The stress intensity factor for a flat elliptical crack in an elastic solid under uniform tension

Making use of simple results concerning 2-dimensional Fourier transforms an expression is derived for the stress-intensity factor at the rim of a flat elliptical crack in an infinite elastic solid under uniform tension.     

Approximate stress intensity factor for an embedded elliptical crack near two parallel free surfaces

An approximate stress intensity factor is derived for an embedded elliptical crack in a plate which is subjected to uniaxial tension in the direction perpendicular to the crack surface. The major axis of an eccentrically located elliptical crack is assumed to be parallel with the two plate surfaces. The approximate stress intensity factors on the minor axis of the elliptical crack are then determined as Ba where a is a correction factor due to the curvature of the ellipse and 6 is a correction factor due to the eccentricity of the crack in the wall.

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Zusammenfassung Es wird ein angenaeherter Faktor fuer die Spannungskonzentration an einem elliptischen Riss, der in einen Platte unter einachsiger Zugspannung eingeschlossen ist, abgeleitet. Die Zugspannungsrichtung ist senkrecht zur Rissoberflaeche. Es wird angenommen, dass die Hauptachse des exzentrisch gelagerten Risses parallel zu den beiden Plattenoberflaechen ist. Fuer den angenaeherten Faktor der Spannungskonzentration an der kleineren Hauptachse des elliptischen Risses ergibt sich dann Ba wobei ein Korrekturfaktor fuer die Ellipsenkruemmung ist und einen Korrekturfaktor fuer die Exzentrizitaet des Risses in der Platte bedeutet.

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Résumé Un facteur approché d'intensité de contrainte est obtenu pour une fracture elliptique encastrée dans une plaque soumise à une tension uniaxiale dans la direction perpendiculaire à la surface de la fracture. Le grand axe d'une fracture elliptique excentrique est supposé être parallèle aux deux surfaces de la plaque. Les facteurs approches d'intensité de contrainte, le long du petit axe de la fracture elliptique sont déterminés par Ba où a est un facteur de correction dû à la courbure de l'ellipse et est un facteur de correction dû à l'excentricité de la fracture dans le mur.

     

Accurate stress intensity factor solutions for corner cracks at a hole

Laboratory test and in-service experience shows fatigue cracks at holes exhibit unsymmetric growth; thus, the need for the new solutions is paramount. Stress intensity factor, K, solutions for symmetric and unsymmetric corner cracks at a hole subject to general loading were determined using a hp-version of the finite element method (FEM) in conjunction with a mathematical splitting scheme to enable efficient, accurate calculations. In traditional applications of the FEM, mesh generation is labor intensive; however, using the splitting scheme, stress intensity functions are obtained without explicitly including the crack in the FE mesh of the global structure. By using the hp-version of FEM, a set of K-solutions converging exponentially fast to the exact solution is obtained. The crack is analyzed in the local domain with easily generated FE meshes. All structurally significant crack shapes were considered; specifically, crack depth to crack length ratios (a/c) of 0.1–10.0, crack depth to sheet thickness ratios (a/t) of 0.10–0.99, and hole radius to sheet thickness ratios (r/t)=1.0. The loading conditions were remote tension, remote bending, and pin loading (bearing). In addition, all combinations of a/c and a/t are analyzed at each side of the hole; thus 226,875 solutions were developed with control of the error in the computed K solutions. Calculated relative error is generally much smaller than 1% along the entire crack front including the vertex regions. Comparisons are made to solutions in the open literature. The new K solutions show the literature solutions are, in general, accurate for all three load conditions; however, for the extreme cases of a/c, a/t, and r/t; the literature solutions differ by as much as 26%.     

Determination of stress intensity factor for embedded elliptical crack in turbine rotor

The stress intensity factor (SIF) for an embedded elliptical crack in a turbine rotor and the thermal shock stress intensity factor for a semi-elliptical surface crack in a finite plate are determined by means of Vainshtok's weight function method. The solution for the semi-elliptical surface crack is in good agreement with the previous one. The value of the SIF for the embedded elliptical crack in the turbine rotor under centrifugal and thermal loading is larger at the crack contour near the inner radius surface and almost constant at the opposite crack contour. The SIF decreases by increasing the crack ratio, and the distance between the inner radius surface and the crack center.     

