Dissimilar Piezoelectric Layers Research Articles

Multiple interfacial cracks in dissimilar piezoelectric layers under time harmonic loadings

AbstractIn this study, the dislocation‐based model is developed to study the interaction between time‐harmonic elastic waves and multiple interface cracks in 2 bonded dissimilar piezoelectric layers. In this model, cracks are represented by a distribution of so‐called electro‐elastic dislocations whose density is to be determined by satisfying the boundary conditions. Using the Fourier transform, this formulation leads to 2 singular integral equations, which can be solved numerically for the densities of electro‐elastic dislocations on a crack surface. The formulation is used to determine dynamic field intensity factors for multiple interface cracks without limitation of number of cracks. The dynamic field intensity factors are then calculated for both permeable and impermeable crack, and finally, numerical results are presented to illustrate the variation of these quantities with the electromechanical coupling, crack spacing, and the frequency of loading.

Transient response of dissimilar piezoelectric layers with multiple interacting interface cracks

In this study, we examine the dynamic behavior of two bonded dissimilar piezoelectric layers containing multiple interfacial cracks subjected to electro-mechanical impact loading. The problem was formulated through Fourier transformation into singular integral equations in which the unknown variables are the jumps of displacement and electric potential across the crack surface in the Laplace transform domain. The resulting integral equations together with the corresponding single-valued conditions are solved numerically for the densities of electro-elastic dislocations on a crack surface. The dynamic field intensity factors and dynamic energy release rate (DERR) history are obtained for both permeable and impermeable crack. The stress field is also obtained for the interface crack under impact loads. The results show that the field intensity factors at the crack tips and dynamic energy release rate depend on the interfacial crack geometry, electromechanical coupling and the electric boundary conditions on the crack surface.

Transient fracture of a piezoelectric-piezomagnetic sandwich structure: anti-plane case

In this article, we investigate the transient fracture behavior of piezoelectric (PE)–piezomagnetic (PM) sandwich structures under combined anti-plane shear mechanical and in-plane electrical impacts. A PM layer with an eccentric crack is sandwiched between two dissimilar PE layers. The Laplace and Fourier transforms are employed to reduce the mixed boundary valued problem to a standard Cauchy singular integral equation of the first kind in the Laplace transform domain. Then the Cauchy singular integral equation is solved by the Gauss–Chebyshev collocation method. By utilizing the numerical Laplace inversion, the dynamic stress intensity factors (DSIFs) are obtained in the time domain. Numerical results are presented to show the effects of the material combinations, crack location, structure geometries and electromechanical coupled loads on DSIFs. The findings of the present paper may be useful for the design and fracture prediction of layered PE–PM structures.

Multiple moving interfacial cracks between two dissimilar piezoelectric layers under electromechanical loading

The dynamic problem of several moving cracks at the interface between two dissimilar piezoelectric materials is analyzed. The combined out-of-plane mechanical and in-plane electrical loads are applied to the layers. Fourier transforms are used to reduce the problem to a system of singular integral equations with simple Cauchy kernel. The integral equations are solved numerically by converting to a system of linear algebraic equations and by using a collocation technique. The results presented consist of the stress intensity factors and the electric displacement intensity factors. It is found that generally the field intensity factors increase with increasing crack propagation speed.

Transient response of a crack in a functionally graded piezoelectric strip between two dissimilar piezoelectric strips

Transient response of a crack in a functionally graded piezoelectric material (FGPM) interface layer between two dissimilar homogeneous piezoelectric layers under anti-plane shear is analyzed using integral transform approaches. The properties of the FGPM layer vary continuously along the thickness. The FGPM layer and two homogeneous piezoelectric layers are connected weak-discontinuously. Laplace and Fourier transforms are used to reduce the problem to two sets of dual integral equations, which are then expressed to the Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate (DERR) are presented for the FGPM to show the effects on electric loading, gradient of the material properties, and thickness of the layers. Computed results yield following conclusions: (a) the DERR increases with the increase of the gradient of the material properties of the FGPM layer; (b) certain direction and magnitude of the electric impact loading impedes crack extension; and (c) increase of the thickness of the FGPM layer and the homogeneous piezoelectric layer which has larger material properties than those of the crack plane are beneficial to increase of the resistance of transient fracture of the FGPM layer.

Transient response of a semi-permeable crack between dissimilar anisotropic piezoelectric layers by time-domain BEM

Abstract This paper studied the transient response of a semi-permeable crack between two dissimilar anisotropic piezoelectric layers by a time-domain BEM with a sub-domain technique and an iterative process for the non-linear crack-face boundary conditions. The present time-domain BEM uses a quadrature formula for the temporal discretization to approximate the convolution integrals and a collocation method for the spatial discretization. A universal matrix-form displacement extrapolation formula and its explicit formula are used to determine the dynamic intensity factors. Several examples are presented and discussed to show the effects of the electrical crack-face boundary condition on dynamic intensity factors.

