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.     

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.     

Nonstationary frictional heat production in the course of sliding of a composite layer over the surface of a half space

We obtain the analytic solution of a nonstationary thermal problem of friction for a system formed by a composite plane-parallel layer and a homogeneous semiinfinite base. The layer slides over the surface of the base with a constant velocity. Due to the action of friction forces, the bodies are heated. In the course of interaction, convective heat transfer with the environment takes place on the outer surface of the layer. For the rectangular shape of the cross section of composite fibers, we study the influence of the thermal properties of the materials of the fiber and the matrix on the distribution of temperature in the tribosystem.     

重力对具有表面层的半空间中Rayleigh波的影响

重力对具有表面层的半空间中Rayleigh波具有重要的影响,假设表面层和半空间均为均匀各向同性介质,首先利用考虑重力作用的运动方程得出了重力影响下具有表面层的半空间中Rayleigh波的弥散方程。该方程经退化后得出了不受重力作用时的弥散方程,且与忽略重力时得到的方程完全一致。然后利用数值方法得到了重力影响下的Rayleigh波弥散曲线,分析了泊松比和表面层的厚度的影响,结果表明泊松比和表面层的厚度对弥散曲线具有明显影响。     

Partial closure of cracks at the interface between a layer and a half space

The paper treats the crack at the interface between a layer and a substrate. Using a formulation based on dislocations, the problem is reduced to a pair of singular integral equations which can be solved numerically. It is found that a large contact zone exists whenever the interface transmits shear. The dependence of the contact zone size on the load parameters is determined for several combinations of materials. Also the shapes of the open part of the crack are shown for illustration.     

Propagation of torsional waves in a viscoelastic layer over an inhomogeneous half space

This paper presents a theoretical study on propagation of torsional surface waves in a homogeneous viscoelastic isotropic layer with Voigt type viscosity over an inhomogeneous isotropic infinite half space. The non-homogeneity in half space is assumed to arise due to exponential variation in shear modulus and density. A closed-form solution has been obtained for the displacement in the layer as well as for a infinite half space. The dispersion and absorption relations for an torsional wave under the assumed geometry have been found. Numerical results are presented for propagation characteristics in terms of a number of non-dimensionalized parameters and have been produced graphically. This study investigates the effect of various parameters, namely non-homogeneity parameter, internal friction, the layer width and complex wave number on dissipation function and phase velocity of the torsional wave. Results in some special cases are also compared with existing solutions available from analytical methods, which show a close agreement.     

Stress in the vicinity of a griffith crack at the interface of a layer bonded to a half plane—an approximate method

Approximations to the stress field in the vicinity of a Griffith crack located at the interface of a layer bonded to a dissimilar half plane are determined. A systematic use of Fourier transforms reduces the problem to that of solving a set of simultaneous dual integral equations with trigonometric kernels and weighting functions. This latter problem is reduced to the solution of an uncoupled pair of singular integral equations. An approximate technique using Legendre polynomial expansions is discussed. The analysis shows that when a constant pressure is applied to the faces of the crack, the stress components have the distinctive oscillatory singularities at the crack tip. Expressions up to the order of $\text{h}{}^{\mathrm{?4}}$, where $\text{h}$ is the thickness of the layer and is much greater than 1, are derived for the stress components.     

Pressure of the lateral surface of a cylinder on a periodically layered half space

We consider a two-dimensional contact problem of indentation of an absolutely rigid cylinder into an inhomogeneous half space with periodic structure. The zone of periodicity consists of two homogeneous elastic layers. The solution of the classical problem of the theory of elasticity is compared with the solution of the problem in which the inhomogeneous half space is replaced by a homogenized space. We propose simple engineering formulas for the evaluation of contact characteristics (the width of the contact zone and the distribution of contact pressure) approximating the solution of the problem in the case where the homogenized medium inadequately models the inhomogeneous medium. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 3, pp. 51–57, May–June, 2007.     

Axially-symmetric buckling of the surface of a laminated half space with bendinh stiffness

An investigation is made of conditions that admit surface-instability in a laminated half-space that is subjected to radial compressional initial stress. In the formulation of the bifurcation problem, the laminated half-space is represented as a homogeneous half-space of Cosserat material. Constitutive relations are formulated that describe the material behavior of a laminated half-space as a Cosserat continuum. Relationships are derived between the incremental moduli defined in the Cosserat continuum and the moduli of the individual layers, the lamination consisting of adhesive layers of periodically varying stiffness. The stability condition is evaluated, and results are discussed in the particular case when one type of layer is thin, in comparison to layers of the other type.     

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.     

The transient response of bonded piezoelectric and elastic half space with multiple interfacial collinear cracks

Summary This paper investigates the dynamic behavior of a bonded piezoelectric and elastic half space containing multiple interfacial collinear cracks subjected to transient electro-mechanical loads. Both the permeable and impermeable boundary conditions are examined and discussed. Based on the use of integral transform techniques, the problem is reduced to a set of singular integral equations, which can be solved using Chebyshev polynomial expansions. Numerical results are provided to show the effect of the geometry of interacting collinear cracks, the applied electric fields, and the electric boundary conditions along the crack faces on the resulting dynamic stress intensity and electric displacement intensity factors.     

