Stress intensity factors for long axial surface cracks at the outer wall of a pipe loaded by stress gradients

By means of the finite element method crack opening displacements were calculated for long axial surface cracks at the outer wall of a pipe. The wall thickness to inner radius ratio of the pipe was 1 to 10. Following a procedure introduced be Mattheck et al. weight functions were evaluated by means of the finite element results. Using these weight functions it is possible to calculate stress intensity factors for arbitrary radially varying stress distributions. In this paper stress intensity factors were evaluated for a constant hoop stress loading as well as for stress distributions with a linear and a quadratic dependence on the radius.     

Stress intensity factor at the surface and at the deepest point of a semi-elliptical surface crack in plates under stress gradients

The weight function method is used to calculate stress intensity factors for a semi-elliptical surface crack in a plate exposed to stress gradients. Starting from a reference load and stress intensity factor an approximate reference displacement field is calculated analytically. The present method allows to calculate stress intensity factors with minimal numerical effort at the deepest point and at the surface. Comparisons with FEM-results from the literature are presented to show satisfying agreement.     

Stress intensity factors and weight functions for deep semi-elliptical surface cracks in finite-thickness plates

ABSTRACT Three-dimensional finite element analyses have been conducted to calculate the stress intensity factors for deep semi-elliptical cracks in flat plates. The stress intensity factors are presented for the deepest and surface points on semi-elliptic cracks with a/t -values of 0.9 and 0.95 and aspect ratios ( a/c ) from 0.05 to 2. Uniform, linear, parabolic or cubic stress distributions were applied to the crack face. The results for uniform and linear stress distributions were combined with corresponding results for surface cracks with a/t = 0.6 and 0.8 to derive weight functions over the range 0.05 ≤  a/c  ≤ 2.0 and 0.6 ≤  a/t  ≤ 0.95. The weight functions were then verified against finite element data for parabolic or cubic stress distributions. Excellent agreements are achieved for both the deepest and surface points. The present results complement stress intensity factors and weight functions for surface cracks in finite thickness plate developed previously.     

Stress intensity factors of semi-elliptical surface cracks in pressure vessels by global-local finite element methodology

In the present study the problem of calculation of the stress intensity factors (SIF) of semi-elliptical cracks located in the stress concentration areas of a pressure vessel is numerically solved by advanced global-local finite element (FE) analysis. The common characteristic of the cases solved is that the stress field at the crack area varies along the axial, the circumferential, as well as, the through-the-thickness directions. SIF solutions for such problems are not available, neither analytically, nor numerically, as the currently existing solutions in the literature (numerical results, Newman-Raju empirical equations, weight function solutions, etc.) are only valid for uniform stress distribution along the axial and circumferential directions of the pressure vessel and allow variation only through-the-thickness. The crack locations considered are the intersection of the cylinder to a nozzle and the connection of the cylinder with its hemi-spherical ends. The stress intensity factors are presented in a suitable table format for various geometrical configurations of both the pressure vessel and the semi-elliptical crack, thus providing a useful tool for the fracture mechanics design of cracked pressure vessels. The modeling details of the sub-structuring methodology, employed in the analysis, are extensively discussed and the numerical approach is proven to be very efficient for the SIF calculation of pressure vessel semi-elliptical cracks.     

Stress intensity factor solution for a semi-elliptical crack in an arbitrarily distributed stress field

An equation for the stress intensity factor (SIF) for semi-elliptical crack has been developed. It is based on the Newman-Raju's solution for the crack in a plate under bending or tension. The equation can be applied when a stress distribution is described by a power function. Using the approach outlined, the SIF for a surface crack in a T-butt welded connection has been estimated. The results obtained can be used in a fracture-mechanics-based fatigue analysis.     

Calculation of Stress Intensity Factors for axial semi-elliptical surface cracks in a pipe with cladding loaded thermally

By means of the weight functions method stress intensity factors were calculated for axial semi-elliptical surface cracks in a pipe with cladding. The component is loaded by a thermoshock. Starting from a stress-free state the inner surface of the cladding is suddenly cooled down. The time-dependent temperature and hoop stress distributions of the uncracked component were calculated for the loading case considered. Numerical values of the stress intensity factors at the deepest point and at the surface points of the crack were evaluated at different time steps for a wide range of crack depths and crack lengths.     

