压电螺位错与含界面裂纹圆形涂层夹杂的干涉

研究位于基体或夹杂中任意点的压电螺型位错与含界面裂纹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一般解答. 典型例 子给出了界面含有一条裂纹时，复势函数的精确级数形式解. 基于已获得的复势函数和广 义Peach-Koehler公式，计算了作用在位错上的像力. 讨论了裂纹几何条件，涂层厚度和材 料特性对位错平衡位置的影响规律. 结果表明，界面裂纹对涂层夹杂附近的位错运动有很大 的影响效应，含界面裂纹涂层夹杂对位错的捕获能力强于完整粘结情况；并发现界面裂纹长 度和涂层材料常数达到某一个临界值时可以改变像力的方向. 解答的特殊情形包含了以 往文献的几个结果.     

Electroelastic interaction between a piezoelectric screw dislocation and a circular inhomogeneity with interfacial cracks

A piezoelectric screw dislocation in the matrix interacting with a circular inhomogeneity with interfacial cracks under antiplane shear and in-plane electric loading at infinity was dealt with. Using complex variable method, a general solution to the problem was presented. For a typical case, the closed form expressions of complex potentials in the inhomogeneity and the matrix regions and derived explicitly when the interface containsthe electroelastic field intensity factors weresingle crack. The image force acting on the piezoelectric screw dislocation was calculated by using the perturbation technique and the generalized Peach-Koehler formula. As a result, numerical analysis and discussion show that the perturbation influence of the interfacial crack on the interaction effects of the dislocation and the inhomogeneity is significant which indicates the presence of the interfacial crack will change the interaction mechanism when the length of the crack goes up to a critical value. It is also shown that soft inhomogeneity can repel the dislocation due to their intrinsic electromechanical coupling behavior.     

Interaction between a screw dislocation and an elastic elliptical inhomogeneity with interfacial cracks

The elastic interaction between a screw dislocation and an elliptical inhomogeneity with interfacial cracks is studied. The screw dislocation may be located outside or inside the inhomogeneity. An efficient complex variable method for the complex multiply connected region is developed, and the general solutions to the problem are derived. As illustrative examples, solutions in explicit series form for complex potentials are presented in the case of one or two interfacial cracks. Image forces on the dislocation are calculated by using the Peach-Koehler formula. The influence of crack geometries and material properties on the image forces is evaluated and discussed. It is shown that the interfacial crack has a significant effect on the equilibrium position of the dislocation near an elliptical-arc interface. The main results indicate, when the length of the crack goes up to a critical value, the presence of the interfacial crack can change the interaction mechanism between a screw dislocation and an elliptical inclusion. The present solutions can include a number of previously known results as special cases.The project supported by the National Natural Science Foundation of China(10272009 and 10472030) and the Natural Science Foundation of Hunan Province(02JJY2014)     

压电螺型位错和共线界面刚性线夹杂的干涉效应

研究了压电材料中压电螺型位错和共线界面导电刚性线夹杂的电弹干涉效应．运用复变函数解析延拓技术与奇性主部分析方法,获得了该问题的一般解答．作为算例,求出了界面含一条刚性线夹杂时两种压电介质区域广义应力函数的封闭形式解．导出了作用在位错上的像力和刚性线夹杂表面剪应力和电位移的解析表达式．讨论了界面刚性线长度,两种材料的剪切模量比和压电系数比对位错力和刚性线表面剪应力的影响规律．为进一步研究该类问题提供了一个基本解。     

Piezoelectric screw dislocations interacting with a circular inclusion with imperfect interface

The electroelastic coupling interaction between multiple screw dislocations and a circular inclusion with an imperfect interface in a piezoelectric solid is investigated. The appointed screw dislocation may be located either outside or inside the inclusion and is subjected to a line charge and a line force at the core. The analytic solutions of electroelastic fields are obtained by means of the complex-variable method. With the aid of the generalized Peach–Koehler formula, the explicit expressions of image forces exerted on the piezoelectric screw dislocations are derived. The motion and the equilibrium position of the appointed screw dislocation near the circular interface are discussed for variable parameters (interface imperfection, material electroelastic mismatch, and dislocation position), and the influence of the nearby parallel screw dislocations is also considered. It is found that the piezoelectric screw dislocation is always attracted by the electromechanical imperfect interface. When the interface imperfection is strong, the impact of material electroelastic mismatch on the image force and the equilibrium position of the dislocation becomes weak. Additionally, the effect of the nearby dislocations on the mobility of the appointed dislocation is very important.     

