增强相/夹杂内螺位错偶极子与含共焦钝裂纹椭圆夹杂的干涉效应

运用弹性力学的复势方法,研究了纵向剪切下增强相/夹杂内螺型位错偶极子与含共焦钝裂纹椭圆夹杂的干涉效应,得到了该问题复势函数的封闭形式解答,由此推导出了夹杂区域的应力场、作用在螺型位错偶极子中心的像力和像力偶矩以及裂纹尖端应力强度因子级数形式解。并分析了位错偶极子倾角 、钝裂纹尺寸和材料常数对位错像力、像力偶矩以及应力强度因子的影响。数值计算结果表明：位错像力、像力偶矩以及应力强度因子均随位错偶极子倾角做周期变化;夹杂内部的椭圆钝裂纹明显增强了硬基体对位错的排斥,减弱了软基体对位错的吸引,且对于硬夹杂,位错出现了一个不稳定平衡位置,该平衡位置随钝裂纹曲率的增大不断向界面靠近;变化 值将出现改变位错偶极子对应力强度因子作用方向的临界值。     

螺型位错偶极子与圆形界面刚性线的干涉效应研究

本文重点研究螺型住错偶极子和圆形夹杂界面刚性线的弹性干涉效应。利用复变函数方法,得到了该问题的一般解;此外还求出了只含一条界面刚性线时的封闭解答,得到了刚性线尖端的应力强度因子以及作用在螺型位错偶板子中心的像力和像力偶矩。研究结果表明：位错偶板子对应力强度因子具有很强的屏蔽或反屏蔽效应;软夹杂吸引位错偶极子,而刚性线排斥位错偶板子,在一定条件下,位错偶极子在刚性线附近出现一个平衡位置;当刚性线的长度争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;刚性线长度对位错偶极子中心像力偶矩也有很大的影响。     

含非完整界面涂层夹杂中螺型位错的弹性分析

研究了含非完整界面圆形涂层夹杂内部一个螺型位错在夹杂、涂层与无限大基体材料中产生的弹性场.运用复变函数函数方法,获得了三个区域复势函数的解析解答.利用求得的应力场和Peach-Koehler公式,得到了作用在螺型位错上位错力的精确表达式.主要讨论了两个非完整界面对位错力的影响规律.结果表明,涂层界面对夹杂内部螺型位错的吸引力随着界面粘结强度的弱化而变大.界面非完整程度增加削弱材料弹性失配对位错力的影响.在一定条件下,非完整界面可以改变夹杂内位错与涂层/基体系统之间的引斥干涉规律,并使位错在夹杂内部产生一个稳定或非稳定的平衡点.     

穿透夹杂界面的半无限楔形裂纹尖端螺型位错的发射研究

摘要：研究了穿透圆形夹杂界面的半无限楔形裂纹与裂纹尖端螺型位错的干涉问题。应用复变函数解析延拓技术与奇性主部分析方法,得到了位错位于半圆形夹杂内部时,半无限基体和半圆形夹杂内复势函数的解析解。然后利用保角映射技术得到了穿透圆形夹杂界面的半无限楔形裂纹尖端螺型位错产生的应力场以及作用在位错上的位错力的解析表达式。主要讨论了螺型位错对裂纹的屏蔽效应以及从楔形裂纹尖端发射位错的临界载荷条件。研究结果表明正的螺型位错可以削弱楔形裂纹尖端的应力强度因子,屏蔽裂纹的扩展,屏蔽效应随位错方位角的增大而减小。位错发射所需的无穷远临界应力随发射角的增加而增大,最可能的位错发射角度为零度,直线裂纹尖端位错的发射比楔形裂纹尖端位错的发射更容易,硬基体抑制位错的发射。     

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。     

含界面刚性线夹杂与广义压电位错双压电介质的电弹性分析

研究了双压电材料中广义压电位错与分布于界面的刚性共线线夹杂相互作用问题.基于线性压电理论Stroh框架,相应的混合边值问题,可化为常见的Hilbert问题.求解Hilben问题,得到存在界面刚性线夹杂与位错时,压电体内所有场变量的显式表达.给出了由于界面和刚性线夹杂的存在,作用于广义压电位错上的广义Peach-Koehler镜像力.对均匀压电材料这一特殊情况,给出了数值算例,讨论了位错对刚性线夹杂端部场强度因子的干涉和它们之间的相互作用.结果可作为求解界面刚性线夹杂与微裂纹交互作用问题的Green函数,也可作为边界元方法的核函数.     

含界面效应纳米尺度圆环形涂层中螺型位错分析

研究了纳米尺度圆环形涂层(界面层)中螺型位错与圆形夹杂以及无限大基体材料的干涉效应.涂层与夹杂的界面和涂层与基体的界面均考虑界面应力效应.运用复势方法,获得了三个区域复势函数的解析解答.利用求得的应力场和Peach-Koehler公式,得到了作用在螺型位错上位错力的精确表达式.主要讨论了界面应力对涂层(界面层)中螺型位错运动和平衡稳定的影响规律.结果表明,界面应力对界面附近位错的运动有大的影响,由于界面应力的存在,可以改变涂层内位错与夹杂/基体干涉的引斥规律,并使位错在涂层内部产生三个稳定或非稳定的平衡点.考虑界面效应后,有一个额外的排斥力或吸引力作用在位错上,使原有的位错力增加或减小.     

