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.     

Determining stress intensity factors of composites using crack opening displacement

The main purpose of this paper is to find the mixed-mode stress intensity factors of composite materials using the crack opening displacement (COD). First, a series solution of the composite material with a crack was used to evaluate COD values. Then, the least-squares method was used to calculate mixed-mode stress intensity factors. This algorithm can be applied to any method that generates or measures COD values. The major advantage of this method is that COD values very near the crack tip are not necessary. Both finite element simulations and laboratory experiments were applied to validate this least-squares method with acceptable accuracy if the even terms of the series solution are removed.     

Weight function,stress intensity factor and crack opening displacement solutions to periodic collinear edge hole cracks

Periodic collinear edge hole cracks and arbitrary small cracks emanating from collinear holes, which are two typical multiple site damages occurred in the aircraft structures, are studied by using the weigh function method. An explicit closed form weight function for periodic edge hole cracks in an infinite sheet is obtained and further used to calculate the stress intensity factor and crack opening displacement for various loading cases. Compared to finite element method, the present weight function is accurate and highly efficient. The interactions of the holes and cracks on the stress intensity factor and crack opening displacement are quantitatively determined by using the present weight function. An approximate weight function method is also proposed for arbitrary small cracks emanating from multiple collinear holes. This method is very useful for calculating the stress intensity factor for arbitrary small cracks.     

An effective numerical stress intensity factor calculation with no crack discretization

An effective numerical procedure for calculating stress intensity factors (SIF) in plane problems based on a modified boundary element technique not requiring any crack discretization was proposed by Snyder [1]. Instead of the usual fundamental solution, he used Green's function for the problem of a traction-free central crack in an anisotropic plate.In the first part of the present paper, the corresponding Green's function for the isotropic problem, not explicitly included in [1], is presented. In addition to the central crack, a semi-infinite edge crack is considered. Both Green's functions are given for the case of the anti-plane state of strain as well. In the first step of the proposed procedure, the tractions and displacements along the outer boundary are calculated. In the second step, the SIF for modes I, II and III are derived in terms of simple boundary integrals over quantities known from the previous step. Contrary to Snyder's derivation, the determination of the SIF is based on the asymptotic displacement field at the crack tip. The method can easily be extended to multiple crack problems by using the subregion technique. Some illustrative examples demonstrate the effectiveness of the method.

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Résumé Snyder a proposé une procédure numérique pour le calcul des facteurs et intensité de contraintes dans les problèmes plans, en se basant sur une modification de la technique des éléments aux limites ne requérant pas de discrétisation de la fissure. Au lieu d'une solution fondamentale habituelle, il a utilisé une fonction de Green pour traiter le problème d'une fissure centrale libre de contraintes dans un plaque anisotrope.Dans la première partie de la présente étude, on présente la fonction de Green qui correspond à un problème isotrope, qui n'était pas explicitement couvert par le travail de Snyder. Outre le cas de la fissure centrale, on considère le cas de la fissure de bord dans un milieu semi-infini. Les deux fonctions de Green relatives au cas d'un état de déformation antiplanaire sont également communiquées. Dans une première étape de la procédure proposée, on calcule les sollicitations et déplacements le long du contour extérieur; dans une deuxième étape, on établit les facteurs d'intensité de contraintes relatifs aux modes I, II et III en terms d'intégrals sur un contour simple défini par les valeurs résultant de l'étape précédente. Contraitement à l'approche de Snyder, on détermine le facteur d'intensité des contraintes sur base du champs de déplacement asymptotique à l'extrémité de la fissure. Par la technique des sous-régions, on peut aisément étendre la méthode à des problèmes de fissuration multiples. L'efficacité de la méthode est illustrée par divers exemples.

     

Explicit calculation of the crack tip stress intensity factor for the double slip plane model crack

A more rigorous analysis is presented for the stationary double slip plane (DSP) crack loaded in mode III with constant friction stress on the slip planes. This analysis gives the dislocation distributions on the slip and crack planes. More important, the analysis leads to an explicit calculation of the crack tip stress intensity factor K_t without resort to use of the J-integral or the Rice-Thompson expression for dislocation crack tip shielding/antishielding factor. It is shown that K_t ≈ K for the stationary crack. With the results of this paper there are now essentially three independent methods of obtaining K_t for a DSP crack.     

Variational bounds of the stress intensity factor at the edge of a plane opening mode crack

Criteria for opening mode critical stress intensity factors in three-dimensional elastic or viscoelastic solids are proposed based upon variational bounds similar in principle to those developed by Lavrent'ev for problems in gas dynamics.     

