Stress intensity factors around a crack in a nonhomogeneous interfacial layer between two dissimilar elastic half-planes

The stresses around a crack in an interfacial layer between two dissimilar elastic half-planes are obtained. The crack is parallel to the interfaces. The material constants of the layer vary continuously within a range from those of the upper half-plane to those of the lower half-plane. An internal gas pressure is applied to the surfaces of the crack. To derive the solution, the nonhomogeneous interfacial layer is divided into several homogeneous layers with different material properties. The boundary conditions are reduced to dual integral equations, which are solved by expanding the differences of the crack face displacements into a series. The unknown coefficients in the series are determined using the Schmidt method, and a stress intensity factor is calculated numerically for epoxy-aluminum composites.     

Dynamic stress intensity factors around two rectangular cracks in a half space under impact load

Summary In this paper, the mixed boundary value problem for two rectangular cracks,which are embedded in a half-space, is analyzed under the action of an impact load. The cracks are situated perpendicular to the plane surface of the half space. The wave front of the incident stress impinges on the cracks at right angles to their surfaces. In the Laplace transform domain, the boundary conditions at the plane surface are satisfied using the Fourier transform technique, while those at the surfaces of the cracks are satisfied using the Schmidt method. The stress intensity factors defined in the Laplace transform domain are inverted in the physical space with the aid of a numerical method.     

Dynamic stress intensity factors around four rectangular cracks in an infinite elastic medium under impact load

The 3-D dynamic problem is presented for an infinite elastic medium weakened by four plane rectangular cracks of equal size. The surfaces of the cracks are loaded by a uniform pressure with Heaviside-function time dependence. Fourier-Laplace transform technique is utilized to reduce the problem to a solution of two simultaneous integral equations which can be solved by using the series expansion method. The Laplace transformed stress intensity factors are defined and are inverted numerically in the physical space.     

Transient analysis of stress waves around two rectangular cracks under impact load

The three-dimensional response of two rectangular cracks in an infinite elastic medium to impact load is investigated in this paper. Fourier and Laplace transforms are applied and the problem is reduced to that of solving dual integral equations in the Laplace transform domain. To solve these equations, the crack surface displacement is expanded in a double series of functions which are zero outside of the cracks. The unknown coefficients accompanied in that series are solved with the aid of the Schmidt method. The dynamic stress intensity factors are computed numerically.     

Stress intensity factors for two parallel interface cracks between a nonhomogeneous bonding layer and two dissimilar orthotropic half-planes under tension

In composite materials, which are constructed of two dissimilar orthotropic half-planes bonded by a nonhomogeneous orthotropic layer, one interface crack is situated at the lower interface between the layer and the lower half-plane, and another crack is located at the interface between the upper half-plane and the bonding layer. The stress intensity factors are solved under uniform tension normal to the cracks. The material properties of the bonding layer vary continuously from the lower half-plane to the upper half-plane. The stress intensity factors are calculated numerically for perpendicularly bonded unidirectional glass fiber reinforced epoxy laminae.     

Dynamic stress intensity factors around two coplanar Griffith cracks in an orthotropic layer sandwiched between two elastic half-planes

Dynamic stresses around two coplanar Griffith cracks in an orthotropic layer sandwiched between two elastic half-planes are determined. To the surfaces of the cracks, an internal pressure is applied suddenly. Application of the Fourier and Laplace transforms reduces the problem to the solution of a pair of dual integral equations in the Laplace transform plane. To solve these equations, the crack surface displacement is expanded in a series of functions which are zero outside of the cracks. The unknown coefficients accompanied in that series are solved with the aid of the Schmidt method. The stress intensity factors defined in the Laplace transform plane are inverted numerically in the physical plane. Numerical calculations are carried out for the case that the layer of carbon fiber is sandwiched by the two elastic half-planes of plastic.     

Transient analysis of stress waves around two coplanar griffith cracks under impact load

The problem of determining the transient stress distribution in an infinite elastic medium weakened by two coplanar Griffith cracks is considered. To the surfaces of the cracks, an internal pressure is applied suddenly. The problem is reduced to that of solving dual integral equations in the Laplace transform domain and those are solved by a series-expansion method. The dynamic stress intensity factors are computed numerically.     

Dynamic stress intensity factors around a rectangular crack in an infinite plate under impact load

A three-dimensional solution is presented for the transient response of an infinite plate which contains a rectangular crack. The Laplace and Fourier transforms are used to reduce the problem to a pair of dual integral equations. These equations are solved with the series expansion method. The stress intensity factors are defined in the Laplace transform domain, and they are inverted numerically in the physical space.     

Two semi-infinite interfacial cracks between two bonded dissimilar elastic strips

The complex stress intensity factor and energy release rate are obtained for two semi-infinite interfacial cracks between two bonded dissimilar elastic strips with equal thickness under inplane deformations. During the procedure, by means of conformal mapping technique, the mixed boundary-value problem is reduced to a standard Riemann-Hilbert problem, which is further solved in closed-form. In some limiting cases, the present explicit solutions can cover the well-known results in the literature.     

Dynamic stress intensity factors around two parallel cracks in an infinite elastic plate

Summary Dynamic stresses around two parallel cracks in an infinite elastic plate are obtained. An incoming shock stress wave impinges on the cracks at right angles to their faces. The Fourier-Laplace transform technique is utilized to reduce the problem to dual integral equations. To solve these equations, the differences in the crack surface displacements are expanded in a series of functions which are zero outside the cracks. The unknown coefficients occurring in those series are solved using the Schmidt method. The stress intensity factors defined in the Laplace transform domain are inverted numerically, in the physical space.     