A generalized screw dislocation interacting with interfacial cracks along a circular inhomogeneity in magnetoelectroelastic solids

The interaction of a generalized screw dislocation with circular arc interfacial cracks under remote antiplane shear stresses, in-plane electric and magnetic loads in transversely isotropic magnetoelectroelastic solids is dealt with. By using the complex variable method, the general solutions to the problem are presented. The closed-form expressions of complex potentials in both the inhomogeneity and the matrix are derived for a single circular-arc interfacial crack. The intensity factors of stress, electric displacement and magnetic induction are provided explicitly. The image forces acting on the dislocation are also calculated by using the generalized Peach–Koehler formula. For the case of piezoelectric matrix and piezomagnetic inclusion, the shielding and anti-shielding effect of the dislocation upon the stress intensity factors is evaluated in detail. The results indicate that if the distance between the dislocation and the crack tip remains constant, the dislocation in the interface will have a largest shielding effect which retards the crack propagation. In addition, the influence of the interfacial crack geometry and materials magnetoelectroelastic mismatch upon the image force is discussed. Numerical computations show that the perturbation effect of the above parameters upon the image force is significant. The main result shows that a stable or unstable equilibrium point may be found when a screw dislocation approaches the surface of the crack from infinity which differs from the perfect bonded case under the same conditions. The present solutions contain a number of previously known results which can be shown to be special cases.     

Electroelastic interaction between piezoelectric screw dislocation and circularly layered inclusion with imperfect interfaces

The interaction between a piezoelectric screw dislocation and an interphase layer in piezoelectric solids is theoretically investigated.Here,the dislocation located at arbitrary points inside either the matrix or the inclusion and the interfaces of the interphase layer are imperfect.By the complex variable method,the explicit solutions to the complex potentials are given,and the electroelastic fields can be derived from them.The image force acting on the dislocation can be obtained by the generalized PeachKoehler formula.The motion of the piezoelectric screw dislocation and its equilibrium positions are discussed for variable parameters.The important results show that,if the inner interface of the interphase layer is imperfect and the magnitude of degree of the interface imperfection reaches the certain value,two equilibrium positions of the piezoelectric screw dislocation in the matrix near the interface are found for the certain material combination which has never been observed in the previous studies(without considering the interface imperfection).     

Interaction of a screw dislocation with an interfacial edge crack in a two-phase piezoelectric material

The interaction of a screw dislocation with an interfacial edge crack in a two-phase piezoelectric medium is investigated. Closed-form solutions of the elastic and electrical fields induced by the screw dislocation are derived using the conformal mapping method in conjunction with the image principle. Based on the electroelastic fields derived, the stress and electric displacement intensity factors, the image force acting on the dislocation are given explicitly. We find that the stress and electric displacement intensity factors depend on the effective electroelastic material constants. In the case where one of two phases is purely elastic, the stress intensity factor and image force are plotted to illustrate the influences of electromechanical coupling effect, the position of the dislocation and the material properties on the interaction mechanism. The project supported by the Doctoral Foundation of Hebei Province (B2003113)     

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.     

On the electroelastic interaction of a piezoelectric screw dislocation with an elliptical inclusion in piezoelectric materials

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Electroelastic interaction between a piezoelectric screw dislocation and a confocal elliptic blunt crack with elliptical inhomogeneity

The electroelastic interaction between a piezoelectric screw dislocation and an elliptical inhomogeneity containing a confocal blunt crack under infinite longitudinal shear and in-plane electric field is investigated. Using the sectionally holomorphic function theory, Cauchy singular integral, singularity analysis of complex functions and theory of Rieman boundary problem, the explicit series solution of stress field is obtained when the screw dislocation is located in inhomogeneity. The intervention law of the interaction between blunt crack and screw dislocation in inhomogeneity is discussed. The analytical expressions of generalized stress and strain field of inhomogeneity are calculated, while the image force, field intensity factors of blunt crack are also presented. Moreover, a new matrix expression of the energy release rate and generalized strain energy density (SED) are deduced. With the size variation of blunt crack, the results can be reduced to the case of the interaction between a piezoelectric screw dislocation and a line crack in inhomogeneity. Numerical analysis are then conducted to reveal the effects of the dislocation location, the size of inhomogeneity and blunt crack and the applied load on the image force, energy release rate and strain energy density. The influence of dislocation on energy release rate and strain energy density is also revealed.     

