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.     

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 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.     

Effect of a variation in material properties on the crack tip opening displacement

This paper investigates the effect of a variation in material properties on the crack tip opening displacement, a parameter often used in the prediction of fatigue and fracture. This situation is typical when a component is subjected to a relatively slow temperature fluctuation or the material properties undergo direct changes, such as due to a phase transformation. An analytical strip‐yield model is developed using the small‐scale yielding assumption and theory of complex potentials. Four cases of crack tip plasticity behaviour are identified for the different combinations of parameters controlling the variation in material properties. Results of calculations over a wide range of material properties are presented and show a significant effect on the crack tip opening displacement. Finite element simulations are conducted to verify the analytical findings. The implications of the outcomes in relation to several practical situations are also discussed.     

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.     

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 fatigue crack growth rate and crack opening displacement in 18G2A-steel under tension

In the paper, the results of crack tip opening displacement (CTOD) and crack opening displacement (COD) in place of crack initiation as well as the fatigue crack growth rate in higher strength steel are presented. The investigation were carried out on flat specimens with central notch under constant amplitude tensile fatigue loading at stress ratio R = 0.2 and different value of the stress σ_max. The test results showed that with growth of crack length l grew values of the CTOD and COD. In the work, it was proposed calculation of the CTOD value on basis various dependence of plastic zone radius on crack tip.     

A crack opening stress equation for fatigue crack growth

International Journal of Fracture -     

The cyclicJ-integral as a criterion for fatigue crack growth

The definition of the cyclic J-integral is offered and its physical significance for fatigue crack growth is discussed using the Dugdale model on the assumption that the crack closure, cycle dependent creep deformation, and crack extension under cycling can be neglected. It is shown that the cyclic J-integral for small scale yielding is equivalent to theJ-integral for linear elastic crack independent of loading processes, while the value for large scale yielding varies with the loading processes. However, in both cases, the cyclicJ-integral remains constant during the reversal of loading under a constant stress range, if the first monotonic loading stage is excluded. In this situation, the cyclicJ-integral can be applied as a criterion for fatigue crack growth, since it is evaluated as a generalized force on dislocations to be moved or the energy flow rate to be dissipated to heat by the dislocation movements in an element just attached to the fatigued crack tip during one cycle of loading. It is suggested that the available experimental data of different materials for fatigue crack growth can be generalized to a unified formulation on the basis of the energy criterion. It is also deduced that the threshold J corresponding to K _th should be larger than 4 where is the surface energy of the material. Finally the operational definition of the cyclicJ-integral on single loadversus displacement curves is given for center cracked plate with wide uncracked ligaments in tension.

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Résumé On présente la définition de l'intégrale J cyclique et sa signification physique dans le cas d'une croissance de fissure de fatigue est discutée en utilisant le modèle de Dugdale et l'hypothèse que la fermeture de la fissure, la déformation de fluage liée au cycle, et l'extension de la fissure au cours du cycle peuvent être négligées. On montre que l'intégraleJ cyclique est, dans le cas d'écoulement plastique à faible échelle, équivalente à l'intégraleJ utilisée pour les fissures élastiques linéaires indépendamment des processus de mise en charge, tandis que la valeur de déformation plastique macroscopique varie avec le processus de mise en charge. Cependant, dans les 2 cas, l'intégraleJ cyclique demeure constante au cours du renversement de charge appliquée à tension constante si l'on exclut le premier stade de mise en charge monotone. Dans cette situation, l'intégraleJ cyclique peut être appliquée comme critère de la croissance d'une fissure de fatigue puisqu'elle représente une forme généralisée de force, un effort sur les dislocations à mouvoir ou à l'écoulement d'énergie dissipée en chaleur par les mouvements de dislocation dans un élément immédiatement solidaire de l'extrémité de la fissure de fatigue, au cours d'un cycle de mise en charge. On suggère que les données expérimentales disponibles sur différents matériaux pour la croissance d'une fissure de fatigue puissent être généralisées à une formulation unifiée, sur base d'un critère d'énergie. On déduit également que le seuil J correspondant à K _th devrait être plus grand que 4, où est l'énergie de surface du matériau. Finalement, la définition opérationnelle de l'intégraleJ cyclique sous simple charge en fonction des courbes de déplacement est fournie dans le cas d'une plaque comportant une fissure centrale et de larges ligaments non fissurés, soumises à traction.

     

Crack tip opening displacement of a Dugdale crack in a three-phase cylindrical model composite material

The analytical investigation of the plastic zone size of a crack in three-phase cylindrical model composite material was carried out. The physical problem is simulated as a crack near a circular inclusion (a single fiber) in the composite matrix, while the three-phase cylindrical composite model is used to represent the composite matrix. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small scale yielding, a thin strip of yielded plastic zone is introduced at each crack tip. Using the solution for a three-phase model with a single dislocation in the matrix phase as the Green’s function, the physical problem is formulated into a set of singular integral equations. By employing Erdogan and Gupta’s method, as well as iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacements.     