Stress analysis of an elastic layer attached to an elastic half space of the same material

The problem of an elastic layer attached to a half space of the same material by a spot weld is formulated for the case when the loading is tension shear. The problem is reduced to the solution of three simultaneous Fredholm integral equations of the second kind. Solution is obtained to integral equations for several values of the ratio of radius of weld to thickness of layer and quantities of physical interest are calculated.     

Stress intensity near a crack in the composition of a half space and a layer under harmonic loading

We consider a three-dimensional problem for an elastic bimaterial body formed by a half space and a layer and containing a circular crack. The surface of the crack is subjected to the action of stationary torsional forces. The problem is reduced to the solution of a system of boundary integral equations of Helmholtz-potential type for the unknown jumps of displacements on the crack surfaces. The dynamic stress concentration in the vicinity of the crack contour is investigated. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 2, pp. 27–32, March–April, 2008.     

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.     

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.     

Static response of a rigid strip bonded to an elastic layer

Summary The problem of a rigid, bonded, rectangular indenter acting on a plane, transversely isotropic elastic layer is solved. The layer is fixed to a rigid foundation and the cases of applied moment and horizontal displacement are considered. In the first case the moment per unit rotation and horizontal displacement are calculated, while in the latter case the horizontal load per unit displacement and the associated torque are found. From the two problems influence coefficients are calculated and their values are given for different materials and layer thicknesses.

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Das statische Verhalten eines mit einer elastischen Schicht verschweißten starren Streifens

Zusammenfassung Gelöst wird das Problem eines mit einer auf einer starren Unterlage befestigten orthotropen elastischen Schicht verschweißten starren Streifens. Betrachtet werden die Fälle eines auf den Streifen wirkenden äußeren Momentes und einer reinen Horizontalverschiebung des Streifens. Im ersten Fall werden das für eine bestimmte Verdrehung nötige Moment und die zugehörige Horizontalverschiebung ermittelt, im zweiten Fall die Horizontalkraft und das Moment pro Einheitsverschiebung. Einflußzahlen werden berechnet und ihre Werte für verschiedene Werkstoffe und Schichtdicken angegeben.

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Head waves in a piezoelectric half space

Head waves are an interesting phenomenon that is often ignored in harmonic piezoelectric wave study. They present a noise source in SAW devices, but carry useful information in seismology and ultrasonic NDE. In this work, a model based on exact Newtonian and Maxwell's equations of motion is used instead of the commonly used quasi-static approximation, because the former behaves better analytically than the latter and correctly describes certain waves that the latter cannot even predict, We identify three types of head waves. One type, called electromagnetic acoustic (EMAC) head waves, is new and unique to piezoelectric materials. The directivity of a head wave depends only on its critical angles, while the intensity changes with the kind of source that excites it. The polarization, on the other hand, is constant, independent of the observation angle and the kind of the excitation source. It is found that a metallized surface reduces the number of head waves in a piezoelectric medium and affects intensities of existing head waves, but does not change their propagation characteristics. Numerical examples are given for all three types of head waves, for both mechanical and electrical sources, and with both free and metallized surfaces     

Torsional impact of a layer or a cylinder bonded to an elastic half-space

In this paper two torsional impact problems are considered. The first problem deals with the solution of a layer bonded to an elastic half-space when the layer is driven by the torsional impact over a bonded rigid circular disc. In the second problem sudden torsion by a rigid disc attached over the plane face of a circular cylinder is considered and the rest of the plane surface of the cylinder is stress free. The cylinder is bonded to the half-space, making use of Laplace and Hankel transforms the solution of each problem is reduced into Fredholm integral equations of the second kind. A numerical Laplace inversion technique is then used to recover the time depencence of the solution. The numerical values for the applied torque at the surface of rigid disc are calculated for each problem and then are displayed graphically.     

Torsion of a transversely isotropic elastic layer bonded to a transversely isotropic half-space

Torsional stresses and displacement of a transversely isotropic elastic layer of finite thickness for which torsional shearing forces are prescribed on its boundary surface are considered. The solutions are given for a few particular cases.     

Generalized plane problem of a cracked piezoelectric layer bonded to dissimilar layers

Summary In this paper, we proposed a model to study the electro-elastic crack problem for a cracked piezoelectic layer bonded to two elastic layers of finite thickness. The crack is assumed to be through thez-direction and the crack faces perpendicular to they-direction. Fourier transforms technique is used to reduce the problem to the solution of singular integral equations. The model is general enough to account for arbitrary electrical polarized direction and material anisotropy, for any mechanical or electrical mode of loading. Numerical results are plotted to illustrate the influence of the crack face electrical boundary condition on crack tip fields for different layer thickness.