Fracture of a piezoelectric material layer bonded by two elastic layers

A piezoelectric material layer bonded by two elastic layers under mechanical and electrical loads is studied. The piezoelectric material layer contains a central crack or two collinear cracks. Both mixed-mode crack and anti-plane crack are considered for the impermeable crack assumption and the permeable crack assumption. The effect of electric boundary conditions on electrical and mechanical field intensity factors are discussed. Some new observations are found.     

Transient anti-plane crack problem of a functionally graded piezoelectric strip bonded to elastic layers

Summary. This paper examined the dynamic electromechanical behavior of a crack in a functionally graded piezoelectric layer bonded between two elastic layers under the combined anti-plane mechanical shear and in-plane electric impacts. Fourier cosine transforms are used to reduce the problem to the solution of a set of singular integral equations. It is found that the impermeable crack condition is more reasonable than the permeable crack condition to analyze the influence of electric loading, and the energy density factor is more acceptable than the energy release rate to be used as the fracture criterion. In addition, numerical results are also presented to show the influences of the crack position, electromechanical combination factor and material gradient parameter on the fracture behavior.     

Pull-off test for a cracked layer bonded to a rigid foundation

This paper is concerned with the plane strain problem of an elastic incompressible layer bonded to a rigid foundation. An upward tensile force is applied to the top surface of the layer through a rigid strip of finite thickness. The layer contains either a finite central crack or two semi-infinite external cracks. The analysis leads to a system of singular integral equations. These integral equations are solved numerically and the interface stress distributions, stress intensity factors at the crack tips and at the corners of the rigid strip, probable cleavage angle for the finite crack and strain energy release rate are calculated for various geometries.     

Pull-off test for a cracked layer bonded to a rigid foundation

This paper is concerned with the plane strain problem of an elastic incompressible layer bonded to a rigid foundation. An upward tensile force is applied to the top surface of the layer through a rigid strip of finite thickness. The layer contains either a finite central crack or two semiinfinite external cracks. The analysis leads to a system of singular integral equations. These integral equations are solved numerically and the interface stress distributions, stress intensity factors at the crack tips and at the corners of the rigid strip, probable cleavage angle for the finite crack and strain energy release rate are calculated for various geometries.     

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

Summary. 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).     

Penny-shaped crack in an elastic layer bonded to dissimilar half spaces

Two axially symmetric mixed boundary value problems in an elastic dissimilar layered medium are considered. It is assumed that an elastic layer is bonded to two semi-infinite half spaces along its plane surfaces, and contains a penny-shaped crack parallel to the interfaces. In the first problem the two half spaces are assumed to have the same elastic properties and the crack is located in the mid-plane of the layer. In the second problem we consider the case of three different materials and arbitrary crack location in the layer. The numerical examples are given for a constant pressure on the crack surface. The stress intensity factors are evaluated and are plotted as functions of the layer thickness-to-crack radius ratio or the relative distance of the crack from an interface.     

The interface crack problem for bonded piezoelectric and orthotropic layers under antiplane shear loading

The primary objective of this paper is to study the influence of the electroelastic interactions on the stress intensity factor in bonded layers of piezoelectric and orthotropic materials containing a crack along the interface under antiplane shear. Attention is given to a two-layer hybrid laminate formed by adding a layer of piezoelectric ceramic to a unidirectional graphite/epoxy composite or an aluminum layer. Electric displacement or electric field is prescribed on the surfaces of the piezoelectric layer. The problem is formulated in terms of a singular integral equation which is solved by using a relatively simple and efficient technique. A number of examples are given for various material combinations. The results show that the effect of the electroelastic interactions on the stress intensity factor and the energy release rate can be highly significant. This revised version was published online in July 2006 with corrections to the Cover Date.     

Antiplane problem of curvilinear cracks in bonded dissimilar materials

A general solution to the antiplane problem of curvilinear cracks in bonded dissimilar materials is provided. The analysis is based upon the Hilbert problem formulation and the technique of analytical continuation. To illustrate the use of the present approach, detailed results are given for a single circular-arc crack lying along the interface between dissimilar materials. The expressions of the complex potentials are derived explicitly in both the unit disk and the surrounding medium. Both the stress intensity factors and contact stress are provided in an explicit form and the former are verified by comparison with existing ones. The effect of material and geometrical parameters upon the contact stress and stress intensity factors has also been discussed and shown in graphic form.     