The crack tip opening angle associated with the growth of a crack in a nonuniform stress field

A general analysis gives the crack tip opening angle associated with the growth of a crack in an infinite solid that is subject to a nonuniform stress distribution. The results allow one to study the effect of nonuniform stresses e.g. residual stresses, on inert environment crack growth and also environmentally assisted crack growth.     

A simple analytical crack tip opening displacement approximation under random variable loadings

A simple analytical approximation is proposed in this paper to calculate the crack tip opening displacement under general random variable amplitude loadings. This approximation is based on a modified Dugdale model for cyclic loadings. The discussion is first given under constant amplitude loading and is extended to several simple cases under variable amplitude loadings. Following this, a general algorithm is proposed under general random variable loadings. Numerical examples are verified with finite element simulations. Following this, hardening effect is included by including a hardening correction function. The proposed analytical approximation is very efficient compared to the direct finite element simulation. The solution can be used for detailed fatigue crack growth analysis under random variable amplitude loadings.     

Cyclic crack tip deformation and its relation to fatigue crack growth

Characteristics and mechanism of fatigue crack growth in mild steel have been investigated taking account of crack tip deformations: crack tip opening displacement δt and the size of highly deformed zone ahead of crack tip Rx0.2 (the size of the zone with accumulated strain above 0.2). δt was measured directly at midsection of the specimen with a profile projector. Rx0.2 was obtained from strain distribution ahead of crack tip determined by the use of the recrystallizalion phenomenon.It is revealed that crack growth rates ranging from 0.02 μm/cycle to 200 μm/cycle are expressed well by a second power function of both δt and Rx0.2. Abrupt increases in μt and Rx0.2 occured at a growth rate of about 1 μm/cycle. At this growth rate, fracture appearance changed from striation to dimple. These transitions are due to the transition of stress state. It is also shown that fatigue fracture strain is constant independently of crack growth rate and is equal to the ductile fracture strain in monotonic loading. The constant fracture strain is the criterion for fatigue failure of ductile steels.     

Simulation of ductile crack growth in thin panels using the crack tip opening angle

The aim of this work is the assessment of the efficiency of the crack tip opening angle (CTOA) with respect to the transferability from one geometry to another, in particular the transferability obtained from Kahn tear tests to M(T) panels. The load-displacement behaviour recorded during a Kahn tear test was reproduced by means of finite element analysis using a variable CTOA as a function of crack length. The CTOA extracted from Kahn tests has then been used to simulate the R-curve of M(T) panels with different widths. Experiments and simulations were run first on a 6013-T6 aluminium alloy and then also on butt, friction stir welded butt joints of the same material.     

The relationship between crack tip opening displacement,local strain and specimen geometry

A method is described whereby values of crack tip opening displacement (COD) can be measured at any section of a pre-cracked or slotted specimen. The relationship between COD and the degree of transverse strain at the notch root of a Charpy specimen has been investigated. A specimen will show some portion in plane strain up to a COD of about one twenty-fifth of the thickness. Transverse contraction results in smaller COD values, for a particular clip gauge displacement, at the outside than at the specimen midsection. An equation is presented relating COD to longitudinal notch root strain for Charpy specimens with root radius 0.002 in. COD and notch root strain are found to be not directly proportional. This finding is discussed in relation to the concept of a “miniature tensile specimen” at the notch root. The effect of specimen geometry on the value of COD at fracture initiation, (COD)_c, has been investigated. Neither a change in specimen thickness nor a change from a fatigue pre-crack to a 0.002 in. root radius notch has been found to significantly affect (COD)_c. The material used in this research was, for the most part, a low alloy pressure vessel steel, A533B.     

疲劳裂纹扩展中裂纹尖端应变变化的详细考察

传统的ASTM2%偏差法和卸载弹性法是以柔度轨迹的线性区段确定开闭口载荷(Pop和Pcl),往往因人工误差导致结果相差很大.本文注重裂纹尖端塑性变形带给柔度变化的物理意义,描述了一个载荷循环下柔度变化与裂纹开闭口以及弹塑性行为的关系.采用自行开发的高精度局部柔度测量法,针对结构钢进行了疲劳试验,记录了裂纹尖端应变与载荷关系的系列迟滞回线,并以微分法定量求出迟滞回线上的特征载荷.根据试验考察结果,分析了文献中几种疲劳裂纹扩展参量的关系.结果表明,ΔKRPG比ΔKcl和ΔKop更适合作为裂纹扩展驱动力参量.