Anti-plane moving crack in a functionally graded piezoelectric layer between two dissimilar piezoelectric strips

The dynamic propagation of a crack in a functionally graded piezoelectric material (FGPM) interface layer between two dissimilar piezoelectric layers under anti-plane shear is analyzed using integral transform approaches. The properties of the FGPM layers vary con- tinuously along the thickness. The FGPM layer and two homogeneous piezoelectric layers are connected weak-discontinuously. A con- stant velocity Yoffe-type moving crack is considered. The Fourier transform is used to reduce the problem to two sets of dual integral equations, which are then expressed to the Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate (DERR) are presented for the FGPM to show the effects on electric loading, gradient of the material properties, crack moving velocity, and thickness of the layers. The following are helpful to increase resistance to crack propagation in the FGPM interface layer: (a) certain direction and magnitude of the electric loading, (b) increasing the thickness of the FGPM interface layer, and (c) increasing the thickness of the homogeneous piezoelectric layer to have larger material properties than those of the crack plane in the FGPM interface layer. The DERR always increases with the increase of crack moving velocity and the gradient of the material properties.

Transient response of an annular interfacial crack between dissimilar piezoelectric layers under mechanical and electrical impacts

AbstractThe dynamic response of an annular interfacial crack between dissimilar piezoelectric layers subjected to mechanical and electrical impact loadings is investigated. Laplace and Hankel transforms are employed to reduce the mixed boundary value problem to Cauchy singular integral equations. The integral equations are further reduced to a system of algebraic equations with the aid of Jacobi polynomials. The dynamic field intensity factors and dynamic energy release rates are determined. Numerical results reveal the effects of crack configuration, electrical impact loading on crack propagation, and growth.

DYNAMIC CRACK PROPAGATION IN A FUNCTIONALLY GRADED PIEZOELECTRIC INTERFACE LAYER BETWEEN TWO DISSIMILAR PIEZOELECTRIC LAYERS UNDER ELECTROMECHANICAL LOADING

The dynamic propagation of a crack in a functionally graded piezoelectric material (FGPM) interface layer between two dissimilar piezoelectric layers under anti-plane shear is analyzed using the integral transform approaches. The properties of the FGPM layers vary continuously along the thickness. FGPM layer and the two homogeneous piezoelectric layers are connected weak-discontinuously. A constant velocity Yoffe-type moving crack is considered. Numerical values on the dynamic energy release rate (DERR) are presented for the FGPM. Followings are helpful to increase of the resistance of the crack propagation of the FGPM interface layer: (a) certain direction and magnitude of the electric loading; (b) increase of the thickness of the FGPM interface layer; (c) increase of the thickness of the homogeneous piezoelectric layer which has larger material properties than those of the crack plane in the FGPM interface layer. The DERR always increases with the increase of crack moving velocity and the gradient of the material properties.

Electroelastic behaviour of an annular interfacial crack between dissimilar piezoelectric layers

An annular interfacial crack between dissimilar piezoelectric layers subjected to electroelastic loadings was investigated under an electrically impermeable boundary condition on the crack surface by using the Hankel transform technique and the Cauchy singular integral equation method. The stress intensity factors and energy release rates were determined. Numerical results reveal the effects of crack configuration, electric loads and material parameters on crack propagation and growth. The results should be useful for the design of piezoelectric composite structures and devices of high performance.

Magnetoelectroelastic shear body waves in periodically layered metalized ferrite–piezoelectric media

A method of deriving the dispersion equations for magnetoelectroelastic shear waves in periodically layered media is proposed. The media are formed by uniting identical metalized laminates, each consisting of two dissimilar piezoelectric layers separated by a layer with the properties of ferrite. A numerical analysis is carried out and the propagation of body waves in different structures consisting of ZnO and GaYtC layers is described within wide ranges of frequencies and wave numbers. The influence of the physical, mechanical, and geometrical parameters of the layers on the structure of the transmission and suppression zones and the effect of the piezoelectric effect of the position of transmission edges are examined

Out-of-plane interface cracks in dissimilar piezoelectric materials

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.

Interaction of a Screw Dislocation with an Interfacial Crack in Two Dissimilar Piezoelectric Layers

A screw dislocation interacting with a semi-infinite interfacial crack in two dissimilar piezoelectric layers is studied. The complex variable method and the conformal mapping technique are employed to obtain the solution of the problem. The stress and electric displacement intensity factors are given explicitly. We find that the stress and electric displacement intensity factors depend on the effective electro-elastic material constants. Numerical example shows that the influence of piezoelectric effect on the crack tip shielding is significant.

