A screw dislocation near a non-parabolic open inhomogeneity with internal uniform stresses

We use conformal mapping techniques and analytic continuation to prove that the stress field inside a non-parabolic open inhomogeneity embedded in a matrix subjected to uniform remote anti-plane stresses can nevertheless remain uniform despite the presence of a screw dislocation in its vicinity. Furthermore, the internal uniform stresses inside the inhomogeneity are found to be independent of both the shape of the inhomogeneity and the presence of the screw dislocation. On the other hand, we find that the existence of the nearby screw dislocation exerts a significant influence on the non-parabolic shape of the inhomogeneity.     

A screw dislocation near a coated non-elliptical inhomogeneity with internal uniform stresses

We consider the anti-plane shear deformation of a three-phase inhomogeneity-coating-matrix composite containing a coated non-elliptical inhomogeneity whose surrounding matrix is subjected to the action of a screw dislocation and uniform remote anti-plane shear stresses. Our objective is to establish conditions under which the inhomogeneity maintains an internal uniform stress field. Our analysis, which is based on a carefully chosen conformal mapping function, clearly indicates that such an internal uniform stress distribution can be achieved independently of the action of the screw dislocation, which influences the shape of the inhomogeneity depending on its proximity to the dislocation. In fact, we find that when the screw dislocation is located far from the coated inhomogeneity, the corresponding material interfaces become two confocal ellipses as reported previously in the literature. A simple criterion for the convergence of the series in the conformal mapping function is established.     

A screw dislocation near a non-elliptical piezoelectric inhomogeneity with internal uniform electroelastic field

Conformal mapping and analytic continuation are employed to prove the existence of an internal uniform electroelastic field inside a non-elliptical piezoelectric inhomogeneity interacting with a screw dislocation. We focus specifically on the case when the piezoelectric matrix surrounding the inhomogeneity is subjected to uniform remote anti-plane mechanical and in-plane electrical loading and a constraint is imposed between the remote loading and the screw dislocation. The constraint can be expressed in a relatively simple decoupled form by utilizing orthogonality relationships between two corresponding eigenvectors. The internal uniform electroelastic field is found to be independent of the presence of the screw dislocation; moreover, it can be expressed in decoupled form.     

The interaction of a screw dislocation with a circular inhomogeneity near the free surface

The interaction of a screw dislocation with a circular inhomogeneity near the free surface is discussed in this paper. By using the complex potential and conformal mapping technique, an explicit series solution is obtained. Then, the solution is cast into a new expression to separate the interaction effects between the dislocation, inhomogeneity, and free surface. The new expression is not only convenient to reveal the coupling interaction effects, but also helpful to improve the convergence of the solution. As an application of the new expression, a simple approximate formula is presented with high accuracy. Finally, the full-field interaction energy and image force are evaluated and studied graphically. It is found that when the screw dislocation, inhomogeneity, and free surface are close to each other, their interaction effects strongly and intricately couple in the near field. In the case of a soft inhomogeneity or a hole, there is an unstable equilibrium point of the screw dislocation between the inhomogeneity and free surface, whereas in the case of a hard or rigid inhomogeneity, there is an unstable equilibrium point on the opposite side of the inhomogeneity.     

Shielding effect and emission condition of a screw dislocation near a blunt crack in elliptical inhomogeneity

The shielding effect and emission condition of a screw dislocation near a blunt crack in elastic elliptical inhomogeneity is dealt with. Utilizing the Muskhelishvili complex variable method, the explicit series form solutions of the complex potentials in the matrix and the inclusion regions are derived. The stress intensity factor and critical stress intensity factor for dislocation emission are also calculated. The influences of the orientation of the dislocation and morphology of the blunt crack as well as the material elastic dissimilarity upon the shielding effect and emission criterion are discussed in detail. As a result, numerical analysis and discussion show that the positive screw dislocation can reduce the stress intensity factor of the crack tip (shielding effect) only when it is located in the certain region. The shielding effect increases with the increase of the shear modulus of the matrix and the curvature radius of the blunt crack tip, but decreases with the increase of dislocation azimuth angle. The critical loads at infinity for dislocation emission increases with the increment of the emission angle and the curvature radius of the blunt crack tip, and the most probable angle for screw dislocation emission is zero. The present solutions contain previous results as the special cases.     