Stress intensity factors for semi-elliptical surface cracks in pressurised cylinders using the boundary integral equation method

Three dimensional linear elastic fracture mechanics analyses of the problem of an internally pressurised thick-walled cylinder with a semi-elliptical surface crack are carried out using the Boundary Integral Equation method. The cases treated are for ratios of external to internal cylinder radii of 2 and 3, with maximum crack depths ranging from 20% to 80% of the wall thickness. For a typical crack, the predicted value of stress intensity factor decreases slightly along the crack front moving away from the point of deepest penetration, reaching a minimum before increasing rapidly as the free internal surface of the cylinder is approached. The results presented will be of considerable use in the prediction of residual or safe life of, for example, chemical reactor tubes known to be cracked to a certain depth.

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Résumé Une analyse tri-dimensionnelle élastique et linéaire en mécanique de rupture du problème d'un cylindre à paroi épaisse soumis à pression interne et comportant une fissure de surface semi-elliptique a été effectuée en utilisant la méthode d'équation intégrale aux limites. Les cas envisagés dans l'étude sont relatifs à des rapports des rayons de cylindre externe et interne de 2 et de 3 avec des profondeurs maximum de fissure s'étalant de 20% à 80% de l'épaisseur de paroi. Dans le cas d'une fissure typique, la valeur prédite pour le facteur d'intensité des contraintes décroit légèrement le long du front de la fissure lorsque l'on se meut du point de pénétration le plus profond, et passe par un minimum pour ensuite s'accroître rapidement lorsqu'on approche de la surface libre interne du cylindre. Les résultats présentés s'avèreront d'une aide considérable pour prédire la vie résiduelle ou la durée de service fiable, par exemple, de tubes de réacteur chimique dont on sait qu'ils sont fissurés sur une certaine profondeur.

     

Stress intensity factors for semi-elliptical surface cracks in a plate under tension based on the Isida's solution

The stress intensity factor solution given by Isida et al. for semi-elliptical surface cracks in plates is improved and extended. The data tabulated for the ranges 0a/t0.6 and 0.25a/c1.0 were checked using the energy relation and found to be superior to solutions available in the literature.     

Variation of stress intensity factor and crack opening displacement of semi-elliptical surface crack

In this paper a singular integral equation method is applied to calculate the stress intensity factor along crack front of a 3D surface crack. Stress field induced by body force doublet in a semi infinite body is used as a fundamental solution. Then the problem is formulated as an integral equation with a singularity of the form of r ^-3. In solving the integral equations, the unknown functions of body force densities are approximated by the product of a polynomial and a fundamental density function; that is, the exact density distribution to make an elliptical crack in an infinite body. The calculation shows that the present method gives the smooth variation of stress intensity factors along the crack front and crack opening displacement along the crack surface for various aspect ratios and Poisson's ratio. The present method gives rapidly converging numerical results and highly satisfactory boundary conditions throughout the crack boundary.     

Stress intensity factors for a wide range of long-deep semi-elliptical surface cracks, partly through-wall cracks and fully through-wall cracks in tubular members

To calculate the rate of fatigue crack growth in tubular members, one approach is to make use of the fracture mechanics based Paris law. Stress intensity factors (SIF) of the cracked tubular members are prerequisite for such calculations. In this paper, stress intensity factors for circumferential deep semi-elliptical surface crack (a/t > 0.8), semi-elliptical partly through-wall crack and fully through-wall crack cracks in tubular members subjected to axial tension are presented. The work has produced a comprehensive set of equations for stress intensity factors as a function of a/T, c/πR and R/T for deep surface cracks. For the partly through-wall cracks and fully through-wall cracks, two sets of bounding stress intensity factor equations were produced based on which all stress intensity factors within the range of parameters can be obtained by interpolation.     

Stress intensity factors for curvilinear cracks loaded by bending and torsional moments

The geometry of a thin flat plate containing a curvilinear crack of finite size is investigated. The plate is loaded by uniform bending and torsional moments at infinite distance from the crack contour, while distributed normal bending moments and torques exist at the upper and lower crack surfaces. The bending stress intensity factors for the curvilinear crack are calculated on the basis of classical plate theory. The displacements and internal moments are represented by two complex analytic functions. Extra conditions are imposed to ensure the univalence of the displacements, which is not evident because the plate comprises a multiply connected domain due to the presence of the crack. A linearization with respect to the crack-curvature function has been performed and the bending stress intensity factors are calculated as the first-order solutions for slightly curved cracks. The results are illustrated with a few examples, such as uniform loading configurations and the geometry of a crack along a circular arc. The loading of thin flat plates by a combination of tensile forces and bending moments is also investigated. In analogy with the variation of the stress components over the cross section of the plate, two combined stress intensity factors are introduced having the same dependence on the perpendicular coordinate and being related to the symmetric and anti-symmetric stress intensity factors of the separate plane-stress and bending problems. The resulting energy release rate is shown to be in full agreement with known results in the literature.     

