Stress intensity factors for axial cracks in hollow cylinders subjected to thermal shock

Stress intensity factors are determined for one and two, internal and external axial cracks in hollow cylinders subjected to stress gradients arising from a thermal shock. A closedform weight function formula was used in the calculation. Results covering a wide range of cylinder geometries are presented in graphical form.     

Computation of membrane and bending stress intensity factors for thin,cracked plates

The crack tip stress fields for plate bending and membrane loading problems are reviewed and the four stress intensity factors that determine these fields are defined. These four stress intensity factors arise from use of Kirchhoff plate theory to account for the bending loads and two dimensional plane stress elasticity to account for the membrane loads. The energy release rate is related to the stress intensity factors and to the stress resultants of plate theory. Virtual crack extension, nodal release and modified crack closure integral methods are discussed for computing components of the energy release rate from finite element analyses of cracked plates. Sample computations of stress intensity factors for single and mixed mode cases are presented for a crack in an infinite plate. Sample computations of stress intensity factors for a double edge notched tension-torsion test specimen are given as well.School of Civil and Environmental Engineering, Cornell University     

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 for an edge cracked circular bar in tension and bending

The variation of the stress intensity factor along the front of an edge crack in an elastic bar of circular cross-section is determined. Both straight and circular-arc crack fronts are modelled using a three-dimensional tinite element analysis of the tension and bending problems. Results are obtained for crack depth to bar diameter ratios ranging from 0.1 to 0.594, in the case of cracks with straight fronts, and from 0.175 to 0.6, in the case of cracks with curved fronts.

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Résumé On détermine la variation du facteur d'intensité de contraintes sur le front d'une fissure latérale dans un barreau élastique de section circulaire. On modélise des points de fissure droits et à arc circulaire à l'aide d'une analyse par éléments finis à trois dimensions des problèmes en traction et en flexion. Les résultats sont obtenus pour des rapports de profondeur de fissure à diamètre de barreaux compris entre 0.1 et 0.594, pour des fissures a front droit, et entre 0,175 et 0,6 dans le cas de fissures à front incurvé.

     

Plastic intensity factors for cracked plates subjected to biaxial loading

An elastic-plastic analysis is performed for an infinite plate under plane stress conditions which contains a finite line crack and is subjected to biaxial loading. In the large scale yielding range, the amplitude of the dominant singularity at the crack tip, the plastic stress (or strain) intensity factor, is found to depend on the magnitude of loading parallel to the crack direction. The predicted value for the fracture initiation stress which is based on a plastic intensity factor fracture criterion, increases under lateral, tensile loading. Compressive loading parallel to the crack has the opposite effect on the fracture initiation stress.

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Zusammenfassung Man untersucht im elastoplastischen Gebiet den Fall eines unendlichen Bleches, im ebenen Spannungszustand, mit einem endlichen linearen Riß, der biaxial belastet wird.Im Gebiet der großen plastischen Verformungen hat man gefunden daß die Amplitude der überwiegenden Sonderbarkeit an der Spitze des Risses und zwar der plastische Spannungsintensitätsfaktor (oder Dehnung) von der Größe der Belastung parallel zur Richtung des Risses abhängt.Der vorausgesetzte Wert der bruchauslösenden Spannung die sich auf einem plastischen Bruchintensitätsfaktor Kriterium gründet, nimmt zu mit der seitlichen Zugbelastung.Druckbelastung parallel zum Riß hat einen entgegengesetzten Einfluß auf die bruchauslösende Spannung.

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Résumé On procède à une analyse élastoplastique du cas d'une tôle infinie en conditions d'état plan de tension, qui comporte une fissure linéaire finie et qui est sujette à une mise en charge biaxiale.Dans le domaine des grandes déformations plastiques, on a trouvé que l'amplitude de la singularité dominante à la pointe de la fissure—à savoir le facteur d'intensité des contraintes (ou des déformations) plastiques—dépen de l'importance de la charge parallèle à la direction de la fissure.Le niveau de contrainte que l'on prédit conduire à l'amorçage de la rupture, et qui est basé sur un critère de rupture relevant du facteur d'intensité plastique, s'accroît en présence de charges de traction latérales.Une mise en charge par compression, parallèlement à la fissure, a un effet inverse sur la contrainte d'amorçage de la rupture.

     

Stress intensity factors for functionally graded solid cylinders

This paper presents the mode I stress intensity factors for functionally graded solid cylinders with an embedded penny-shaped crack or an external circumferential crack. The solid cylinders are assumed under remote uniform tension. The multiple isoparametric finite element method is used. Various types of functionally graded materials and different gradient compositions for each type are investigated. The results show that the material property distribution has a quite considerable influence on the stress intensity factors. The influence for embedded cracks is quite different from that for external cracks.     

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.     

