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.     

Stress intensity factors for cracked I-beams

We present simple, closed-form expressions for stress intensity factors for cracked I-beams subjected to a bending moment. The estimates are based on the elementary strength theory for cracked beams forwarded by Herrmann and co-workers, coupled with dimensional considerations and a finite element calibration. The expressions given here are valid for the case when the crack has propagated through the flange and into the web of the beam. The simple expressions are accurate to within 5% of detailed finite element calculations for the range of practical applicability. To further demonstrate the validity of the stress intensity factor expression, we measured fracture loads for cracked polymethyl methacrylate (PMMA) I-beams in four-point flexure. Using the failure loads and our expression for the stress intensity factor, we deduce the fracture toughness. The fracture toughness so-obtained results in excellent fracture correlation for the cracked I-beams.     

Stress intensity factors in a reinforced thick-walled cylinder

In this paper an elastic thick-walled cylinder containing a radial crack is considered. It is assumed that the cylinder is reinforced by an elastic membrane on its inner surface. The model is intended to simulate pressure vessels with cladding. The formulation of the problem is reduced to a singular integral equation. Various special cases including that of a crack terminating at the cylinder-reinforcement interface are investigated and numerical examples are given. Among the interesting results found one may mention the following: In the case of the crack touching the interface the crack surface displacement derivative is finite and consequently the stress state around the corresponding crack tip is bounded, and generally, for realistic values of the stiffness parameter, the effect of the reinforcement is not very significant.     

Stress intensity factors for a crack in planar disking

Disking is a relatively new manufacturing process for cutting/slicing brittle plates and rods. In the planar disking configuration, a pre-cracked plate is placed against an elastic plate and the two are squeezed together by fluid pressure. At a critical pressure the crack runs across the thickness of the brittle plate producing a clean cut. In this paper a fracture criterion is developed for the process using linear elastic fracture mechanics. The geometry of the process is modeled here as two perfectly bonded, infinite elastic layers with a crack perpendicular to the interface. The problem is formulated in terms of a singular integral equation with the derivative of the crack surface displacement (dislocation density) as the unknown function. Numerical quadrature is used to determine the stress intensity factors as a function of the parameters of the problem.     

Stress intensity factors in cracked cylindrical shells under tension

The singular stress field at the tip of a circumferential crack in a cylindrical shell under axial tension was studied by the optical method of caustics. The material of the shell was considered as linearly elastic and optically anisotropic. A complete study of the influence of the optical anisotropy of the material of the shell, the shell curvature and the characteristics of the optical set-up, on the shape and size of the caustics formed by illuminating the shell by a divergent or parallel light beam was undertaken. The stress intensity factor for the crack tip was evaluated by interrelating this quantity with the geometric characteristics of the caustics. Stress intensity factors evaluated experimentally on shells made either of an optically inert material (plexiglas) or of an optically active material (polycarbonate) compared favorably with the already existing theoretical solutions.

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Résumé On étudie la singularité du champ de tensions à l'extrémité d'une fissure circulaire dans une enveloppe cylindrique sous tension axiale par la méthode optique des caustiques. On considère que le matériau de l'enveloppe est linéaire élastique et anisotrope du point de vue optique. On entreprend une étude complète de l'influence de l'anisotropie optique du matériau, de la courbure de l'enveloppe et des caractéristiques de l'installation optique sur la forme et de la dimension des caustiques qui se forment lorsqu'on éclaire l'enveloppe par un rayon lumineux divergent ou parallèle. Le facteur d'intensité des contraintes relatif à l'extrémité de la fissure est évalué en le mettant en relation avec les caractéristiques géométriques des caustiques. On constate que les facteurs d'intensité des contraintes qui sont évalués par voie expérimentale sur des enveloppes en matériau optiquement inerte (plexiglas) ou en matériau optiquement actif (polycarbonate) soutiennent la comparaison avec les solutions existantes établies par voie théorique.

     

The calculation of dynamic stress intensity factors for a cracked thick walled cylinder

The finite element method for calculating dynamic stress intensity factors of a thick walled cylinder is studied in this paper, reasonable computational schemes are provided, and the regularity of stress intensity factors for a thick walled cylinder subjected to dynamic inner pressure is obtained. Furthermore, the superposition integral method is presented to compute dynamic stress intensity factors for the thick walled cylinder, which is convenient for calculating dynamic stress intensity factors of different kinds of dynamic inner pressures     

Stress intensity factors for cracked rectangular cross-section thin-walled tubes

For cracked structural rectangular thin-walled tubes, an exact and very simple method to determine the stress intensity factors has been proposed based on a new concept of crack surface widening energy release rate. Unlike the classical crack extension energy release rate, the crack surface widening energy release rate can be expressed by the G^*-integral and elementary strength theory of materials for slender cracked structures. From present discussions, a series of new and exact solutions of stress intensity factors are derived for cracked rectangular and square tubes. The present method can also be applied to cracked polygon thin-walled tubes.     

Stress intensity factors for a semiinfinite crack with branches

The stressed state of an elastic plane weakened by a semiinfinite branching crack whose branches are either shear cracks or cracks of a mixed type is determined by the method of singular integral equations for the case where the stressed state at the tip of the semiinfinite crack without branches is characterized by stress intensity factorsK ₁ ⁰ andK _II ⁰ . The values of these factors are obtained for the cases of one, two, and three branches and different values of geometric parameters. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 1, pp. 45–50, January–February, 1997.     

