Some axially symmetric thermal stress distributions in an elastic solid containing an annular crack

The present paper seeks to solve the axisymmetric thermal stress distribution in an infinite, isotropic solid containing an annular crack. The problem is reduced to triple integral equations, which are ultimately reduced to the solution of an infinite set of simultaneous equations.     

Interaction of torsional waves with an annular crack in an infinitely long cylinder

The Hankel transform is used to obtain a complete solution for the dynamic stresses and displacements around a flat annular surface of a crack embedded in an infinite elastic cylinder, which is excited by normal torsional waves. The curved surface of the cylinder is assumed to be stress free. Solution of the problem is reduced to three simultaneous Fredholm integral equations. By finding the numerical solution of the simultaneous Fredholm integral equations the variations of the dynamic stress-intensity factors are obtained which are displayed graphically.     

Axisymmetric elastodynamic response of a flat annular crack to normal impact waves

The axisymmetric response of a flat annular crack in an infinite medium subjected to normal impact load is investigated in this study. A step stress is applied to the crack surface. The singular solution is equivalent to solutions of the problem of diffraction of normally incident tension wave by a flat annular crack, and the problem of the sudden appearance of a flat annular crack in a uniform tensile stress field. Laplace and Hankel transforms are used to reduce the problem to the solution of a set of triple integral equations in the Laplace transform domain. These equations are solved by using a integral transform technique and the result is expressed in terms of a singular integral equation of the first kind with the kernel which is improved by means of a contour integration on the Riemann surface. A numerical Laplace inversion routine is used to recover the time dependence of the solution. Numerical results of the dynamic stress intensity factor are obtained to show the influence of inertia, the ratio of the inner radius to the outer one and Poisson's ratio on the load transmission to the crack tip.     

Annular crack surrounding an elastic fibre in transversely isotropic elasticity

The axisymmetric problem of an infinitely long transversely isotropic elastic fibre perfectly bonded to a dissimilar transversely isotropic elastic matrix containing an annular crack is considered. The annular crack, surrounding the fibre, is subjected to prescribed longitudinal tension. A potential function approach is used to find the solution of the basic equations. The mixed boundary value problem is reduced to the solution of a singular integral equation, which is further reduced, by using Chebyshev polynomials, to a system of algebraic equations.     

Mixed boundary value problem of an infinite thick elastic slab containing a flat annular crack under torsion

In the present paper we consider the problem of determining the stress distribution in an infinitely long isotropic, compressible, homogeneous elastic slab containing a flat annular crack which is opened by internal shear stress. The faces of the slab are assumed to be stress free and the crack is located in the middle plane of the slab. The problem is formulated in triple integral equations which reduce to an infinite system of simultaneous equations, which are solved numerically.     

An annular crack in microelasticity

In this paper, the problem of an annular crack in a transverse field of constant uniexial tension is studied applying linear theory of microelasticity. By means of Hankel transforms and triple integral equations the problem is reduced to a set of simultaneous equations and is then solved numerically. Also the numerical results for the physical interest are illustrated graphically and compared with those of the couple stress theory. The classical results have been presented finally as limiting case.     

Singular stresses in an infinite solid with a flat annular crack around a spherical cavity under tension

The problem of singular stresses in an infinite elastic solid containing a spherical cavity and a flat annular crack subjected to axial tension is considered. By application of an integral transform method and the theory of triple integral equations the problem is reduced to that of solving a singular integral equation of the first kind. The singular integral equation is solved numerically, and the influence of the spherical cavity upon the stress intensity factor and the influence of the annular crack upon the maximum stress at the surface of the spherical cavity are shown graphically in detail.     

Interaction of axially symmetric waves with an annular crack in an infinitely long hollow cylinder

In this paper an analysis of the interaction of longitudinal waves with an annular crack in an infinitely long hollow cylinder is presented. Using Fourier sine and cosine as well as Hankel integral transforms, formal complete solutions to the governing equations are given. By means of Abel integral transform, the problem is reduced to the solution of a Fredholm integral equation of the second kind which is, then, solved numerically for a range of values of the frequencies of the incident waves. The numerical values of the dynamic stress intensity factor at the rim of the crack have been calculated.     

Thermal stresses in a slab containing an annular crack

A linear thermoelastic problem of a slab containing an annular crack is solved. Using integral transform techniques, the problem is reduced to that of solving two singular integral equations of the first kind. The solution of the singular integral equation is obtained in the form of the product of the series of Chebyshev polynomials of the first kind and their weight functions. Thus the essential feature of the singular stress field near the crack is preserved and the crack tip stress intensity factor is easily evaluated. Numerical calculations are also carried out and the variations of the stress intensity factors are plotted against the geometry for various values of physical properties.     

