On stress field near a stationary crack tip

It is well known that the stress and elastic-plastic deformation fields near a crack tip have important roles in the corresponding fracture process. For elastic-perfectly-plastic solids, different solutions are given in the literature. In this work we examine and compare several of these solutions for Mode I (tension), Mode II (shear), and mixed Modes I and II loading conditions in plane strain. By consideration of the dynamic solution, it is shown that the assumption that the material is yielding all around a crack tip may not be reasonable in all cases. By admitting the existence of some elastic sectors, we obtain continuous stress fields even for mixed Modes I and II.     

Creep crack growth modeling and near tip stress fields

The problem of near tip stress fields in a cracked body subjected to Mode I loading at elevated temperatures is studied. Specifically, the superalloy, IN 718, is examined in the standard compact tension specimen geometry. The simulation is at 650°C. The specimen is assumed to be under dead load conditions. For a stationary crack, the near tip stress fields are calculated and compared with the asymptotic solutions available in the literature. While the results assuming small strains agree very well with the asymptotic solutions, the large strain analysis does not. The results indicate that both the amplitude and the asymptotic exponent are dependent on the applied load level which is in disagreement with the asymptotic predictions. In addition, the zone effected by creep deformation is larger when large strains are considered. An algorithm is developed and tested for the modeling of stable crack growth. Both convergence and stability are investigated. Explicit time integration is used for crack growth studies as it is demonstrated to be computationally more efficient. The algorithm is employed to study the near tip stress fields for a growing crack. The near tip stress fields for a growing crack (with constant velocity) are generated using the developed algorithm. The results demonstrate that the asymptotic behavior of the stress field is load dependent. Comparison is made with the limited analyses available. Recommendations for future research are discussed.     

Plane stress dynamic plastic field near a propagating crack tip

In this paper the asymptotic solution to the plane stress dynamic plastic field surrounding a propagating crack tip is given. The perfectly plastic model and Mises yield condition as well as J₂ flow theory are adopted. The force of inertia is considered in the equations of motion. The asymptotic expansions of displacements, strains and stresses are given and solved for the dominant terms. The results show that strain possesses ln (A/r) singularity at the crack tip. Finally, the stress distribution surrounding the crack tip are given numerically.

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Résumé On fournit dans cette étude une solution asymptotique pour le champ de déformations pastiques dynamiques sous contraintes planes qui entoure l'extrémité d'une fissure au cours de sa propagation. On adopte comme hypothèse un modèle parfaitement plastique, la conditions de passage en plasticité de von Mises et la théore de l'écoulement J₂. Dans les équations de mouvement, on considère la force d'inertie. Les développements asymptotiques des déplacements, des déformations et des contraintes sont fournis et résolus pour leur termes principaux. Les résultats montrent qu'à l'extrémité d'une fissure, la déformation présente une singularité de caractère ln A/Y. Enfin, on fournit une expression numérique de la distribution des contraintes dans la zone enrobant l'extrémité de la fissure.

     

A near optimal crack tip mesh

The near optimal crack tip mesh obtained by the authors in a previous paper is tested for a set of problems. The accuracy is maintained within the desired values. The direct displacement extrapolation method for SIF estimation is compared to the virtual crack extension. The methodology for crack tip mesh design discussed previously is validated.     

Nonlocal elastic damage near crack tip

A constitutive modeling for nonlocal elastic damage near crack tip is proposed. A calculation method for nonlocal elastic damage is introduced and the computational results for stress and damage are given by means of finite element method.     

The stress field near the blunt crack tip and the fracture criterion

The asymptotic expansion solution containing two terms for the stress field near the blunt crack tip is obtained. It is proposed that the slit be divided into the ideal crack, blunt crack I, blunt crack II and the notch in accordance with the geometrical structure of the slit tip. Whether the blunt crack can be considered as the ideal crack will depend mainly on the following three factors: $\text{√}\text{2R}{}_0\text{C}$, $\text{√}\text{R}{}_0\text{r}{}_{\mathrm{c}}$ and the profile of the crack. In this paper, the influence of the crack tip radius on the fracture criterion is studied and it is shown that the classical strength theories belong to the unconditional extremum criteria while the S criterion, etc. in fracture mechanics belong to the conditional extremum criteria. A modified maximum tension stress theory is developed, in which the fracture theories of the crack and the notch can be roughly unified.     

