Size effect on creep energy dissipation during stable crack growth

Creep energy dissipation (CED) due to crack tip creep zone is determined under steady state conditions for centre cracked thin specimen of 1.25CrO.5Mo steel, with different widths and crack length to width ratios. The creep energy rate increases when the increment in crack length Δa increases and the slope increases with increase in aspect ratio a/W and decreases with increase in width W.     

Some properties of stable crack growth

A survey is given on the results of stable crack growth studies done at DFVLR. The tests were done under both cyclic and monotonic loads. Special attention was given to the effects of specimen size and material on crack growth. It was found that certain similarities exist between crack growth under cyclic and monotonic loads, respectively. Some simple calculations are compared with experimental results.     

Model analysis of stable crack growth

The results of a numerical model study of quasi-static crack growth are reported. This study made use of an elastic-plastic stringer sheet in which the stringers were broken in an appropriate manner to simulate crack growth. The stringer-sheet model was used to demonstrate the qualitative effect of material properties, specimen geometry, initial crack length, and type of applied load on crack growth. In addition, stringer sheet analogs were constructed for both the R-curve concept of linear elastic fracture mechanics and for a modification of this concept in which K is replaced by the J-integral. The modified R curve was called the R^p curve. Calculated stringer sheet R and R^p curves were not material properties, but were influenced by the extent of plastic yielding during stable crack growth. In general, however, the R^p curve provided a somewhat better correlation of crack growth than the R curve.     

On the calculation of plastic energy dissipation rate during stable crack growth

An approximate analysis is presented for the calculation of the plastic energy dissipation rate during stable growth of a centrally located through crack. in a sheet subjected to gradually increasing uniaxial tension normal to the crack plane.It is shown that the plastic energy dissipation rate is a function of the slow growth parameter (_p/)·(d/da)+(_p/a), where _p is the plastic enclave width in the plane of the crack and d/da is the rate of increase of the gross stress with respect to stable growth. At the point of instability this parameter becomes equal to _p/a. By assuming that this parameter is zero at the point of instability, a simple expression is obtained for the plastic energy dissipation rate.The analysis excludes the energy dissipation rate resulting from energy changes in an inner fracture zone in the immediate neighborhood of the crack tip in which it is presumed that fracture processes such as vacancy formation, crack initiation by dislocation pile ups etc., are active. The analysis is not applicable in this inner zone as deformation is not homogeneous.

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Zusammenfassung Es wurde eine mehr oder weniger genaue Analyse für die Kalkulation eines plastischen Energiezerstreuungsverhältnisses während stabilem Wachstums eines zentral lokalisierten Durchrißes in einer einfachen Anspannungsplatte präsentiert.Man zeigte, daß das plastische Energiezerstreuungsverhältnis eine Funktion des langsam wachsenden Parameters ist, wobei _p die eingeschlossene, plastische Weite in der Rißebene und d/da das Wachstumsverhältnis des Rohdruckes mit Rücksicht auf das stabile Wachstum, darstellt.Diese Analyse schließt das Energiezerstreuungsverhältnis vom Energiewechsel in einer inneren Bruchzone in der unmittelbaren Nähe der Rißspitze aus. Man nahm nicht an, daß these Veränderung homogen, sondern auf Vakanzen, Verschiebungen, etc. begründet sei.

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Résumé On présente une analyse approchée pour le calcul de la vitesse de dissipation de l'érgie de déformation plastique au cours de l'extension stable d'une fissure située au centre d'une tôle et traversant celle-ci de part en part, lorsque cette tôle est sujette à une contrainte uniaxiale, normale au plan de la fissure, et graduellement croissante.On montre que cette vitesse de dissipation est fonction du paramètre d'extension lente: où _p est la largeur de l'enclave de déformation plastique dans le plan de la fissure, et d/da le taux d'accroissement de la tension nominale par rapport à l'extension de la fissure dans des conditions stables.Au point d'instabilité, ce paramètre devient égal à _p/a, en supposant que sa valeur soit nulle, on aboutit à une expression simple de la vitesse de dissipation de 1'énergie de déformation plastique.L'analyse ne considère pas la vitesse de dissipation qui résulte de modifications de l'énergie au sein d'une zone de rupture interne, et située dans le voisinage immédiat de la pointe de la fissure. Dans cette zone, l'on présume que les processus de fissuration tels que la formation de lacunes, ou l'amorçage d'une fissure par empilements de dislocations, etc., sont particulièrement actifs. L'analyse n'est pas applicable dans cette zone interne, car les déformations n'y sont pas homogènes.