含界面层圆形夹杂中螺旋位错的弹性分析

研究了复合材料含界面层圆形夹杂内部的一个螺旋位错在夹杂，界面层与基体材料中产生的弹性干涉，将复变函数的分区亚纯函数理论与柯西型积分，罗朗级数相结合，求出了各分区复势的解析关系，化为一个关于界面层复势的函数方程，用显示式表达了问题的结果，揭示了界面层参数对位错干涉能与位错力的影响规律。该解析方法较经典级数方法未知量大量减少，表达式更加简洁，结果的特殊情形包含了若干已有成果。     

弹性椭圆夹杂纵向剪切问题

获得纵向剪切下弹性椭圆夹杂问题的精确解。将复变函数的分区全纯函数理论，Cauchy型积分和Riemann边值问题相结合，求得各复势函数之间的解析关系，从而得到问题的封闭形式解，并给出了界面应力的解析表达式。本文解答与已有文献结果一致。本文发展的分析方法，为求解复杂多连通域的平面弹性问题提供了一条有效途径。     

压电材料椭圆夹杂界面开裂问题的电弹性耦合解

本文研究了在反平面剪切和面内电场的共同作用下，压电材料椭圆夹杂的界面开裂问题，假定夹杂是刚性的导体，采用复变函数保角变换和级数展开方法，可确定压电材料基体的复势表达式，进而求得夹杂界面开裂的电弹性耦合的能量释放率。     

The interaction between a screw dislocation and a rigid wedge inhomogeneity with an elastic circular inhomogeneity at the tip

The interaction between a screw dislocation and an elastic semi-cylindrical inhomogeneity abutting on a rigid half-plane is investigated. Utilizing the image dislocations method, the closed form solutions of the stress fields in the matrix and the inhomogeneity region are derived. The image force acting on the dislocation is also calculated. The results were used to study the interaction between a screw dislocation and a rigid wedge inhomogeneity with an elastic circular inhomogeneity at the tip by means of conformal mapping. The results show that an unstable equilibrium point of the dislocation near the semi-cylindrical inhomogeneity is found when the inhomogeneity is softer than the matrix. Moreover, the force on the dislocation is strongly affected by the position of the dislocation and the shear modulus of the semi-circular inhomogeneity. Positive screw dislocations can reduce the SIF of the rigid wedge inhomogeneity (shielding effect) only when it located in the lower half-plane. The shielding effect increases with the increase of the shear modulu of both the matrix and the inhomogeneity and increases with the increase of the wedge angle. The shielding effect (or anti-shielding effect) reaches the maximum when the dislocation tends to the wedge inhomogeneity interface.     

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.     

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)     

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.     

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.     

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.     

Size-dependent interaction of an edge dislocation with an elliptical nano-inhomogeneity incorporating interface effects

The elastic behavior of an edge dislocation, which is positioned outside of a nanoscale elliptical inhomogeneity, is studied within the interface elasticity approach incorporating the elastic moduli and surface tension of the interface. The complex potential function method is used. The dislocation stress field and the image force acting on the dislocation are found and analyzed in detail. The difference between the solutions obtained within the classical-elasticity and interface-elasticity approaches is discussed. It is shown that for the stress field, this difference can be significant in those points of the inhomogeneity-matrix interface, where the radius of curvature is smaller and which are closer to the dislocation. For the image force, this difference can be considerable or dispensable in dependence on the dislocation position, its Burgers vector orientation, and relations between the elastic moduli of the matrix, inhomogeneity and their interface. Under some special conditions, the dislocation can occupy a stable equilibrium position in atomically close vicinity of the interface. The size effect is demonstrated that the normalized image force strongly depends on the inhomogeneity size when it is in the range of several tens of nanometers, in contrast with the classical solution where this force is always constant. The general issue is that the interface elasticity effects become more evident when the characteristic sizes of the problem (inhomogeneity size, interface curvature radius and dislocation-interface spacing) reduce to the nanoscale.     

The interaction between a screw dislocation and a circular inhomogeneity in gradient elasticity

The interaction between a screw dislocation and a circular inhomogeneity in gradient elasticity is investigated. The screw dislocation is located inside either the inhomogeneity or the matrix. By using the Fourier transform method, closed analytical solutions are obtained when the inhomogeneity and the matrix have the same gradient coefficient. The explicit expressions of image forces exerted on screw dislocations are derived. The motion of the appointed screw dislocation and its equilibrium positions are discussed. The results show that the classical singularity is eliminated. Especially, for the case of a tiny inhomogeneity, the relation of dislocations and inhomogeneities become quite different. The screw dislocation may be attracted by the stiff inhomogeneity and repelled by the soft inhomogeneity when it tends to the interface. So there is an unstable equilibrium position when a dislocation tends to a tiny stiff inhomogeneity and there is a stable equilibrium position when a dislocation tends to a tiny soft inhomogeneity.