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．     

压电复合材料圆形夹杂中螺型位错和界面裂纹的干涉分析

研究了无穷远纵向剪切和面内电场共同作用下,压电复合材料圆形夹杂中螺型位错与界面裂纹的电弹耦合干涉作用．运用Riemann-Schwarz 对称原理,并结合复变函数奇性主部分析方法,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和电弹性场的封闭形式解．应用广义Peach-Koehler公式,导出了位错力的解析表达式．分析了裂纹几何参数和材料的电弹性常数对位错力的影响规律．结果表明,界面裂纹对位错力和位错平衡位置有很强的扰动效应,当界面裂纹长度达到临界值时,可以改变位错力的方向．该结果可以作为格林函数研究圆形夹杂内裂纹和界面裂纹的干涉效应．其公式的退化结果与已有文献完全一致．     

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.     

压电材料椭圆夹杂界面局部脱粘问题的分析

利用复变函数方法,研究在反平面剪切和面内电场共同作用下压电材料椭圆夹杂的界面脱粘问题．假定夹杂界面脱粘导致了界面电绝缘型裂纹的产生．通过保角变换和解析延拓,将原问题化为两个黎曼-希尔伯特问题,获得了夹杂和基体复势的级数解,进而求得应力变形场以及夹杂-基体界面脱粘的能量释放率的一般表达式．通过理想粘结的椭圆夹杂、完全脱粘的椭圆夹杂、局部脱粘的刚性导体椭圆夹杂、局部脱粘的圆形夹杂等特例的分析说明了该解的有效性和通用性．     

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。     

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.     

压电基体中部分脱开的刚性导体椭圆夹杂分析

通过利用八维Stroh公式以及共形映射、解析延拓和奇点分析技术,获得了对一压电基体中已部分脱开的刚性导体椭圆夹杂二维问题的闭合形式全场解答。也推导了一些新的恒等式和求和式,通过这些恒等式及求和式可获得沿界面应力和电位移分布以及刚性夹杂转动的实形式表示。正如所预料的,在脱开界面的端部应力及电位移显现出与在压电材料Griffith界面裂纹的研究中所发现的相似的奇异行为。最后也给出了几个算例以展示所得到解答的一般性以及各种载荷条件、几何参数和机电常数等对界面处应力及电位移分布的影响。     

含椭圆形夹杂的压电体平面应变问题

利用复变函数理论,对在无限远处均匀应力和电位移载荷作用下的含有椭圆形弹性夹杂的横观各向同性压电材料,作了力电分析．在该文有限元结果和前人相关理论解的基础上,提了出一个可接受的认为弹性夹杂体内的应力场为常应力场的假设．在采用了不导通电边界条件之后,获得了以复势形式表示的压电基体的和弹性夹杂体内部的应力场解．     

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.     

圆形界面刚性线夹杂的平面问题

研究了圆弧形界面刚性线夹杂的平面弹性问题．集中力作用于夹杂或基体中的任意点,并且无穷远处受均匀载荷作用．利用复变函数方法,得到了该问题的一般解答．当只含一条界面刚性线夹杂时,获得了分区复势函数和应力场的封闭形式解答,并给出刚性线端部奇异应力场的解析表达式．结果表明,在平面荷载下界面圆弧形刚性线夹杂尖端应力场和裂纹尖端相似具有奇异应力振荡性．对无穷远加载的情况,讨论了刚性线几何条件、加载条件和材料失配对端部场的影响．     

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.     

Imperfect interface effect for nano-composites accounting for fiber section shape under antiplane shear

This paper investigates the elastic responses of fibrous nano-composites with imperfectly bonded interface under longitudinal shear. The proposed imperfect interface model is the shear lag (or the spring layer) model; the presented nano interfacial stress model is the Gurtin–Murdoch surface/interface model; and the three-phase confocal elliptical cylinder model is the geometry model accounting for the fiber section shape. By virtue of the complex variable method, a generalized self-consistent method is employed to derive the closed from solution of the effective antiplane shear modulus of the fibrous nano-composites with imperfect interface. Five existing solutions can be regarded as the limit form the present analytic expression. The influences of the interface elastic constant, the interfacial imperfection parameter, the size of the elliptic section fiber, the fiber section aspect ratio, the fiber volume fraction and the fiber elastic property on the effective antiplane shear modulus of the nano-composites are discussed. Particularly, numerical results demonstrate that the interfacial elastic imperfection will always cause a significant reduction in the effective antiplane shear modulus; and the fiber interface stress effect on the effective modulus of the fibrous nano-composites will weaken with the interfacial imperfection increases.     

Micro-statistical modeling of an imperfect interface in a piezoelectric bimaterial under inplane static deformations

A micro-statistical model is proposed for investigating the effective properties of a micro-damaged interface between a piezoelectric layer and a piezoelectric half-space under inplane electroelastostatic deformations. The interface is modeled as damaged by periodic arrays of micro-cracks. The lengths and the positions of the micro-cracks on a period interval of the interface are randomly generated. The conditions on the interfacial micro-cracks are formulated in terms of hypersingular integro-differential equations with the displacement and electrical potential jumps across the interface being unknown functions to be determined. To gain new useful physical insights into the behaviors of the imperfect interface, the influences of the material constants, the width of the layer and the crack densities of the interface on the effective properties of the interface are examined in details.     

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.     

Dynamic electromechanical behavior of a triple-layer piezoelectric composite cylinder with imperfect interfaces

The dynamic electromechanical behavior of a triple-layer piezoelectric composite cylinder with imperfect interfaces is investigated. The composite cylinder is constructed by two elastic layers and an embedded piezoelectric layer. A linear spring model is adopted to describe the weakness of imperfect interface. The exact analysis is performed by the state space method and normal mode expansion method. The determining procedure for the eigenfunction and the proof of the orthogonal property of the eigenfunction is presented for an imperfectly bonded triple-layer piezoelectric composite cylinder. The obtained solution is valid for analyzing the dynamic electromechanical behavior of composite cylinder with arbitrary thickness for both elastic and piezoelectric layers. Numerical results show that the weakness of imperfect interface has significant effect on the transient electromechanical responses of piezoelectric composite cylinder.     

On the uniform stress state inside an inclusion of arbitrary shape in a three-phase composite

The stress field inside a two-dimensional arbitrary-shape elastic inclusion bonded through an interphase layer to an infinite elastic matrix subjected to uniform stresses at infinity is analytically studied using the complex variable method in elasticity. Both in-plane and anti-plane shear loading cases are considered. It is shown that the stress field within the inclusion can be uniform and hydrostatic under remote constant in-plane stresses and can be uniform under remote constant anti-plane shear stresses. Both of these uniform stress states can be achieved when the shape of the inclusion, the elastic properties of each phase, and the thickness of the interphase layer are properly designed. Possible non-elliptical shapes of inclusions with uniform hydrostatic stresses induced by in-plane loading are identified and divided into three groups. For each group, two conditions that ensure a uniform hydrostatic stress state are obtained. One condition relates the thickness of the interphase layer to elastic properties of the composite phases, while the other links the remote stresses to geometrical and material parameters of the three-phase composite. Similar conditions are analytically obtained for enabling a uniform stress state inside an arbitrary-shape inclusion in a three-phase composite loaded by remote uniform anti-plane shear stresses.