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Notations 2a Crack length - t Thickness of sheet - W Width of sheet - Gross stress applied at infinity normal to the crack plane - A, ₀, n Parameters in a Ramburg-Osgood representation of the octahedral shear stresss-hear strain curve - _oct Octahedral shear stress at any point near the crack tip - _oct Octahedral shear strain at any point near the crack tip. - _infoct ^supel Octahedral shear stress at any point near the crack tip given by elastic analysis - _oli Octahedral shear stress at yield - _oli/₀ - _infoct ^supel /_oli - \5m _oct/_oli - E Young's modulus - E _s Secant modulus - G Shear modulus - G _s Secant modulus of the octahedral stress-strain curve - u _p Plastic energy density at any point inside the plastic enclave at the crack tip - U _p Plastic energy dissipated in the plastic enclave per unit thickness - v Poisson's ratio - r, Polar co-ordinates with the crack tip as origin - K Stress intensity factor - _p Plastic enclave width given by Irwin's formula - f ₁, f ₂, f ₃ Functions of , defining the stress field near the crack tip - f _e f _inf1 ^sup2 –f ₁ f ₂+f _inf2 ^sup2 +3f _inf3 ^sup2 - _oct Limiting octahedral shear stress beyond which homogeneous plastic deformation is not possible since fracture processes such as vacancy formation etc., become active. - \5m_{0 infoct} ^supu /_oli - C (_p/)·(d/da)+(_p/da); slow growth parameter - B (G·A/_o1i)· ⁿ      

On retardation effects during fatigue crack growth under random overloads

A stochastic approach to fatigue crack growth under random overload sequences, superimposed on a base-line cyclic load, is described. The approach consists in presentation of the delay time due to the retardation effect associated with the overload peaks as a purely discontinuous Markov process. A numerical procedure based on the Kolmogarov-Feller integrodifferential equation is developed. Application of the model is illustrated by examples.     

Creep crack growth by grain boundary cavitation: crack tip fields and crack growth rates under transient conditions

Transient creep crack growth due to grain boundary cavitation, and under plane strain and small scale creep conditions, is investigated. Full account is taken of the finite geometry changes accompanying crack tip blunting and the material is characterized as an elastic-power law creeping solid with an additional contribution to the creep rate arising from a given density of cavitating grain boundary facets. All voids are assumed present from the outset, distributed on a given density of cavitating grain boundary facets. Our analyses show the competing effects of stress relaxation due to creep, diffusion and crack tip blunting, and the stress increase due to crack growth. Another outcome of our analyses is the crack growth rate under various conditions of loading and for various values of material properties and for various characterizations of the failure process. Prior to crack growth, Hutchinson-Rice-Rosengren type singular fields dominate over the crack tip region, outside of a finite strain zone that has dimensions of the order of the crack opening displacement. These singular fields scale with the path integral C(t), which to a good approximation decays as K _I ²/t, with t being the elapsed time since load application and K _Ithe imposed stress intensity factor. When the crack growth rate is faster than the growth rate of the creep zone, our finite element results show that Hui-Riedel singular fields dominate over the crack tip region and the magnitude of the Hui-Riedel fields scales with the crack growth rate. For a crack that grows more slowly than the creep zone, Hutchinson-Rice-Rosengren type fields dominate over the crack tip region. In these circumstances, the crack growth rate is found to scale as C(t) to a power. Regardless of which of the two singular fields dominates for the growing crack, finite strain effects are found to be significant over a size scale of the order of the crack opening displacement at crack growth initiation. The effect of increased mesh refinement is also considered and very little mesh dependence is found.

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Résumé On étudie la croissance d'une fissure en fluage transitoire, associée à la cavitation aux frontières des grains, sous des conditions d'état plan de déformation et de fluage à petite échelle. On tient compte des modifications finies de géométrie accompagnant l'arrondisement de l'extrémité de la fissure, et le matériau suit une loi de fluage elasto-parabolique, avec une contribution additionnelle à la vitesse de fluage venant d'une densité donnée de facettes de joints de grains comportant de la cavitation. On suppose que toutes les cavités sont présentes dès le début, et qu'elles sont distribuées selon une densité déterminée de ces facettes. L'analyse montre les effets rivaux d'une relaxation des contraintes associée au fluage, à la diffusion et à l'arrondisement des extrémités de fissure, et d'une augmentation de contraintes due à la croissance de fissure. Un autre résultat de l'analyse est l'établissement de la vitesse de croissance de la fissure sous diverses conditions de mise en charge, pour diverses valeurs des propriétés du matériau, et pour divers modes de caractérisation du processus de rupture. Avant croissance de la fissure, ce sont des champs singuliers de type Hutchinson-Rice-Rosengren (HDR) qui prédominent sur la région de l'extrémité de la fissure, à l'extérieur d'une zone de déformations finies dont la taille est de l'ordre de grandeur du COD. Ces champs singulier sont proportionnels à l'intégrale de parcours C(t) laquelle, avec une bonne approximation, s'atténue en fonction de K _I ²/t, où t est le temps qui s'est écoulé depuis la mise en charge et K _Ile facteur d'intensité de contraintes imposés. Lorsque la vitesse de croissance de la fissure dépasse la vitesse de croissance de la zone en fluage, les résultats de l'analyse par éléments finis montre que ce sont les champs singuliers de Hui-Riedel qui prédominent sur la zone de l'extrémité de la fissure, et que l'amplitude de ces champs est proportionnelle à la vitesse de croissance de la fissure. Pour une fissure qui croit moins vite que la vitesse de fluage, es champs de type HRR sont prédominants et on trouve que la vitesse de croissance de la fissure est proportionelle C(t) à une certaine puissance. Quel que soit le type de champs singulier qui détermine la croissance de la fissure, on trouve que les effets de déformation finies sont significatifs sur une échelle de dimension de l'ordre du COD à l'amorçage de la fissuration. On considère également l'effet d'un affinage plus important du réseau, et l'on trouve me très faible dépendance par rapport à ce paramètre.

