Diffraction of shear waves by an edge crack in an elastic wedge

Low frequency diffraction of plane harmonic shear (SH) wave by an edge crack in an elastic wedge of arbitrary vertex angle is studied. Kontorowich-Lebedev transform is used to solve the mixed boundary value problem under consideration. For low frequency case, i.e. wavelength large compared to the length of the crack, the displacement field is obtained by successive approximation of the resulting Wiener-Hopf equation. For the limiting case of an elastic half space the results agree with those obtained by the method of matched asymptotic expansions.     

Diffraction of SH waves by a moving crack

Summary The problem of diffraction of anti-plane shear waves by a running crack of finite length is investigated analytically. Fourier transform method is used to solve the mixed boundary value problem which reduces to two pairs of dual integral equations. These dual integral equations are further reduced to a pair of Fredholm integral equations of the second kind. The iterative solution of the integral equations has been obtained for small wave number. The solution is used to calculate the dynamic stress intensity factor at the edge of the crack.With 2 Figures     

Diffraction of elastic sphericalP waves by a cylindrical cavity

Summary This paper deals with the three dimensional diffraction of impulsive compressional waves by a cylindrical cavity. The cavity is embedded in an unbounded, isotropic, homogeneous elastic medium. The compressional point source, generating the incident pulse, is supposed to be situated outside the cavity. The formal solution to the problem is obtained in integral form. The integrals are evaluated asymptotically for the early time motion by the residue-Cagniard method.With 6 Figures     

Diffraction of high frequency torsion waves by a penny-shaped crack

The diffraction of high frequency torsion waves by a penny-shaped crack situated in an infinite isotropic elastic solid is considered. Asymptotic expressions for the dynamic stress intensity factors are derived for a variety of incident excitations, and the results predict an oscillatory behaviour of these factors at high frequencies.     

Diffraction of horizontal shear waves by a moving interface crack

Summary An analysis of the diffraction of horizontally polarized shear waves by a finite crack moving on a bimaterial interface is carried out. Fourier transform method is used to reduce the mixed boundary value problem to the solutions of two pairs of dual integral equations. These equations are further reduced to a pair of Fredholm integral equations of the second kind. The dynamic stress intensity factors are obtained for several values of wave number, incident angle, crack velocity, and material constants.With 7 Figures     

Diffraction of transient horizontal shear waves by a running crack

An analysis of the diffraction of horizontally polarized shear waves of arbitrary profile by a finite crack extending uniformly is investigated. Transform techniques and a generalized Wiener-Hopf method are employed to solve the mixed boundary-value problem exactly from the instant the incident wave first strikes the crack until the diffracted wave reaches the opposite edge, is rediffracted, and then returns the original edge. The dynamic stress-intensity factors for an incident wave with a step function stress profile are obtained as functions of time, the angle of incidence and the speed of crack propagation. The effects of the aforementioned system parameters on the dynamic stress-intensity factors are shown graphically.     

Diffraction of torsional waves by a flat annular crack at the interface of two bonded dissimilar elastic solids

The paper deals with the problem of finding the stress distribution near an annular crack located at the interface of two bonded dissimilar elastic solids. The crack is opened by the interaction of a torsional wave incident normally on the annular crack. The problem is reduced to the solution of three simultaneous Fredholm integral equations. The numerical solution of these simultaneous integral equations has been obtained. The solution is used to calculate the stress-intensity factors at the tips of the crack.     

Diffraction of elastic waves by two coplanar Griffith cracks in an infinite transversely-isotropic medium

Summary The problem of diffraction of normally incident longitudinal waves by two parallel and coplanar Griffith cracks embedded in an infinite transversely-isotropic medium is considered. Approximate formulas are derived for stress intensity factors when the wave lengths are large compared, to the distance between the outer edges of the two cracks By taking appropriate limits we derive various interesting and new results.     

Diffraction of elastic waves by four rigid strips embedded in an infinite orthotropic medium

In the present paper, the elastodynamic response of four coplanar rigid strips embedded in an infinite orthotropic medium due to elastic waves incident normally on the strips is analyzed. The resulting mixed boundary-value problem is solved by an integral-equation method. The normal stress and the vertical displacement are derived in closed analytic form. Numerical values of stress-intensity factors at the edges of the strips and vertical displacements at point in the plane of the strips for several orthotropic materials are calculated and plotted graphically to show the effect of material orthotropy.     

Interaction of elastic waves by a Griffith crack in an infinite transversely-isotropic medium

The paper deals with the problem of finding the stress distribution near a Griffith crack located in an infinite transversely-isotropic medium. The crack is opened by the interaction of a plane harmonic elastic wave incident normally on the crack. A Fredholm integral equation is derived for the determination of diffracted field. From the integral equation asymptotic solution is obtained which is valid for wavelength long compared to the crack length. For wave lengths comparable with the size of the crack, the integral equation is solved numerically. The stress intensity factor and displacement field in the vicinity of crack are computed for a range of values of the frequency. The approximate solution is compared with exact solution.

