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.     

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.     

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. The 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.     

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。     

Uniformly moving screw dislocation interacting with interface cracks in anisotropic bimaterials

This paper attempts to investigate the problem for the interaction between a uniformly subsonic moving screw dislocation and interface cracks in two dissimilar anisotropic materials. Using Riemann–Schwarz’s symmetry principle integrated with the analysis singularity of complex functions, we present the general elastic solutions of this problem and the closed form solutions for interface containing one and two cracks. The expressions of stress intensity factors at the crack tips and image force acting on moving dislocation are derived explicitly. The results show that the stress intensity factors at the crack tips decrease with increasing velocity of dislocation, and larger dislocation velocity leads to the equilibrium position of dislocation leaving from crack tips. The presented solutions contain previously known results as the special cases.     

Interaction of an anti-plane singularity with interfacial anti-cracks in cylindrically anisotropic composites

Anti-plane problem for a singularity interacting with interfacial anti-cracks (rigid lines) under uniform shear stress at infinity in cylindrically anisotropic composites is investigated by utilizing a complex potential technique in this paper. After obtaining the general solution for this problem, the closed solution for the interface containing one anti-crack is presented analytically. In addition, the complex potentials for a screw dislocation dipole inside matrix are obtained by the superimposing method. Expressions of stress singularities around the anti-crack tips, image forces and torques acting on the dislocation or the center of dipole are given explicitly. The results indicate that the anisotropy properties of materials may weaken the stress singularity near the anti-crack tip for the singularity being a concentrated force but enhance the one for the singularity being a screw dislocation and change the equilibrium position of screw dislocation. The presented solutions are valid for anisotropic, orthotropic or isotropic composites and can be reduced to some new or previously known results.     

A moving screw dislocation near interfacial rigid lines in two dissimilar anisotropic media

This paper attempts to investigate the problem for the interaction between a uniformly moving screw dislocation and interface rigid lines in two dissimilar.anisotropic. materials. Integrating Riemann-Schwarz＇s symmetry principle with the analysis singularity of complex functions, we present the general elastic solutions of this problem and the closed form solutions for interfaces containing one and two rigid lines. The expressions of stress intensity factors, at the rigid line tips and image force acting on moving dislocation are derived explicitly. The results show that dislocation velocity has an antishielding effect on the rigid line tip and a larger dislocation velocity leads to the equilibrium position of dislocation closing with the rigid line. The presented solutions contain previously known results as the special cases.     

Some basic problems in anisotropic bimaterials with a viscoelastic interface

This research is devoted to the study of anisotropic bimaterials with Kelvin-type viscoelastic interface under antiplane deformations. First we derive the Green’s function for a bimaterial with a Kelvin-type viscoelastic interface subjected to an antiplane force and a screw dislocation by means of the complex variable method. Explicit expressions are derived for the time-dependent stress field induced by the antiplane force and screw dislocation. Also presented is the time-dependent image force acting on the screw dislocation due to its interaction with the Kelvin-type viscoelastic interface. Second we investigate a rectangular inclusion with uniform antiplane eigenstrains embedded in one of the two bonded anisotropic half-planes by virtue of the derived Green’s function for a line force. The explicit expressions for the time-dependent stress field induced by the rectangular inclusion are obtained in terms of the simple logarithmic and exponential integral functions. It is observed that in general the stresses exhibit the logarithmic singularity at the four corners of the rectangular inclusion. Our results also show that when one side of the rectangular inclusion lies on the viscoelastic interface, the interfacial tractions are still regular at the two corners of the inclusion which are located on the interface. Last we address a finite Griffith crack normal to the viscoelastic interface by means of the obtained Green’s function for a screw dislocation. The crack problem is formulated in terms of a resulting singular integral equation which is solved numerically. The time-dependent stress intensity factors at the two crack tips are obtained and some interesting features are discussed.     

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。     

Concentrated impact loading on one face of a semi-infinite crack in an anisotropic elastic material

The response of an unbounded anisotropic elastic body containing a semi-infinite crack subjected to a concentrated impact force on one of the crack faces is studied. An exact solution of the dynamic stress intensity factors is obtained from a linear superposition of the solution of Lamb’s problem and a solution of a dislocation emitting from the crack tip. The stress intensity factors exhibit square-root singularity upon the arrival of the Rayleigh wave at the crack tip. As the Rayleigh wave passes through the crack tip, the stress intensity factors either instantaneously assume the static values or gradually approach to zero. Several numerical examples are given for isotropic, cubic and orthotropic materials.     

