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1.
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.  相似文献   

2.
The elastic interaction of screw dislocations and a star crack with a central hole was investigated. The complex potential of the present problem was obtained from that of an internal crack in an infinite medium using the conformal mapping technique. The stress field, image force and strain energy of dislocation, and stress intensity factor at the crack tip were derived. The critical stress intensity factor for dislocation emission was calculated based on the spontaneous dislocation emission criterion. The influence of the ratio of crack length to hole radius, crack number, and dislocation source on the above mechanical variables were studied. The present solution was reduced to several special cases previously reported in the literature.  相似文献   

3.
Interface and interfacial cracks interacting with screw dislocations in piezoelectric bimaterials subjected to antiplane mechanical and in-plane electrical loadings are studied within the framework of linear piezoelectricity theory. Straight dislocations with the Burgers vector normal to the isotropic basal plane near the interface or interfacial crack are considered. The dislocations are characterized by a discontinuous electric potential across the slip plane and are subjected to a line-force and a line-charge at the core. An explicit solution for the screw dislocation in piezoelectric bimaterial with straight interface is found based on the solution of a similar problem for infinite homogenous medium. The obtained relation is independent of the nature of singularity. This fundamental result is used to analyze dislocation interacting with a set of collinear interfacial cracks in piezoelectric bimaterials. Three solutions for the screw dislocation interacting with a semi-infinite crack, finite crack, and edge crack between two bonded dissimilar piezoelectric materials are obtained in closed-form. These solutions can be used as Green’s functions for the analyses of interfacial cracks in piezoelectric bimaterials.  相似文献   

4.
Electro-elastic stress investigation on the interaction between a piezoelectric screw dislocation and collinear rigid lines under anti-plane mechanical and in-plane electrical loading is carried out. The lines are considered, respectively, as dielectrics or conductors. The screw dislocation is subjected to a line charge and a line force at the core. Closed-form analytical solutions are derived by means of complex variable method. Explicit expressions for the field variables, the singularity of the field variables at the line tip and the force on the dislocation are obtained for a single rigid line.  相似文献   

5.
An interfacial edge crack of a length a in two bonded dissimilar anisotropic quarter planes having an anti-plane singularity such as a screw dislocation or anti-plane line force is analyzed. The energy release rate and stress intensity factor are explicitly expressed in terms of complex potentials. The interaction problems in two bonded orthotropic quarter planes are exemplified. It is confirmed that the present solution reduces to the known solutions dealing with particular cases of the present problem.  相似文献   

6.
The elastic interaction between screw dislocation and the internal crack near a free surface has been investigated. The stress intensity factor at the crack tip, crack extension force, the image force on the dislocation are affected by the free surface. The number and nature of dislocations, m, inside the crack also play an important role in fracture. In order to understand the plastic zone, the zero-force points of dislocation along the x-axis are involved. The dislocation emitted from the right-hand crack tip is enhanced by positive m and reduced by negative m. On the other hand, if the internal crack is closer to the free surface, a dislocation generated from the right-hand crack tip is easier for negative m and more difficult for positive m. However, the role of m on the dislocation emission for the left-hand crack tip is opposite to that for the right-hand crack tip. Finally, three special cases can be obtained from our results. (1) The interaction between a dislocation and a surface crack; (2) the interaction between a dislocation and an internal crack; (3) the interaction between two dislocations.  相似文献   

7.
This article provides a comprehensive theoretical treatment of the interaction between an arbitrarily located and oriented microdefect and a finite interfacial crack under antiplane loading. The analysis is based upon the use of an integral transform method and a self-consistent iterative superposition technique. The closed form expression for the resulting stress intensity factors at the interfacial crack are obtained by solving the appropriate singular integral equations, using Chebyshev polynomials. Typical examples are provided to show the effect of the location and orientation of the microdefect and the material combination upon the stress intensity factor of the interfacial crack.  相似文献   