Thermal stress in an elastic layer containing a penny-shaped crack and bonded to dissimilar half-spaces

This paper gives an analysis of the distribution of thermal stress in an elastic layer bonded to two half-spaces along its plane surfaces and contains a penny-shaped crack parallel to the interfaces. The crack is situated in the mid-plane of the layer. The thermal and elastic properties of the layer and of the half-spaces are assumed to be different. The problem is first reduced to dual integral equations. These equations are further reduced to Fredholm integral equations of the second kind which are solved iteratively. Expressions for quantities of physical interest are derived.

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Résumé Le mémoire fournit une analyse de la distribution des contraintes thermiques dans une couche élastique solidaire de deux demi-espaces situés le long de ses surfaces planes et comportant une fissure en forme de disque parallèle à ses interfaces. La fissure est située dans le plan moyen de la couche élastique. Les propriétés thermiques et élastiques de cette couche ainsi que celles des demi-espaces sont supposées différentes. Le problème est en premier lieu ramené à des équations intégrales. Ces équations sont ensuite ramenées à des équations intégrales de Fredholm du second genre qui sont résolues par itération. Des expressions pour les quantités présentant un intérêt physique sont déduites de ce travail.

     

Contact problem for two perfectly bonded dissimilar infinite strips

In this paper a finite contact problem for two perfectly bonded dissimilar infinite strips is formulated in terms of singular integral equations. Both of the strips are assumed to be isotropic and uniaxial tension is applied to the lower strip away from the contact region. The contact stresses, stress intensity factors and stress distributions in the strips are obtained for various geometries and material combinations. It is also shown that the contact stresses become infinite at the contact ends with a typical square-root singularity.

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Résumé On exprime un problème de contact fini de deux bandes infinies différentes et parfaitement assemblées sur une longueur finie sous la forme d'intégrales singulières. On Suppose que chacune des bandes est isotrope, et qu'une tension uniaxiale est appliquée à la bande inférieure, à une distance suffisante de la zone de contact. On obtient pour diverses géométries et combinaisons de matériaux les contraintes de contact, les facteurs d'intensité de contraintes et les distributions des contraintes dans les bandes. On montre également que les contraintes de contact deviennent infinies aux extrémités de la zone de contact, et présentent une singularité typiquement exprimée par la racine carrée de leur valeur.

     

T-shaped crack problem for bonded orthotropic layers

The plane elasticity problem of two perfectly bonded orthotropic layers containing cracks perpendicular to and along the interface is considered. Cracks are extended to intersect the boundaries and each other in such a way that a crack configuration suitable to study the T-shaped crack problem is obtained. The problem is reduced to the solution of a system of singular integral equations with Cauchy type singularities. Numerical results for stress intensity factors and energy release rates are presented for various loading conditions and for isotropic as well as orthotropic material pairs. These results indicate that elementary strength of material type calculations for energy release rates provide a good approximation to the actual elasticity solution even for relatively short cracks, as long as the layer thicknesses are not very different.     

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

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.     

用无网格法分析带压电层的裂纹板的振动特性

将无网格伽辽金法（EFGM）应用于求解含压电层裂纹板的横向自由振动问题。建立了系统的能量泛函,根据弹性动力学推广的Hamilton原理和引入无量纲量,推导了含压电层的裂纹矩形薄板的变分式;建立了无网格伽辽金法离散的控制方程。通过数值计算,得出了薄板的无量纲固有频率随裂纹和压电片几何参数的变化曲线,分析了裂纹的参数和数量对矩形薄板的横向振动特性的影响。     

Multiple interfacial cracks in dissimilar piezoelectric layers under time harmonic loadings

In 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.     

