crack in an electrostrictive solid

Based on the assumption that the elastic strain of electrostrictive materials is a higher-order small quantity, this paper studies the 3D problem of an infinite electrostrictive solid with a flat elliptical crack which is electrically permeable. According to existing solutions of similar problems in pure elastic materials, with the displacement function method, we first derived explicit expression for displacement potential function and obtained stress field near the crack and open displacement of crack surface. Then, the general solution for the stress intensity factor was derived, and the corresponding solutions were also presented for a penny-shaped crack and a permeable line-crack as two special cases of the present problem. Finally, numerical results were given to discuss the effect of environment at infinity and electric field inside the crack on the stress-intensity factors.     

Interaction integrals for fracture analysis of functionally graded piezoelectric materials

This paper presents domain form of the interaction integrals based on three independent formulations for computation of the stress intensity factors and electric displacement intensity factor for cracks in functionally graded piezoelectric materials. Conservation integrals of J-type are derived based on the governing equations for piezoelectric media and the crack tip asymptotic fields of homogeneous piezoelectric medium as auxiliary fields. Each of the formulation differs in the way auxiliary fields are imposed in the evaluation of interaction integral and each of them results in a consistent form of the interaction integral in the sense that extra terms naturally appears in their derivation to compensate for the difference in the chosen crack tip asymptotic fields of homogeneous and functionally graded piezoelectric medium. The additional terms play an important role of ensuring domain independence of the presented interaction integrals. Comparison of the numerically evaluated intensity factors through the three consistent formulations with those obtained using displacement extrapolation method is presented by means of two examples.     

插值矩阵法分析与复合材料界面相交的平面裂纹奇异应力场

提出了用插值矩阵法分析与各向异性材料界面相交的平面裂纹应力奇异性。基于V形切口尖端附近区域位移场渐近展开,将位移场的渐近展开式的典型项代入线弹性力学基本方程,得到关于平面内与复合材料界面相交的裂纹应力奇异性指数的一组非线性常微分方程的特征值问题,运用插值矩阵法求解,获得了平面内各向异性结合材料中与界面以任意角相交的裂纹尖端的应力奇异性指数随裂纹角的变化规律,数值计算结果与已有结果比较表明,本文方法具有很高的精度和效率。     

Singularities of an interface crack in electrostrictive materials

In the present work, the singularities of an interface crack between two dissimilar electrostrictive materials under electric loads are investigated. Within the framework of two-dimensional deformation, the problem is solved using the complex variable method. Three crack models, that is, permeable, impermeable and conducting crack models are considered individually. Complex potentials and intensity factors of total stresses are derived by considering both the Maxwell stresses in the surrounding space at infinity and inside the crack. It is found that, for the above three crack models, the singularities of total stress are the same as those in traditional bi-materials with an interface crack; however, the intensities of the total stress depend on the actual crack model used.     

轴对称界面端的扭转问题

基于弹性力学轴对称扭转问题的通解,研究了具有任意几何形状的双材料轴对称界面端,给出了界面端的应力奇异性及其附近的位移场和奇应力场,定义了扭转问题的Ｄｕｎｄｕｒｓ双材料参数。研究结果表明,应力奇异性只与界面端的结合角和扭转问题的Ｄｕｎｄｕｒｓ双材料参数有关,而与界面的角度以及界面端与对称轴之间的距离无关,在任何情况下,特征值均为实数,不会产生振荡应力奇异性。     

电弹性体力学中的偏场方法及其应用

主要综述了当前有关叠加于偏场之上的电弹性体小位移问题的求解方法,即偏场方法.首先介绍了作为偏场方法理论基础的非线性电弹性力学理论,接着总结了偏场方法的研究进展以及受偏场作用后,电弹性梁、板、壳结构的分析方法,随后综述了偏场方法的诸多应用:其中,包括在薄壁电弹性结构屈曲分析中的应用、在记时与通信压电谐振器和基于频率漂移原理所设计的声波传感器的频率稳定性分析方面的应用、在非线性电弹性材料系数的测定以及偏场作用下电致伸缩陶瓷特征的分析等方面的应用.最后给出了该领域当前和未来的一些可能的研究课题.全文参考文献166篇.      

压电材料中切口/接头端部平面电弹性场奇异性有限元分析

为了对平面载荷作用下压电材料中切口或接头端部附近电弹性场奇异性问题进行分析，首先以应力平衡方程、Maxwell方程和和边界条件为基础，得到一种求解压电材料特征问题的弱式方程；其次，假定楔形切口或接头端部附近单元内位移和电势沿径向分布为指数形式，而周向方向分布则采用泡函数插值，将其代入弱式方程，建立一种只需对楔形切口或接头端部附近周边进行离散的一维简单有限元方法．压电材料的极化轴可以是任意方向．利用该有限元模型讨论了楔形切口角度、极化轴方向和边界条件对奇性场的影响．通过和其它特定情况下的现有解相比，证实了该文有限元数值方法的有效性，而且精度很高．     

