压电材料反平面应变状态的椭圆夹杂及界面裂纹问题

本文采用共法求解了压电材料反平面变形的椭圆夹杂及界面裂纹问题，前者的解答表明当远场外力均匀分布对夹杂内的应力场及电位移场是常量，后者解答表明在界面裂纹的裂尖处，应力及电位移都具有γ＾－１／２的奇异性。     

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。     

压电介质中受拉伸与弯曲联合作用的圆币形裂纹问题

以弹性位移分量和电势函数为基本未知量时，横观各向同性压电介质非轴对称三维问题的控制微分方程是四个二阶线性偏微分方程相联立的方程组。本文导出了用四个调和函数表示位移及电势的该方程组的势函数通解。作为通解的应用举例，文中求解了压电陶瓷材料中受拉伸与弯曲联合作用的圆币形裂纹问题，得到了裂纹尖端附近应力场及电位移场的解析表达式。结果表明裂尖场以及应力强度因子和电位移强度因子均表现出复杂的机－电耦合行为。     

压电陶瓷中圆币形裂纹在横向剪力下的机－电耦合行为

以弹性位移分量和电势函数为基本未知量时，横观各向同性压电介质三维问题的场方程可化为四个联立的二阶线性偏微分方程组，本文导出了用四个调和函数表示位移分量及电势函数的表达式，即得到了该场方程的势函数通解，作为通解的应用举例，文中求解了圆币形裂纹受横向剪切作用的问题，得到了裂尖附近应力场及电位移场的解析表达式，结果表明，在横向剪切载荷下圆币形裂纹的尖端场及应力、电位移强度因子均具有明显的机－电耦合性质，而应力和电位移分量在裂尖仍具有－１／２的奇异性。     

横观各向同性压电材料半无限体Green函数解

按以四个调和函数表示的通解，用镜像法，对材料特征根ｓ１≠ｓ２≠ｓ３≠ｓ１情形，给出了横观各向同性压电材料半无限体的两类闭合形式Ｇｒｅｅｎ函数。     

各向同性材料接头和界面相交裂纹应力奇异性特征分析

提出了用插值矩阵法分析各向同性材料接头以及与界面相交的平面裂纹应力奇异性。基于接头和裂纹端部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,得到关于平面内各向同性材料接头以及与两相材料界面相交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,获得了两相材料平面接头端部应力奇异性指数以及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。     

横观各向同性轴对称界面端奇异性研究

套筒模型是复合材料中常用的进行纤维、基体间应力传递分析的轴对称模型.在套筒模型中,中心为纤维,纤维外包裹的"套筒"有假设为各向同性基体材料的,也有假设为横观各向同性复合材料的.不失一般性,本文将纤维和基体均视作横观各向同性材料,建立了任意楔形角的横观各向同性复合材料基体包裹横观各向同性纤维的轴对称模型,采用两次坐标变换、逐次渐近等求解方法,得到了求解该模型界面端应力奇异性指数的特征方程.考虑常见的碳纤维/环氧树脂复合材料制成的压入和拔出试件,根据得到的特征方程计算了两种试件的界面端奇异性指数随碳纤维体积百分含量的变化情况,结果发现,随纤维体积百分含量的增加,两种试件界端的奇异性均呈减弱趋势.     

含有多个涂层压电纤维复合材料的平面问题研究

压电纤维在未来的复合材料结构健康监测中具有重要作用.本文基于横观各向同性压电材料位移和应力连续条件以及经典的复势函数理论,讨论了同时受到平面内机械载荷和出平面电载荷作用时含有多个带涂层压电纤维的无限大线弹性基体的平面力学问题.首先将线弹性基体、涂层和压电纤维的应力场、位移场表示成复势函数,然后通过横观各向同性压电材料和线弹性材料的位移和应力连续条件确定复势函数表达式.将得到的复势函数表达式代入线弹性基体、涂层和压电纤维的的应力场、位移场公式可确定其应力场和位移场.最后,通过定量的案例讨论了涂层的材料属性对线弹性基体应力场的影响.案例分析表明涂层的材料属性对压电复合材料的应力场有重要的影响.     