Temperature fields near a running crack tip

Near a running crack tip, the plastic work rate is high. According to the theory of irreversible thermodynamics, the plastic work will be almost completely converted into heat which may lead to high temperature rise at the running crack tip. The plastic zone is regarded as the zone of the heat source, and the plastic work rate as the strength of the heat source. In this paper, the plastic work rate is derived from the solution of stress and strain fields obtained by Chitaley and McClintock[1] for a steady state crack growth under anti-plane shear in an elastic perfectly-plastic material. The dependence of the thermal conductivity on temperature has been considered and a non-linear model for temperature fields has been proposed. The numerical results for glass have been given and compared with other papers.     

Semi-empirical crack tip analysis

Experimentally observed crack opening displacements are employed as the solution of the multiple crack interaction problem. Then the near and far fields are reconstructed analytically by means of the double layer potential technique. Evaluation of the effective stress intensity factor fesulting from the interaction of the main crack and its surrounding crazes in addition to the remotely applied load is presented as an illustrative example. It is shown that crazing (as well as microcracking) may constitute an alternative mechanism to Dugdale-Barenblatt models responsible for the cancellation of the singularity at the crack tip.

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Résumé Pour solutionner le problème d'interactions multiples des fissures, on utilise les COD observées expérimentalement. On reconstitue ensuite analytiquement les champs proche et lointain à l'aide de la technique du potentiel en deux couches. Comme exemple illustratif, on présente une évaluation du facteur effectif d'intensité de contraintes résultant de l'interaction d'une fissure principale avec les brisures qui l'entourent, ainsi que de la charge appliquée à distance. On montre que le phénomène de brisures-comme celui de microfissuration-constitue une alternative aux modèles de Dugdale-Barenblatt auxquels on doit la suppression de la singularité à l'extrémité de la fissure.

     

Residual stress induced crack tip constraint

This paper studies the effect of welding residual stresses on the near tip stress field in single edge notched bending and tensile specimens. A combined effect of mechanical stresses by the applied load and residual stress on the crack tip constraint is analyzed. Three initial residual stress distributions were considered. It has been shown that the crack tip stress field is strongly influenced by the residual stresses and a new parameter, R, is proposed to characterize the residual stress induced crack tip constraint. The results therefore suggest a three-parameter approach (CTOD, Q and R) to characterize the crack tip stress field in the presence of residual stress where CTOD sets the size scale over which large stresses and large strains develop, and the geometry constraint parameter Q and the new residual stress induced constraint parameter R control the actual crack tip constraint level. For the cases analyzed, R is in general positive, which indicates that residual stress can enhance the crack tip constraint. However, the results also indicate that the R decreases towards zero and the effect of residual stress on crack tip constraint can be neglected when a full plastic condition is approached in the specimen.     

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.

     

Large strain field near an interface crack tip

In this paper the elastostatic field near the tip of an interface crack between two materials is analyzed with the fully nonlinear theory. By dividing the crack tip field into narrowing sectors and an expanding sector, the asymptotic equations for the crack tip field are derived and solved. The singular characters of stress and strain near the crack tip are revealed. The crack opening shape is discussed for various cases. It is shown that when large deformation is taken into account the oscillatory singularity does not occur.     

The analysis of thermoelastic isopachic data from crack tip stress fields

A computer program—FACTUS (fracture analysis of crack tips using SPATE)—has been developed for the efficient analysis of thermoelastic data obtained from around a crack tip. The program is based on earlier work for the determination of stress intensity factors (SIFs), and also includes a novel solution procedure for the derivation of the non-singular stress term σ _{0 x} . The program has been used in the analysis of a series of large plate specimens with central or edge slots/cracks. The derived SIFs are compared with independent values. Issues, e.g. crack closure and the extent and effect of the plastic zone, are discussed.     