Exact solutions for piezoelectric screw dislocations near two asymmetrical edge cracks emanating from an elliptical hole

The interaction between piezoelectric screw dislocations and two asymmetrical interfacial cracks emanating from an elliptic hole under combined mechanical and electric load at infinity is dealt with. The closed-form solutions are derived for complex potentials and generalized stress fields. In the limiting cases, some well-known results can be obtained from the present solutions. Moreover, some new exact solutions are shown. The stress intensity factor and the energy release rate at the right tip due to a screw dislocation near the right interfacial crack are also calculated. The results show that the shielding effect of dislocation on crack expanding decreases with the increase in dislocation azimuth angle and the distance between the dislocation and the crack tip, and the repulsion acting on the dislocation from the other half plane demotes crack propagation. The increasing of the length of the other crack promotes crack growth, but the increasing of the minor semi-axis demotes it.     

A SCREW DISLOCATION IN A THREE-PHASE COMPOSITE CYLINDER MODEL WITH INTERFACIAL RIGID LINES

The problem of the elastic interaction between a screw dislocation and a three-phase circular inclusion with interracial rigid lines （anti-cracks） is investigated. An efficient and concise method for the complex multiply connected region is developed, with which explicit series form solutions of the complex potentials in the matrix, and the interphase layer and inclusion regions are derived. Based on the complex potentials, the image force on the screw dislocation is then calculated by using the Peach-Koehler formula. The equilibrium position of the dislocation is discussed in detail for various rigid line geometries, interphase layer thicknesses and material property combinations. The main results show that the interracial rigid lines exert a significant perturbation effect on the motion of the screw dislocation near the circular inclusion surrounded by an interphase layer.     

Analysis of a piezoelectric screw dislocation inside an elliptical inhomogeneity with confocal rigid line in piezoelectric material

This paper deals with the electro-elastic coupling interaction between a piezoelectric screw dislocation which is located inside the elliptical inhomogeneity and an electrically conductive confocal rigid line under remote anti-plane shear stresses and in-plane electrical loads in piezoelectric composite material. The analytical-functions of the complex potentials, stress fields and the image force acting on the piezoelectric screw dislocation are obtained based on the principle of conformal mapping, the method of series expansion, the technical of analytic continuation and the analysis of singularity of complex potentials. The rigid line and the piezoelectric material property combinations upon the image force and the equilibrium position of the dislocation are discussed in detail by the numerical computation.     

On a semi-infinite crack penetrating a piezoelectric circular inhomogeneity with a viscous interface

We investigate a semi-infinite crack penetrating a piezoelectric circular inhomogeneity bonded to an infinite piezoelectric matrix through a linear viscous interface. The tip of the crack is at the center of the circular inhomogeneity. By means of the complex variable and conformal mapping methods, exact closed-form solutions in terms of elementary functions are derived for the following three loading cases: (i) nominal Mode-III stress and electric displacement intensity factors at infinity; (ii) a piezoelectric screw dislocation located in the unbounded matrix; and (iii) a piezoelectric screw dislocation located in the inhomogeneity. The time-dependent electroelastic field in the cracked composite system is obtained. Particularly the time-dependent stress and electric displacement intensity factors at the crack tip, jumps in the displacement and electric potential across the crack surfaces, displacement jump across the viscous interface, and image force acting on the piezoelectric screw dislocation are all derived. It is found that the value of the relaxation (or characteristic) time for this cracked composite system is just twice as that for the same fibrous composite system without crack. Finally, we extend the methods to the more general scenario where a semi-infinite wedge crack is within the inhomogeneity/matrix composite system with a viscous interface.     