Stress intensity factors of microstructurally small crack

The stress intensity factor (SIF) is widely used for evaluating integrity of cracked components. Averaging the anisotropy of each crystal, the macroscopic behavior of polycrystalline materials is isotropic and homogenous in terms of elastic deformation. However, the anisotropic and/or inhomogeneous property influences on the stress field around a crack if the crack size is small in comparison with the grain. Thus, the SIF of the microstructurally small crack may differ from that in the isotropic body. In present study, the effect of anisotropic/inhomogeneous elasticity on the SIF is investigated by using the finite element analysis (FEA). At first, the SIFs of semi-circular crack in a single crystal and a polycrystalline material are calculated. These reveal that the magnitude of SIF is dependent not only on the crystal orientation but also on the deformation constraint by the neighboring crystals. Then, the statistical scatter of SIF due to the random orientation of crystal orientation in a polycrystal is examined by a Monte Carlo simulation.     

Stress intensity factors in a cracked infinite elastic wedge loaded by a rigid punch

The paper considers splitting a plane elastic wedge-shaped solid through the application of a rigid punch. It is assumed that the coefficient of friction on the contact area is constant, the problem has a plane of symmetry with respect to loading and geometry, and the crack lies in the plane of symmetry. The problem is formulated in terms of a system of integral equations with the contact stress and the derivative of the crack surface displacement as the unknown functions. The solution is obtained for an internal crack and for an edge crack. The results include primarily the stress intensity factors at the crack tips, and the measure of the stress singularity at the wedge apex, and at the end points of the contact area.     

Stress intensity factors for cracked T-sections and dynamic behaviour of T-beams

This paper presents an extension of a simple and convenient method proposed by Kienzler and Herrmann [An elementary theory of defective beams. Acta Mech 1986;62:37-46] to estimate the stress intensity factors of cracked beams and bars. This method is based on an elementary beam theory estimation of the strain energy release as the crack is widened into a fracture band. As an extension, the power of the simple beam theory analysis is demonstrated by application to cracked T-beams subjected to a bending moment, shear forces and a torsion. Moreover, the present work addresses the coupled bending-torsional vibration of cracked T-beams within the context of the dynamic stiffness matrix method of analysing structures.     

Stress intensity factors and crack propagation in a single crystal nickel-based superalloy

A three-dimensional finite element method was used to calculate the stress intensity factors for corner cracked specimens of a single crystal nickel-based superalloy. The anisotropic material properties and inclinations of the cracks were shown to have significant effects on the stress intensities. Then the two-dimensional resolved shear stress approach for predicting the crack planes and crack growth directions in single crystals was extended to the three-dimensional case. Using this approach, the fatigue crack growth behaviour in single crystal corner cracked specimens could be explained.     

Stress intensity factors for an ARC crack in a rotating disc

Numerical solutions are obtained to the problem of an arc crack in a rotating disc. Two boundary element methods are used, one dependent on the problem symmetry and the other capable of solving rotational problems with quite general boundaries. Good agreement is obtained between the two methods, and the results cast some doubt on the validity of published values.     

Stress intensity factors for an inclined edge crack in a semiplane

Mode I and II Stress Intensity Factors under uniform general biaxial loadings were derived for an inclined edge crack in a semiplane. By interpolating Finite Element results in the angular range [0°÷80°], analytical expressions were obtained for both K_I and K_II with an accuracy better than 1%. Influence coefficients were defined in the crack reference frame thus highlighting the coupling effects between Modes I and II due to the loss of symmetry when the crack is not normal to the surface.     

Stress intensity factors in a circular cylinder containing a pair of radial cracks

The elasticity problem of a circular cylinder having a pair of radial cracks subject to mode I loading is studied in this article. Stress intensity factors of the cracked cylinder under mode I loading are systematically and effectively evaluated with use of an equivalent procedure established in this paper. The equivalent procedure reduces the problem under consideration to that of a simpler geometry—an infinite medium with two similar collinear cracks. Numerical results are obtained for a uniform tension and for a pair of concentrated forces acting on the circumferential boundary of the cylinder. The relative merit of the solution method presented in this paper is also discussed.     

Elastic stress intensity factors and crack opening displacements for circumferential through-walled cracked elbows

This paper provides tabulated solutions of elastic stress intensity factors and crack opening displacements for circumferential through-wall cracked elbows under internal pressure and under in-plane bending, based on extensive three-dimensional elastic finite element analyses covering a wide range of crack lengths and elbow/pipe geometries. The effect of crack length and elbow/pipe geometry on the results is discussed, with particular emphasis on the crack closure behaviour under in-plane bending.     

Calculation of stress intensity factors for a longitudinal semi-elliptical crack in a finite-length thick-walled cylinder

The purpose of this paper is to present the effect of finite boundary on the stress intensity factor of an internal semi-elliptical crack in a pressurized finite-length thick-walled cylinder  ( R _i/ t = 4)  . The three-dimensional finite element method, in conjunction with the weight function method, is used for computing the stress intensity factor at the deepest and surface points of an axial semi-elliptical crack in a cylinder. The transition aspect ratios, the aspect ratios in which the maximum stress intensity factor translates from the deepest to the surface points of the crack, are calculated for different relative depths and cylinder lengths. The results show that the stress intensity factor increases as the cylinder length decreases, especially at the corner point of the crack compared with the deepest point. The major advantage of this paper is that a closed-form expression is extracted for the stress intensity factor at the surface point of a semi-elliptical crack, which experiences higher changes due to the effect of the finite boundary of the cylinder.