压电螺型位错与含界面裂纹椭圆夹杂的干涉效应

运用求解复杂多连通域问题的复变函数方法，获得了压电螺型位错与含界面裂纹椭圆夹杂的干涉问题，复势函数的精确级数形式解。利用广义Peach-Koehler公式导出作用于螺型位错的位错力公式。分析结果表明，当裂纹的曲率或长度达到临界值，界面裂纹的存在会改变压电螺型位错与椭圆夹杂的干涉性质。     

压电螺型位错与椭圆夹杂界面导电刚性线的干涉效应

研究了无限大压电基体材料中压电螺型位错与含界面导电刚性线椭圆夹杂的电弹耦合干涉问题。运用求解复杂多连通域问题的复变函数方法,获得了椭圆夹杂和基体区域复势函数以及电弹性场的精确级数形式解答。利用广义Peach-Koehler公式导出作用于压电螺型位错上的位错力公式。主要讨论了刚性线几何尺寸和椭圆曲率对位错力的影响规律。分析结果表明:界面刚性线排斥基体中的位错,对靠近椭圆夹杂界面的螺型位错的运动和平衡位置有重要的影响。当刚性线的长度达到临界值,界面刚性线的存在会改变螺型位错与压电椭圆夹杂的干涉规律。椭圆夹杂的压缩系数变大,刚性线尺寸对位错力的影响也越大。     

压电材料中螺型位错与含界面刚性线圆形涂层夹杂的干涉

研究了压电材料中位于基体的螺型位错与含界面刚性线圆形涂层夹杂的电弹耦合干涉问题。运用复变函数方法,获得了基体、涂层和夹杂中复势函数的精确级数形式解答。基于广义Peach-Koehler公式,计算了作用在位错上的像力。讨论了刚性线几何条件、界面层厚度和材料电弹特性对位错力和位错平衡位置的影响规律。结果表明:对于软夹杂和软涂层的情况,刚性线长度存在一个临界值改变像力的方向。螺型位错先被吸引后被排斥,在夹杂附近有一个稳定的平衡点。对于硬夹杂和硬涂层的情况,位错一直被排斥,刚性线对位错力的影响较小。     

电磁材料中广义螺型位错与圆形界面刚性线夹杂的干涉效应

研究了广义螺型位错和圆形界面刚性导体线夹杂的磁电弹耦合干涉效应.采用Riemann-Schwarz对称原理并结合复势函数奇性主部分析,得到该问题的一般解答.当界面只含一条刚性线时,获得了封闭形式解.运用扰动技术,求解了位错点的扰动应力、电位移和磁感应强度场.由推广的Peach-Koehler公式求出了作用在位错上的位错力,讨论了圆弧形刚性线几何条件和材料失配对位错力的影响规律.解答不但可作为格林函数获得任意分布位错的相应解答,而且可以用于研究无穷远纵向剪切和面内电磁场作用下界面刚性线夹杂和任意形状裂纹的磁电弹耦合干涉效应问题.     

压电螺位错与圆夹杂的电弹相互作用

研究压电材料中压电螺位错与圆夹杂的相互作用问题，分析基体与夹杂的相对刚度以及压电效应对作用于位错上像力的影响，得到了新的相互作有机理。     

位错与含裂纹非理想界面圆形夹杂的干涉效应

研究了基体中任意位置的螺型位错与含裂纹非理想界面圆形弹性夹杂的干涉力学问题。运用复变函数的解析延拓技术与奇性主部分析方法,获得了该问题复势函数的一般解答。作为典型例子,求出了非理想圆形界面含一条裂纹时基体和夹杂区域复势函数的封闭形式解。计算了作用在螺型位错上的位错力。讨论了含裂纹的非理想界面以及材料失配对位错力的影响规律。结果表明:与含裂纹理想界面相比,非理想界面对位错力的影响更大,对位错的捕获能力更强。硬夹杂时,可能存在非稳定平衡点,使得非理想界面、界面裂纹和夹杂对位错的作用力为零;软夹杂时,非理想界面、界面裂纹和夹杂则始终吸引位错。     

一维六方准晶复合材料界面层中螺型位错分析

本文研究了一维六方准晶复合材料夹杂界面层中螺型位错与夹杂以及无限大基体的干涉效应。运用复变函数方法,得了该问题的解析解答,所得退化结果与已有文献结果一致,并得到了作用在圆环形界面层中螺型位错的位错力的精确表达式。讨论了一维六方准晶材料弹性常数对位错运动以及位错力的影响规律。结果表明,一维六方准晶中的材料弹性常数对位错力的变化影响是显著的。随着相位子场弹性常数或者声子场-相位子场耦合弹性常数的增大,其相应区域对位错的排斥或者吸引作用也分别增强。在夹杂界面或者基体界面附近,随着相位子场弹性常数和声子场-相位子场耦合弹性常数同时增大,夹杂或者基体对位错的吸引作用增强,但是并不改变位错平衡点的位置。     

