Crack opening displacement and the rate of fatigue crack growth

Using a direct proportionality between the rate of fatigue crack growth and crack opening displacement above a threshold, it is shown that fatigue crack growth data for a wide variety of different materials can be accurately described in terms of the mechanical properties and two material constants; the constant of proportionality A and the threshold stress intensity factor K _th. Some 65 sets of data for tests at R 0 were analysed by computer and it is shown that the approach is valid to growth rates up to about 10^–4 in./cycle, i.e. until the onset of crack propagation by dimple formation. It is found that A can be related to the yield strain for crack growth in non-aggressive environments, and is increased by increasingly severe environments, while K _th is decreased. These changes provide a measure of the severity of the environment. Crack growth rate in non-aggressive environments is shown to be independent of the yield stress and proportional to the strain intensity factor above the threshold. The tabulation of A and K _th values as a function of material, environment and loading conditions provides a systematic engineering approach to estimating rates of fatigue crack growth and in determining the residual lifetimes of flawed structures.

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Zusammenfassung Unter Zuhilfenahme einer direkten Proportionalität zwischen der Rißfortpflanzungsgeschwindigkeit von Ermudungsrissen und dem COD oberhalb eines gewissen Grenzwertes, konnte gezeigt werden, daß die Fortpflanzungsgeschwindigkeit von Ermüdungsrissen in verschiedenen Werkstoffen befriedigenderweise in Abhängigkeit von den mechanischen Eigenschaften der gegebenen Werkstoffe und von zwei Konstanten ausgedrückt werden kann. Diese beiden Konstanten sind ein Proportionalitätsfaktor A und ein Spannungsintensitatsfaktor K _th welcher einem kritischen Grenzwert entspricht.Die numerische Auswertung der Ergebnisse von rund 65 Versuchsreihen bei R0 ermöglichte es zu zeigen daß these Annäherung für Fortpflanzungsgeschwindigkeiten bis zu rund 10^–4 Zoll pro Lastspiel anwendbar ist, d.h. für einen Geschwindigkeitsbereich in dem die Rißfortpflanzung mit der Bildung von Schuppen gekoppelt ist.Außerdem fand man, daß im Falle wo die Fortpflanzungsgeschwindkeit in einer nich agressiven Umwelt stattfindet, die Konstante A mit der Elastizitätsgrenze in Zusammenhang gebracht werden kann und, daß diese Konstante mit der Aggresivität der Umgebung ansteigt, während der Wert der Konstanten K _th abfällt. Diese Veränderungen ermöglichen es die Aggressivität der Umwelt abzuschätzen.Es wird weiter gezeigt, daß in einer nicht aggressiven Umwelt die Fortpflanzungsgeschwindigkeit von der Elastizitätsgrenze unabhängig und dem Intensitätsfaktor der über der kritischen Grenze liegenden Spannungen proportional ist.Durch das Aufstellen von Tabellen der Werte von A und K_th in Abhängigkeit vom Werkstoff, der Umwelt und der Beanspruchungsbedingungen, verfügt man über ein praktisches und systematisches Hilfsmittel zur Abschätzung der Fortpflanzungsgeschwindigkeiten von Ermüdungsrissen und der noch verbleibende Lebensdauer von gerissenen Bauelementen.