刚性圆形压头作用下热电材料半平面的无摩擦接触问题

热电材料可以将热能转化为电能,反之亦然,这一优良的性质将有助于研发更具成本效益的设备和器件。本文研究了刚性圆形压头作用在热电材料半平面的无摩擦接触问题。假定压头为电导体、热导体,且压头压入深度及与材料的接触区域宽度未知。首先求解电场和温度场,利用傅里叶变换得到了电势函数、温度、电流密度和能量通量的解析表达式。然后求解弹性场,利用积分变换和边界条件,将该热弹性接触问题转化为第一类奇异积分方程并数值求解。数值结果讨论了压头半径和热电载荷对法向接触应力、电流强度因子和能量通量强度因子的影响。结果表明,对于圆压头,热电材料的法向电流密度、法向能量通量在接触边缘表现出奇异性,而表面法向接触应力在接触边缘为零。本文建立的研究模型有助于更深层次的了解热电材料的接触行为。     

Surface contact behavior of functionally graded thermoelectric materials indented by a conducting punch

The contact problem for thermoelectric materials with functionally graded properties is considered. The material properties, such as the electric conductivity, the thermal conductivity, the shear modulus, and the thermal expansion coefficient, vary in an exponential function. Using the Fourier transform technique, the electro-thermoelastic problems are transformed into three sets of singular integral equations which are solved numerically in terms of the unknown normal electric current density, the normal energy flux, and the contact pressure. Meanwhile, the complex homogeneous solutions of the displacement fields caused by the gradient parameters are simplified with the help of Euler's formula. After addressing the non-linearity excited by thermoelectric effects,the particular solutions of the displacement fields can be assessed. The effects of various combinations of material gradient parameters and thermoelectric loads on the contact behaviors of thermoelectric materials are presented. The results give a deep insight into the contact damage mechanism of functionally graded thermoelectric materials(FGTEMs).     

Stress analysis in two dimensional electrostrictive material with an elliptic rigid conductor

This paper presents the governing equations of electrostrictive materials. The stress and electric field solutions for an infinite plate with a rigid elliptic conductor under applied load at infinity are given. The asymptotic expansions of the solution for a narrow elliptic conductor show that the stresses and the electric fields near the end of a narrow elliptic conductor possess r⁻¹ and r^−1/2 forms respectively in a local coordinate system with the origin at its focus.     

电致伸缩材料内电极附近应力奇异性研究

应用复变函数的方法,研究电致伸缩材料内置电极附近的应力奇异性.基于精确的电边界条件,采用Hilbert理论以及复变函数中的Cauchy积分与留数定理,首先分别给出了柔性电极和刚性电极的复势函数解,然后就这两种极限情况,讨论了电极刚度对应力场奇异性的影响.研究结果表明:无论对柔性电极还是刚性电极,Max-well应力的应力场均呈现r-1阶的奇异性,但对于前者总应力奇异性系数为零,而对于后者总应力奇异性系数与基体的材料常数有关.     

不同压电介质界面上的反平面运动裂纹

利用积分变换技术,得到不同压电介质界面上的平面运动裂纹问题的分析解。结果表明应力及电位移强度因子均与界面裂纹扩展速度及材料参数相关,这不同于均匀压电介质中运动裂纹的结论,当两种压电介质完全相同时,本文结果将退化为均匀压电介质中反平面运动裂纹问题的解。     

刚度微分法计算压电材料平面断裂问题

把计算应变能释放率的刚度微分法推广到压电材料平面断裂问题．在此基础上，利用压电材料平面断裂问题的有限元数值解作为真实场，用Ｓｏｓａ的平面问题裂端渐近解作为辅助场，由推广的交互Ｍ积分法求得了应力强度因子ＫＩ，ＫＩＩ和电位移强度因子ＫＩＶ．算例表明，计算结果与理论解符合得很好     

Stress and electric fields in an infinite electrostrictive plate with an elliptic inhomogeneity

The stress and electric fields in electrostrictive materials under general electric loading at infinity are obtained in this paper. It is shown that the pseudo total stresses are continuous in the whole body. The elliptic inhomogeneity problem is first discussed in this paper and its solution is also given. The results show that the stress in the inhomogeneity is not uniform which is different from the solution of Eshelby theory for elastic materials. When the inhomogeneity and matrix have the same dielectric permittivity or the matrix is a non-electrostrictive material, the stress field is uniform in the inhomogeneity. The form of stress function is simple when the inhomogeneity degenerates to a circle.     

Modeling of pre-fracture zones for limited permeable crack in piezoelectric materials

A plane-strain problem for a limited permeable crack in an adhesive thin interlayer between two semi-infinite piezoelectric spaces is considered. The tensile mechanical stress and the electric displacement are applied at infinity. The interlayer is assumed to be softer than the connected materials; therefore, the zones of mechanical yielding and electric saturations can arise at the crack tips on the continuations of the crack. These zones are considered in this work. It was assumed that the length of electric saturation zones is larger than the length of mechanical yield zones. The zones of mechanical yielding are modeled by the crack continuations with normal compressive stresses applied at its faces. The electric saturation zones are modeled by segments at the crack continuations with prescribed saturated electric displacements. These electric displacements can linearly vary along the mechanical yielding zones. The problem is reduced to the Hilbert–Riemann problem of linear relationship, which is solved exactly. The equation for the determination of the yielding zones length, the expressions for the crack-opening displacement jump, electric potential jump, and J-integral is obtained in an analytical form. In case of finite size body, the finite elements method is used and the variation in the fracture mechanical parameters with respect to this size is demonstrated.