压电螺型位错和含界面裂纹圆形夹杂的电弹干涉效应

研究了在无穷远反平面剪切和面内电场共同作用下压电材料基体中一个压电螺型位错与含界面裂纹圆形弹性夹杂的电弹耦合干涉作用．运用复变函数方法,获得了该问题的一般解答．作为典型算例,求出了界面含一条裂纹时,基体和夹杂区域复势函数的封闭形式解以及裂纹尖端应力和电位移场强度因子．应用扰动技术和广义Peach-Koehler公式,导出了位错力的解析表达式．数值结果表明,界面裂纹对压电螺型位错与夹杂的干涉具有强烈扰动效应,当裂纹长度达到临界值时,可以改变其干涉机理．同时,分析说明压电材料中软夹杂可以排斥基体中的位错．     

压电螺型位错与含非理想界面层圆形夹杂的干涉效应

研究了位于压电材料基体或夹杂中任意点的压电螺型位错与含非理想界面层圆形夹杂的电弹性干涉问题．运用复变函数方法,获得了复势函数的精确解．由广义Peach-Koehler公式,导出了作用在螺型位错上的像力的精确表达式．讨论了不同参数对压电螺型位错的运动和平衡位置的影响规律．研究结果表明,对某些材料组合,当界面层的内界面是非理想界面且界面的非理想度达到一定值时,在基体中靠近界面处会出现两个位错的平衡位置,此现象未在以往研究(不考虑非理想界面)中观察到．     

夹杂与基体对界面层螺旋位错的干涉效应

研究圆形夹杂与基体对有限厚度界面层螺旋位错的干涉问题。结合复变函数的分区亚纯函数理论、施瓦兹对称原理与柯西型积分运算,发展了多连通域联结问题的一个有效分析方法,将3个区域应力函数的联结问题化归为界面层应力函数的函数方程,并求得了显式级数解。利用该结果,研究与讨论了界面层螺旋位错能与位错力。     

SH波对界面含有半圆形脱胶的圆柱形弹性夹杂的散射的近似分析

采用Green函数法、复变函数法研究了SH波对界面附近含有半圆形脱胶的圆柱形弹性夹杂的散射,并给出了动应力集中系数的数值结果．首先,界面将整个空间分成上下两部分．在下半空间,给出在含有半圆形凸起的圆柱形弹性夹杂的弹性半空间中,水平表面上任意一点承受时间谐和的出平面线源荷载作用时的位移函数．其次,取该位移函数作为Green函数．上下空间连接时在界面处满足连续性条件,构造出半圆形脱胶裂纹,进而求出应力和位移的表达式．最后作为算例,给出了动应力集中系数的数值结果,分析了介质参数和入射波参数对动应力集中的影响情况．     

楔型向错偶极子和裂纹的干涉效应

研究了晶体材料中一个楔型向错偶极子与裂纹的弹性干涉效应．运用复变函数方法获得了复势函数和应力场的封闭形式解答,导出了裂纹尖端应力强度因子和作用在向错偶极子中心点像力的解析表达式．获得了向错偶极子的位置、方向和偶臂长度对裂纹尖端应力强度因子的影响规律,并讨论了裂纹附近向错偶极子的平衡位置．结果表明向错偶极子靠近裂纹尖端时,对应力强度因子有明显的屏蔽或反屏蔽作用．     

半无限一维六方准晶压电双材料中的螺型位错

研究了半无限大一维六方准晶压电双材料中的螺型位错问题,利用镜像位错法,获得了电弹性场的解析表达式,分析了含螺型位错半无限大准晶压电双材料中声子场应力,相位子场应力以及电位移的分布特征.基于广义Peach Koehler公式,得到了作用在位错上的像力,讨论了声子场-相位子场耦合弹性常数对作用在位错上像力的影响,为实际应用奠定了理论基础.为实际应用奠定了理论基础.     

各向异性双材料中运动螺型位错与界面刚性线的干涉

研究了各向异性双材料中匀速运动螺型位错与界面刚性线的干涉问题.运用Riemann Schwarz解析延拓技术与复势函数奇性主部分析方法,获得了该问题的一般弹性解答,求出了界面含一条和两条刚性线情况下的封闭形式解,并给出了刚性线尖端的应力强度因子和作用于运动位错上的像力的显式表达式.结果表明,位错速度增大可以削弱位错对应力强度因子的反屏蔽效应;位错速度越大,位错平衡点越靠近刚性线,退化结果与已有的解答完全吻合.     

压电螺位错与椭圆夹杂的电弹相互作用

研究了压电材料中压电螺位错与椭圆夹杂的电弹相互作用.基于扰动概念和级数展开方法,推导了基体和夹杂的弹性场和电场,在此基础上给出了作用于位错上像力的表达式.通过分析基体与夹杂的相对刚度和机电耦合强弱对像力的影响,得到了新的相互作用机理.     

热偶极子与圆形界面裂纹的作用

热偶极子由热源和热汇组成.应用解析延拓方法、广义Liouville 定理及Muskhelishvili 边值问题理论,研究了在热源偶极子作用下含圆形夹杂复合材料的界面裂纹问题.导出温度场和应力场之后,分析了温度场和夹杂对界面断裂的效应.作为实例,针对若干种组合材料及热偶极子处于不同位置,给出了界面裂纹热应力强度因子的数值变化曲线.结果表明,界面裂纹特性取决于材料的弹性常数和热学性能及偶极子的情况.     