Derivation of applied stress-crack opening displacement relationships for the evaluation of effective stress intensity factor range

Linear elastic fracture mechanics (LEFM) integrated with the interference of fracture surface asperities has been formulated. The asperities are considered to simulate the influence of the microstructures and possibly oxide debris. The applied stress/load-crack opening displacement (COD) relationships in several cases have been derived. In the original LEFM, the stress-COD relationship is represented by a straight line passing through the origin of the stress-COD plot. The insert of one asperity results in a deviation of the stress-COD response from the LEFM relationship, leading to the exhibition of an inflection point (first contact point, σ_op), a larger slope, and a residual COD. In the case of two asperities, the slope and the residual COD of the stress-COD relationship become further larger, and two inflection points emerge. A general stress-COD expression in the case of multiple asperities has been derived. The slope of the stress-COD equation, the residual COD, and the minimum COD all increase with increasing number of asperities for a given loading condition, resulting in a smaller ΔCOD and Δσ_eff. The number of the inflection points is the same as that of the asperities. To the authors' knowledge, this paper is the first to derive analytically an applied stress-COD curve with a gradual variation below σ_op, caused by the asperity-/roughness-, or oxide-induced crack closure.     

On the uniqueness of the stress intensity factor — crack velocity relationship

Experimental results due to several different investigators on the K _I – a relationship are reviewed and the apparent differences in results leading to questions regarding the uniqueness of this relationship are discussed. The influence of the errors due to the three dimensional state of stress at the crack tip, the effects of non-singular stresses, velocity, transient loading and velocity measurement is presented. These errors have obscured resolution of the uniqueness question and an experiment is described to resolve the issue.

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Résumé On passe en revue les résultats expérimentaux obtenus par différents chercheurs sur la relation K _I – a et l'on discute des différences apparentes dans les résultats qui conduisent à des questions en ce qui regarde l'unicité de cette relation. On présente l'influence des erreurs dues à l'état tridimensionnel des tensions à l'extrémité de la fissure, les effets des contraintes non singulières de la vitesse de la mise en charge transitoire et de la mesure de la vitesse. Ces erreurs ne contribuent pas à éclaircir la question de l'unicité et, en vue de la résoudre, on décrit une expérience possible.

     

Limitations of the Petroski-Achenbach crack opening displacement approximation for the calculation of weight functions

The displacement fields of edge cracks under tensile stress can be described by an approximation given by Petroski and Achenbach. Using this approximation and the weight function method, the displacement fields for single forces and varying stress distributions can be obtained. This is done for the examples of an edge cracked and a through cracked plate, showing good agreement with FE and analytical calculations, respectively.     

A crack opening displacement approach to crack patching

The results of a numerical investigation into crack patching indicate that a modified form of the crack opening displacement approach may be useful in estimating the effect that fibre composite patches have on cracks in thin sheets.     

On the compatibility between J-Integral and crack opening displacement

An investigation of the relationship between the resistances J_R and δ_R during crack growth in several medium strength steels is reported in this paper. The results show that we can find out some reasonable rules governing their relationship only after analysing the plastic components of the resistances J_P and δ_P. As can be seen from the tests, the J_P/δ_S?δ_P relationship is linear within the range of crack growth amount investigated and is probably affected by the material property and the specimen geometry. A comparison between P-V and P-Δ curves made by the plastic hinge model shows that the two kinds of records are essentially equivalent. Therefore, the compatibility between J-integral and COD is proved by extensive experiments.     

Boundary element crack closure calculation of three-dimensional stress intensity factors

A general method for boundary element-crack closure integral calculation of three-dimensional stress intensity factors is presented. An equation for the strain energy release rate in terms of products of nodal values of tractions and displacements is obtained. Embedded and surface cracks of modes I, II, and III are analyzed using the proposed method. The multidomain boundary element technique is introduced so that the crack surface geometry is correctly modeled and the unsymmetrical boundary conditions for mode's II and III crack analysis are handled conveniently. Conventional quadrilateral elements are sufficient for this method and the selection of the size of the crack front elements is independent of the crack mode and geometry. For all of the examples demonstrated in this paper, 54 boundary elements are used, and the most suitable ratio of the width of the crack front elements to the crack depth is 1/10 and the calculation error is kept within ±1.5 percent. Compared to existing analytical and finite element solutions the boundary element-crack closure integral method is very efficient and accurate and it can be easily applied to general three-dimensional crack problems.