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Résumé En recourant à une proportionlialité directe entre la vitesse de propagation des fissures de fatigue et le COD d'une valeur supérieure à un certain seuil, on démontre que les données de vitesse de propagation des fissures de fatigue relatives à des matériaux différents peuvent être exprimées de manière satisfaisante en fonction des propriétés mécaniques de ces matériaux et de deux constantes: une constante de proportionnalité A et can facteur d'intensité de contraintes K _th correspondant à un seuil critique.L'analyse numérique de quelques 65 séries de données d'essais de fatigue à R0 a permis de montrer que cette approche est applicable à des vitesses de propagation allant jusqu'à 10^–4 pouces/cycle environ, c'est-à-dire une gamme de vitesses où la propagation de fissures est associée à la formation de cupules.On trouve que la constante A pent être mise en relation avec la limite élastique dans le cas où la propagation s'effectue en milieu non agressif, et que cette constante s'accroit avec l'agressivité du milieu tandis que décroît la constante K _th. Ces modifications permettent d'apprécier la sévérité dun milieu ambiant.Dans un milieu non agressif, on montre que la vitesse de propagation est indépendante de la limite élastique, et qu'elle est proportionnelle au facteur d'intensité des contraintes excédant le seuil critique.En présentant les valeurs de A et de K _th sous la forme de tables en fonction du matériau du milieu ambiant et des conditions de sollicitation, on dispose d'une approche pratique et systématique permettant d'estimer les vitesses de propagation des fissures de fatigue et de déterminer l'endurance résiduelle d'éléments de construction fissurés.

     

Elastic–plastic fatigue crack growth in 18G2A steel under proportional bending with torsion loading

The paper presents the results of fatigue crack growth on low‐alloy 18G2A steel under proportional bending with torsion loading. Specimens with square sections and a stress concentration in the form of external one‐sided sharp notch were used. The tests were performed under the stress ratios R=?1, ?0.5 and 0. The test results were described by the ΔJ‐integral range and compared with the ΔK stress intensity factor range. It has been found that there is a good agreement between the test results and the model of crack growth rate, which includes the ΔJ‐integral range.     

A crack opening stress equation for fatigue crack growth

International Journal of Fracture -     

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.

     

Cyclic AE count rate and crack growth rate under low cycle fatigue fracture loading

In the low cycle fatigue fracture testing with KS (or JIS) SS41 steel, crack growth rate, AE count rate and J-integral range are measured to get empirical relationships between crack growth rate and J-integral range, AE count rate and J-integral range as well as AE count rate and crack growth rate. All the relationships are shown to be linear on the log—log graphs. It is also shown that the linear relationships can be formulated by using Dunegan's assumption and elastic-plastic fracture mechanics along with the well-known relationships of crack growth rate and J-integral range. It is concluded that the differences between experimental and theoretical values are due to the problem of Dunegan's assumption.     

A relative crack opening time correlation for corrosion fatigue crack growth in offshore structures

A considerable amount of research has been carried out on the prediction of mean stress effects on fatigue crack growth in structures. Newer types of structure are now being developed for use in highly dynamic, harsh marine environments, particularly for renewable energy applications. Therefore, the extent to which mean stresses can enhance corrosion‐assisted fatigue damage in these structures needs to be better understood. A new theoretical model that accounts for mean stress effects on corrosion fatigue crack growth is proposed. The model is developed based on the relative crack opening period per fatigue cycle and by considering only the damaging portion of the stress cycle. The baseline data for the modelling exercise are the data obtained at a stress ratio of 0.1 in air and seawater tests conducted on compact tension specimens. The model is validated by comparison with experimental data and with other fatigue crack propagation models. The proposed model correlates fairly well with experimental data and the other models examined.     

The prediction of fatigue crack growth under flight-by-flight loading

A large number of crack growth computations were made for flight-by-flight loading using several varieties of a fighter spectrum. Various retardation models were applied. With proper adjustment of the retardation model the experimental data could be closely reproduced in a calculation. It is concluded that satisfactory crack growth predictions can be made. The application of safety factors to predictions is discussed.     

Plasticity and the crack opening displacement in shells

The plastic deformations and the crack opening displacement, , in cylindrical shells with an axial or circumferential crack and spherical shells with a meridional crack are considered. It is assumed that outside the perturbation zone of the crack the shell is subjected to uniform membrane loads perpendicular to the crack. The plastic strip model is used to calculate the plastic zone size. The crack opening displacement is calculated as the crack surface displacement at the crack tips by using the conventional superposition technique. In cylindrical shells with an axial crack the crack surface displacement perpendicular to the shell surface (i.e., the bulging) is also evaluated. The results are applied to a set of existing experimental data on the fracture of cylindrical shells. The tentative conclusion is that in dealing with the fracture of thin-walled structures, among various fracture models =constant appears to be the most satisfactory criterion.

