Variation of mixed modes stress intensity factors of an inclined 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 inclined semi-elliptical surface crack in a semi-infinite body under tension. The stress field induced by displacement discontinuities in a semi-infinite body is used as the fundamental solution. Then, the problem is formulated as a system of integral equations with singularities of the form r ^–3. In the numerical calculation, the unknown body force doublets are approximated by the product of fundamental density functions and polynomials. The results show that the present method yields smooth variations of mixed modes stress intensity factors along the crack front accurately for various geometrical conditions. The effects of inclination angle, elliptical shape, and Poisson's ratio are considered in the analysis. Crack mouth opening displacements are shown in figures to predict the crack depth and inclination angle. When the inclination angle is 60 degree, the mode I stress intensity factor F _I has negative value in the limited region near free surface. Therefore, the actual crack surface seems to contact each other near the surface.     

On the calculation of crack opening displacement from the stress intensity factor

For the application of the weight function method the crack opening displacements for a reference case have to be known. An approximate method to derive the crack opening field from the stress intensity factor was proposed by Petroski and Achenbach [Engng Fracture Mech. 10, 257 (1978)]. The limited accuracy of their method becomes evident in cases where the stresses differ strongly from the homogeneous loading case (σ = const.). By expanding the crack opening displacement field in a power series it is demonstrated here how the approximative solutions can be improved by simple additional conditions.     

Variations of stress intensity factor of a semi-elliptical surface crack subjected to mixed mode loading

Maximum stress intensity factors of a surface crack usually appear at the deepest point of the crack, or a certain point along crack front near the free surface depending on the aspect ratio of the crack. However, generally it has been difficult to obtain smooth distributions of stress intensity factors along the crack front accurately due to the effect of corner point singularity. It is known that the stress singularity at a corner point where the front of 3 D cracks intersect free surface is depend on Poisson's ratio and different from the one of ordinary crack. In this paper, a singular integral equation method is applied to calculate the stress intensity factor along crack front of a 3-D semi-elliptical surface crack in a semi-infinite body under mixed mode loading. The body force method is used to formulate the problem as a system of singular integral equations with singularities of the form r ⁻³ using the stress field induced by a force doublet in a semi-infinite body as fundamental solution. In the numerical calculation, unknown body force densities are approximated by using fundamental density functions and polynomials. The results show that the present method yields smooth variations of mixed modes stress intensity factors along the crack front accurately. Distributions of stress intensity factors are indicated in tables and figures with varying the elliptical shape and Poisson's ratio.     

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.     

The crack opening displacement field of semi-elliptical surface cracks in tension for weight functions applications

Application of the weight function method for calculating energy release rates or averaged weighted stress intensity factors requires that both the stress intensity factors and the crack opening displacements are known for a reference load case. This report gives an approximative solution for the crack opening displacement field of a semi-elliptic surface crack under pure tension loading. As a practical example the energy release rates are calculated for bending and compared with results available in the literature. Also a test procedure is described for checking the quality of approximative stress intensity factors.

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Résumé Pour appliquer la méthode des fonctions pondérées au calcul des vitesses de relaxation de l'énergie ou des facteurs d'intensité de contraintes moyens pondérés, il faut que soient connus les facteurs d'intensité de contraintes et les déplacements d'ouverture de la fissure, dans un cas de sollicitation de référence. La rapport fournit une solution approximative pour le champ de COD correspondant à une fissure superficielle semi-elliptique soumise à une charge de traction pure. Comme exemple pratique, on calcule les vitesses de relaxation de l'énergie correspondant à la flexion, et on se compare avec les résultats publiés dans la littérature. On décrit également une procédure d'essai en vue de vérifier la qualité des facteurs d'intensité de contraintes approchés.

     

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.     

Calculating stress intensity factors for a semi-elliptical surface crack in a heterogeneous stress field

The author proposes an equation for calculating the stress intensity factor (SIF) for a semi-elliptical surface crack for uniform, linear, and quadratic laws of variation of the load applied to its edges. The derivation of the equation is based on the well-known Newman—Raju solution for a bent plate. The distribution of the values of SIF along the crack front, obtained using the empirical equations, coincides with the results of calculations carried out using the finite element method (FEM).Translated from Problemy Prochnosti, No. 7, pp. 38–41, July, 1990.     

弯扭组合载荷下圆管半椭圆表面裂纹应力强度因子的有限元分析

对表面裂纹复合型应力强度因子的研究一直是线弹性断裂力学中的重要课题,例如弯扭组合载荷下圆管半椭圆表面裂纹应力强度因子的计算,到现在也没有一个正确的分析解。考虑到裂尖的应力奇异性,在裂纹前沿手动设置三维奇异单元,用三维有限元法中的1/4点位移法计算弯扭组合载荷下圆管表面椭圆裂纹前沿的Ⅰ型、Ⅱ型和Ⅲ型应力强度因子,并分析其随裂纹深度增加时的变化规律。运用该方法计算了有关模型的应力强度因子,并与该模型的实验值进行了比较,计算结果和实验结果吻合良好。     

Stress intensity factor for semi-elliptical surface cracks loaded by stress gradients

The stress intensity factor at the deepest point of a semi-elliptical surface crack is calculated for stress gradients in direction of depth. The method is based on weight functions. The crack opening displacement for the reference problem is calculated with a method proposed by Petroski and Achenbach. The results are compared to finite element solutions given in the literature. As an example, the stress intensity factor is calculated for a crack in a thermally shocked pipe.     

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.     

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 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.     

Stress intensity factor calculation of steel-lined hoop-wrapped cylinders with internal semi-elliptical circumferential crack

The purpose of this paper is to present mode I stress intensity factor for a circumferential semi-elliptical crack on the inner surface of a hoop-wrapped steel-lined CNG cylinder. The stress intensity factors along the crack front are directly computed by 3D finite element method for a wide range of variations of the crack geometry. Also influence of many parameters such as cylinder internal pressure, composite layer thickness, composite material properties and undertaking Auto-Frettage pressure are studied on the stress intensity factor of the crack and some conclusive results are drawn. For the sake of validation of the results and because of lack of the results for a circumferential semi-elliptical crack in the literature, a semi-elliptical axial crack in a composite hoop-wrapped cylinder has been modeled and the results have been compared with those in the literature showing a good agreement.     

Stress intensity factors for a semi-elliptical crack in the surface of a semi-infinite solid

The stress intensity factors are presented for a vertical semi-elliptical surface crack in an elastic semi-infinite body which is subjected to a constant pressure on the crack surface. The approach utilizes a singular integral equation which is defined over the crack area only, where the weakness of the stress singularity is taken into account near the corner points at which the crack periphery intersects the surface of the semi-infinite body.This pertinent approach provides the proper assessment of the stress intensity factors in the vicinity of the corner points, and reveals that the stress intensity factor reaches a maximum value near the corner point and then decreases to zero as the point is approached.

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Résumé On présente les facteurs d'intensité de contrainte pour une fissure de surface verticale semi-elliptique dans un corps élastique semi-infini soumis à une pression constante sur la surface de la fissure. L'approche utilisée recourt à une intégrale singulière définie uniquement sur la superficie de la fissure, où l'on prend en considération l'affaiblissement de la singularité des contraintes au voisinage des points où la périphérie de la fissure est en intersection avec la surface du corps semi-infini.Cette approche permet d'obtenir les facteurs d'intensité de contrainte au voisinage des points considérés et révèle que le facteur d'intensité des contraintes passe par un maximum en ceux-ci et décroît vers zéro lorsqu'on s'en éloigne.

     

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.     

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.