Numerical solution of cracked thin plates subjected to bending, twisting and shear loads

A semi-analytical method namely fractal finite element method is presented for the determination of mode I and mode II moment intensity factors for thin plate with crack using Kirchhoff's theory. Using the concept of fractal geometry, infinite many of finite elements is generated virtually around the crack border. Based on the analytical global displacement function, numerous degrees of freedom (DOF) are transformed to a small set of generalised coordinates in an expeditious way. The stress intensity factors can be obtained directly from the generalized coordinates. No post-processing and special finite elements are required to develop for extracting the stress intensity factors. Examples of cracked plate subjected to bending, twisting and shear loads are given to illustrate the accuracy and efficiency of the present method. The influence of finite boundaries on the calculation of the moment intensity factors is studied in details. Very accuracy results when compare with the theoretical and numerical counterparts are found.     

Stress intensity factors for cylindrical cracks in long cylinders

Stress intensity factors for a long cylindrical crack in a long cylinder have been calculated using the energy release rate approach. The investigated loading cases include centrifugal forces (Mode I), radial surface forces (Mode I), forces parallel to the axis (Mode II), and twisting moments (Mode III).     

Analysis of thermal stress intensity factors for cracked cylinders using weight function method

In this paper a general weight function was derived to evaluate the thermal stress intensity factors of a circumferential crack in cylinders. The weight function derived is valid for a wide range of thin- to thick-walled cylinders and relative crack depth. Closed-form stress intensity factor based on the weight function method was derived as a function of the Biot number and relative depth and various inner-to-outer radius ratios of cylinders. The accuracy of the analysis has been examined using the finite element method results and were compared to existing solutions for uniform loading in the literature for special geometries, indicating an excellent agreement.     

New plastic collapse moment equations of defect-free and throughwall circumferentially cracked elbows subjected to combined internal pressure and in-plane bending moment

Closed-form plastic collapse moments (PCM) equations were earlier proposed for throughwall circumferentially cracked (TCC) elbow subjected to pure in-plane bending moment. However, an elbow is often subjected to combined internal pressure and bending moment in actual service condition. Therefore, the present study investigates the effect of internal pressure on the in-plane PCM of a TCC elbow. The PCM of a cracked elbow is usually expressed as a product of two parameters: PCM of a defect-free elbow multiplied by a weakening factor due to the crack. Therefore, the present study also includes analysis of defect-free elbows. Elastic-plastic finite element analysis is employed for the present analysis. A total of 396 cases of elbows with various sizes of circumferential cracks (2θ = 0-150°), different wall thickness (R/t = 5-20), different levels of normalized internal pressure (p = PR/(tσ_y) = 0-1), different elbow bend radii (R_b/R = 2,3) and two different bending modes, namely closing and opening are considered in the analysis. Elastic-perfectly plastic stress-strain response of material is assumed. The load in the elbows is split in two components: a constant internal pressure applied initially followed by in-plane bending moment monotonically increasing in definite steps. PCM are evaluated from moment—end rotation curves by twice-elastic slope method. From these results, closed-form equations are proposed to evaluate PCM of TCC and defect-free elbows subjected to combined internal pressure and in-plane closing/opening bending moment. Attempt has been made to compare the predictions of the proposed equations with the available experimental/numerical results and to rationally explain the behaviour where no experimental/numerical data is available for comparison.     

Stress intensity factors for an edge-cracked strip in bending

International Journal of Fracture -     

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.

     

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 for cracks in thin plates

This paper presents stress intensity factor solutions for several crack configurations in plates. The loadings considered include internal pressure, and also combined bending and tension. The dual boundary element method is used to model the plate and mixed mode stress intensity factors are evaluated by a crack surface displacement extrapolation technique and the J-integral technique. Several cases including centre crack, edge crack and cracks emanating from a hole in finite width plates are presented.     

Crack closure effect on stress intensity factors of an axially and a circumferentially cracked cylindrical shell

Crack-face closure occurs when a shell or plate containing a through-the-thickness crack is subjected to a bending load, which leads to lower stress-intensity factors than those expected from non-closure assumption. This article presents a theoretical analysis of the effect of crack-face closure on the stress intensity factors of an axially and a circumferentially cracked cylindrical shell subjected to bending moment respectively. The presented analysis extends the shallow shell theories of Delale and Erdogan by incorporating the effect of crack-face closure. In keeping consistent with the shear deformation shell theory, crack-face closure is modeled by a line contact at the compressive edges of the crack face. The unknown contact force is computed by solving a mixed-boundary value problem iteratively, i.e. along the crack length, either the normal displacement of the crack face at the compressive edges is equal to zero or the contact pressure is equal to zero. The results show that the distribution of the contact force along the crack is generally nonuniform. Furthermore, it is found that, similar to the case of spherical shells, crack closure may occur over the full length or only some segments of the crack in cylindrical shells, depending on the geometry of the shell and the nature (direction) of applied bending load. Comparisons of the stress intensity factor ratios between the closure solutions and the non-closure solutions reveal that the crack-face closure influences significantly the magnitude of the stress intensity factors and it tends to reduce the maximum stress intensity factor. The closure effect of crack face on the stress intensity factors is highest when the shell radius becomes very large for a given crack length and shell thickness.