     

Influence of residual stresses on stable crack growth

Abstract

The influence of residual stresses resulting from thermal shock and pressure loading on the initiation and stable growth of cracks in pressure vessels and pipes is considered and preliminary calculations have been made. The residual stresses of a precracked vessel of a 0·22Cr–0·75Ni–0·7Mo–Cr steel at an arbitrarily chosen temperature transient have been analysed using the finite element method. After reheating to normal operating temperature, the influence of the remaining residual stresses on the initiation of the assumed crack is considered. The results provide the initial conditions for stable crack growth analysis based on the J–integral method, which is implemented into the non–linear finite element program ADINA.

MST/27     

Mechanisms of stable crack growth in ductile polycarbonate

An extensive study of the phenomena appearing during crack propagation in ductile polycarbonate during the phase of stable crack growth (SCG) was undertaken. It has been shown that this phase starts at a critical loading step where a blunted crack was established and a damaged ligament in front of the crack tip developed and stabilized. This phase may be divided into two successive steps. The first is characterized by the step by step advancement of the blunted crack by exhausting respective parts of the damaged ligament so that the overall length of crack and ligament remains stationary. In this step the crack tip opening angle is increasing and attains its final value of the order of 55 degrees.This progressive crack growth, at the expense of the damaged ligament, is replaced by the proper steady crack growth where the crack advances steadily under almost constant external load and under constant CTOA up to a limit where catastrophic fracture occurs. The influence of the in-plane and transverse constraint factors was studied and important results concerning the mechanisms of fracture under predominating plane-stress or plane-strain conditions were established.     

Estimation of the effects of plasticity and resulting crack closure during small fatigue crack growth

On the basis of a plastic-strip model and the method of singular integral equations, a closed-form analytical solution of the problem of an elastic-plastic plate containing a rectilinear fatigue crack is considered. The solution is used for the prediction of fatigue growth of `mechanically-small' crack by accounting for reverse plastic yielding and plasticity-induced crack closure in the material. The main effects of these factors on the crack-growth rate are analyzed, and the predicted results are compared with experimental data on small fatigue-crack growth in a aluminum-lithium alloy 2091-T351 and Fe-3% Si alloy.     

A new finite-element technique for modelling stable crack growth

This paper presents a new technique for simulating crack extension in conjunction with the finite-element method. The technique uses spring and gap elements to control the motion of nodes on the crack plane. These elements are available in many proprietary finite-element codes, thereby obviating the need for a user-written finite-element code. Numerical results for stable crack growth are in excellent agreement with corresponding experiments. The technique is also applied to rapid fracture in ductile materials, as discussed in a companion paper.     

The criteria and stable form of nonthrough crack growth during cyclic loading. Report 1

Mechanisms controlling the development of surface and corner cracks during cyclic loading on samples of steel 15Kh2MFA having a variety of stress gradients has been studied. Kinetic diagrams of fatigue failure (KDFF) were plotted, and their association to the KDFF of standard samples was established. On the basis of a comparative analysis of the data showing the kinetic growth of surface and corner cracks, the possibility of using the local, mean, and effective stress intensity coefficient ranges as criteria for the growth of nonthrough cracks were examined. The conditions necessary for transferring the cyclic crack resistance characteristics obtained on standard samples to those obtained on structural elements with nonthrough cracks was established.Translated from Problemy Prochnosti, No. 8, pp. 3–10, August, 1990.     

