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.     

Interaction of a screw dislocation with a semi-infinite interfacial crack in a magneto-electro-elastic bi-material

The interaction between a screw dislocation and a semi-infinite interfacial crack in a transversely isotropic magneto-electro-elastic bi-material is investigated. The dislocation line is perpendicular to the isotropic basal plane of the bi-material. The elastic and electromagnetic fields induced by the dislocation are obtained through the use of the complex variable method together with the superposition scheme. The stress, electric displacement and magnetic intensity factors as well as the image exerted on the dislocation are given explicitly. We find that the intensity factors are expressed in terms of the so-called effective materials and the radial component of the image force is only dependent on the elastic modulus of the material with the dislocation. As an illustrative example, the bi-material that consists of piezoelectric and piezomagnetic phases is analyzed.     

Electro-elastic interaction between a piezoelectric screw dislocation and circular interfacial rigid lines

The electro-elastic interaction between a piezoelectric screw dislocation located either outside or inside inhomogeneity and circular interfacial rigid lines under anti-plane mechanical and in-plane electrical loads in linear piezoelectric materials is dealt with in the framework of linear elastic theory. Using Riemann–Schwarz’s symmetry principle integrated with the analysis of singularity of complex functions, the general solution of this problem is presented in this paper. For a special example, the closed form solutions for electro-elastic fields in matrix and inhomogeneity regions are derived explicitly when interface containing single rigid line. Applying perturbation technique, perturbation stress and electric displacement fields are obtained. The image force acting on piezoelectric screw dislocation is calculated by using the generalized Peach–Koehler formula. As a result, numerical analysis and discussion show that soft inhomogeneity can repel screw dislocation in piezoelectric material due to their intrinsic electro-mechanical coupling behavior and the influence of interfacial rigid line upon the image force is profound. When the radian of circular rigid line reaches extensive magnitude, the presence of interfacial rigid line can change the interaction mechanism.     

Analysis of a piezoelectric screw dislocation inside an elliptical inhomogeneity with confocal rigid line in piezoelectric material

This paper deals with the electro-elastic coupling interaction between a piezoelectric screw dislocation which is located inside the elliptical inhomogeneity and an electrically conductive confocal rigid line under remote anti-plane shear stresses and in-plane electrical loads in piezoelectric composite material. The analytical-functions of the complex potentials, stress fields and the image force acting on the piezoelectric screw dislocation are obtained based on the principle of conformal mapping, the method of series expansion, the technical of analytic continuation and the analysis of singularity of complex potentials. The rigid line and the piezoelectric material property combinations upon the image force and the equilibrium position of the dislocation are discussed in detail by the numerical computation.     

Electro-elastic green's functions for a piezoelectric half-space and their application

I.IntroductionItiswell'knownthatoneofthemostpowerfultoolsinlinearfieldtheoriesistheGreen'sfunction.Fore1asticity,considerableresearchcanbefoundintheliterature.However,theGreen'sfunctionforpiezoe1ectricityisratherlimitedduetotheanisotropyandelectromechanic…     

Interaction of a screw dislocation with an interfacial edge crack in a two-phase piezoelectric material

The interaction of a screw dislocation with an interfacial edge crack in a two-phase piezoelectric medium is investigated. Closed-form solutions of the elastic and electrical fields induced by the screw dislocation are derived using the conformal mapping method in conjunction with the image principle. Based on the electroelastic fields derived, the stress and electric displacement intensity factors, the image force acting on the dislocation are given explicitly. We find that the stress and electric displacement intensity factors depend on the effective electroelastic material constants. In the case where one of two phases is purely elastic, the stress intensity factor and image force are plotted to illustrate the influences of electromechanical coupling effect, the position of the dislocation and the material properties on the interaction mechanism. The project supported by the Doctoral Foundation of Hebei Province (B2003113)     

A piezoelectric screw dislocation interacting with a half-plane trimaterial composite

The electro-elastic stress investigation on the interaction between a screw dislocation and a half-plane trimaterial composite composed of three bonded dissimilar transversely isotropic piezoelectric materials is analyzed in the framework of linear piezoelectricity. Each layer is assumed to have the same material orientation with x ₃ in the poling direction. The dislocations are characterized by a discontinuous displacement and electric potential across the slip plane and are subjected to a line force and a line charge at the core. Based on the complex variable and the method of alternating technique, the solution of electric field and displacement field is expressed in terms of explicit series form. The solutions derived here can be applied to a variety of problems, for example, a half-plane bimaterial, a quarter-plane bimaterial, a quarter-plane material and a rectangular strip etc. Numerical results are provided to show the influences of the material combinations and geometric configurations on the electro-elastic fields and image force calculated through the generalized Peach-Koehler formula. The solutions proposed here can be served as Green??s functions for the analyses corresponding piezoelectric cracking problems.     

Out-of-plane interface cracks in dissimilar piezoelectric materials

Summary This paper investigates the problem of an anti-plane interfacial crack between two dissimilar piezoelectric material layers. A single crack is first considered. The effect of interaction of two collinear cracks in the medium on the field intensity factors is investigated. The solutions of several particular cases, including an infinite piezoelectric bi-material and a piezoelectric material bonded to an elastic medium, are given. The bi-material constants governing the behavior of the crack tip fields are identified. By considering the crack as a notch of finite thickness, it is shown that the thickness of the notch has a pronounced influence on the crack tip field. The results for the assumption of a permeable crack represent the limit case where the notch thickness is reduced to zero.BLW would like to thank the National Science Foundation of China (#10102004) and the City University of Hong Kong (DAG #7100219) for the support of this work. YGS also thanks the Multidiscipline Scientific Research Foundation Project (HIT. MD 2001. 39) of the Harbin Institute of Technology and the SRF for ROCS, SEM.accepted for publication 3 April 2003     

Green's functions for anisotropic piezoelectric bimaterials with a slipping interface

An explicit full-field expression of the Green's functions for anisotropic piezoelectric bimaterials with a slipping interface is derived. When the electro-elastic singularity reduces to a pure dislocation in displacement and electric potential, interaction energy between the dislocation and the bimaterials is obtained explicitly while the generalized force on the dislocation is given in a real form which is also valid for degenerate materials. The investigation demonstrates that the boundary conditions at the slipping interface between two piezoelectric materials will exert a prominent influence on the mobility of the dislocation. Project supported by the National Natural Science Foundation of China (No. 59635140).     

Interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional hexagonal quasicrystal with piezoelectric effect

The interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional(1 D) hexagonal quasicrystal with piezoelectric effect is considered. A general formula of the generalized stress field, the field intensity factor, and the image force is derived, and the special cases are discussed. Several numerical examples are given to show the effects of the material properties and the dislocation position on the field intensity factors and the image forces.     

Analysis of a screw dislocation inside an elliptical inhomogeneity in piezoelectric solids

This paper formulates and examines the electro-elastic coupling effects resulting from the presence of a screw dislocation inside an elliptical piezoelectric inhomogeneity embedded in an infinite piezoelectric matrix. The general solution to this problem is obtained by conformal mapping and Laurent series expansion of the corresponding complex potentials. The appropriate expressions of the field potentials and the field components are given explicitly in both the inhomogeneity and the surrounding matrix using a perturbation technique. The internal energy and the force on the dislocation are computed and several specific examples are provided to illustrate the validity and versatility of the developed formulations.     

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.     

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.     

Study on a straight dislocation in an icosahedral quasicrystal with piezoelectric effects

An electro-elastic analysis is performed on an icosahedral quasicrystal with piezoelectric effects containing a straight dislocation. The closed-form expressions for the elastic and electric fields are obtained using the extended Stroh formalism. The effects of piezoelectric constant on the phonon displacement, phason displacement, and electric potential are discussed in detail.     

Analysis of an interfacial crack in a piezoelectric bi-material via the extended Green’s functions and displacement discontinuity method

Based on the extended Stroh formalism, we first derive the extended Green’s functions for an extended dislocation and displacement discontinuity located at the interface of a piezoelectric bi-material. These include Green’s functions of the extended dislocation, displacement discontinuities within a finite interval and the concentrated displacement discontinuities, all on the interface. The Green’s functions are then applied to obtain the integro-differential equation governing the interfacial crack. To eliminate the oscillating singularities associated with the delta function in the Green’s functions, we represent the delta function in terms of the Gaussian distribution function. In so doing, the integro-differential equation is reduced to a standard integral equation for the interfacial crack problem in piezoelectric bi-material with the extended displacement discontinuities being the unknowns. A simple numerical approach is also proposed to solve the integral equation for the displacement discontinuities, along with the asymptotic expressions of the extended intensity factors and J-integral in terms of the discontinuities near the crack tip. In numerical examples, the effect of the Gaussian parameter on the numerical results is discussed, and the influence of different extended loadings on the interfacial crack behaviors is further investigated.     

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.     

Electro-elastic fundamental solutions of anisotropic piezoelectric materials with an elliptical hole

By using Stroh' complex formalism and Cauchy's integral method, the electro-elastic fundamental solutions of an infinite anisotropic piezoelectric solid containing an elliptic hole or a crack subjected to a line force and a line charge are presented in closed form. Particular attention is paid to analyzing the characteristics of the stress and electric displacement intensity factors. When a line force-charge acts on the crack surface, the real form expression of intensity factors is obtained. It is shown through a special example that the present work is correct. The project supported by the Fund of the State Education Commission of China for Excellent Young Teachers     

Compensation of stress intensity factors in hollow cylinders containing several cracks under torsion by electro-elastic coating

In this article, a formulation for a hollow cylinder reinforced with an electroelastic layer is investigated. The hollow cylinder and its electro-elastic coating are under the Saint-Venant torsional loading. First, the solution to the problem containing a Volterra-type screw dislocation is obtained by using the Fourier transform. The problem is then reduced to a set of Cauchy singular integral equations by the distributed dislocation method. Finally, several examples are presented to show the effect of the electro-elastic coating on the reduction of the stress intensity factors at the crack tips.     

Interfacial coplanar cracks in piezoelectric bi-material systems under pure mechanical impact loading

In this paper, we examine the dynamic behaviour of different piezoelectric bi-material combinations containing two interfacial cracks subjected to mechanical impact loading. The problem is formulated in terms of integral transforms techniques and the collocation method to obtain the solution for the resulting singular integral equation in the transformed plane. Laplace inversion was then used to obtain the resulting dynamic stress intensity factors in the physical plane. Numerical examples are provided for five different types of piezoelectric bi-material systems to illustrate the effect of the presence of collinear interacting cracks and the different material combinations upon the resulting dynamic stress intensity factors.     

The interaction between a screw dislocation and a piezoelectric fiber composite with a wedge crack

The interaction problem between a screw dislocation and a piezoelectric fiber composite with a semi-infinite wedge crack is investigated in this paper. The piezoelectric media are assumed to be transversely isotropic with the poling direction along the x ₃ direction. The screw dislocation considered here involves a Burgers vector parallel to the poling direction with a line force and a line charge being applied at the core of the dislocation. Both cases of the screw dislocation located at the matrix and inclusion are observed. The analytical derivation is based on the complex variable and the conformal mapping methods. The exact solutions are obtained to calculate the forces on the dislocation and the crack-tip stress and electric displacement intensity factors. Based on these results, the anti-shielding and shielding effects for different loadings, material combinations, and geometric configurations are discussed in detail.