Modeling of fatigue crack growth threshold development for a microstructurally small crack

A method for predicting the fatigue crack growth threshold using finite element analysis is investigated. The proposed method consists of monitoring the plastic strain hysteresis energy dissipation in the crack tip plastic zone, with the threshold being defined in terms of a critical value of this dissipated energy. Two-dimensional plane-strain elastic-plastic finite element analyses are conducted to model fatigue crack growth in a middle-crack tension M(T) specimen. A single-crystal constitutive relationship is employed to simulate the anisotropic plastic deformation near the tip of a microstructurally small crack without grain boundary interactions. Variable amplitude loading with a continual load reduction is used to generate the load history associated with fatigue crack growth threshold measurement. Load reductions with both constant load ratio R and constant maximum stress intensity K_max are simulated. In comparison with a fixed K_max load reduction, a fixed R load reduction is predicted to generate a 35% to 110% larger fatigue crack growth threshold value.     

Stress intensity factors for a semiinfinite crack with branches

The stressed state of an elastic plane weakened by a semiinfinite branching crack whose branches are either shear cracks or cracks of a mixed type is determined by the method of singular integral equations for the case where the stressed state at the tip of the semiinfinite crack without branches is characterized by stress intensity factorsK ₁ ⁰ andK _II ⁰ . The values of these factors are obtained for the cases of one, two, and three branches and different values of geometric parameters. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 1, pp. 45–50, January–February, 1997.     

Stress intensity factors for a crack in planar disking

Disking is a relatively new manufacturing process for cutting/slicing brittle plates and rods. In the planar disking configuration, a pre-cracked plate is placed against an elastic plate and the two are squeezed together by fluid pressure. At a critical pressure the crack runs across the thickness of the brittle plate producing a clean cut. In this paper a fracture criterion is developed for the process using linear elastic fracture mechanics. The geometry of the process is modeled here as two perfectly bonded, infinite elastic layers with a crack perpendicular to the interface. The problem is formulated in terms of a singular integral equation with the derivative of the crack surface displacement (dislocation density) as the unknown function. Numerical quadrature is used to determine the stress intensity factors as a function of the parameters of the problem.     

Stress intensity factors of an elliptical crack or a semi-elliptical crack subject to tension

This paper is concerned with the analysis of stress intensity factors of a semi-infinite body with an elliptical or a semi-elliptical crack subject to tension. Analysis is based on the body force method [1] which has been applied to the various plane stress problems. In this paper the method is extended to three-dimensional problems. The numerical calculations are performed for various shapes and configurations of ellipses and the results are in agreement with the two-dimensional cases by M. Isida asb/a→0. The stress intensity factor of a semi-elliptical crack in a plate of finite width is also discussed.     

Stress intensity factors of a surface crack near an interface end

Due to the singular behavior of the stress field near the interface edge of bonded dissimilar materials, fracture generally initiates near the interface edge, or just from the interface edge point. In this paper, an edge crack near the interface, which can be considered as being induced by the edge singularity and satisfying two conditions, is analyzed theoretically, based on the singular stress field near the interface edge and the superposition principle. It is found that the stress intensity factor can be expressed by the stress intensity coefficient of the edge singular stress field, the crack length, the distance between the interface and the crack, as well as the material combination. Boundary element method analysis is also carried out. It is found that the theoretical result coincides well with the numerical result when the crack length is small. Therefore, the theoretical representation obtained by this study can be used to simply evaluate the stress intensity factor of an edge singularity induced crack for this case. However, when the crack length becomes larger than a certain value, a significant difference appears, especially for the case with large edge singularity.     

Stress intensity factors for an interface crack along an elliptical inclusion

The problem of a crack along the interface of an elliptical elastic inclusion embedded in an infinite plate subjected to uniform stresses at infinity is analyzed by the body force method. The crack tip stress intensity factors are calculated for various inclusion geometries and material combinations. Based on numerical results, the effect of the inclusion geometry on the stress intensity factors is investigated. It is found that for small interface cracks the stress intensity factors are mainly determined by the stresses, occurring at the crack center point before the crack initiation, and interface curvature radius alone.     