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Zusammenfassung Der Bericht handelt über die plastische Verformung und die Rißausbreitung in einer zylindrischen Hülle mit einem Axial- oder einem Peripherieriß und in Kugelhüllen mit Meridionalrissen. Es wird vorausgesetzt, daß die Hülle außer-halb der gestörten Rißzone gleichmäßigen Membranspannungen unterworfen ist. Die Abmessungen der plastischen Zone werden an Hand des Dugdale-Modells bestimmt. Die Rißausweitung wird durch das Ausbreiten der Rißoberfläche an der Rißspitze gekennzeichnet und auf Grund des Überfagerungsverfahrens berechnet.In zylindrischen Hüllen mit einem Axialriß wird außerdem die Rißoberflächenausweitung senkrecht zur Hüllen-oberfläche (Schwellen) ermittelt. Die Rechenergebnisse werden auf sine Reihe Experimentalwerte für den Bruch von zylindrischen Hüllen angewandt. Man zeigt zur Schlußfolgerung, daß für die Behandlung von Brüchen in dünnwandigen Konstruktionen der Ausdruck =konstant anscheinend das befriedigendste der verschiedenen möglichen Bruchmodelle ergibt.

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Résumé Le mémoire traite des déformations plastiques et du déplacement d'ouverture d'un défaut, , dans des enveloppes cylindriques possédant une fissure axiale ou circonférencielle, et dans des enveloppes sphériques.On suppose que l'enveloppe est sujette à des contraintes uniformes de membrane, perpendiculaires à la fissure, en toute zone non perturbée par celle-ci.La dimension de la zone plastifiée est déterminée en utilisant le modèle de Dugdale. Le COD est calculé en le considérant comme le déplacement des surfaces de la fissure à l'extrémité de cells-ci, et en recourant à la technique classique de superposition.Dans le cas d'enveloppes sphériques, contenant une fissure axiale, on a également évalué le déplacement de la surface de la fissure dans le sens perpendiculaire à la surface de denveloppe (ballonnement). Les résultats de l'analyse sont appliqués à une série de résultats expérimentaux sur la rupture d'enveloppes cylindriques.On tend à conclure que, dans le cas de constructions en parois minces, le critère qui semble le plus satisfaisant est, parmi divers modéles de rupture, celui exprimant que est une constante.

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Symbols 2a: a _p + a + p crack length - A _m, A _b, B _ij: c ₁ = N ₀ a _p/(hE) c _N + Na _p/(hE) c _M = 6Ma _p/(Eh ²) c _w = ² RN ₀/(2Eh) d = a_y/E stress intensity factor ratios - E, v elastic constants - F stress function - h shell thickness - k ^m, k ^b: k = k ^m + k ^b membrane and bending components of the stress intensity factor - k _p plasticity corrected stress intensity factor - N _ij, M _ij, (i, j) = (x, y, z) stress and moment resultants - N ₀ membrane load perpendicular to the crack - N, M tractions in the plastic zone - p the plastic zone size - R meam radius of the shell - u, v, w x, y, z-components of the displacement vector - u ₁, u ₂ auxiliary functions - x, y, z: = a/a _p dimensionless coordinates - crack opening displacement - = [12(1 – ²)]^1/4 a (Rh)^1/2 shell parameter - _p = [12(1 – ²)]^1/4 a _p/(Rh)^1/2 _Y yield strength This work was supported by the National Aeronautics and Space Administration under the Grant NGR 39-007-011.     