The effect of an elliptical inclusion on a crack

The interaction between an elliptical inclusion and a crack is analyzed by body force method. The investigated stress field is simulated by superposing the fundamental solutions for a point force applied at a point in an infinite plate containing an elliptical inclusion. Based on numerical results, effects of the inclusion shape on the crack tip stress intensity factor are discussed. It is found that for small cracks emanating from a stress-higher point on the inclusion interface the stress intensity factors are mainly determined by the stresses, occurring at the crack starting point before the crack initiation, and the inclusion root radius, besides the crack length. However, for the cracks occurring in a stress-lower region around the inclusion, it is difficult to characterize the effect of the inclusion geometry on the stress intensity factors of small cracks by the inclusion root radius alone. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analytic evaluation of the difference between Oore-Burns and Irwin stress intensity factor for elliptical cracks

Summary. The mode-I weight function proposed by Oore and Burns is an efficient and empirical mathematical relationship capable of estimating the Stress Intensity Factor in the presence of a generic planar flaw. In the case of penny shaped cracks or tunnel cracks the Oore-Burns equation provides the classic analytical expressions. In this paper, the authors prove analytically that the Oore-Burns equation is not the weight function for an ellipse in an infinite solid under traction loading. The absolute novelty is given by the analytic evaluation between the Oore-Burns integral and the Irwin solution in terms of an algebraic expression, which is independent from any numerical procedures for an ellipse close to a circle.     

The effect of water on the critical stress intensity factor of unsaturated polyester resins

The effect of water on the critical stress intensity factor,K _IC, of a highly unsaturated isophthalic polyester resin has been measured for periods of immersion of up to 2200 h in water at temperatures of 35, 70 and 80° C.K _IC decreased from 0.84±0.1 MN m^–3/2 to 0.24±0.03 MN m^–3/2 after immersion for 2200 h in water at 80° C. The observed changes in the critical stress intensity factor indicate that a constant value is eventually reached. This is consistent with the decline being attributable to the leaching of extractable matter from the polyester resin.     

Investigation of the stress intensity factor changing on the hole crack subject to laser shock processing

Laser shock processing (LSP) is a new surface modification technology. The effect of the compressive residual stresses generated due to laser shock processing (LSP) on the stress intensity factor (SIF) of a through-the-thickness radial crack at the edge of the circular hole was investigated. The residual stresses around the hole induced by LSP were measured by using X-ray method. The relationship between the SIF and the residual stress was determined on the basis of the weight function theory in fracture mechanics. Crack propagation characteristics for such cracks subjected to the combination of the applied stress and residual stress were discussed. And the results showed that the compressive residual stress could lead to the decrement of the SIF. Moreover, the number of the laser shocks had an important influence on the SIF.     

The stress intensity factor of an edge crack in a finite elastic disc

In this paper, a Mellin transform technique is used to express the stress intensity factor and the crack energy of an edge crack in a finite elastic disc directly in terms of the solution of a Fredholm integral equation of the second kind. The constant loading case is considered in detail and the results given in graphical form.     

The stress intensity factor of a crack emanating from a circular hole in a finite plate by boundary collocation method

The problem of a finite plate containing a circular hole with a crack subjected to a uniform remote stress is analysed by boundary collocation method. For an infinite plate with dimensions large in comparison with the crack length and the radius of the hole, the stress intensity factor (SIF) values calculated by this method coincide very well with the existing solution. Numerical results of the SIF values are obtained for varying crack-length-to-hole-radius ratios, l/r, and equivalent crack-length-to-plate-width ratios, a/b. The analysis for finite plates can provide useful results for practical applications.

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Résumé On analyse par la méthode de collocation des limites le problème d'une plaque finie comportant un trou circulaire avec une fissure, soumis à une contrainte uniforme appliquée à une certaine distance. Dans le cas d'une plaque infinie et de grandes dimensions par rapport à la longueur de la fissure et le rayon du trou, les valeurs du facteur d'intensité de contraintes calculées à l'aide de cette méthode coincident bien avec la solution existante. On obtient des résultats numériques du facteur d'intensité de contrainte pour différents rapports l/r de la fissure sur le rayon du trou, et pour les rapports a/b de la longueur de fissure équivalente sur la largeur de la plaque. L'analyse relative à des plaques finies peut fournir des résultats utiles à des applications pratiques.