Studies of stable crack growth under two independent loads

SEN specimens of two different materials were tested under different combinations of independently applied bending and tension. J _R-curves were determined and showed to be independent of the load combinations. Stability analysis using the tearing modulus concept showed to be possible but difficult.

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Résumé Des éprouvettes à entaille latérale simple en deux matériaux différents ont été soumises à essai sous diverses combinaisons de charges de flexion et de traction appliquées de manière indépendante. On a déterminé les courbes J _R et on a montré qu'elles étaient indépendantes de la combination de charge adoptée. Une analyse de stabilité recourant au concept de module d'arrachement s'est révélée possible encore que difficile à mettre en veuvre.

     

Numerical investigation on stable crack growth in plane stress

Large deformation finite element analysis has been carried out to investigate the stress-strain fields ahead of a growing crack for compact tension (a/W=0.5) and three-point bend (a/W=0.1 and 0.5) specimens under plane stress condition. The crack growth is controlled by the experimental J-integral resistance curves measured by Sun et al. The results indicate that the distributions of opening stress, equivalent stress and equivalent strain ahead of a growing crack are not sensitive to specimen geometry. For both stationary and growing cracks, similar distributions of opening stress and triaxiality can be found along the ligament. During stable crack growth, the crack- tip opening displacement (CTOD) resistance curve and the cohesive fracture energy in the fracture process zone are independent of specimen geometry and may be suitable criteria for characterizing stable crack growth in plane stress. This revised version was published online in August 2006 with corrections to the Cover Date.     

Inertial effects on fatigue crack growth

In this paper, a cohesive zone model is used to study the influence of inertial effects on crack growth considering cyclic loading in homogenous rate‐independent materials. Quasi‐static and dynamic solutions are compared in order to establish the conditions in which the inertial effects become important in the analysis. It is discussed how speed and frequency of the loading and specimen sizes modify crack growth characteristics. In general, an increase in the loading frequency leads to a higher propagation velocity. Very high loading frequencies may lead to the formation of microcracks ahead of the crack tip and may change the failure mode of the cracked structure from crack propagation to uniform debonding. This work shows that inertial effects are specially noticeable for frequencies in the kHz range. However, applied frequencies close to natural frequencies of the cracked specimen can give rise to strong inertial effects and then a substantial reduction of fatigue life for much lower frequencies. This work also shows that critical frequencies depend on the specimen size.     

A mathematical description of transient crack growth behaviour in glass

Transient crack growth behaviour resulting from time-dependent changes in crack-tip radius can occur near the fatigue limit. In the present work, mathematical expressions describing this transient behaviour are developed assuming that a dissolution reaction is responsible for changes in crack geometry. An elliptical crack is analysed because of its mathematical simplicity. The theoretical model slightly underestimates the extent of crack-tip blunting occurring below the fatigue limit. However, the predicted transient behaviour associated with the crack-tip sharpening processes which take place above the fatigue limit compares favourably with experimental data for glass.     

Constraint effect on the ductile crack growth resistance of circumferentially cracked pipes

A systematic study has been carried out by using 2D axisymmetric models to understand the ductile fracture behavior of pipes with internal and external circumferential cracks. Crack growth resistance curves have been computed using the complete Gurson model. Pipes with various diameter-to-thickness ratios, internal pressure, crack depths and material properties are analyzed. The results have been compared with those of corresponding SENT and standard SENB specimens. It clearly indicates that the SENT specimen is a good representation of circumferentially flawed pipes and an alternative to the conventional standard SENB specimen for the fracture mechanics testing in engineering critical assessment of pipes.     

A numerical analysis on stable crack growth under increasing load

A simple and flexible method of analysis on stable crack growth in ductile materials is presented. The analysis is based on an elastic-plastic finite element method to calculate the stress and displacement fields in the vicinity of a growing crack under monotonically increasing load. A special type of element known as a breakable element and a nodal force relaxation technique have been adopted in a usual elastic-plastic analysis to simulate stable crack growth. A new fracture criterion which is suitable for mixed mode fracture is also used. The computational scheme was verified by excellent correlation with some experimental results.

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Résumé On présente une méthode simple et flexible pour l'analyse de la croissance stable d'une fissure dans les matériaux ductiles. L'analyse est basée sur une méthode par éléments finis élasto-plastiques permettant de calculer les champs de contrainte et de déplacement au voisinage d'une fissure en croissance sous charges monotonique croissante. On a adopté un type spécial d'éléments, dénommé éléments fragmentables, et une technique de relaxation des forces nodales dans une analyse élasto-plastique habituelle, pour simuler la croissance stable d'une fissure. Le nouveau critère de rupture applicable à une rupture de mode mixte a également été utilisée; certains résultats expérimentaux ont permis de vérifier l'excellente corrélation du schéma de calcul proposé.