A Strip-Yield algorithm for the analysis of closure evaluation near the crack tip

“Plasticity-induced crack closure” phenomenon is the leading mechanism of different effects (R-ratio, overload retardation, … ) acting on crack growth rate in many metallic materials. Experimental tests are carried out to quantify the physical phenomenon, while Strip-Yield analytical models have been developed for predicting life of components. In the present work, an additional module to be applied to a Strip-Yield model is proposed in order to derive the strains near the crack tip. Particularly, the module is based on the Westergaard’s elastic complex potential. The presented algorithm allowed us to obtain the correlation between “local compliance” experimental results and the corresponding Strip-Yield analyses. This method can be taken as a semi-analytical procedure for calibrating the constraint factor, i.e., the most delicate parameter for Strip-Yield models.     

Optical analysis of crack tip stress fields: a comparative study

Four optical techniques for evaluating stress intensity factors in opaque specimens are described in outline, and compared for both an artificial crack and a fatigue crack. The results are compared to a standard solution for the geometry considered. All the techniques gave acceptable results over a range of stress levels and crack lengths. The methods of caustics and strain gauges were less good, whilst photoelasticity gave consistent results over a wide range of stress levels. Comments on the ease of application and the resource implications are also made in order to assist practitioners.     

On the elasticT-term of a main crack induced by near tip microcracks

In the expansion form of the stress field near a crack tip, the nonsingular and constant stress acting parallel to the crack plane is called the elasticT-term, which is very important in fracture analysis. The elasticT-term of a main crack induced by near tip microcracks is analyzed. The original problem considered consists of a main crack accompanied by near tip microcracks, which are loaded remotely by the first three terms of the crack tip stress field expansion parameterized by stress intensity factorsK _I ,K _II , and the nonsingular stress, i.e., theT-term,. With the principle of superposition, the problem can be reduced to a system of Fredholm integral equations which can be solved numerically. After obtaining the solution, the induced elasticT-term is evaluated. Several typical numerical examples are given and the results are shown in Figures, from which some useful discussion and conclusions are obtained.     

Microscale characterization of granular deformation near a crack tip

This paper presents a study of microscale plastic deformation at the crack tip and the effect of microstructure feature on the local deformation of aluminum specimen during fracture test. Three-point bending test of aluminum specimen was conducted inside a scanning electron microscopy (SEM) imaging system. The crack tip deformation was measured in situ utilizing SEM imaging capabilities and the digital image correlation (DIC) full-field deformation measurement technique. The microstructure feature at the crack tip was examined to understand its effect on the local deformation fields. Microscale pattern that was suitable for the DIC technique was generated on the specimen surface using sputter coating through a copper mesh before the fracture test. A series of SEM images of the specimen surface were acquired using in situ backscattered electronic imaging (BEI) mode during the test. The DIC technique was then applied to these SEM images to calculate the full-field deformation around the crack tip. The grain orientation map at the same location was obtained from electron backscattered diffraction (EBSD), which was superimposed on a DIC strain map to study the relationship between the microstructure feature and the evolution of plastic deformation at the crack tip. This approach enables to track the initiation and evolution of plastic deformation in grains adjacent to the crack tip. Furthermore, bifurcation of the crack due to intragranular and intergranular crack growth was observed. There was also localization of strain along a grain boundary ahead of and parallel to the crack after the maximum load was reached, which was a characteristic of Dugdale–Barenblatt strip-yield zone. Thus, it appears that there is a mixture of effects in the fracture process zone at the crack tip where the weaker aspects of the grain boundary controls the growth of the crack and the more ductile aspects of the grains themselves dissipate the energy and the corresponding strain level available for these processes through plastic work.