     

Stress intensity factor for an embedded elliptical crack under arbitrary normal loading

In this paper we introduce the boundary value problem of three-dimensional classical elasticity for an infinite body containing an elliptical crack. Using the method of simultaneous dual integral equations, the problem is transformed to the system of linear algebraic equations. Stress intensity factor is obtained in the form of the Fourier series expansion. Several solutions for specific cases of applied polynomial stress fields are derived and compared with existing results. Eligibility of the method for more complicated stress fields is demonstrated on the example of partially loaded elliptical crack.     

Transverse shear stress distribution through thickness near an internal part-through elliptical hole in a stretched plate

A semi-analytical post-processing method, termed the equilibrium/compatibility method here, is used for computation of hitherto unavailable through-thickness variation of transverse shear stresses in the vicinity of the circumferential re-entrant corner line of an internal part-through elliptical cylindrical hole weakening an edge-loaded rectangular plate. A C⁰-type triangular “composite” plate element, based on the assumptions of transverse inextensibility and piece (“layer”)-wise constant shear-angle theory (LCST), is employed to first compute the inplane stresses and “layer”-wise through-thickness average transverse shear stresses. These serve as the starting point for computation of through-thickness distribution of transverse shear stresses in the vicinity of the circumferential re-entrant corner line of the internal part-through elliptical hole. As in the case of its circular counterpart, the transverse shear stresses computed by the conventional equilibrium method (EM) are, in contrast, in serious error in the presence of the circumferential re-entrant corner line singularity arising out of the internal part-through elliptical hole, and are found to violate the compatibility condition. The computed maximum transverse shear stress can be high enough to cause catastrophic transverse shear fracture in the shape of a cone, of elliptical cross-section starting from the circumferential re-entrant corner line of the internal part-through hole. The results computed by the present analysis are in line with a three-dimensional asymptotic analysis.     

Averaged stress intensity factors for embedded elliptical cracks

As an extension of well-known two-degree-of-freedom models describing virtual crack extensions in weight function applications for surface crack configurations different possibilities are suggested of four-degree-of-freedom models used for embedded elliptical cracks. As a result, the geometric function for an elliptical crack in a strip of finite width is presented for tension and bending. FEM-calculations have been carried out to check the quality of the solution.     

The stress intensity factor of an edge crack in a finite rotating elastic disc

In this paper the problem of determining the stress intensity factor and crack formation energy of an edge crack in a finite rotating elastic disc is reduced to the solution of a Fredholm equation. Numerical results are given.     

The effect of partial closure on the stress intensity factor of a Griffith crack opened by a parabolic pressure distribution

The problem of a Griffith crack in a thin plate, which is opened by a parabolic pressure acting on its surfaces is considered. The crack is then partially closed in a symmetric manner by ties, idealized by point loads in the material, and the effect upon the stress intensity factors is discussed.

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Zusammenfassung Man betrachtet das Problem eines Griffith-Risses in einem dünnen Blech, dessen Seitenflächen einem Öffnungsdruck parabolischer Verteilung ausgesetzt sind.Anschließend wird der Riß unter Einfluß lokaler, quer zur Rißachse wirkender Bindungen wieder teilweise symmetrisch geschlossen. Diese Bindungen werden durch Punktbelastungen ideal dargestellt und es wird ihr Einfluß auf die Spannungsintensität erörtert.

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Résumé On considère le problème de la fissure de Griffith dans une tôle soumise à une pression d'ouverture, de distribution parabolique, sur ses faces.La fissure est ensuite partiellement refermée, de manière symétrique, sous l'action de liaisons localisées, perpendiculaires à l'axe de la fissure. Ces liaisons sont idéalisées par des charges ponctuelles.On discute de leur effet sur les facteurs d'intensité de contrainte.

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This work was supported by Grant AFOSR-69-1779.