Stress intensity factors in a hollow cylinder containing a radial crack

In this paper an exact formulation of the plane elasticity problem for a hollow cylinder or a disk containing a radial crack is given. The crack may be an external edge crack, an internal edge crack, or an embedded crack. It is assumed that on the crack surfaces the shear traction is zero and the normal traction is an arbitrary function ofr. For various crack geometries and radius ratios, the numerical results are obtained for a uniform crack surface pressure, for a uniform pressure acting on the inside wall of the cylinder, and for a rotating disk.

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Résumé Dans le mémoire, on donne une formulation exacte du problème de l'élasticité plane d'un cyclindre creux ou d'un disque comportant une fissure radiale. La fissure peut être une fissure externe de bord, une fissure interne de bord ou une fissure noyée. On suppose que les surfaces de la fissure sont soumises à une contrainte de cisaillement nulle et à une contrainte normale suivant une fonction arbitraire der. On obtient, pour diverses géométries de fissure et divers rapports de rayon, les résultats numériques dans le cas d'une pression uniforme sur la surface de la fissure, dans le cas d'une pression uniforme agissant sur la paroi interne du cylindre et dans le cas d'un disque en rotation.

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This work was supported by the Department of Transportation under the Contract DOT-RC-82007, by NASA-Langley under the Grant NGR-007-011, and by NSF under the Grant ENG. 78-09737.     

Axisymmetric crack problem for a hollow cylinder imbedded in a dissimilar medium

The analytical solution for the linear elastic problem of flat annular crack in a transversely isotropic hollow cylinder imbedded in a transversely isotropic medium is considered. The hollow cylinder is assumed to be perfectly bonded to the surrounding medium. This structure, which can represent a cylindrical coating-substrate system, is subjected to uniform crack surface pressure. Because of the geometry and the loading, the problem is axisymmetric. The z = 0 plane on which the crack lies, is also a plane of symmetry. The composite media consisting of the hollow cylinder and the surrounding medium extends to infinity in z and r directions. The mixed boundary value problem is formulated in terms of the unknown derivative of the crack surface displacement by using Fourier and Hankel transforms. By extending the crack to the inner surface and to the interface, the cases of surface crack and crack terminating at the interface are obtained. Asymptotic analyses are performed to derive the generalized Cauchy kernel and associated stress singularities. The resulting singular integral equation is solved numerically. Stress intensity factors for various crack configurations, crack opening displacements and stresses along the interface and on z = 0 plane are presented for sample material combinations and geometric parameters.     

Transient thermal contact problem for axial crack in a hollow circular cylinder

The transient behavior of an axial-cracked hollow circular cylinder subjected to a sudden heating is investigated. It is shown that surface heating may induce compressive thermal stress near the inner surface of the cylinder which in turn may force the cracked surfaces to close together. Assuming that the existence of the crack does not alter the temperature distribution, this problem can be divided into two parts and solved by the principle of superposition. First, the temperature and transient thermal stress distributions along the axisymmetric surface of the imaginary cylinder without a crack are obtained by finite element/implicit time integration method. The calculated temperature and thermal stress distributions are in good agreement with the values predicted by the analytical method. Secondly, the opposite senses of the stress distributions along the cracked surfaces, which are obtained previously, are treated as the traction boundary conditions, and the contact length and contact pressure of the real cracked cylinder are obtained by a modified elimination finite element scheme. In this scheme, the concepts of contact-node-pairs' penetration, contact-double-forces and compliance matrix are introduced. The calculated results indicate that the contact length ratio becomes smaller when the crack length ratio increases, and becomes larger as the radius ratio increases. Finally, the normalized stress intensity factor for the crack tip of the cylinder is obtained. It is shown that the larger the crack length ratio the higher the stress intensity factor.     

Thermal Shock loading of a surface crack in a hollow sphere

Temperature and stress distributions in a hollow sphere are calculated, caused by a sudden cooling (thermal shock) of the inner surface of a hollow sphere. The thermal stresses are acting as load of surface cracks of approximate semi-elliptic shape. By means of the weight functions method stress intensity factors are estimated at the deepest point of the cracks using the well-known Newman-Raju solution for semi-elliptical surface cracks in a plate as reference solution.     