Experimental solution of the problem of a curvilinear crack in bonded dissimilar materials

An experimental technique based on the optical method of caustics for the solution of the two-dimensional problem of an arc-shaped crack lying along the interface of a circular inclusion embedded in a matrix and subjected to a uniaxial tension at infinity was developed. The study was directed towards the determination of the complex stress intensity factorK ^*characterizing the near to the crack tip stress field. A detailed analysis of the caustics obtained by illuminating the near to the crack tip region by a coherent light beam was undertaken and nomograms for the direct experimental determination ofK ^*in the Dundurs parallelogram, incorporating all the physically relevant material combinations of the two bodies, were given. Extensive experimental evidence for the new technique was given.

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Résumé Une technique expérimentale basée sur une méthode optique par caustiques a été développée pour établir la solution d'un probléme bidimensionnel d'une fissure en forme d'arc située le long de l'interface d'une inclusion circulaire noyée dans une matrice et soumise à une tension uniaxiale à l'infini. L'étude a été dirigée en vue de la détermination du facteur d'intensité des contraintes complexesK ^*caractérisant le champ de contrainte situé au voisinage de l'extrémité de la fissure. Une analyse détaillée des caustiques obtenues en illuminant la région située au voisinage de la pointe de l'entaille à l'aide d'un rayon lumineux cohérent a été effectuée, et des nomogrammes ont été obtenus pour une détermination expérimentale directe deK ^*dans un parallélogramme de Dundurs, en incorporant toutes les combinaisons physiquement possibles des matériaux constituant les deux corps. Plusieurs vérifications expérimentales de la nouvelle technique sont fournies.

     

A cracked elastic strip bonded to a rigid support

The elastostatic plane problem of an infinite strip containing a transverse crack is considered. It is assumed that one side of the strip is perfectly bonded to a rigid support whereas the other side is free of traction. The problem is formulated in terms of a singular integral equation. Internal crack, edge crack, crack terminating at the rigid support, and completely broken strip cases are considered in some detail. The singular integral equation is solved numerically by employing collocation schemes developed by Erdogan, Gupta and Cook. The stress intensity factor, which may be regarded as the most important fracture parameter, and the crack surface displacement are calculated for various crack geometries and given in graphical form.

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Résumé On considère le problème élastostatique et plan d'un feuillard infini comportant une fissure transversale. On suppose qu'un côté de la bande est parfaitement fixé à un support rigide tandis que l'autre côté est libre de contrainte. On formule le problème sous forme d'une équation intégrale singulière. On considère avec quelques détails la fissure interne, la fissure de coin, la fissure se terminant au support rigide et le cas de la bande complètement rompue. L'équation intégrale singulière est résolue numériquement en utilisant les schémas de collocation développés par Erdogan, Gupta et Cook. Le facteur d'intensité de contrainte qui peut être considéré comme le paramètre le plus important de rupture et le déplacement de surface de la fissure sont calculés pour diverses géométries de fissure; ils sont fournis sous une forme graphique.

     

A thin cracked layer bonded to an elastic half-space under an antiplane concentrated load

The antiplane elasticity problem for a thin cracked layer bonded to an elastic half-space under an antiplane concentrated load is considered. The fundamental solution is obtained as a rapidly convergent series in terms of the complex potentials via iterations of Möbius transformation. The singular integral equation with a logarithmic singular kernel is derived to model a crack problem that can be solved numerically in a straightforward manner. The dimensionless mode-III stress intensity factors obtained for various crack inclinations and crack lengths are discussed in detail and provided in graphic form. A strip problem with an arbitrarily oriented crack is also considered.     

Generalized thermal conductivity of dissimilar heat-sensitive bodies connected by a thin intermediate layer

Generalized conditions are formulated for the nonideal contact of dissimilar heat-sensitive crystalline solids in order to determine their Kirchhoff variables.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 55, No. 4, pp. 650–656, October, 1988.     

Antiplane piezoelectric surface waves over a ceramic half-space with an imperfectly bonded layer

We study surface wave propagation over a piezoelectric half-space with an imperfectly bonded mass layer. The imperfect interface between the half-space and the layer is described by the so-called shear-lag model with an elastic constant characterizing the interface physical property. An analytical solution is obtained. Discussion and numerical solutions are presented.