压电材料中螺型位错偶极子与圆弧形界面裂纹的电弹干涉效应

研究了在无穷远力电荷载作用下广义螺型位错偶极子与圆弧形界面裂纹的电弹干涉作用。运用复变函数方法,导出了该问题的一般解答,并获得了界面上只有一条裂纹时的封闭形式解,求得了基体及夹杂区域复势函数、广义应力场、裂纹尖端的广义应力强度因子以及作用在螺型位错偶极子上的位错力和力偶矩。讨论了裂纹长度、压电材料电弹常数以及位错偶极子的位置对裂纹尖端应力强度因子、偶极子中心的位错力和像力偶矩的影响。     

含椭圆孔压电材料的电弹场

采用复变函数的方法,研究了含椭圆孔的压电材料在无限远处受力电荷载作用的平面问题。与已有文献不同,通过求解10元一次方程,得到了满足可导通和不可导通电边界条件,孔内和压电材料体内电弹场的通解。以PZT一4压电陶瓷为例,给出了孔内的电场、压电材料体内电弹场沿孔边和坐标轴向的分布情况。得出了以下新的结论:含椭圆孔压电材料的电弹场与边界条件、力电荷载的方向、椭圆孔的形状有关,但在水平方向的拉伸载荷和电位移的作用下,椭圆孔的形状对长半轴处的环向电位移和正应力的最大值没有影响。     

螺型位错偶极子与界面刚性线的弹性干涉

研究了晶体材料中螺型位错偶极子和界面刚性线夹杂的弹性干涉作用。利用复变函数方法,得到了该问题的复势函数以及应力场的封闭形式解答。求出了作用在螺型位错偶极子中心的像力和力偶矩,并分析了界面刚性线几何条件和不同材料特征组合对位错偶极子平衡位置的影响规律。研究结果表明:当位错偶极子不断靠近刚性线时,刚性线对螺型位错偶极子的运动有很强的排斥作用。当刚性线的长度和材料剪切模量比达到临界值时,可以改变偶极子和界面之间的干涉机理。同时,偶极子偶臂的方向对其自身的平衡也有很大的影响。     

Electro-elastic interaction between a moving screw dislocation and collinear interfacial rigid lines

This paper attempts to investigate the problem for the electro-elastic interaction between a piezoelectric moving dislocation and interfacial collinear rigid lines under combined longitudinal shear and in-plane electric field. Using Riemann–Schwarz's symmetry principle integrated with the analysis singularity of complex functions, we present the general elastic solution of this problem and the closed form solution for interface containing single rigid line. The expressions of electro-elastic fields and image force acting on moving dislocation are derived explicitly. The results show that the velocity of moving dislocation has significant effect on the image force. The present solutions contain previously known results as the special cases.     

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

Electro-elastic stress investigation on the interaction between a piezoelectric screw dislocation and collinear rigid lines under anti-plane mechanical and in-plane electrical loading is carried out. The lines are considered, respectively, as dielectrics or conductors. The screw dislocation is subjected to a line charge and a line force at the core. Closed-form analytical solutions are derived by means of complex variable method. Explicit expressions for the field variables, the singularity of the field variables at the line tip and the force on the dislocation are obtained for a single rigid line.     

Micro-crack initiation at tip of a rigid line inhomogeneity in piezoelectric materials

For the square-root singularity shear stress found at the tip of a rigid line inhomogeneity (an anti-crack) in piezoelectric media, one possible way of releasing high strain energy is to initiate a micro-crack at the inhomogeneity tip. In our current study, a dislocation pileup model for micro-crack initiation at the inhomogeneity tip is proposed based on Zener-Stroh crack initiation mechanism. An interesting and important physical result that emerges from the analysis is that the critical stress intensity factor for the anti-crack (the line inhomogeneity) can be related to the fracture toughness of a conventional Griffith crack in the same material. Analytical results further show that under mechanical loading, the critical stress and electric displacement intensity factors of an anti-crack are only related to the corresponding intensity factors of stress and electric displacement of the crack, respectively. While if the anti-crack is under displacement loading (with net dislocation pile-up at the inhomogeneity tip), the critical stress and electric displacement intensity factors of an anti-crack depend on both of the total mechanical dislocations b_T and electricity dislocations b_D.     

Viscoelastic interaction between a screw dislocation and a piezoelectric inhomogeneity with an interfacial rigid line

Summary The problem for the interaction between a screw dislocation and a piezoelectric circular inhomogeneity with one interfacial rigid line in a viscoelastic matrix is investigated in this paper. Based on the elastic-viscoelastic correspondence principle, the analytical stress fields and image force for the problem are presented. The results show that the influences of the viscoelastic properties of the material together with rigid line's length and inhomogeneity's piezoelectricity upon the time-dependent image force are significant. The time-dependent image force evolves toward a constant value as time elapses. Results presented in this paper are in agreement with the previous solution as special cases.     

