Electro-elastic interaction between a screw dislocation and an elliptical inhomogeneity in piezoelectric materials

Meguid, S. A.; Wei, Deng

doi:10.1016/s0020-7683(97)00116-9

Cited by 54 publications

(23 citation statements)

References 17 publications

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“…These adaptive structures are capable of monitoring and adapting to their environments, providing a smart response to external conditions. Investigations on piezoelectric materials in the presence of defects such as dislocations, cracks, and inclusions are many [Pak 1990a;1990b;1992;Meguid and Deng 1998;Liu et al 1999;Ru and Mao 1999;Lee et al 2000;Chen et al 2002;Xiao et al 2007] due to the fact that these defects can adversely influence the performance of the piezoelectric devices. Recently He and Lim [2003] analyzed the electromechanical response of a piezoelectric fibrous composite with a viscous interface described by the linear law of rheology [Ray and Ashby 1971;Suo 1997].…”

Section: Introductionmentioning

confidence: 99%

Interaction between a screw dislocation and a piezoelectric circular inclusion with viscous interface

Wang

Pan

Roy

2008

JOMMS

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Exact closed-form solutions in terms of elementary functions are derived for the problem of a screw dislocation embedded in an unbounded piezoelectric matrix interacting with a piezoelectric circular inclusion with a linear viscous interface. By means of the complex variable method, the original boundary value problem is reduced to an inhomogeneous first-order partial differential equation whose solution can be expressed in terms of elementary functions. The time dependent electroelastic fields such as stresses, strains, electric fields, and electric displacements are then obtained. In particular the image force acting on the piezoelectric screw dislocation, due to its interaction with the circular viscous interface, is presented. Some special cases of practical importance are discussed to verify and to illustrate the obtained solution. Finally we present a specific example of a screw dislocation located in a piezoelectric PZT-5 matrix interacting with a piezoelectric BaTiO 3 fiber to graphically demonstrate the influence of the viscosity of the interface on the mobility of the screw dislocation.

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Section: Introductionmentioning

confidence: 99%

Interaction between a screw dislocation and a piezoelectric circular inclusion with viscous interface

Wang

Pan

Roy

2008

JOMMS

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“…According to the singular behavior of the complex potential [2,15] and the perturbation concept [17,23], the complex potential in the matrix in the z -plane can be taken the form [15,17] 2 0 2 0…”

Section: Original Papermentioning

confidence: 99%

Electroelastic interaction between a piezoelectric screw dislocation and an elliptical inclusion with interfacial cracks

Fang

Liu

Jiang

2005

Physica Status Solidi (b)

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The electroelastic interaction between a piezoelectric screw dislocation, which is located inside either the inclusion or the matrix, and an elliptical inclusion with interfacial cracks under antiplane mechanical and inplane electrical loads is dealt with. An efficient and concise complex variable method for complex multiply connected region is developed, in terms of which general solutions of complex potentials in the matrix and the inclusion regions are derived. The explicit series-form solutions are then given for the interface with a finite crack. The image force on the piezoelectric screw dislocation due to the elliptical inclusion, interfacial crack and remote uniform loadings is calculated by using the generalized PeachKoehler formula. The influence of the curvature and the length of the crack, the shape of the inclusion and electroelastic mismatch between two materials on the image force is evaluated and discussed. Numerical examples show that the elliptical arc interfacial crack has significant effect on the equilibrium position of the dislocation near the interface. Further analysis implies that, when the curvature or the length of the crack goes up to a critical value, existence of the interfacial crack can change the interaction mechanism between a piezoelectric screw dislocation and the elliptical inclusion. In addition, a significative result is that there exists a same value of the crack angle to change the direction of the image force regardless of the shape of the inclusion as the area of the elliptical inclusion taking a constant. The present solutions contain a number of previously known results which can be shown to be special cases.

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“…Xiao and Zhao [2004] analyzed a Zener-Stroh crack at the interface of metal/piezoelectric bimaterials by means of Green's function. Contributions have also been made to study the dislocation-inclusion/interface/crack interaction in piezoelectric materials, for example [Meguid and Deng 1998;Fang et al 2005;Chen et al 2005a;Chen et al 2005b] and [Gao et al 2005].…”

Section: Introductionmentioning

confidence: 99%

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2008

JOMMS

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See inside back cover or http://www.jomms.org for submission guidelines.Regular subscription rate: $500 a year.Subscriptions, requests for back issues, and changes of address should be sent to Mathematical Sciences Publishers, 798 Evans Hall, Department of Mathematics, University of California, Berkeley, CA 94720-3840. ELASTIC CONSTANTS AND THERMAL EXPANSION AVERAGES OF A NONTEXTURED POLYCRYSTAL ROLAND DEWITThis paper gives expressions for the overall average elastic constants and thermal expansion coefficients of a polycrystal in terms of its single crystal components. The polycrystal is assumed to be statistically homogeneous, isotropic, and perfectly disordered. Upper and lower bounds for the averages are easily found by assuming a uniform strain or stress. The upper bound follows from Voigt's assumption that the total strain is uniform within the polycrystal while the lower bound follows from Reuss' original assumption that the stress is uniform. A self-consistent estimate for the averages can be found if it is assumed that the overall response of the polycrystal is the same as the average response of each crystallite. The derivation method is based on Eshelby's theory of inclusions and inhomogeneities. We define an equivalent inclusion, which gives an expression for the strain disturbance of the inhomogeneity when external fields are applied. The equivalent inclusion is then used to represent the crystallites. For the self-consistent model the average response of the grains has to be the same as the overall response of the material, or the average strain disturbance must vanish. The result is an implicit equation for the average polycrystal elastic constants and an explicit equation for the average thermal expansion coefficients. For the particular case of cubic symmetry the results can be reduced to a cubic equation for the selfconsistent shear modulus. For lower symmetry crystals it is best to calculate the self-consistent bulk and shear modulus numerically. IntroductionA polycrystal, whose properties vary in a complicated fashion from point to point over a small microscopic length scale, may appear on average to be uniform or perhaps, more generally, its properties appear to vary smoothly. The determination of such overall properties from the properties and geometrical arrangement of the constituent monocrystal grains is our aim. In the simplest case the polycrystal is assumed to be statistically homogeneous, isotropic, and perfectly disordered. General expressions for averages can then be derived. Many different properties can be averaged, such as dielectric constants, diffusivity, elastic constants, electrical conductivity, magnetic permeability, magnetostriction, piezoelectric constants, thermal conductivity, or thermal expansion. In this paper we treat the elastic constants, which have already received more attention than most other physical properties, and the thermal expansion. Elastic constants are fundamental physical data needed for the characterization of materials. In addition to their fundam...

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Electro-elastic interaction between a screw dislocation and an elliptical inhomogeneity in piezoelectric materials

Cited by 54 publications

References 17 publications

Interaction between a screw dislocation and a piezoelectric circular inclusion with viscous interface

Interaction between a screw dislocation and a piezoelectric circular inclusion with viscous interface

Electroelastic interaction between a piezoelectric screw dislocation and an elliptical inclusion with interfacial cracks

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