压电陶瓷中圆币形裂纹在横向剪力下的机—电耦合行为

以弹性位移分量和电热函数基本未知量时，横观各向同性压电介质三维问题的场方程可化为四个联立的二阶线性偏微分方程组，本文导出了用四个调和函数表示位移分量及电势函数的表达式，即得到了该场方程的势函数能通解，作为通解的应用举例，文中求解了圆币形裂纹受横向剪切载荷下圆币形裂纹的尖端场及应力、电位移强度因子均具有明显的机－电耦合性质，而应力和电位移分量在裂尖仍具有－１／２的奇异性。     

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．     

Antiplane electro-mechanical field of a piezoelectric finite wedge under shear loading and at fixed-grounded boundary conditions

This paper presents the general solutions of antiplane electro-mechanical field solutions for a piezoelectric finite wedge subjected to a pair of concentrated forces and free charges. The boundary conditions on the circular segment are considered as fixed and grounded. Employing the finite Mellin transform method, the stress and electrical displacement at all fields of the piezoelectric finite wedge are derived analytically. In addition, the singularity orders and intensity factors of stress and electrical displacement can also be obtained. These parameters can be applied to examine the fracture behavior of the wedge structure. After being reduced to the problem of an antiplane edge crack or an infinite wedge in a piezoelectric medium, the results compare well with those of previous studies.     

Mode III crack problems for two bonded functionally graded piezoelectric materials

This paper investigates the singular electromechanical field near the crack tips of an internal crack. The crack is perpendicular to the interface formed by bonding two half planes of different functionally graded piezoelectric material. The properties of two materials, such as elastic modulus, piezoelectric constant and dielectric constant, are assumed in exponential forms and vary along the crack direction. The singular integral equations for impermeable and permeable cracks are derived and solved by using the Gauss–Chebyshev integration technique. It shows that the stresses and electrical displacements around the crack tips have the conventional square root singularity. The stress intensity and electric displacement intensity factors are highly affected by the material nonhomogeneity parameters β and γ. The solutions for some degenerated problems can also be obtained.     

Electro-elastic interaction between a piezoelectric screw dislocation and circular interfacial rigid lines

The electro-elastic interaction between a piezoelectric screw dislocation located either outside or inside inhomogeneity and circular interfacial rigid lines under anti-plane mechanical and in-plane electrical loads in linear piezoelectric materials is dealt with in the framework of linear elastic theory. Using Riemann–Schwarz’s symmetry principle integrated with the analysis of singularity of complex functions, the general solution of this problem is presented in this paper. For a special example, the closed form solutions for electro-elastic fields in matrix and inhomogeneity regions are derived explicitly when interface containing single rigid line. Applying perturbation technique, perturbation stress and electric displacement fields are obtained. The image force acting on piezoelectric screw dislocation is calculated by using the generalized Peach–Koehler formula. As a result, numerical analysis and discussion show that soft inhomogeneity can repel screw dislocation in piezoelectric material due to their intrinsic electro-mechanical coupling behavior and the influence of interfacial rigid line upon the image force is profound. When the radian of circular rigid line reaches extensive magnitude, the presence of interfacial rigid line can change the interaction mechanism.     

结合材料界面端的三维应力奇异性

本文利用特殊有限元方法，开发了一个用来求解结合材料界面端三维应力奇异性问题的数值分析程序。该方法只需对界面端的角度方向进行离散即可求得应力奇异性。结合材料的应力奇异性取决于两种材料的材料常数和界面端形状。选用三个材料参数作为变量，用来研究结合材料三维应力奇异性随材料常数的变化规律。文中计算了几种重要而且常见的情况，并以此为基础建立了数据库。同时，还分析了应力奇异性随界面端形状的变化规律，并得到了应力函数的分布图。     

Crack-tip field on mode Ⅱ interface crack of double dissimilar orthotropic composite materials