Analysis of a screw dislocation interacting with an elliptical nano inhomogeneity

The interaction between a screw dislocation and an elliptical nano inhomogeneity embedded in an infinite matrix is investigated. The interface stress effects of the nano inhomogeneity are accounted for with the Gurtin-Murdoch model. The stress fields inside the inhomogeneity and matrix are then solved with the complex variable and conformal mapping method. The solution is of semi-analytical nature and is verified by studying a degenerated case wherein a screw dislocation interacts with a circular nano inhomogeneity. The image force on the screw dislocation is then calculated. The influences of the elastic mismatch between the inhomogeneity and matrix, the interfacial properties, the aspect ratio of the elliptic nano inhomogeneity and the position of the screw dislocation on the image force are systematically discussed.     

A screw dislocation interacting with an interphase layer between a circular inhomogeneity and the matrix

The interaction of a screw dislocation with an interphase layer between a circular inhomogeneity and the matrix is dealt with. By combining the sectionally holomorphic function, Cauchy integral and Laurent series expansion techniques, the relation among the complex potentials for the three material regions is given, and the functional equation in complex potential for the interphase layer are derived. Explicit series solutions are given for the two cases when the screw dislocation is located in the inhomogeneity or in the matrix. The influence of the interphase layer parameters on interaction energy and dislocation force is evaluated and discussed. The present solutions contain a number of novel and previously known results which can be shown to be special cases.     

Electro-elastic stress analysis for a wedge-shaped crack interacting with a screw dislocation in piezoelectric solid

The electro-elastic stress investigation on the interaction problem of a screw dislocation near the tip of a semi-infinite wedge-shaped crack in piezoelectric material has been carried out. Explicit closed-form analytical solutions are obtained for the stress intensity factor (SIF) and the electric displacement intensity factor (EDIF) of the crack, as well as the force on dislocation. The derivation is based on the conformal mapping method and the perturbation technique. The dislocation has Burger's vector normal to the isotropic basal plane, with a line force and a line charge being applied at the core of the dislocation. The influence of the location and the wedge angle of the crack on the image force of the dislocation has been discussed in detail. At the same time the effect of the dislocation on the crack behavior has been also examined under different configurations. Two types of PZT materials are used to numerically illustrate the influences of the wedge angle and the location of the dislocation on the image force and the crack intensities. Results obtained in the current study can be fully reduced to various special cases available in the literatures.     

Electro-elastic behavior induced by an external circular crack in a piezoelectric material

The electro-elastic problem of a transversely isotropic piezoelectric material with a flat crack occupying the outside of a circle perpendicular to the poling axis is considered in this paper. By using the Hankel transform technique, a mixed boundary value problem associated with the considered problem is solved analytically. The results are presented in closed form both for impermeable crack and for permeable crack. A full field solution is given, i.e., explicit expressions for electro-elastic field at any point in the entire piezoelectric space, as well as field intensity factors near the crack front, are determined. A numerical example for a cracked PZT-5H ceramic is given, and the effects of applied electric fields on elastic and electric behaviors are presented graphically.     

压电复合材料的共线周期性裂纹平面问题的电弹性场分析

利用复变函数知识、半逆解法及待定系数法, 研究了压电复合材料的共线周期性裂纹问题, 给出了在电不可渗透边界条件下的应力、电位移、应力强度因子、电位移强度因子和机械应变能释放率的解析解。当裂纹间距趋于无穷时, 共线周期性裂纹退化为一条单裂纹, 得到了压电复合材料一条单裂纹的结果。通过数值算例讨论了共线周期性裂纹的裂纹长度、裂纹间距和机电载荷对机械应变能释放率的影响规律。结果表明, 机械应变能释放率随着共线周期性裂纹的裂纹长度、共线周期性裂纹的裂纹间距、机械载荷和正电场的增大而增大, 随着负电场的增大而减小。     

A piezoelectric screw dislocation in a three-phase composite cylinder model with an imperfect interface

The electroelastic coupling interaction between a piezoelectric screw dislocation and the embedded circular cross-section inclusions with imperfect interfaces in piezoelectric solids is investigated by using a three-phase composite cylinder model. By means of a complex variable technique, the explicit solutions of electroelastic fields are obtained. With the aid of the Peach-Koehler formula, the explicit expression for the image force exerted on the piezoelectric screw dislocation is derived. The image force on the dislocation and its equilibrium positions near one of the inclusions are discussed for variable parameters (interface imperfection and material electroelastic dissimilarity) and the influence of nearby inclusions is also considered. The results show that when compared with the previous solution (the perfect interface), more equilibrium positions of the screw dislocation in the matrix may be available due to the effect of the interface imperfection when the dislocation is close to the electroelastic stiff inclusion. It is also found that the magnitude of the image force exerted on the piezoelectric screw dislocation produced by multiply inclusions is always smaller than that produced by a single inclusion and the impact of nearby inclusions on the mobility of the screw dislocation is very important.