Stable crack growth in ductile polymers

Growth of a crack in ductile polymers (polyarylate, PTFE, and PU/PMMA blends) was studied. The crack growth was described assuming that local yielding in the crack tip is similar to large-scale shear yielding in rigid-plastic materials. Crack growth was stable, and a wedge shaped crack tip was formed. The crack tip opening displacement and the crack extension in the initial stage of the crack growth were proportional to the square of the strain up to 11% elongation. Dugdale’s equation was modified to describe the magnitude of the crack tip opening. In PA, a yield subzone near the crack tip was observed. This revised version was published online in November 2006 with corrections to the Cover Date.     

Regular regime for a hollow cylinder heated at its inner surface

The initial stage of the regular regime is analyzed. The features found in the evolution of this stage may be useful in research on thermal physics.     

The torsion of an infinite hollow cylinder with an external crack

This paper deals with the axially symmetric torsion of a hollow cylinder with an external crack. The mixed boundary value problem is reduced to a pair of dual series equations. These equations are shown to be equivalent to an infinite system of simultaneous equations. Numerical results are presented for stresses, displacement and stress intensity factors.     

Temperature distribution in a rotating hollow cylinder

The temperature distribution in a hollow cylinder rotating with a given angular velocity is found for steady-state boundary conditions of the first kind.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 4, pp. 705–711, October, 1979.     

Analysis of a crack in a disclinated cylinder

In this paper, the stress intensity factors and the opening displacement of a crack loaded by a negative wedge disclination in an isotropic cylinder are numerically determined. The disclination axis coincides with the long axis of the cylinder, and one end of the crack coincides with the disclination location. The cylinder may also be subjected to equal and opposite line loads on its surface. An exact formulation leads to a pair of decoupled singular integral equations of the Cauchy type. Numerical solutions show that if the cylinder represents a grain in a polycrystal, (i) unstable submicroscopic cracks 10^-5 to 10^-1 times the grain size and stable microscopic cracks of the order of the grain size, are predicted, (ii) the submicroscopic crack length to grain size ratio decreases, while the microscopic crack length to grain size ratio increases, as the grain size increases, (iii) significant differences exist, even in the case of the submicroscopic cracks, between the predictions of the exact theory and the approximate theory which ignores stress redistribution, and (iv) the opening displacement is independent of the elastic constants and the crack profile is wedge-shaped.     

Fatigue crack growth for a surface crack in a round bar under multi-axial loading condition

In this paper, the fatigue life, surface crack extension direction and crack growth rate in an elastic bar with a circular cross section are determined through experiments under cyclic torsion with axial static and cyclic tension/compression loading. The effects of the loading type, loading value and stress ratio on the crack growth behaviour are discussed. The results show that, under pure fatigue torsion loading, the crack extension direction is almost the same whatever the value of torsion loading. Under fatigue torsion with cyclic tension loading, it is found that the crack extension direction is mainly determined by the alternating parts of the stresses and is almost independent of the average parts of the stresses, whereas the fatigue life is obviously dependent on the average stress.     

Edge cracks in a transversely isotropic hollow cylinder

The analytical solution for the linear elastic, axisymmetric problem of inner and outer edge cracks in a transversely isotropic infinitely long hollow cylinder is considered. The z = 0 plane on which the crack lies is a plane of symmetry. The loading is uniform crack surface pressure. The mixed boundary value problem is reduced to a singular integral equation where the unknown is the derivative of the crack surface displacement. An asymptotic analysis is done to derive the generalized Cauchy kernel associated with edge cracks. It is shown that the stress intensity factor is a function of three material parameters. The singular integral equation is solved numerically. Stress intensity factors are presented for various values of material and geometric parameters.     

Nonstationary thermal stresses in a hollow cylinder with heat flux acting on the inside surface

Thermoelastic stresses in a long hollow cylinder are considered when a uniformly distributed heat flux is applied to the inside surface and the outside surface is heat-insulated.     

Acoustical multipole source in a hollow fluid-filled cylinder

The propagation of elastic waves generated by an impulse multipole source in a hollow fluid-filled cylinder was studied. The general solution of the problem is illustrated by calculations for monopole and dipole sources applied in geophysical and geoecological measurement practice. The analysis of the outer boundary influence on the waveforms registered by receivers located in the fluid was performed. The estimation has been carried out to determine a cylinder wall thickness under which its influence on cinematic parameters of the waveforms can be neglected.     

On solutions of crack surface opening displacement of a penny-shaped crack in an elastic cylinder subject to tensile loading

A simple analytical expression for the surface displacement of a penny-shaped crack in an elastic cylinder subject to remote tensile loading is proposed based on a modified shear-lag model. The results are then compared with the dilute solution [1] and those of finite element calculation. It is found that the present work gives much better result than the dilute model.     

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.