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.     

A screw dislocation near and inside a partially bonded circular inclusion

The behaviour of a screw dislocation near and inside a partially bonded circular inclusion in an infinite matrix is investigated. The complex variable method is used to arrive at the solution, and the equilibrium positions of the dislocation are obtained.     

A screw dislocation near a circular nano-inhomogeneity in gradient elasticity

A screw dislocation outside an infinite cylindrical nano-inhomogeneity of circular cross section is considered within the isotropic theory of gradient elasticity. Fields of total displacements, elastic and plastic distortions, elastic strains and stresses are derived and analyzed in detail. In contrast with the case of classical elasticity, the gradient solutions are shown to possess no singularities at the dislocation line. Moreover, all stress components are continuous and smooth at the interface unlike the classical solution. As a result, the image force exerted on the dislocation due to the differences in elastic and gradient constants of the matrix and inhomogeneity, remains finite when the dislocation approaches the interface. The gradient solution demonstrates a non-classical size-effect in such a way that the stress level inside the inhomogeneity decreases with its size. The gradient and classical solutions coincide when the distances from the dislocation line and the interface exceed several atomic spacings.     

A screw dislocation near an elliptic hole in non-local elasticity

Summary The solutions are given for the stress field and elastic energy of a screw dislocation near an elliptic hole in non-local elasticity by a conformal mapping technique. The numerical results are discussed for the stress along thex-axis. Allowing one axis of the ellipse to dwindle to zero, the solution of the finite length crack is obtained.

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Schraubenversetzung neben einem elliptischen Loch bei nichtlokaler Elastizität

Übersicht Durch eine konforme Abbildungstechnik werden die Lösungen für das Spannungsfeld und die elastische Energie der Schraubenversetzung neben einem elliptischen Loch in nichtlokaler Elastizität gegeben. Die numerischen Ergebnisse werden für die Spannung entlang derx-Achse diskutiert. Läßt man eine Ellipsenachse gegen Null gehen, so gewinnt man die Lösung für den Riß endlicher Länge.

     

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)     

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.     

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.     

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.     

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.     

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.     

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.     

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。     

A new analytical-numerical method for calculating interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses

Based on the elementary solutions and new integral equations, a new analytical-numerical method is proposed to calculate the interacting stresses of multiple circular holes in an infinite elastic plate under both remote stresses and arbitrarily distributed stresses applied to the circular boundaries. The validity of this new analytical-numerical method is verified by the analytical solution of the bi-harmonic stress function method, the numerical solution of the finite element method, and the an...     

A technique for studying interaction between a screw dislocation dipole or a concentrated load and a mode III crack crossing an interface

A method of potentially wide application is developed for deriving analytical expressions of the elastic interaction between a screw dislocation dipole or a concentrated force and a crack cutting perpendicularly across the interface of a bimaterial. The cross line composed of the interface and the crack is mapped into a line, and then the complex potentials are educed. The Muskhelishvili method is extended by creating a Plemelj function that matches the singularity of the real crack tips, and eliminates the pseudo tips’ singularity induced by the conformal mapping. The stress field is obtained after solving the Riemann–Hilbert boundary value problem. Based on the stress field expressions, crack tip stress intensity factors, dislocation dipole image forces and image torque are formulated. Numerical curves show that both the translation and rotation must be considered in the static equilibrium of the dipole system. The crack tip stress intensity factor induced by the dipole may rise or drop and the crack may attract or reject the dipole. These trends depend not only on the crack length, but also on the dipole location, the length and the angle of the dipole span. Generally, the horizontal image force exerted at the center of the dislocation dipole is much smaller than the vertical one. Whether the dipole subjected to clockwise torque or anticlockwise torque is determined by whether the Burgers vector of the crack-nearby dislocation of the dipole is positive or negative. A concentrated load induces no singularity to crack tip stress fields as the load is located at the crack line. However, as the concentrated force is not located on the crack line but approaches the crack tip, the nearby crack tip stress intensity factor K_IIIu increases steeply to infinity.