一维六方准晶中螺型位错偶极子与直线纳米裂纹的干涉效应

关于准晶中螺型位错偶极子与直线纳米裂纹干涉效应的问题，提出了一种可获得精确解的新方法。首先，将Gurtin-Murdoch表/界面理论推广运用到准晶材料中的纳米裂纹问题，建立了裂纹表面上含声子场、相位子场的应力边界模型；然后，利用复变函数中的共形映射方法，将直线裂纹问题化为单位圆孔问题；再借助于柯西积分方法获得了问题的封闭解；最后，数值结果表明：当裂纹的尺寸减小到纳米量级时，表面效应将对声子场和相位子场中的应力场、像力及像力偶矩产生显著的影响，从而改变其力学性能，即裂纹尺寸越小，表面效应越强，声子场和相位子场中的应力场、像力及像力偶矩的数值变化越大；螺型位错偶极子力偶臂的方向对像力的极值和自身平衡亦有较大影响。     

Elastic interaction between edge dislocation,concentrated force,point heat source and edge crack in a semi-infinite plane

We investigate the interaction between edge crack and edge dislocation as well as concentrated force and point heat source. The stress intensity factors at the edge crack tip and the image forces acting on the edge dislocation are calculated. The influence of the concentrated force, point heat source and edge dislocation on the shielding and anti-shielding effects to edge crack as well as the glide and climb forces acting on the edge dislocation is examined in detail. The results indicate that the shielding and anti-shielding effects increase acutely with the increment of concentrated force and point heat source. In addition, the glide and climb forces increase acutely with the decrement of the distance between dislocation and crack tip.     

Transient analysis of a propagating crack with finite length subjected to a horizontally polarized shear wave

In this study, the transient response of a finite crack subjected to an incident horizontally polarized shear wave and then propagated with a constant speed in an unbounded elastic solid is investigated. Initially, the finite crack with crack length l is stress-free and at rest. At time t = 0, an incident horizontally polarized shear wave strikes at one of the crack tips and will arrive at the other tip at a later time. Then, two crack tips propagate along the crack tip line with different velocities as the corresponding stress intensity factors reach their fracture toughness. The correspondent configuration is shown in Fig. 1

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Fig. 1. Configuration and coordinate systems of a finite crack in an unbounded medium.

. In analyzing this problem, diffracted waves generated by two propagating crack tips must be taken into account and it makes the analysis extremely difficult. In order to solve this problem, the transform formula in the Laplace transform domain between moving and stationary coordinates is first established. Complete solutions are determined by superposition of proposed fundamental solutions in the Laplace transform domain. The fundamental solutions to be used are from the problems of applying exponentially distributed traction and screw dislocation on crack faces and along the crack tip line, respectively. The exact transient solutions of dynamic stress intensity factor for the first few diffracted waves that arrive at two crack tips are obtained and expressed in compact formulations. Numerical calculations of dynamic stress intensity factors for both tips are evaluated and the results are discussed in detail.     

Finite element analysis of a bimaterial interface crack

In this investigation, the enriched element method developed by Benzley was extended to treat the stress analysis problem involving a bimaterial interface crack. Unlike crack problems in isotropic elasticity, where the stress singularity at the crack tip is of the inverse square root type, the interface crack contains an additional oscillatory singularity. Although the effect of this oscillatory characteristic is confined to a region very close to the crak tip, it nevertheless requires proper treatment in order to obtain accurate predictions on the stress intensity factors. Using appropriate crack tip stress and displacement expressions, the enriched element method can model the stress singularity for an interface crack exactly. The finite element implementation of this method has been made on the code APES. Stress intensity factor results predicted by the modified APES program compare favorably with those available in the literature. This indicates tha the enriched element technique provides an accurate and efficient numerical tool for the analysis of bimaterial interface crack problems.     

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.     

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.     

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.     

纤维增强复合材料圆柱型界面裂纹分析

以裂纹面上的位错函数为未知量将圆柱型界面裂纹问题化成一组奇异积分方程的求解问题．应用Ｍｕｓｋｈｅｌｉｓｈｖｉｌｉ的奇异积分方程理论，分析了圆柱型界面裂纹尖端应力场．针对裂纹尖端分别存在和不存在接触区两种情况，确定了裂纹尖端应力场的奇异性．利用数值方法计算了圆柱型界面裂纹尖端接触区尺寸对剪应力强度因子的影响．     

A piezoelectric screw dislocation near a wedge-shaped bi-material interface

The electro-elastic stress field due to a piezoelectric screw dislocation near the tip of a wedge-shaped bi-material interface is derived. The screw dislocation is subjected to a line charge and a line force at the core. The explicit closed-form analytical solutions for the stress field are derived by means of the complex variable and conformal mapping methods. The stress and electric intensity factors of the wedge tip induced by the dislocation and the image force acting on the dislocation are also formulated and calculated. The influence of the wedge angle and the different bi-material constant combinations on the image force is discussed. Numerical results for three particular wedge angles are calculated and compared.     

Dynamic self-similar debonding of interface at very high velocity: Anti-plane case

This paper analyzes the anti-plane problem of dynamic self-similar debonding of interface at very high velocity. The debonding is modeled as an interface crack propagating self-similarly from zero-length. The extending speed is assumed to be transonic or supersonic. We first consider the dynamic debonding under moving concentrated loads. The moving dislocation model of self-similar propagation of an interface crack is used to formulate the problem to a singular integral equation which is solved analytically. The singularity of stresses near the crack tip is discussed and the dynamic stress intensity factors are presented. Finally the solution of dynamic debonding underx ²-type loads is obtained by using the superposition method.