Acoustic diffraction by a rigid annular disk

Summary The subject of this paper is the problem of acoustic diffraction by a perfectly rigid annular disk. The method of solution rests on formulating the problem in terms of an integral equation which embodies the steady state wave equation as well as the boundary conditions. This Fredholm integral equation of the first kind is converted into four simultaneous integral equations of the second kind by using Williams' integral equation technique. These four integral equations are subsequently solved by the standard iterative procedure when the frequency of the incident wave is low and the inner radius of the annulus is small.     

The stress field near a griffith crack at the interface of two bonded dissimilar elastic half-planes

The stress and displacement fields in the vicinity of a Griffith crack located at the interface of two bonded dissimilar elastic half-planes are determined. A systematic use of Fourier transforms reduces the problem to that of a solving a set of simultaneous dual integral equations and this in turn is shown to be equivalent to a Riemann boundary value problem with closed form solution. The particular case in which the crack is opened by constant pressure is discussed.     

Problem of an infinite solid containing a flat annular crack under torsion

An analytic method is developed to find the axisymmetric stress distribution in an infinite elastic solid containing a flat annular crack under axial torsion. By use of Hankel transforms, the solution to the problem is reduced to triple-integral equations involving Bessel functions of order 1. Modifying the method discussed by Cooke[Quart. J. Mech. Appl. Math. 16, 193–203 (1963).], the solution of the triple-integral equations is reduced to a pair of Fredholm integral equations of the second kind. Finally, the approximate expressions for the stress intensity factors are obtained by finding the iterative solution of the pair of Fredholm integral equations.     

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     

An Annular Crack in a Magnetoelectroelastic Layer

A flat annular crack in a magnetoelectroelastic layer subjected to mechanical, electric and magnetic loadings is investigated under magnetoelectrically impermeable boundary condition on the crack surface. Using Hankel transform technique, the mixed boundary value problem is reduced to a system of singular integral equations. With the aid of Gauss-Chebyshev integration technique, the integral equations are further reduced to a system of algebraic equations. The field intensity factor and energy release rate are determined. Numerical results reveal the effects of electric and magnetic loadings and crack configuration on crack propagation and growth.     

Dynamic stress intensity factor of a cracked dielectric medium in a uniform electric field

Summary We consider the scattering of normally incident longitudinal waves by a finite crack in an infinite isotropic dielectric body under a uniform electric field. By the use of Fourier transforms, we reduce the problem to that of solving two simultaneous dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind having the kernel that is a finite integral. The dynamic stress intensity factor versus frequency is computed, and the influence of the electric field on the normalized values is displayed graphically.     

On the axisymmetric loading of an annular crack by a disk inclusion

This paper examines the axisymmetric elastostatic problem related to the loading of an annular crack by a rigid disk–shaped inclusion subjected to a central force. The integral equations associated with the resulting mixed–boundary–value problem are solved numerically to determine the load–displacement result for the rigid inclusion and the Mode II stress–intensity factors at the boundaries of the annular crack. The results presented are applicable to a wide range of Poisson's ratios ranging from zero to one half.     

Scattering of antiplane shear wave by a kinked crack

In this paper the scattering of antiplane shear waves by a kinked crack for a linearly elastic medium is considered. In order to solve the proposed problem, at first the broken crack problem is reduced to two coupled single cracks. Fourier integral transform method is employed to calculate the scattered field of a single crack. In order to derive the Cauchy type integral equations of a broken crack and analyze the singular stresses at the breakpoint, the scattered field of a single crack is separated into a singular part and a bounded part. The single crack solution is applied to derive the generalized Cauchy type integral equations of a broken crack. The singular stress and singular stress order are analyzed in the paper and the dynamic stress intensity factor (DSIF) at breakpoint is defined. Numerical solution of the obtained Cauchy type integral equations gives the DSIF at the crack tips and at the breakpoint. Comparison of the present results in some special cases with the known results confirms the proposed method. Some typical numerical results and corresponding analysis are presented at the end of the paper.     

An arbitrarily-oriented plane crack in an anisotropic elastic slab

The problem of an arbitrarily-oriented plane crack in an anisotropic elastic slab is considered. Through the use of a Fourier transform technique, the problem is reduced to a system of simultaneous Fredholm integral equations of the second kind. Once these integral equations are solved, relevant quantities such as the crack energy can be readily computed. Numerical results pertaining to the stability of a plane crack in a particular elastic slab are given.     

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.     

Transient response of a crack in an anisotropic strip

Summary The problem of an anisotropic elastic strip containing a crack which is opened by stresses suddenly applied on the crack faces is considered here. The problem is reduced to a set of simultaneous Fredholm integral equations of the second kind which may be solved iteratively. Once the solutions of these integral equations are obtained, the dynamic stress intensity factors may be evaluated numerically. Numerical results are obtained for a particular transversely isotropic strip.With 1 Figure