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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. 相似文献
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《International Journal of Solids and Structures》2007,44(10):3344-3358
A general method is presented for the analytical solution of a piezoelectric screw dislocation located within one of two joined piezoelectric half-planes. The bonding along the half-plane is considered to be imperfect with the assumption that the imperfect interface is mechanically compliant and dielectrically weakly (or highly) conducting. For a mechanically compliant interface tractions are continuous but displacements are discontinuous across the imperfect interface. In this context, jumps in the displacement components are assumed to be proportional to their respective interface traction components. Similarly, for a dielectrically weakly conducting interface the normal electric displacement is continuous but the electric potential is discontinuous across the interface. The jump in electric potential is proportional to the normal electric displacement. In contrast, for a dielectrically highly conducting interface the electric potential is continuous across the interface whereas the normal electric displacement has a discontinuity across the interface which is proportional to a certain differential expression of the electric potential. Explicit expressions are derived for the complex field potentials. The results show that there are two dimensionless parameters measuring the interface “rigidity” as compared to one for the purely elastic case. When the imperfect interface is compliant and weakly conducting, the two dimensionless parameters can be positive real values or complex conjugates with positive real parts. When the imperfect interface is compliant and highly conducting the two dimensionless parameters can only be positive real values. An expression for the image force acting on the screw dislocation due to its interaction with a compliant and weakly conducting interface is also given. It is found that the image force is only dependent on two dimensionless generalized Dundurs constants as well as two dimensionless parameters measuring the interface “rigidity”. 相似文献
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A Zener-Stroh crack interacting with an edge dislocation is studied. The crack faces are assumed to be traction free. The applied ‘generalized loading’ for crack is the initial displacement jump and the intervention of the edge dislocation. Through decomposing the problem into two sub-simple problems, using the superposition principle, its solution is obtained. To demonstrate both the validity of the solution and its potential application, two simple examples related to the crack stress intensity factors are presented on the basis of the solution. The application of the solution to model crack initiations arising from dislocation-pileup is discussed. 相似文献
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《International Journal of Solids and Structures》2003,40(21):5781-5797
The elastic interaction of an edge dislocation, which is located either outside or inside a circular inhomogeneity, with an interfacial crack is dealt with. Using Riemann–Schwarz’s symmetry principle integrated with the analysis of singularity of the complex potentials, the closed form solutions for the elastic fields in the matrix and inhomogeneity regions are derived explicitly. The image force on the dislocation is then determined by using the Peach–Keohler formula. The influence of the crack geometry and material mismatch on the dislocation force is evaluated and discussed when the dislocation is located in the matrix. It is shown that the interfacial crack has significant effect on the equilibrium position of the edge dislocation near a circular interface. The results also reveal a strong dependency of the dislocation force on the mismatch of the shear moduli and Poisson’s ratios between the matrix and inhomogeneity. 相似文献
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P.S. Yang J.Y. Liou J.C. Sung 《International Journal of Solids and Structures》2007,44(25-26):8556-8578
In this paper, the problem of a crack embedded in a half-plane piezoelectric solid with traction-induction free boundary is analyzed. A system of singular integral equations is formulated for the materials with general anisotropic piezoelectric properties and for the crack with arbitrary orientation. The kernel functions developed are in complex form for general anisotropic piezoelectric materials and are then specialized to the case of transversely isotropic piezoelectric materials which are in real form. The obtained coupled mechanical and electric real kernel functions may be reduced to those kernel functions for purely elastic problems when the electric effects disappear. The system of singular integral equations is solved numerically and the coupling effects of the mechanical and electric phenomena are presented by the generalized stress intensity factors for transversely isotropic piezoelectric materials. 相似文献
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《International Journal of Solids and Structures》2003,40(13-14):3477-3492
Approximate dynamic boundary conditions of different orders are derived for the case of a thin piezoelectric coating layer bonded to an elastic material. The approximate boundary conditions are derived using series expansions of the elastic displacements and the electric potential in the thickness coordinate of the layer. All the expansion functions are then eliminated with the aid of the equations of motion and boundary/interface conditions of the layer. This results in boundary conditions on the elastic material that may be truncated to different orders in the thickness of the layer to obtain approximate boundary conditions. The approximate boundary conditions may be used as a replacement for the piezoelectric layer and thus simplify the analysis significantly. Numerical examples show that the approximate boundary conditions give good results for low frequencies and/or thin piezoelectric layers. 相似文献
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《European Journal of Mechanics - A/Solids》2007,26(3):442-459
The plane problem of a Griffith crack steadily propagating in an anisotropic piezoelectric medium is investigated through an analytical approach which is new in this topic. Complete solutions are provided in the subsonic regime under permeable and impermeable boundary conditions and the combined effects of mechanical and electrical far-fields are pointed out. 相似文献