Stress intensity factors for internal semi-elliptical surface cracks in pressurized thick-walled cylinders using the hybrid boundary element method

The purpose of this paper is to present a comprehensive range of results of mode I SIFs of three-dimensional surface cracks in internally pressurized thick-walled cylinders. The hybrid boundary element method is summarily reviewed and used to calculate the SIFs of surface cracks in pressurized thick-walled cylinders. The analyzed ratio of crack depth to wall thickness ranges from 0.2 to 0.8; the ratio of crack depth to crack length ranges from 0.25 to 1.0; and the ratio of wall thickness to cylinder radius is 0.5, 1.0 and 2.0. The present normalized SIFs are also compared with other solutions from the literature. The recent results of the body force method and the finite element method agree well (ca 3%), and the early ones of the boundary integral equation and the finite element method agree fairly well (ca 10%) with the present results.     

Local weight functions for stress intensity factor evaluation for a surface semi-elliptical crack under polynomial loading

The stress intensity factor distribution along the front of a surface semi-elliptical crack under polynomial loads is computed. Approximate formulas for the large number of ranges are obtained.     

Stress intensity factors for semi-elliptical surface cracks in plates and cylindrical pressure vessels using the hybrid boundary element method

At first, a hybrid boundary element method used for three-dimensional linear elastic fracture analysis is established on the basis of the first and the second kind of boundary integral equations. Then the concerned basic theories and numerical approaches including the discretization of boundary integral equations, the divisions of different boundary elements, and the procedures for the calculations of singular and hypersingular integrals are presented in detail. Finally, the stress intensity factors of surface cracks in finite thickness plates and cylindrical pressure vessels are computed by the proposed method. The numerical results show that the hybrid boundary element method has very high accuracy for the analysis of surface crack.     

Application of the weight function method for determining stress intensity factors of semi-elliptical cracks

The weight function method is applied to solving three-dimensional linear elastic fracture mechanics (LEFM) problems. Within the framework of the present approach the fundamental equations of LEFM are satisfied and the minimum of additional assumptions are used.The crack opening displacement field and stress intensity factors for a semi-elliptical surface crack in the nonuniform stress fields are obtained. Comparison of the calculated results with the numerical data from the literature confirms the efficiency of the proposed method for the solution of three-dimensional crack problems.

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Zusammenfassung Die Gewichtsfunktionsmethode wird für die Lösung dreidimensionaler Aussgaben der linearen Bruchmechanik gebraucht.Im Rahmen der vorgeschlagenen Methode werden fundamentale Gleichungen der linearen Bruchmechanik befriedigt und nur minimale Anzahl der Zuschlagsvermutungen benutzt. Es wird gefunden die Ausdrücke für Verschiebungen der Risskanten und die Bedeutungen der Spannungsintensitätsfaktoren bei ungleichartiger Belastung für halbelliptischen Riss im Halbraum.Der Vergleich der Ergebnisse vorliegender Arbeit mit bekannten Zahlenangaben hat die Effektivität der vorgeschlagenen Methode für die Lösung dreidimensionaler Aufgaben der linearen Bruchmechanik gezeigt.

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Résumé La méthode des fonctions pondérées est appliquée à la solution de problèmes de mécanique de rupture linéaire et élastique (MRLE) à trois dimensions. Dans le cadre de la présente approche, on satisfait aux équations fondamentales de la MRLE et l'on recourt à un minimum d'hypothèses supplémentaires. On obtient le champ de déplacement d'ouverture de la fissure et les facteurs d'intensité des contraintes pour une fissure de surface semi-elliptique, pour des champs de contraintes non uniformes. En comparant les résultats du calcul avec les données numériques en provenance de la littérature, on confirme l'efficacité de la méthode proposée pour solutionner les problèmes de fissuration sur trois dimensions.