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Résumé Le mémoire est relatif au problème de déterminer la distribution de contraintes au voisinage d'une fissure de Griffith localisée dans un milieu infini transversalement isotrope. La fissure est ouverte par l'interaction d'une onde élastique harmonique plane incidente sur une direction normale au plan de la fissure. On dérive une équation intégrale de Fredholm pour la détermination du champ de diffraction. Une solution asymptotique est obtenue à partir de l'équation intégrale, qui se révèle valide dans le cas de longueur d'onde grande par rapport à la longueur de la fissure. Lorsque les longueurs d'onde sont comparables à la taille de la fissure, l'équation intégrale peut être résolue de manière numérique. Le facteur d'intensité de contrainte et le champ des déplacements au voisinage de la fissure sont calculées pour une gamme large de valeur de la fréquence. La solution approximative obtenue est comparée avec la solution exacte.

     

Diffraction of transient horizontal shear waves by a finite crack at the interface of two bonded dissimilar elastic solids

Scattering of transient horizontal shear waves by a finite crack located at the interface of two bonded dissimilar elastic solids is investigated in this study. Laplace and Fourier transform technique is used to reduce the problem to a pair of dual integral equations. The solution of the dual integral equation is expressed in terms of the Fredholm integral equation of the second kind having the kernel of a finite integration. Dynamic stress intensity factor is obtained as a function of the material and geometric properties and time.     

Scattering of elastic waves by an elastic sphere

The problem of scattering of plane compressional wave by an elastic sphere embedded in an isotropic elastic medium of different material properties is solved. Approximate formulas are derived for the displacement field, stress tensor, stress intensity factors, far-field amplitudes and the scattering cross-section. It is assumed that the wave length is large compared to the radius of the scatterer. Various elastostatic limits are also presented.     

Scattering of elastic waves by an elastic sphere

The problem of scattering of plane compressional wave by an elastic sphere embedded in an isotropic elastic medium of different material properties is solved. Approximate formulas are derived for the displacement field, stress tensor, stess intensity factors, far-field amplitudes and the scattering cross section. It is assumed that the wave length is large compared to the radius of the scatterer. Various elastostatic limits are also presented.     

Scattering of elastic waves by a crack with spring-mass contact

The scattering problem of elastic waves by a crack with spring-mass contact is investigated. Such a crack may be regarded as a simplified model of a thin elastic inclusion. Boundary integral equations are formulated for both displacement and traction on crack faces and are solved numerically. Numerical results are presented for stress intensity factors, crack-opening displacements and scattering cross-sections. Our results are in good agreement with other published solutions. It is also found that the effect of a mass can not be neglected in evaluation of scattering cross-sections, even if the mass is small.     

Diffraction of torsional waves by a penny-shaped crack in an infinitely long cylinder bonded to an infinite medium

This paper contains an analysis of the interaction of torsional waves with penny-shaped crack located in an infinitely long cylinder which is bonded to an infinite medium. Both the cylinder and infinite medium are of homogeneous and elastic but dissimilar materials. The solution of the problem is reduced to a Fredholm integral equation of the second kind which is solved numerically. The numerical solution is used to calculate the stress intensity factor at the rim of the penny-shaped crack.     

Diffraction of normal compression waves by a penny-shaped crack in the presence of an axial magnetic field

The problem of diffraction of normally incident compressional waves by a penny-shaped crack located in a perfectly conducting, infinite, isotropic, elastic solid permeated by an uniform magnetostatic field is considered. Using an integral transform technique, the problem is reduced to that of solving a Fredholm integral equation of the second kind having a finite integral kernel. The dynamic singular stress distributions near the crack tip are obtained in closed form and the effects on the dynamic stress-intensity factors due to the presence of the magnetic field are shown graphically. For low frequencies, the dynamic stress-intensity factors are expressed in series of ascending powers of the normalized frequency. The approximate solutions are compared with exact solutions.     

Diffraction of shear waves on cylindrical inclusions and cavities in an elastic half space

Dynamic problems of the steady-state oscillations of a half space with different types of cylindrical homogeneities (cavities, rigid and stiff inclusions) are examined. The boundary of the half space is assumed to be fixed or free of forces. A harmonic shear wave radiating from infinity or a concentrated harmonic source may be radiators of the exciting wave field. Integral representations of displacement amplitudes, which automatically satisfy fixity conditions on the boundary of the half space and radiation conditions at infinity are constructed. The edge problems are reduced to Fredholm integral equations of the second kind and to singular integral equations. Selection of additional conditions for the latter is substantiated. Some computer-generated results are presented.Translated from Problemy Prochnosti, No. 11, pp. 90–94, November, 1990.     

Interaction of a penny-shaped crack with an elliptic crack

Three-dimensional problem of crack-microcrack interaction is solved. Both the crack and microcrack are embedded in an infinite isotropic elastic medium which is subjected to constant normal tension at infinity. One of the cracks is circular while the other is elliptic and they are coplanar and are positioned in such a way that the axis of the elliptic crack passes through the centre of the circular crack. A recently developed integral equation method has been used to solve the corresponding two dimensional simultaneous dual integral equation involving the displacement discontinuity across the crack faces that arises in such an interaction problem. A series of transformations first reduce them to a quadruplet infinite system of equations. A series solution is finally obtained in terms of crack separation parameter which depends on the separation of the crack microcrack centre. Analytical expression for the stress intensity factors have been obtained up to the order ⁶. Numerical values of the interaction effect have been computed for and results show that interaction effects fluctuate from shielding to amplification depending on the location of each crack with respect to the other and crack tip spacing as well as the aspect ratio of the elliptic crack. The short range interaction can play a dominant role in the prediction of crack microcrack propagation.