Three-dimensional dynamic stress intensity factors around two parallel square cracks in an infinite elastic medium subjected to a time-harmonic stress wave

Summary Dynamic stresses around two parallel square cracks in an infinite elastic medium are determined. A time-harmonic stress wave impinges on the two cracks normal to their surfaces. The two-dimensional Fourier transform technique is applied to reduce the mixed boundary value conditions to dual integral equations. To solve the equations, differences of the displacements in the upper square crack are expanded using a double series of functions which are equal to zero outside the crack. Those in the lower crack are also expanded using a similar series. Unknown coefficients in the series are determined by applying the Schmidt method. Dynamic stress intensity factors are calculated numerically assuming that the shape of the upper crack is identical to that of the lower crack.     

Dynamic stress intensity factors around two parallel cracks in a functionally graded layer bonded to dissimilar half-planes subjected to anti-plane incident harmonic stress waves

The time-harmonic problem of determining the stress field around two parallel cracks in functionally graded materials (FGMs) is studied. The Fourier transform technique is used to reduce the boundary conditions to four simultaneous integral equations which are then solved by expanding the differences of crack surface displacements in a series. The unknown coefficients in the series are obtained by the Schmidt method. Numerical calculations are carried out for dynamic stress intensity factors (DSIF) in FGMs.     

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.

     

On the dynamic behaviour of interfacial cracks between a piezoelectric layer and an elastic substrate

Surface-bonded piezoelectric layers can be used as actuators/sensors for advanced structural applications. The current paper provides a theoretical study of the dynamic behaviour of interacting cracks between a piezoelectric layer and an elastic medium under antiplane mechanical loads. The electromechanical field of a single interfacial crack is determined first using Fourier transform technique and solving the resulting integral equations. This fundamental solution is then imple- mented into a pseudo-incident wave method to account for the interaction between different cracks. The dynamic behaviour of the resulting stress field is studied with special attention being paid to the stress intensity factors at the crack tips. Typical examples are provided to show the effect of the size and position of the cracks, the material combination and the loading frequency upon the stress intensity factors.     

Stress intensity factors for two rectangular cracks in three-dimensions

In this paper an analytical solution is developed for two three-dimensional coplanar rectangular-shaped cracks embedded in an infinite elastic medium and subjected to normal loading. Employing two-dimensional integral transforms, the solution of the problem is reduced to triple integral equations. Assuming the plane strain solution across the lengths of the narrow cracks, an approximate solution of the triple integral equations for large values of the lengths of the cracks is obtained. Finally, expressions are obtained for the stress intensity factors along the sides of the cracks and these results are given in the form of graphs.     

Near-tip fields and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media

A complete form of stress and electric displacement fields in the vicinity of the tip of an interfacial crack, between two dissimilar anisotropic piezoelectric media, is derived by using the complex function theory. New definitions of real-valued stress and electric displacement intensity factors for the interfacial crack are proposed. These definitions are extensions of those for cracks in homogeneous piezoelectric media. Closed form solutions of the stress and electric displacement intensity factors for a semi-infinite crack as well as for a finite crack at the interface between two dissimilar piezoelectric media are also obtained by using the mutual integral.     

Dynamic stress intensity factors around three cracks in an infinite elastic plane subjected to time-harmonic stress waves

The time-harmonic problem for an infinite elastic plane weakened by three parallel cracks has been solved. In this problem, two cracks are situated symmetrically on either side of a central crack and incident stresses impinge perpendicular to the cracks. Using the Fourier transform technique, the boundary conditions are reduced to four simultaneous integral equations. To solve the equations, the differences of displacements inside the cracks are expanded in a series. The unknown coefficients in the series are solved by the Schmidt method. The dynamic stress intensity factors are calculated numerically for several crack configurations. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the stress intensity factors associated with cracks interacting with an interface between two elastic media

Closed form expressions are obtained for the stresses at a crack tip when a crack is approaching a welded boundary (or a free surface) and when it has just passed through the interface. The solutions which are obtained in terms of a small parameter, the distance from or through the interface, are given in explicit form for the mode 3 situation and for some mode 1 and 2 cases. The importance of the change of stress singularity when the crack meets the interface is demonstrated.     

Dynamic stress intensity factors of two 3D rectangular permeable cracks in a transversely isotropic piezoelectric material under a time‐harmonic elastic P‐wave

The dynamic behavior of two 3D rectangular permeable cracks in a transversely isotropic piezoelectric material is investigated under an incident harmonic stress wave by using the generalized Almansi's theorem and the Schmidt method. The problem is formulated through double Fourier transform into three pairs of dual integral equations with the displacement jumps across the crack surfaces as the unknown variables. To solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. Finally, the relations among the dynamic stress field and the dynamic electric displacement filed near the crack edges are obtained, and the effects of the shape of the rectangular crack, the characteristics of the harmonic wave, and the distance between two rectangular cracks on the stress and the electric intensity factors in a piezoelectric composite material are analyzed. Copyright © 2015 John Wiley & Sons, Ltd.     

Random dynamic response and reliability of a crack in a functionally graded material layer between two dissimilar elastic half-planes

An analytical approach is presented for the random dynamic analysis of a functionally graded material (FGM) layer between two dissimilar elastic half-planes. This FGM layer contains a crack and its material properties vary randomly in the thickness direction, while their mean values are exponential functions of field position. The transient loadings applied on the crack faces are assumed to be stochastic processes of time. In order to obtain the solution, the FGM layer is divided into several sub-layers, and the material properties of each layer are reduced to random variables by an average method. A fundamental problem is constructed for the solution. Based on the use of Laplace and Fourier transforms, the boundary conditions are reduced to a set of singular integral equations, which can be solved by the Chebyshev polynomial expansions. Both stress intensity factor history with its statistics and dynamic reliability are analytically derived. Numerical calculations are provided to show the effects of related parameters.