In-plane Electric Loading Research Articles

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

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.

Transversely isotropic piezoelectric materials with an arbitrarily shaped boundary

In this paper, a two-dimensional electro-elastic analysis is performed on transversely isotropic piezoelectric materials containing an arbitrarily shaped boundary under out-of-plane mechanical and in-plane electrical loads at infinity. General closed-formed solutions are provided in terms of complex functions by using the conformal mapping technique. Using such solutions, several numerical examples are shown by graphical representation for various arbitrarily shaped boundaries. The effects of stress concentration on arbitrarily shaped boundaries are discussed. The stress intensity factors of mode III at the cusp are computed.

Transient response of a center crack in a functionally graded piezoelectric strip under electromechanical impact

The dynamic fracture problem for a functionally graded piezoelectric strip containing a center crack parallel to the free boundaries is considered in this study. It is assumed that the electroelastic properties of the medium vary continuously in the thickness direction, and that the strip is under in-plane mechanical and electric impact loadings. Integral transform techniques and dislocation density functions are employed to reduce the problem to the solutions of a system of singular integral equations. The dynamic stress and electric displacement intensity factors versus time are presented for various values of dimensionless parameters representing the crack size, the material nonhomogeneity and the loading combination.

Moving crack at the interface between two dissimilar magnetoelectroelastic materials

Analytical solutions for an anti-plane Griffith crack moving at the interface between two dissimilar magnetoelectroelastic media under the conditions of permeable crack faces are formulated using the integral transform method. The far-field anti-plane mechanical shear and in-plane electrical and magnetic loadings are applied to the magnetoelectroelastic materials. Expressions for stresses, electric displacements, and magnetic inductions in the vicinity of the crack tip are derived. Field intensity factors for magnetoelectroelastic material are obtained. The stresses, electric displacements and magnetic inductions at the crack tip show inverse square root singularities, and it is found that the dynamic stress intensity factor (DSIF), the dynamic electric displacement intensity factor (DEDIF) and the dynamic magnetic induction intensity factor (DMIIF) are independent of the remote electromagnetic loads. The moving speed of the crack has influence on the DEDIF and the DMIIF. When the crack is moving at lower speeds 0 ≤ M≤ Mc1 or higher speeds Mc2 < M < 1, the crack will propagate along its original plane, while in the range of Mc1 < M < Mc2 , the propagation of the crack possibly brings about the branch phenomena in magnetoelectroelastic media.

3652 平行き裂を有する傾斜機能圧電セラミックス厚板の電気弾性相互干渉(S24-4 特異応力・刃状転位,S24 数理・数値解析による先端材料評価)

In this paper, the mixed-mode crack problem for a functionally graded piezoelectric material (FGPM) strip is considered. It is assumed that the electroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under in-plane electric loading. The problem is formulated in terms of a system of singular integral equations. The stress and the electric displacement intensity factors, and the energy density factor are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity.

Transient Response of a Symmetric Functionally Graded Piezoelectric Slab with a Parallel Crack under Electromechanical Impact

The dynamic fracture problem for a functionally graded piezoelectric slab containing a center crack parallel to the free boundaries is considered in this study. It is assumed that the electroelastic properties of the medium vary continuously in the thickness direction, and that the slab is under inplane mechanical and electric impact loadings. Integral transform techniques and dislocation density functions are employed to reduce the problem to the solutions of a system of singular integral eqations. The dynamic stress and electric displacement intensity factors versus time are presented for various values of dimensionless parameters representing the crack size, the material non-homogeneity and the loading combination.

A finite crack in a semi-infinite strip of a graded piezoelectric material under electric loading

In this paper, the mixed-mode crack problem for a functionally graded piezoelectric material (FGPM) strip is considered. It is assumed that the electroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under in-plane electric loading. The problem is formulated in terms of a system of singular integral equations. The stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity.

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

AbstractThe 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 Peach–Koehler 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. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

A closed form solution to the antiplane problem of doubly periodic cracks of unequal size in piezoelectric materials

The problem of doubly periodic cracks in piezoelectric materials under far-field antiplane mechanical load and inplane electric load is investigated, where the fundamental cell contains four parallel and unequal cracks. By combining the elliptical function theory and conformal mapping technique, an exact solution in closed form to this problem is obtained. Based on this solution, the exact formulae for the crack tip field intensity factors and the effective electroelastic moduli of such cracked piezoelectric materials are derived. Numerical examples are graphically presented to show the interesting mechanical and electrical coupling phenomena induced by multicrack interactions, especially to reveal the shielding and intensifying effects of small cracks on the main cracks and to quantify the loss of electroelastic properties due to the presence of such arrays of microcracks. New and existing solutions, such as those for doubly periodic cracks in purely elastic materials and a single row or a single stack of periodical unequal cracks in piezoelectric materials are obtained as special cases of the present solution. The present solution can provide benchmark results for other numerical and approximate methods.

