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。     

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。     

位错与含裂纹非理想界面圆形夹杂的干涉效应

研究了基体中任意位置的螺型位错与含裂纹非理想界面圆形弹性夹杂的干涉力学问题。运用复变函数的解析延拓技术与奇性主部分析方法,获得了该问题复势函数的一般解答。作为典型例子,求出了非理想圆形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。计算了作用在螺型位错上的位错力。讨论了含裂纹的非理想界面以及材料失配对位错力的影响规律。结果表明:与含裂纹理想界面相比,非理想界面对位错力的影响更大,对位错的捕获能力更强。硬夹杂时,可能存在非稳定平衡点,使得非理想界面、界面裂纹和夹杂对位错的作用力为零;软夹杂时,非理想界面、界面裂纹和夹杂则始终吸引位错。     

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。     

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。     

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。     

纳米尺度圆孔表面薄膜界面失配位错形核机理

研究了无限大基体内纳米尺度圆孔表面薄膜中界面螺型位错形核的临界条件,薄膜考虑了表/界面效应。运用弹性复势方法,获得了两个区域应力场的解析解答,并导出位错形核能公式,由此讨论了表/界面效应对薄膜界面位错形核的影响规律。算例结果表明,表/界面效应在纳米尺度下对位错形核的影响显著,不同表/界面效应下位错形核的临界薄膜厚度有很大差异,当基体与薄膜的相对剪切模量超过某一值后,只有考虑负的表/界面应力时位错才有可能形核;薄膜厚度在小于某一临界尺寸时负的表/界面应力更容易位错形核,薄膜厚度大于某一临界尺寸时正的表/界面应力更容易位错形核。     

On the interaction between a generalized screw dislocation and circular-arc interfacial rigid lines in magnetoelectroelastic solids

The interaction of a generalized screw dislocation, which is located inside either the inclusion or the matrix, with circular-arc interfacial rigid lines under remote antiplane shear stresses, in-plane electric and magnetic loads in linear magnetoelectroelastic materials is dealt with. By using the complex variable method, the general solutions of the physical problem are presented in this paper. The closed-form solutions for stresses, electric displacement fields and magnetic induction fields are derived explicitly for the interface with a finite rigid line. The image forces acting on the generalized screw dislocation are then calculated by using the generalized Peach–Koehler formula. The influence of the length and the location of the rigid line as well as the material mismatch on the image force is evaluated. Numerical computations and discussions show that, when the length or the position of the interfacial rigid line achieves a critical value, the image force on the dislocation changes its direction due to the existence of the rigid line. In addition, the soft inclusion can repel the dislocation in magnetoelectroelastic materials owing to their intrinsic magnetoelectromechanical coupling behavior.     

Viscoelastic interaction between a screw dislocation and a piezoelectric inhomogeneity with an interfacial rigid line

Summary The problem for the interaction between a screw dislocation and a piezoelectric circular inhomogeneity with one interfacial rigid line in a viscoelastic matrix is investigated in this paper. Based on the elastic-viscoelastic correspondence principle, the analytical stress fields and image force for the problem are presented. The results show that the influences of the viscoelastic properties of the material together with rigid line's length and inhomogeneity's piezoelectricity upon the time-dependent image force are significant. The time-dependent image force evolves toward a constant value as time elapses. Results presented in this paper are in agreement with the previous solution as special cases.     

A piezoelectric screw dislocation interacting with a nonuniformly coated circular inclusion

This paper investigated the interaction of a piezoelectric screw dislocation with a nonuniformly coated circular inclusion in an unbounded piezoelectric matrix subjected to remote antiplane shear and electric fields. In addition to having a discontinuous displacement and a discontinuous electric potential across the slip plane, the dislocation is subjected to a line force and a line charge at the core. The alternating technique in conjunction with the method of analytical continuation is applied to derive the general solutions in an explicit series form. This approach has a clear advantage in deriving the solution to the heterogeneous problem in terms of the solution for the corresponding homogeneous problem. The presented series solutions have rapid convergence which is guaranteed numerically. The image force acting on the piezoelectric screw dislocation is calculated by using the generalized Peach–Koehler formula. The numerical results show that the varying thickness of the interphase layer will exert a significant influence on the shear stress and electric field within the circular inclusion, and on the direction and magnitude of the image force. This solution can be used as Green’s function for the analysis of the corresponding piezoelectric matrix cracking problem.     

Electro-elastic interaction between a moving screw dislocation and collinear interfacial rigid lines

This paper attempts to investigate the problem for the electro-elastic interaction between a piezoelectric moving dislocation and interfacial collinear rigid lines under combined longitudinal shear and in-plane electric field. Using Riemann–Schwarz's symmetry principle integrated with the analysis singularity of complex functions, we present the general elastic solution of this problem and the closed form solution for interface containing single rigid line. The expressions of electro-elastic fields and image force acting on moving dislocation are derived explicitly. The results show that the velocity of moving dislocation has significant effect on the image force. The present solutions contain previously known results as the special cases.     

On the interaction between a screw dislocation and a circular coated inclusion with interfacial cracks

Summary The problem of the elastic interaction between a screw dislocation, which is located at an arbitrary point inside either the matrix or the inclusion, and a circular coated inclusion with interfacial cracks is dealt with. An efficient and concise method for a complex multiply connected region is developed, in terms of which the general solutions to the problem are derived. As an illustrative example, explicit series form solutions for complex potentials are presented in the case of one interfacial crack. Based on the complex potentials, image forces on the screw dislocation are then calculated using the Peach-Koehler formula. The equilibrium position of the dislocation is discussed in detail for various crack geometries, coating layer thicknesses and material constant combinations. It is shown that the influence of interfacial cracks on the motion of the dislocation near the coated inclusion is significant. The present solutions contain a number of previously known results as special cases.     

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.