圆柱型各向异性材料中螺型位错与非理想界面圆形夹杂的干涉效应

研究了圆柱型各向异性材料中螺型位错与含非理想界面圆形夹杂的弹性干涉问题。利用复变函数方法,获得了圆形夹杂和无限大基体区域复势函数的精确级数形式解答。利用Peach-Koehler公式导出作用于螺型位错上的位错力公式。主要讨论了材料各向异性性质与界面非理想性对位错力的影响规律。分析结果表明,界面非理想性吸引位错,而各向异性夹杂排斥各向同性基体材料中的位错。当夹杂的各向异性程度大于基体时,位错在非理想界面附近存在一个平衡位置。当界面非理想程度系数不变时,夹杂各向异性程度系数存在一个临界值改变作用在位错上位错力的方向。     

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。     

螺型位错偶极子与圆形夹杂界面裂纹的弹性干涉

该文研究了螺型位错偶极子和圆形夹杂界面裂纹的弹性干涉作用。利用复变函数方法,得到了该问题的复势函数以及应力场的封闭形式解答。求出了裂纹尖端的应力强度因子以及作用在螺型位错偶极子中心的像力和像力偶矩,并分析了位错偶极子对应力强度因子的影响及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。研究结果表明:位错偶极子对应力强度因子具有很强的屏蔽或反屏蔽效应;硬夹杂排斥位错偶极子,而裂纹吸引位错偶极子,在一定条件下,位错偶极子在裂纹附近出现一个平衡位置;当裂纹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,裂纹长度对位错偶极子中心像力偶矩也有很大的影响。     

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。     

复合材料中压电螺型位错与含刚性核夹杂的电弹干涉

为了研究压电复合材料中位于基体的压电螺型位错与含共焦椭圆导电刚性核椭圆夹杂的电弹相互作用, 基于复变函数方法, 获得了基体和夹杂区域的精确级数形式解析解。运用广义Peach-Koehler公式, 导出了作用在位错上像力的解析表达式。在此基础上讨论了椭圆刚性核和材料电弹特性对位错像力以及位错平衡位置的影响规律, 同时讨论了压电夹杂和弹性基体的复合情况。结果表明: 椭圆刚性核对位错有着明显的排斥作用, 可以增强硬夹杂对位错的排斥, 减弱软夹杂对位错的吸引; 对于软夹杂, 在界面附近位错存在一个不稳定的平衡位置; 在基体和夹杂的界面上, 像力迅速增大; 当夹杂的剪切模量远小于基体时, 界面附近不会出现位错的平衡位置。     

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。     

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。     

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.     

The interaction between a screw dislocation and a nano-inhomogeneity with a semi-infinite wedge crack penetrating the interface

The interaction between a screw dislocation and a circular nano-inhomogeneity with a semi-infinite wedge crack penetrating the interface is investigated. By using Riemann-Schwartz’s symmetry principle integrated with the analysis of singularity of complex functions and the conformal mapping technique, the analytical expressions of the stress field in both the circular nano-inhomogeneity and the infinite matrix, the image force acting on the screw dislocation and the stress intensity factor at the crack tip are obtained. The influence of elastic mismatch of materials, inhomogeneity size, interface stress, wedge crack opening angle and the relative location of dislocation on the image force and on the equilibrium position of the screw dislocation and the shielding effect of the screw dislocation are discussed in detail. The results show that interface stress has a significant impact on the movement of dislocations near the interface, and the effect of interface stress enhances when the inhomogeneity radius decreases. With the decrease in the wedge crack opening angle, the influence of interface stress on the movement of the screw dislocation and on the SIF enhances. With the increment of the relative shear modulus, the influence of interface stress weakens with the screw dislocation locating in the inhomogeneity and strengthens with the screw dislocation locating in the matrix. When the screw dislocation is located in the inhomogeneity, the positive (negative) interface stress increases (decreases) the shielding effect, while this phenomenon is opposite when the screw dislocation locates in the matrix.     

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.     

Image force and stability of a screw dislocation inside a coated cylindrical inhomogeneity with interface stresses

The image force and stability of a screw dislocation inside a coated cylindrical inhomogeneity with interface stresses are analyzed. A three-phase composite cylinder model is utilized to study the issues. The stress boundary condition at the interface of the coating layer is modified by incorporating surface/interface stress. The analytical solution of complex functions of the inhomogeneity, the coating layer, and the infinite matrix is derived by means of the complex variable method. With the aid of the obtained stress fields and the Peach–Koehler formula, the explicit expression of the image force acting on the screw dislocation is obtained. The critical radius of the inhomogeneity where the screw dislocation stays is evaluated. The influence of the interface stresses on the image force and the critical radius of the inhomogeneity is derived. The results indicate that the negative interface stresses attract the dislocation, and the positive interface stresses repel the dislocation. The critical radius of inhomogeneity will increase for considering the negative interface stresses and will decrease for considering the positive interface stresses.     

Interaction between screw dislocations and inclusions with imperfect interfaces in fiber-reinforced composites

A three-phase composite cylinder model is utilized to study the elastic interaction between screw dislocations and embedded multiple circular cross-section inclusions (fibers) with imperfect interfaces in composites. By means of complex variable techniques, the explicit solutions of stress and displacement fields are obtained. With the aid of the Peach–Koehler formula, the explicit expressions of image forces exerted on screw dislocations are derived. The equilibrium positions of the appointed screw dislocation near one of the inclusions are discussed for variable parameters (interface imperfection, material mismatch and dislocation position) and the influence of the nearby inclusions and dislocations is also considered. The results show that, if the inclusion is stiffer than the matrix and the magnitude of the degree of interface imperfection reaches the certain value, a new equilibrium position for the screw dislocation in the matrix can always be produced in comparison with the previous solution (the perfect interface). The effect of elastic constants of the inclusion on the image force and the equilibrium position of the appointed screw dislocation is weak when the interface imperfection is strong. It is also seen that the magnitude of the image force exerted on the appointed dislocation caused by multiple inclusions is always smaller than that produced by a single inclusion. The impact of the closer dislocations on the mobility of the appointed dislocation is very significant.     

A screw dislocation interacting with a coated nano-inhomogeneity incorporating interface stress

Effect of interface stress on the interaction between a screw dislocation and a coated nano-inhomogeneity is investigated in the framework of surface elasticity. By using the complex variable function method, the stress fields in heterogeneous materials and the image force acting on the screw dislocation are derived analytically. The results indicate that, when the radius of the coated inhomogeneity is reduced to nanometers, the influence of interface stress on the motion of the dislocation near the inhomogeneity becomes significant and the image force acting on the screw dislocation depends on the size of the coated inhomogeneity, which differs from the classical solution. And it is showed that the thicker coated layer relative to inclusion decreases or increases the influence of a coated inclusion on the image force of dislocation, not as expected.