The interaction between a screw dislocation and a piezoelectric fiber composite with a wedge crack

The interaction problem between a screw dislocation and a piezoelectric fiber composite with a semi-infinite wedge crack is investigated in this paper. The piezoelectric media are assumed to be transversely isotropic with the poling direction along the x ₃ direction. The screw dislocation considered here involves a Burgers vector parallel to the poling direction with a line force and a line charge being applied at the core of the dislocation. Both cases of the screw dislocation located at the matrix and inclusion are observed. The analytical derivation is based on the complex variable and the conformal mapping methods. The exact solutions are obtained to calculate the forces on the dislocation and the crack-tip stress and electric displacement intensity factors. Based on these results, the anti-shielding and shielding effects for different loadings, material combinations, and geometric configurations are discussed in detail.     

INTERACTION OF A DISLOCATION DIPOLE WITH A MODE Ⅲ INTERFACE CRACK

Interaction between a screw dislocation dipole and a mode Ⅲ interface crack is investigated. By using the complex variable method, the closed form solutions for complex potentials are obtained when a screw dislocation dipole lies inside a medium. The stress fields and the stress intensity factors at the tip of the interface crack produced by the screw dislocation dipole are given. The influence of the orientation, the dipole arm and the location of the screw dislocation dipole as well as the material mismatch on the stress intensity factors is discussed. zThe image force and the image torque acting on the screw dislocation dipole center are also calculated. The mechanical equilibrium position of the screw dislocation dipole is examined for various material property combinations and crack geometries. The results indicate that the shielding or anti-shielding effect on the stress intensity factor increases abruptly when the dislocation dipole approaches the tip of the crack. Additionally, the disturbation of the interface crack on the motion of the dislocation dipole is also significant.     

Edge dislocation interacting with an interfacial crack along a circular inhomogeneity

The elastic interaction of an edge dislocation, which is located either outside or inside a circular inhomogeneity, with an interfacial crack is dealt with. Using Riemann–Schwarz’s symmetry principle integrated with the analysis of singularity of the complex potentials, the closed form solutions for the elastic fields in the matrix and inhomogeneity regions are derived explicitly. The image force on the dislocation is then determined by using the Peach–Keohler formula. The influence of the crack geometry and material mismatch on the dislocation force is evaluated and discussed when the dislocation is located in the matrix. It is shown that the interfacial crack has significant effect on the equilibrium position of the edge dislocation near a circular interface. The results also reveal a strong dependency of the dislocation force on the mismatch of the shear moduli and Poisson’s ratios between the matrix and inhomogeneity.     

刃型位错和圆弧形刚性线夹杂的干涉效应

位错和夹杂的干涉效应对于理解材料的强化和韧化机理具有十分重要的意义。文中研究了晶体材料中刃型位错和多条共圆弧刚性线夹杂的干涉作用。利用Riemann—Schwarz反照原理和复势函数的奇性主部分析技术，得到了问题的一般解答；对于只含一条刚性线夹杂的情况，给出了复势函数的封闭形式解。由Peach-Koehler公式求出了作用在刃型位错上的位错力，并讨论了圆弧形刚性线夹杂对位错力的影响规律，发现弧形刚性线对刃型位错有很强的排斥作用。本文解答不但可作为格林函数获得任意分布位错的相应解答，而且可以用于研究刚性线夹杂和任意形状裂纹的干涉效应问题。     

位错偶极子和Ⅲ型界面裂纹的干涉效应

研究了多晶体材料中螺型位错偶极子和界面裂纹的弹性干涉作用.利用复变函数方法,得到了该问题复势函数的封闭形式解答.求出了由位错偶极子诱导的应力场和裂纹尖端应力强度应子,分析了偶极子的方向,偶臂和位置以及材料失配对应力强度因子的影响.推导了作用在螺型位错偶极子中心的像力和力偶矩,并讨论了界面裂纹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.结果表明,裂纹尖端的螺型位错偶极子对应力强度因子会产生强烈的屏蔽或反屏蔽效应.同时,界面裂纹对螺型位错偶极子在材料中运动有很强的扰动作用.