Stress intensity factors for an ARC crack in a rotating disc

Numerical solutions are obtained to the problem of an arc crack in a rotating disc. Two boundary element methods are used, one dependent on the problem symmetry and the other capable of solving rotational problems with quite general boundaries. Good agreement is obtained between the two methods, and the results cast some doubt on the validity of published values.     

Stress intensity factors for two-dimensional crack problems using constrained finite elements

Two-dimensional crack problems, in common with other elliptic problems containing a boundary singularity, may be solved efficiently with the aid of a constrained finite element. The singularity is surrounded by a superelement containing a refined mesh whose interior nodal values are constrained to agree with the first few terms of the known expansion for the solution. The superelement conforms with linear or bilinear elements, and may thus be included in standard finite element programs. The calculation yields the expansion coefficients directly, and the method has been applied to determine stress intensity factors for a variety of two-dimensional configurations, including mixed-mode. The results are in excellent agreement with those obtained by other methods.

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Résumé Les problèmes de fissures à deux dimensions ont en commun avec d'autres problèmes elliptiques comportant une singularisation de frontière, qu'ils peuvent être solutionnés de manière efficace à l'aide d'éléments finis sous sollicitations.Pour ce faire, on englobe la singularité dans un élément comportant lui-même un maillage fin dont les noeuds sont placés sous contrainte de manière à satisfaire aux premiers termes du développement en série de la solution. L'élément d'enrobage est compatible avec les éléments linéaires ou bilinéaires utilisés par ailleurs, et peut donc être intégré dans des programmes standard d'analyse par éléments finis.Les calculs permettent de déduire directement les coefficents du développement en série, et la méthode a été appliquée avec succès à la détermination des facteurs d'intensité de contrainte dans une large gamme de configurations bidimensionelles, y compris afférentes à des modes de rupture combinés. Les résultats sont en excellent accord avec ceux que fournissent d'autres méthodes de calcul.

     

Stress intensity factors for a crack near broken/intact stiffener

On leave from EMBRAER S.A., Brazil     

Stress intensity factors in a hollow cylinder containing a radial crack

In this paper an exact formulation of the plane elasticity problem for a hollow cylinder or a disk containing a radial crack is given. The crack may be an external edge crack, an internal edge crack, or an embedded crack. It is assumed that on the crack surfaces the shear traction is zero and the normal traction is an arbitrary function ofr. For various crack geometries and radius ratios, the numerical results are obtained for a uniform crack surface pressure, for a uniform pressure acting on the inside wall of the cylinder, and for a rotating disk.

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Résumé Dans le mémoire, on donne une formulation exacte du problème de l'élasticité plane d'un cyclindre creux ou d'un disque comportant une fissure radiale. La fissure peut être une fissure externe de bord, une fissure interne de bord ou une fissure noyée. On suppose que les surfaces de la fissure sont soumises à une contrainte de cisaillement nulle et à une contrainte normale suivant une fonction arbitraire der. On obtient, pour diverses géométries de fissure et divers rapports de rayon, les résultats numériques dans le cas d'une pression uniforme sur la surface de la fissure, dans le cas d'une pression uniforme agissant sur la paroi interne du cylindre et dans le cas d'un disque en rotation.

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This work was supported by the Department of Transportation under the Contract DOT-RC-82007, by NASA-Langley under the Grant NGR-007-011, and by NSF under the Grant ENG. 78-09737.     

Stress intensity factors for an inclined edge crack in a semiplane

Mode I and II Stress Intensity Factors under uniform general biaxial loadings were derived for an inclined edge crack in a semiplane. By interpolating Finite Element results in the angular range [0°÷80°], analytical expressions were obtained for both K_I and K_II with an accuracy better than 1%. Influence coefficients were defined in the crack reference frame thus highlighting the coupling effects between Modes I and II due to the loss of symmetry when the crack is not normal to the surface.     

Stress intensity factors and crack extension in a cracked pressurised cylinder

This paper considers the plane elastic problem corresponding to single or multiple radial cracks emanating from the internal boundary of a circular ring, under uniform external tension and internal pressure. The stress intensity factors are calculated by using the dual boundary element method with the J-integral technique. Accurate data are found for varying crack depths over a representative range of wall ratios for fracture mechanics applications to pressurised circular cylinders. The interaction of multiple cracks and crack extension are investigated in the case of an internal pressure loading condition. The analysis shows that, for a multi-cracked pressurised cylinder, it is sufficient to calculate the stress intensity of the main crack in isolation for the purposes of safety assessment.     

