A crack opening displacement approach to crack patching

The results of a numerical investigation into crack patching indicate that a modified form of the crack opening displacement approach may be useful in estimating the effect that fibre composite patches have on cracks in thin sheets.     

A new expression for crack opening stress determined based on maximum crack opening displacement under tension–compression cyclic loading

The maximum crack opening displacement is introduced to investigate the effect of compressive loads on crack opening stress in tension–compression loading cycles. Based on elastic–plastic finite element analysis of centre cracked finite plate and accounting for the effects of crack geometry size, Young's modulus, yield stress and strain hardening, the explicit expression of crack opening stress versus maximum crack opening displacement is presented. This model considers the effect of compressive loads on crack opening stress and avoids adopting fracture parameters around crack tip. Besides, it could be applied in a wide range of materials and load conditions. Further studies show that experimental results of da/dN ? ΔK curves with negative stress ratios could be condensed to a single curve using this crack opening stress model.     

A new method of crack-tip opening displacement determined based on maximum crack opening displacement

In this paper a new method is presented to determine the crack-tip opening displacement (CTOD) for the center cracked plate with uniaxial uniform tension load. The maximum crack opening displacement (MCOD) is adopted to estimate CTOD. Based on the series of calculation results by elastic–plastic finite element simulation, an explicit function expression for the CTOD versus MCOD is determined, which enables to consider the influence effects of crack geometries, plate sizes, applied loads, plane state and material properties. Hence, the presented method of CTOD determined by MCOD is suitable to any center crack finite plate of any material under uniaxial tension.     

On solutions of crack surface opening displacement of a penny-shaped crack in an elastic cylinder subject to tensile loading

A simple analytical expression for the surface displacement of a penny-shaped crack in an elastic cylinder subject to remote tensile loading is proposed based on a modified shear-lag model. The results are then compared with the dilute solution [1] and those of finite element calculation. It is found that the present work gives much better result than the dilute model.     

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.     

Variation of stress intensity factor and crack opening displacement of 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 surface crack. Stress field induced by body force doublet in a semi infinite body is used as a fundamental solution. Then the problem is formulated as an integral equation with a singularity of the form of r ^-3. In solving the integral equations, the unknown functions of body force densities are approximated by the product of a polynomial and a fundamental density function; that is, the exact density distribution to make an elliptical crack in an infinite body. The calculation shows that the present method gives the smooth variation of stress intensity factors along the crack front and crack opening displacement along the crack surface for various aspect ratios and Poisson's ratio. The present method gives rapidly converging numerical results and highly satisfactory boundary conditions throughout the crack boundary.     

Relationships between crack opening displacement,alloy variables,and crack detection sensitivity

Alloy grain size is known to influence both the propagation path and the closure stress of surface fatigue cracks in many alloys. The general trend is for the path to be more tortuous and the closure stress to be larger, the larger the grain size. By use of Ti Al-4V and Al 7075-T6, the effects of grain size on the nondestructive detection of surface cracks which might arise from closure stress and path irregularity variables were evaluated. Titanium specimens were inspected using an acoustic harmonic generation technique, and it was discovered that the major source of harmonic signals was grain sized crystallographic cracks. Harmonic signals were larger during fatigue in an 8-µm compared to a 4-µm grain sized alloy, as there were more grain sized cracks in the large grain material. Crack closure was found to be extremely important in determining the reflected acoustic amplitude obtained in inspecting small (100–1000 µm) cracks in Al 7075-T6 using a critical angle technique. Average received amplitudes were an order of magnitude smaller for cracks at zero load than for those opened by a tensile stress. The scatter in the reflected amplitude was also large, apparently as the result of variations in the degree of the closure from crack to crack. For the 7075 material, the important effect of larger grain size was to increase the irregularity of the crack path, making the small cracks more visible acoustically at azimuthal angles not normal to the crack plane.     

Comparison of methods for crack tip opening displacement toughness determination

The crack tip opening displacement (CTOD) initiation toughness has been obtained by different methods in Cr and Cr-Mo steels at 30, 200 and 400 C. The crack tip stretching and grain deformation has been investigated by scanning electron microscope and optical microscopic studies and by microhardness measurements. The resistance curve approach is used employing the average and the maximum crack growth and the initiation toughness determined are with respect to 0.2 mm crack growth ( ^0.2), the stretched zone width (SZW) and also using a blunting line approach. In addition, an initiation toughness using stretched zone depth (SZD) measurement is also obtained. The various initiation toughness values have been compared and an attempt has been made to identify the realistic plane strain CTOD toughness amongst the different values. The-CTOD relationship has also been investigated.     

The effect of shallow cracks on crack tip opening displacement

Further results given in the present paper confirm that shallow cracks have larger crack tip opening displacements at initiation than deep cracks. This difference in behaviour is shown to be principally caused by the different hydrostatic stresses existing at the tips of shallow and deep cracks. A new method based on lateral crack growth across the thickness is used in this work to measure crack tip opening displacements in specimens containing machined slots rather than fatigue pre-cracks. Justification and advantages of this method are discussed and compared to the conventional technique.     

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.

     

The stereophotogrammetric determination of the critical crack tip opening displacement

The methods to determine the critical crack tip opening displacement (COD_i) are discussed. Stretched zone regions are analyzed using the method of stereophotogrammetry with the scanning electron microscope. The COD_i is determined on eight sections near the centre of the specimen. The scatter of the individual COD_i-values is surprisingly small.     

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.     

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.     

On the compatibility between J-Integral and crack opening displacement

An investigation of the relationship between the resistances J_R and δ_R during crack growth in several medium strength steels is reported in this paper. The results show that we can find out some reasonable rules governing their relationship only after analysing the plastic components of the resistances J_P and δ_P. As can be seen from the tests, the J_P/δ_S?δ_P relationship is linear within the range of crack growth amount investigated and is probably affected by the material property and the specimen geometry. A comparison between P-V and P-Δ curves made by the plastic hinge model shows that the two kinds of records are essentially equivalent. Therefore, the compatibility between J-integral and COD is proved by extensive experiments.