Two systems of non-homogeneous linear equations with 8 unknowns are obtained.This is done by introducing two stress functions containing 16 undetermined coefficients and two real stress singularity exponents with the help of boundary conditions.By solving the above systems of non-homogeneous linear equations,the two real stress singularity exponents can be determined when the double material parameters meet certain conditions.The expression of the stress function and all coefficients are obtained based on the uniqueness theorem of limit.By substituting these parameters into the corresponding mechanics equations,theoretical solutions to the stress intensity factor,the stress field and the displacement field near the crack tip of each material can be obtained when both discriminants of the characteristic equations are less than zero.Stress and displacement near the crack tip show mixed crack characteristics without stress oscillation and crack surface overlapping.As an example,when the two orthotropic materials are the same,the stress singularity exponent,the stress intensity factor,and expressions for the stress and the displacement fields of the orthotropic single materials can be derived.     

Antiplane stress singularities in a bonded bimaterial piezoelectric wedge

Summary  In this paper, the eigen-equations governing antiplane stress singularities in a bonded piezoelectric wedge are derived analytically. Boundary conditions are set as various combinations of traction-free, clamped, electrically open and electrically closed ones. Application of the Mellin transform to the stress/electric displacement function or displacement/electric potential function and particular boundary and continuity conditions yields identical eigen-equations. All of the analytical results are tabulated. It is found that the singularity orders of a bonded bimaterial piezoelectric wedge may be complex, as opposed to those of the antiplane elastic bonded wedge, which are always real. For a single piezoelectric wedge, the eigen-equations are independent of material constants, and the eigenvalues are all real, except in the case of the combination C–D. In this special case, C–D, the real part of the complex eigenvalues is not dependent on material constants, while the imaginary part is. Received 26 March 2002; accepted for publication 2 July 2002     

Penny-shaped crack in transversely isotropic piezoelectric materials

Using a method of potential functions introduced successively to integrate the field equations of three-dimensional problems for transversely isotropic piezoelectric materials, we obtain the so-called general solution in which the displacement components and electric potential functions are represented by a singular function satisfying some special partial differential equations of 6th order. In order to analyse the mechanical-electric coupling behaviour of penny-shaped crack for above materials, another form of the general solution is obtained under cylindrical coordinate system by introducing three quasi-harmonic functions into the general equations obtained above. It is shown that both the two forms of the general solutions are complete. Furthermore, the mechanical-electric coupling behaviour of penny-shaped crack in transversely isotropic piezoelectric media is analysed under axisymmetric tensile loading case, and the crack-tip stress field and electric displacement field are obtained. The results show that the stress and the electric displacement components near the crack tip have (r ^−1/2) singularity. The project supported by the Natural Science Foundation of Shaanxi Province, China     

纤维与基体的轴对称界面端附近的奇异应力场

基于各向性弹性力学空间轴对称问题的基本方程,研究了纤维与基体的轴对称界面端的应力奇异性,并给出了界最佳 近的奇异应力场。研究结果表明,该轴对称界面端的应力奇异性与平面应变状态下相应模型的应力奇异性完全相同,材料对界面端附近奇异应力场的影响可用丰个双材料组合参数描述。     

Interface crack problems for mode Ⅱ of double dissimilar orthotropic composite materials

The fracture problems near the interface crack tip for mode Ⅱ of double dissimilar orthotropic composite materials are studied. The mechanical models of interface crack for mode Ⅱ are given. By translating the governing equations into the generalized bi-harmonic equations,the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions,a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about himaterial engineering parameters. According to the uniqueness theorem of limit,both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same,the stress singularity exponents,stress intensity factors and stresses for mode Ⅱ crack of the orthotropic single material are obtained.     

压电体中考虑表面效应时开裂孔洞的断裂特征

研究了反平面机械载荷和面内电载荷作用下压电体中考虑表面效应时孔边双裂纹问题的断裂特征。基于Gurtin-Murdoch表面理论模型，通过构造映射函数，利用复势电弹理论获得了应力场和电位移场的闭合解答。给出了裂纹尖端应力强度因子、电位移场强因子和能量释放率的解析解。讨论了开裂孔洞几何参数和施加力电载荷对电弹场强因子和能量释放率的影响。