Electromechanical response of a center crack in a functionally graded piezoelectricstrip

In this paper the problem of a finite crack in a strip of functionally graded piezoelectricmaterial (FGPM) is studied. It is assumed that the elastic stiffness, piezoelectric, anddielectric constants of the FGPM vary continuously along the thickness of the strip, andthat the strip is under an in-plane mechanical and electric loading. The integral transformtechnique is used to reduce the problem to the solution of a singular integral equation. Theenergy density factor is presented for various values of dimensionless parametersrepresenting the crack size, the material inhomogeneity, and the magnitude of the electricloading.

Analysis of a screw dislocation inside a circular inclusion with interfacial cracks in piezoelectric composites

The electroelastic interaction of a screw dislocation inside a circular inclusion with interfacial cracks in piezoelectric composite materials under anti-plane shear and in-plane electric loads at infinity is investigated. The general solution to this problem was obtained by means of Riemann-Schwarz's symmetry principle integrated with analysis of singularities of corresponding complex potentials. As a typical example, closed form expressions of the complex potentials and electroelastic field components in the matrix and inhomogeneity regions were derived explicitly when the interface contains a single crack. The image force acting on the screw dislocation was calculated by using the generalized Peach-Koehler formula. The influence of interfacial crack geometry and piezoelectric material property combinations upon the image force was discussed in detail. The results show that interfacial crack has a significant perturbation effect on the image force and the equilibrium position of the screw dislocation. The presence of the interfacial crack can change the direction of the image force when the length of the crack goes up to a critical value. The obtained explicit solutions can be used as Green's functions to study the problem on the interaction between interfacial cracks and arbitrary shape crack inside the inclusion. The present solutions can lead to previously known results as the special case.

On the interaction between a generalized screw dislocation and circular-arc interfacial rigid lines in magnetoelectroelastic solids

The interaction of a generalized screw dislocation, which is located inside either the inclusion or the matrix, with circular-arc interfacial rigid lines under remote antiplane shear stresses, in-plane electric and magnetic loads in linear magnetoelectroelastic materials is dealt with. By using the complex variable method, the general solutions of the physical problem are presented in this paper. The closed-form solutions for stresses, electric displacement fields and magnetic induction fields are derived explicitly for the interface with a finite rigid line. The image forces acting on the generalized screw dislocation are then calculated by using the generalized Peach–Koehler formula. The influence of the length and the location of the rigid line as well as the material mismatch on the image force is evaluated. Numerical computations and discussions show that, when the length or the position of the interfacial rigid line achieves a critical value, the image force on the dislocation changes its direction due to the existence of the rigid line. In addition, the soft inclusion can repel the dislocation in magnetoelectroelastic materials owing to their intrinsic magnetoelectromechanical coupling behavior.

The dynamic behaviour of a piezoelectric actuator bonded to an anisotropic elastic medium

Surface-bonded piezoelectric actuators can be used to generate elastic waves for monitoring damages of composite materials. This paper provides an analytical and numerical study to simulate wave propagation in an anisotropic medium induced by surface-bonded piezocermic actuators under high-frequency electric loads. Based on a one-dimensional actuator model, the dynamic load transfer between a piezoceramic actuator and an anisotropic elastic medium under in-plane mechanical and electrical loading is obtained. The wave propagation induced by the surface-bonded actuator is also studied in detail by using Fourier transform technique and solving the resulting integral equations in terms of the interfacial shear stress. Typical examples are provided to show effects of the geometry, the material combination, the loading frequency and the material anisotropy of the composite upon the load transfer and the resulting wave propagation.