8.
In this paper, the anti-plane problem for an interfacial crack between two dissimilar magneto-electro-elastic plates subjected to anti-plane mechanical and in-plane magneto-electrical impact loadings is investigated. Four kinds of crack surface conditions are adopted: magneto-electrically impermeable (Case 1), magnetically impermeable and electrically permeable (Case 2), magnetically permeable and electrically impermeable (Case 3), and magneto-electrically permeable (Case 4). The position of the interfacial crack is arbitrary. The Laplace transform and finite Fourier transform techniques are employed to reduce the mixed boundary-value problem to triple trigonometric series equations in the Laplace transform domain. Then the dislocation density functions and proper replacements of the variables are introduced to reduce the series equations to a standard Cauchy singular integral equation of the first kind. The resulting integral equation together with the corresponding single-valued condition is approximated as a system of linear algebra equations, which can easily be solved. Field intensity factors and energy release rates are determined and discussed. The effects of loading combination parameters on dynamic energy release rate are plotted for Cases 1-3. On the other hand, since the magneto-electrically permeable condition is perhaps more physically reasonable for type III crack, the effect of the crack configuration on the dynamic fracture behavior of the crack tips is studied in detail for Case 4. The results could be useful for the design of multilayered magneto-electro-elastic structures and devices.  相似文献   

9.
The interaction between a penny-shape crack and a dislocation in crystalline materials is investigated within the framework of dislocation dynamics. The long-range and singular stress field resulting from the crack is determined by modeling the crack as continuous distribution of dislocation loops. This distribution is determined by satisfying the traction boundary condition at the crack face, resulting into a singular integral equation of the first kind that is solved numerically. This crack model is integrated with the dislocation dynamics simulation technique to yield the stress field of the combine system of crack and different types of dislocations situated at different positions in a three dimensional space. The integrated system is then used to investigate the dislocation behavior and its influence on the crack opening displacement and the characteristic of the stress field near the crack tip. It is shown that, depending on the relative position of the dislocation and its character, the dislocation may result in reduction in the stress amplitude at the crack tip and in some cases in closure of the crack tip. These analyses yield shielding and amplification zones near the crack providing an insight of the dislocation influence on the crack. The full dislocation dynamic analysis reveals the nature of the crack dislocation interaction and the manner in which the dislocation morphology changes as it is attracted to the crack surfaces, as well as the changes it causes to the crack profile.  相似文献   

10.
The principle of superposition is used to solve the problem and the original problem is converted into two particular hole edge crack problems. The remote stresses are applied at infinity in the first problem. Meantime, a dislocation distribution is assumed outside the hole contour in the second problem. Singular integral equation is proposed for the solution of the second problem, in which the right hand side of the integral equation is obtained from the solution of the first problem. The first problem as well as the elementary solution of the second problem are solved by means of the rational mapping approach. Finally, numerical examples with the calculated results of stress intensity factors are presented.  相似文献   

11.
Interaction between screw dislocations and a partially debonded interface in cylindrically anisotropic composites subjected to uniform stress at infinity is investigated in this paper. Using Muskhelishvili’s complex variable method, the closed forms of complex potentials are obtained for a screw dislocation and a screw dislocation dipole located inside either matrix or inhomogeneity. Explicit expressions of stress intensity factors at the crack tips, image forces and image torques acting on dislocation or the center of dipole are provided. The results show that the crack and dislocation geometry combination plays an important role in the interaction between screw dislocations and interface crack. Furthermore, it is found that the anisotropy of solids may change the shielding and anti-shielding effects arising from screw dislocations and the equilibrium position of screw dislocations. The presented solutions are valid for anisotropic, orthotropic or isotropic composites and can be reduced to some novel or previously known results.  相似文献   

12.
In the present work the finite element method is used to analyze the effect of interaction between an interfacial crack and a microcrack in ceramic/aluminum bi-materials. The behaviour is analyzed by the determination of the J integral, the plastic zone at the tips of the interfacial crack and the microcrack. The effects of longitudinal and transversal distance between the tips of the two cracks and the rotation of the microcrack are examined. The obtained results allow us to deduce a correlation between the position of the microcrack and the J integral and the plastic zone.The obtained results shows that the J integral at the interfacial crack tip reaches a maximum value when the microcrack is moved in the vicinity of the interfacial crack. With this distance the effect of interaction is marked more; the stress field at the microcrack tip and that of the interfacial crack generates only one plastic zone at the interfacial crack tip. The maximum size of the plastic zone is localised at the interfacial crack tip. Those of the two tips of the microcrack are very weak and even negligible in front of the zone plasticized at the interfacial crack tip.  相似文献   