半平面压电体的Green函数及其应用

本文研究半平面压电体在线力、电荷和位错作用下的弹性场和电场，即Green函数．基于各向异性弹性力学中的Stroh方法和解析延拓理论，推导了Green函数的封闭形式的解．作为解的应用，分析了含半无限裂纹的无限大压电介质的机电耦合场，给出了应力和电位移强度因子的解析表达式．     

The interaction between a screw dislocation and a rigid line in a confocal elliptical inhomogeneity

The interaction between a screw dislocation and an elastic elliptical inhomogeneity which contains a confocal rigid line is investigated. The screw dislocation is located inside either the elliptical inhomogeneity or the infinite matrix. By using the complex potential method, explicit series solutions of complex potentials are obtained. The image force acting on the screw dislocation and the stress intensity factor at the tip of the rigid line are derived. As a result, the analysis and discussion show that the influence of the rigid line on the interaction effects between a screw dislocation and an elliptical inhomogeneity is significant. The rigid line enhances the repulsive force exerted on the dislocation produced by the stiff inhomogeneity and abates the attractive force produced by the soft inhomogeneity. For the soft inhomogeneity, there is an unstable equilibrium position when the dislocation is inside the matrix and there is a stable equilibrium position when the dislocation is inside the inhomogeneity. The stress intensity factor contour around the rigid line tip shows that when a dislocation with positive burgers vector is in the upper half-plane, stress intensity factor will be positive; while in the lower half-plane, stress intensity factor will be negative; and in the x-axis, it will be zero. The absolute value of the stress intensity factor will increase when the dislocation approaches the tip of the rigid line. The stress intensity factor at the rigid line tip is enhanced by a harder matrix and abated by a softer matrix.     

Joint deformation of a circular inclusion and a matrix

An elastic infinite plane containing a circular inclusion with given jumps of tractions and displacements along the interface and nonzero conditions at infinity is considered. Explicit expressions are derived for the Goursat-Kolosov complex potentials of this problem. The solution constructed can be used to examine various circular interfacial defects, including interfacial cracks and rigid parts of the interface. The problem under consideration is fundamental for the superposition method, which solves many problems in which a circular region is an element of a polyphase elastic medium. In such cases, the well-posedness of the problem, which depends on the interrelation between the jumps of tractions and displacements, follows from the very superposition method. The application techniques of this method are demonstrated for singular problems on the action of a point force and an edge dislocation located inside an inclusion or in the matrix. Computational results for the tractions arising at the interface under the action of a point force concentrated in the inclusion are given.     

On a partially debonded rigid line inclusion penetrating a circular inhomogeneity

We derive closed-form solutions to the mixed boundary value problem of a partially debonded rigid line inclusion penetrating a circular elastic inhomogeneity under antiplane shear deformation. The two tips of the rigid line inclusion are just mutual mirror images with respect to the inhomogeneity/matrix interface, and the upper part of the rigid line inclusion is debonded from the surrounding materials. By using conformal mapping and the method of image, closed-form solutions are derived for three loading cases: (i) the matrix is subjected to remote uniform stresses; (ii) the matrix is subjected to a line force and a screw dislocation; and (iii) the inhomogeneity is subjected to a line force and a screw dislocation. In the mapped ξ-plane, the solutions for all the three loading cases are interpreted in terms of image singularities. For the remote loading case, explicit full-field expressions of all the field variables such as displacement, stress function and stresses are obtained. Also derived is the near tip asymptotic elastic field governed by two generalized stress intensity factors. The generalized stress intensity factors for all the three loading cases are derived.     

Electroelastic State of a Multiply Connected Piezoelectric Half Plane with Holes and Cracks

A method has been proposed [1] for solving two-dimensional electroelasticity problems using generalized complex potentials. General representations of complex potentials for a multiply coupled region have been studied [2] and a method for calculating the stress intensity factors and induction has been introduced. In this article, general expressions are obtained for the complex potentials for a multiply connected half plane with arbitrarily positioned holes and rectilinear cracks and the electroelastic state of a half plane with a single elliptical hole or rectilinear crack is studied.     

Green's functions for a point force and dislocation outside an elliptic inclusion in plane elasticity

The plane elasticity problem of an infinite plate containing an elliptic inclusion is considered. The Green's functions for a point force and/or a dislocation located outside the inclusion are derived. By using the complex potential approach of Muskhelishvili, the general solutions are obtained in a form of carefully selected functions plus an infinite series. The numerical convergence of the solutions is better than that of Stagni-Lizzio's solutions. The proposed solutions can also be applied to the case of a point force and dislocation acting at a point right on the interface.     

A circular inhomogeneity with a mixed-type imperfect interface in anti-plane shear

We present a rigorous study of the problem associated with a circular inhomogeneity embedded in an infinite matrix subjected to anti-plane shear deformations. The inhomogeneity and the matrix are each endowed with separate and distinct surface elasticities and are bonded together through a soft spring-type imperfect interphase layer. This combination is referred to in the literature as a ‘mixed-type imperfect interface’ due to the fact that the soft interphase layer (described by the spring model) is bounded by two stiff interfaces arising from the separate surface elasticities of the inhomogeneity and the matrix. The entire composite is subjected to remote shear stresses and we allow for the presence of a screw dislocation in either the inhomogeneity or the matrix. The corresponding boundary value problem is reduced to two coupled second-order differential equations for the two analytic functions defined in the two phases (as well as their analytical continuations) leading to solutions in either series or closed-form. The analysis indicates that the stress field in the composite and the image force acting on the screw dislocation can be described completely in terms of three size-dependent parameters and a size-independent mismatch parameter. Interestingly, in the absence of the screw dislocation, the size-dependent stress field inside the inhomogeneity is uniform. Several numerical examples are presented to demonstrate the solution for a screw dislocation located inside the matrix. The results show that it is permissible for the dislocation to have multiple equilibrium positions.