Dynamic behavior of a crack in a functionally graded piezoelectric strip bonded to two dissimilar half piezoelectric material planes

The dynamic behavior of a crack in a functionally graded piezoelectric material (FGPM) strip bonded to two half dissimilar piezoelectric material planes subjected to combined harmonic anti-plane shear wave and in-plane electrical loading was studied under the limited permeable and permeable electric boundary conditions. It was assumed that the elastic stiffness, piezoelectric constant and dielectric permittivity of the functionally graded piezoelectric layer vary continuously along the thickness of the strip. By using the Fourier transform, the problem can be solved with a set of dual integral equations in which the unknown variables are the jumps of the displacements and the electric potentials across the crack surfaces. In solving the dual integral equations, the jumps of the displacements and the electric potentials across the crack surfaces were expanded in a series of Jacobi polynomials. Numerical results illustrate the effects of the gradient parameter of FGPM, electric loading, wave number, thickness of FGPM strip and electric boundary conditions on the dynamic stress intensity factors (SIFs).

Anti-plane shear crack in a functionally gradient piezoelectric layer bonded to dissimilar half spaces

In this paper, the problem of a crack located in a functionally gradient piezoelectric interlayer between two dissimilar homogeneous piezoelectric half-planes being subjected to an anti-plane mechanical loading and an in-plane electric loading is considered. The material properties of the interlayer, such as the elastic stiffness, piezoelectric constant and dielectric constant, are assumed to vary continuously along the thickness of the interlayer, and the crack surface condition is assumed to be impermeable or permeable. By using the Fourier transform, the problem is first reduced to two pairs of dual integral equations and then into a Fredholm integral equation of the second kind. Numerical calculations are carried out, and the effects of crack geometric parameters on the stress intensity factor and the energy release rate are shown graphically.

Theoretical Analysis Around Arbitrary-Shaped Hole with Free or Fixed Boundary of Transversely Isotropic Piezoelectric Materials under Out-of-Plane Shear Loadings

In this paper, two-dimensional electro elastic analysis is performed for transversely isotropic piezoelectric materials containing arbitrary-shaped hole under the out-of-plane mechanical and in-plane electrical loads at infinity. General closed-formed solutions are provided in terms of complex functions by using the conformal mapping technique. Using the solution, several numerical examples are shown by graphical representation for various arbitrary-shaped holes. The effect of stress concentration on arbitrary-shaped holes is discussed.

Electoroelastic Interaction of a Symmetric Functionally Graded Piezoelectric Slab with a Crack Parallel to the Boundaries

In this paper the problem of a finite crack in a slab of functionally graded piezoelectric material (FGPM) is studied. It is assumed that the elastic stiffness, piezoelectric, and dielectric constants of the FGPM vary continuously along the thickness of the slab, and that the slab is under in-plane mechanical and electric loadings. Integral transform technique is used to reduce the problem to the solution of a singular integral equation. The stress intensity factor and the energy density factor are presented for various values of dimensionless parameters representing the crack size, the material nonhomogeneity and the magnitude of the electric loading.

Analysis of Anisotropic Piezoelectric Materials with Multilayered Elliptical Inclusion under In-Plane Loadings

In this paper, two-dimensional electro elastic analysis is performed for anisotropic piezoelectric materials containing conformal multilayered elliptical inclusion under the in-plane mechanical and electrical loads at infinity. General formed solutions are provided in terms of complex functions by using the conformal mapping technique. Formulations of mechanical and electrical quantities are expressed analogical formulations of mechanical quantities of 3-Dimensional anisotropic problem. Using the solutions, several numerical examples are shown by graphical representation to examine the effects of the piezoelectricity and anisotropy. And the legitimacy of the solutions are discussed

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 the electroelastic field intensity factors were derived explicitly when the interface contains single 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.

Constant moving crack in a magnetoelectroelastic material under anti-plane shear loading

Analytical solutions for an anti-plane Griffith moving crack inside an infinite magnetoelectroelastic medium under the conditions of permeable crack faces are formulated using integral transform method. The far-field anti-plane mechanical shear and in-plane electrical and magnetic loadings are applied to the magnetoelectroelastic material. Expressions for stresses, electric displacements and magnetic inductions in the vicinity of the crack tip are derived. Field intensity factors for magnetoelectroelastic material are obtained. The stresses, electric displacements and magnetic inductions at the crack tip show inverse square root singularities. The moving speed of the crack have influence on the dynamic electric displacement intensity factor (DEDIF) and the dynamic magnetic induction intensity factor (DMIIF), while the dynamic stress intensity factor (DSIF) does not depend on the velocity of the moving crack. When the crack is moving at very lower or very higher speeds, the crack will propagate along its original plane; while in the range of M c1 < M < M c2 , the propagation of the crack possibly brings about the branch phenomena in magnetoelectroelastic media.