13.
The interaction of a screw dislocation with an interphase layer between a circular inhomogeneity and the matrix is dealt with. By combining the sectionally holomorphic function, Cauchy integral and Laurent series expansion techniques, the relation among the complex potentials for the three material regions is given, and the functional equation in complex potential for the interphase layer are derived. Explicit series solutions are given for the two cases when the screw dislocation is located in the inhomogeneity or in the matrix. The influence of the interphase layer parameters on interaction energy and dislocation force is evaluated and discussed. The present solutions contain a number of novel and previously known results which can be shown to be special cases.  相似文献   

14.
Three-dimensional stress investigation on the interaction between a penny-shaped crack and an expanding spherical inclusion in an infinite 3-D medium is studied in this paper. The spherical transformation area (the inclusion) expands in a self-similar way. By using the superposition principle, the original physical problem is decomposed into two sub-problems. The transient elastic filed of the medium with an expanding spherical inclusion is derived with the dynamic Green's function. A time domain boundary integral equation method (BIEM) is then adopted to solve the current problem. The numerical scheme applied here uses a constant shape function for elements away from the crack front, and a square root crack-tip shape function for elements near the crack tip to describe the proper behavior of the unknown quantities near the crack front. A collocation method as well as a time stepping scheme is applied to solve the BIEs. Numerical examples for the Mode I stress intensity factor are presented to assess the dynamic effect of the expanding inclusion.  相似文献   

15.
This paper describes a framework to study the initiation and arrest of an interfacial crack, using a combination of experiment and computation. We consider a test configuration widely used in the microelectronic industry: a sample of two substrates bonded by a stack of thin films, with a pre-crack in one of the substrates, perpendicularly impinging upon the films. When the sample is loaded to a critical level, the pre-crack initiates a new crack on one of the interfaces in the sample. The new crack often runs rapidly on the interface for a considerable length, and then arrests. We introduce a quantity, the initiation energy, to characterize the condition under which the pre-crack initiates the interfacial crack. The initiation energy is independent of the test configuration on the scale of the substrates, but changes greatly with the materials and stacking sequence of the films. We measure the initiation energy experimentally, interpret the data using mechanistic models, and use the initiation energy to predict the arrest crack length.  相似文献   

16.
J. L. Zheng  B. Li  Y. W. Liu 《Acta Mechanica》2007,193(3-4):129-139
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.  相似文献   

17.
A numerical method described recently[1] is used here to obtain the stress intensity factor for a crack near an inclusion. Results for the variation of the stress intensity factor with the distance of the crack tip from the inclusion, are shown graphically.  相似文献   

18.
In this study, the mode III axisymmetric crack problem in a non-homogeneous interfacial region between two homogeneous half-spaces is considered. The shear modulus of the interfacial layer is assumed to be μ2(z)=μ0 emz. It is also assumed that this shear modulus varies continuously between that of the two half-spaces. By using the Hankel transform technique the problem is reduced to a singular integral equation. The problem is solved for various material combinations, crack geometries and for three different sets of crack surface tractions, and the corresponding stress intensity factors are tabulated. This revised version was published online in August 2006 with corrections to the Cover Date.  相似文献   

19.
The mechanical model is established for a piezoelectric sensor with a mode III permeable crack parallel to the imperfect interface. Fracture analysis is performed by the standard methods of Fourier transform and singular integral equation. Three conclusions are drawn: (a) the imperfect interface has a shielding effect on the crack parallel and very near to it; (b) the shielding effect depends on the structural stiffness and the distance between the crack and interface; (c) for the electrically permeable crack, mechanical imperfection has more remarkable shielding effect than dielectric imperfection does.  相似文献   

20.
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.  相似文献   

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