An assessment of the crack tip opening displacement criterion for predicting creep crack growth

From a set of finite element (FE) simulations of creep crack growth in compact tension specimens, the critical value of the crack tip opening displacement, CTOD, for creep crack growth has been generated for a Ni-base superalloy (Waspaloy) at 700°C. It was found that the critical value is independent of the initial crack length, amount of previous creep crack growth and the load level. Hence, the CTOD seems likely to be a viable criterion for use in creep crack growth rate analysis. Good agreement was also obtained between the experimental test results and FE predictions of the creep crack growth with time and between the crack growth rate, da/dt, versus the C ^* parameter based on load-line displacement rate.     

Description of the kinetics of growth of a fatigue crack on the basis of the criterion of current crack tip opening displacement

We suggest a microprocessor-based data-processing and measuring system and a special device aimed at the determination of current values of the crack tip opening displacement. They are used to establish current values of the crack tip opening displacement at working frequencies of loading of the specimen and describe the kinetics of fatigue crack growth. A decrease in the loading frequency of the specimen from 15 to 0.1 Hz in the course of measuring the current values of the crack tip opening displacement does not affect the reliability of determination of the characteristics of cyclic crack-growth resistance. The reliability of the results is affected only by the inertia of the mass of the gauge case. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 60–67, July–August, 1998.     

Mixed-mode fatigue crack growth under biaxial loading

Studies on crack growth in a panel with an inclined crack subjected to biaxial tensile fatigue loading are presented. The strain energy density factor approach is used to characterize the fatigue crack growth. The crack growth trajectory as a function of the initial crack angle and the biaxiality ratio is also predicted. The analysis is applied to 7075-T6 aluminium alloy to predict the dependence of crack growth rate on the crack angle. The effect of crack angle on the cyclic life of the component and on the cyclic life ratio is presented and discussed.     

Predicting fatigue crack growth under irregular loading

We describe a model for predicting fatigue crack growth (FCG) with the presence in the loading spectrum of peak and block tensile overloads. The model is based on account for the following factors influencing crack growth retardation: change of the quantity K_op as a consequence of the induction of a system of residual compressive stresses at the crack tip and increase of the degree of crack closure that is due to plastic deformation of the material in the wake of the tip of the growing crack; plastic blunting of the crack tip. We propose a technique for quantitative prediction of the residual crack tip opening (radius of the blunted tip) after a peak tensile overload. Experimental verification of the proposed FCG model with differing applied load irregularity showed that the model may serve as the basis of a method for predicting the service life of cracked structural members operating in irregular loading regimes.Translated from Problemy Prochnosti, No. 8, pp. 3–16, August, 1994.     

Finite element analysis of crack mouth opening displacement compliance in crack length evaluation for clamped single edge tension specimens

In the unloading compliance method developed for clamped single edge tension (SE(T)) specimens, six crack mouth opening displacement (CMOD)‐based compliance equations (i.e. a/W = f(BCE′)) were proposed for the crack length evaluation without clearly clarifying the corresponding predictive accuracies. In addition, the effective elastic modulus (E_e) that reflects the actual state of stress should also be introduced in the crack length evaluation for SE(T) specimens, because the actual state of stress in the remaining ligament of the test specimen is neither plane stress (E) nor plane strain (E′). In this study, two‐dimensional (2D) plane strain and three‐dimensional (3D) finite element analyses (FEAs) are carried out to investigate predictive accuracies of the six compliance equations. In both 2D and 3D FEA, specimens with a wide range of crack lengths and geometric configurations are included. For a given specimen, the value of E_e that presents the equivalent stress state in the remaining ligament is calculated on the basis of 3D FEA data. A set of formulae for the clamped SE(T) specimen is proposed that allows to evaluate E_e from the corresponding CMOD compliance. This approach is verified using numerical data. The observations of the numerical verification suggest that the use of E_e instead of E or E′ in CMOD‐based compliance equations markedly improves the accuracy of the predicted crack length for clamped SE(T) specimens.