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《International Journal of Solids and Structures》2003,40(6):1433-1453
In this paper, a mixed electric boundary value problem for a two-dimensional piezoelectric crack problem is presented, in the sense that the crack face is partly conducting and partly impermeable. By the analytical continuation method, the unknown electric charge distributions on the upper and lower conducting crack faces are reduced to two decoupled singular integral equations and then these two equations are converted into algebraic equations to find the full field solution. Though the results suggest that the stress intensity factors at the crack tip are identical to those of conventional piezoelectric materials, but the electric field and electric displacement are related to the electric boundary conditions on the crack faces. The electric field and electric displacement are singular not only at crack tips but also at the junctures between the impermeable part and conducting parts. Numerical results for the variations of the electric field, electric displacement field and J-integral with respect to the normalized impermeable crack length are shown. Some discussions for the energy release rate and the J-integral are made. 相似文献
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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) 相似文献
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《International Journal of Solids and Structures》2002,39(17):4501-4524
A cracked piezoelectric material strip under combining mechanical and electrical loads is considered. The crack is vertical to the top and bottom edges of the strip. The edges of the strip are parallel to the x-axis and perpendicular to the z-axis. When a piezoelectric ceramic is poled, it exhibits transversely isotropic behavior. Among many possible poled axis orientations, a particular orientation when the poling direction lies parallel to x-axis is examined in this paper. Both impermeable crack and permeable crack assumptions are considered. Numerical results are included for three kinds of fracture mechanics specimens, namely an edge-cracked strip, a double edge-cracked strip, and a center-cracked strip, subjected to uniform tensions and uniform electric displacement loads simultaneously, at the far ends. In addition, an edge-cracked strip under pure bending and uniform electric displacement loads at the far ends is also investigated in this paper. 相似文献
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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. 相似文献
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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. 相似文献
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1.IntroductionItiswell-knownthatthefundame,ltalsolutionsorGreen'sfunctionsplayanimportantroleilllinearelasticity.Forexample,theycanbeusedtoconstructmanyanalyticalsolutionsofpracticalproblems.Itismoreimportantthattheyareusedasthefundamentalsolutionsintheboundaryelementmethod(BEM)tosolvesomecomplicatedproblem.Withthewidely-increasingapplicationofpiezoelectricmaterialsinengineeringproblems,thestudyregardingtheGreen'sfLlnctionsinpiezoelectricsolidshasreceivedmuchinterest.The3DGreen'sfunctionsi… 相似文献
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Ralf Müller Petia Dineva Tsviatko Rangelov Dietmar Gross 《Archive of Applied Mechanics (Ingenieur Archiv)》2012,82(1):97-110
The anti-plane dynamic problem of a functionally graded piezoelectric plane containing a hole–crack system is treated by a
non-hypersingular traction-based boundary integral equation method. The material parameters vary exponentially in the same
manner in an arbitrary direction. The system is loaded by an incident SH-type wave, and impermeable boundary conditions are
assumed. Using a frequency-dependent fundamental solution of the wave equation, the boundary value problem is transformed
into a system of integro-differential equations along the boundary of the hole and on the crack line. Its numerical solution
yields the dynamic stress intensity factors and stress concentration factors. A parametric study reveals their dependence
on the hole–crack scenario and its geometry, characteristics of the dynamic load and magnitude and direction of material inhomogeneity. 相似文献
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By invoking the theorem of work reciprocity for piezoelectric media, necessary conditions, which the prescribed edge data of the plate must fulfill in order that it should generate a decaying state within the plate, are established through generalizing the method proposed by Gregory and Wan. These decaying state conditions for the case of axisymmetric deformation of a transversely isotropic piezoelectric circular plate when stress and electric displacement conditions are imposed on the plate edge are derived explicitly, which are then used for the formulation of boundary conditions for the plate theory solution (or the interior solution). Also an analytical solution of the axisymmetric decaying state of transversely isotropic piezoelectric circular plates is derived. Furthermore, the corresponding necessary conditions for the axisymmetric deformation of elastic circular plates are indeed reproduced directly. 相似文献
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Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions 总被引:1,自引:0,他引:1
We present a family of phase-field models for fracture in piezoelectric and ferroelectric materials. These models couple a variational formulation of brittle fracture with, respectively, (1) the linear theory of piezoelectricity, and (2) a Ginzburg–Landau model of the ferroelectric microstructure to address the full complexity of the fracture phenomenon in these materials. In these models, both the cracks and the ferroelectric domain walls are represented in a diffuse way by phase-fields. The main challenge addressed here is encoding various electromechanical crack models (introduced as crack-face boundary conditions in sharp models) into the phase-field framework. The proposed models are verified through comparisons with the corresponding sharp-crack models. We also perform two dimensional finite element simulations to demonstrate the effect of the different crack-face conditions, the electromechanical loading and the media filling the crack gap on the crack propagation and the microstructure evolution. Salient features of the results are compared with experiments. 相似文献