Screw dislocation in two dissimilar piezoelectric layers

AbstractThe elastic and electrical fields produced by a straight screw dislocation in two dissimilar piezoelectric layers are derived through the use of conformal mapping technique, where the solution for a semi‐infinite piezoelectric bimaterial is used as a base. The expression for the image force acting on the dislocation is given explicitly. The equilibrium position of the dislocation is further determined by letting the image force be equal to zero. In the case where one of the two layers is pure elastic, the numerical results for the image force are provided to illustrate the influence of piezoelectric effect on the behavior of the dislocation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Electroelastic analysis of an interface anti-plane shear crack in a layered piezoelectric plate

The problem of an anti-plane interface crack in a layered piezoelectric plate composed of two bonded dissimilar piezoelectric ceramic layers subjected to applied voltage is considered. It is assumed that the crack is either impermeable or permeable. An integral transform technique is employed to reduce the problem considered to dual integral equations, then to a Fredholm integral equation by introducing an auxiliary function. Field intensity factors and energy release rate are obtained in explicit form in terms of the auxiliary function. In particular, by solving analytically a resulting singular integral equation, they are determined explicitly in terms of given electromechanical loadings for the case of two bonded layers of equal thickness. Some numerical results are presented graphically to show the influence of the geometric parameters on the field intensity factors and the energy release rate.

Antiplane interface crack between two bonded dissimilar piezoelectric layers

The problem of an antiplane crack situated in the interface between two bonded dissimilar piezoelectric layers is considered under the permeable crack assumption. It is assumed that applied longitudinal shear stress and electric loading at the layer surfaces are prescribed. By using an integral transform technique, the problem considered is reduced to dual integral equations, which is further transformed into a Fredholm integral equation by introducing an auxiliary function. The field intensity factors and the energy release rate are obtained in explicit form in terms of the auxiliary function. In particular, by solving analytically a resulting singular integral equation, they are determined in closed-form in terms of given electromechanical loading for the case of two bonded layers of equal thickness. Some numerical results are presented graphically to show the influence of the material properties and geometric parameters on the normalized energy release rate.

Transient response of an insulating crack between dissimilar piezoelectric layers under mechanical and electrical impacts

The dynamic response of an interface crack between two dissimilar piezoelectric layers subjected to mechanical and electrical impacts is investigated under the boundary condition of electrical insulation on the crack surface by using the integral transform and the Cauchy singular integral equation methods. The dynamic stress intensity factors, the dynamic electrical displacement intensity factor, and the dynamic energy release rate (DERR) are determined. The numerical calculation of the mode-I plane problem indicates that the DERR is more liable to be the token of the crack growth when an electrical load is applied. The dynamic response shows a significant dependence on the loading mode, the material combination parameters as well as the crack configuration. Under a given loading mode and a specified crack configuration, the DERR of an interface crack between piezoelectric media may be decreased or increased by adjusting the material combination parameters. It is also found that the intrinsic mechanical-electrical coupling plays a more significant role in the dynamic fracture response of in-plane problems than that in anti-plane problems.

Transient response of a Griffith crack between dissimilar piezoelectric layers under anti-plane mechanical and in-plane electrical impacts

The problem of an interface crack between dissimilar piezoelectric layers under mechanical and electrical impacts is formulated by using integral transform and Cauchy singular integral equation methods. The dynamic stress intensity factor and dynamic energy release rate (DERR) are determined through use of the obtained solutions and the effects of the loading ratio, the geometry of crack configuration and the combination of material parameters on the above two quantities are discussed. The numerical calculations indicate that the electrical load can promote or retard the crack growth depending on its magnitude, direction and the existence of the mechanical load and that with the increase of the value of ratio of two material parameters, some material parameters will inhibit the crack growth. On the other hand, some material parameters play the contrary roles. In addition, the geometry of the crack configuration has the significant effects on the DERR. Finally the results are compared with those obtained in a previous investigation.

Transient response of an interface crack between dissimilar piezoelectric layers under mechanical impacts

Using the integral transform and the Cauchy singular integral equation methods, the problem of an interface crack between two dissimilar piezoelectric layers under mechanical impacts is investigated under the permeable electrical boundary condition on the crack surface. The dynamic stress intensity factors (DSIFs) of both mode-I and II are determined. The effects of the crack configuration and the combinations of the constitutive parameters of the piezoelectric materials on the dynamic response are examined. The numerical calculation of the mode-I plane problem indicates that the DSIFs may be retarded or accelerated by specifying different combinations of material parameters. In addition, the parameters of the crack configuration, including the ratio of the crack length to the layer width and the ratio between the widths of two layers, exert a considerable influence on the DSIFs. The results seem useful for design of the piezoelectric structures and devices of high performance.