Analysis of crack tip plasticity for microstructurally small cracks using crystal plasticity theory

Crack tip plastic zone sizes and crack tip opening displacements (CTOD) for stationary microstructurally small cracks are calculated using the finite element method. To simulate the plastic deformation occurring at the crack tip, a two-dimensional small strain constitutive relationship from single crystal plasticity theory is implemented in the finite element code ANSYS as a user-defined plasticity subroutine. Small cracks are modeled in both single grains and multiple grains, and different crystallographic conditions are considered. The computed plastic zone sizes and CTOD are compared with those found using conventional isotropic plasticity theory, and significant differences are observed.     

Stress intensity factors of an inclined elliptical crack near a bimaterial interface

In this paper the stress intensity factors are discussed for an inclined elliptical crack near a bimaterial interface. The solution utilizes the body force method and requires Green’s functions for perfectly bonded semi-infinite bodies. The formulation leads to a system of hypersingular integral equation whose unknowns are three modes of crack opening displacements. 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 stress intensity factors along the crack front accurately. Distributions of stress intensity factors are presented in tables and figures with varying the shape of crack, distance from the interface, and elastic modulus ratio. It is found that the inclined crack can be evaluated by the models of vertical and parallel cracks within the error of 24% even for the cracks very close to the interface.     

Stress intensity factors of a twisted round bar with a circumferential crack

International Journal of Fracture -     

Stress intensity factors for crack tip shielding or anti-shielding by impurity atoms

The average value of the crack tip stress intensity factor produced by a row of impurity atoms is calculated in this paper. The row of impurity atoms lies parallel to the crack front and is situated at an arbitrary position about a crack. The impurity atom produced mode I shielding/antishielding stress intensity factor L _iI for a row of impurity atoms very close to the crack tip is given by the expression: 295-1 where 2a is the crack length, a ^* is either the atomic radius of the host atoms (for substitutional impurities) or the radius of the vacant interstitial site (for interstitial impurities), 295-2 and 295-3 where G is the shear modulus, c is the fraction of impurity atoms in the impurity atom row and is the misfit parameter of the impurity atoms, r ₂ is the distance from the crack tip, and 295-4 is the angle the radius r ₂ makes with the crack plane.

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Résumé On calcule dans ce travail la valeur moyenne du facteur d'intensité de contraintes occasionné par une rangée d'atomes étrangers, située parallèlement à un front the fissure, et en une position arbitraire par rapport à la fissure.L'atome intersticiel ou de substitution génère une facteur d'intensité de contrainte de mode I, qui interfère sur une rangée d'atomes étrangers très proche de l'extrémité de la fissure, selon une expression ou interviennent la longueur de la fissure, le rayon atomique des atomes donnant lieu à une substitution ou à une insertion d'atomes étrangers, le module de cisaillement, la fraction d'atomes étrangers présents sur une rangée, le paramètre de désaxement des atomes étrangers, la distance de la rangée par rapport à l'extrémité de la fissure, et l'angle qui caractérise cette distance par rapport au plan de la fissure.

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This research has been performed under the auspices of the U.S. Department of Energy.     

Stress intensity factors and crack propagation in a single crystal nickel-based superalloy

A three-dimensional finite element method was used to calculate the stress intensity factors for corner cracked specimens of a single crystal nickel-based superalloy. The anisotropic material properties and inclinations of the cracks were shown to have significant effects on the stress intensities. Then the two-dimensional resolved shear stress approach for predicting the crack planes and crack growth directions in single crystals was extended to the three-dimensional case. Using this approach, the fatigue crack growth behaviour in single crystal corner cracked specimens could be explained.     

Stress intensity factors for a crack in two intersecting uniformly stressed sheets

A model is considered for a crack growing simultaneously in the stiffener and the main sheet of a panel in which the stiffener is continuously attached. Stress intensity factors are determined for various ratios in the stiffnesses of the sheet and the stiffener. The panel is modelled with two uniformly stressed mutually perpendicular infinite sheets each containing a crack perpendicular to and bisected by the line of intersection of the sheets. Compatibility of displacements is maintained along the line of intersection of the sheets and the problem is reduced to the solution of a singular integral equation.