A theoretical explanation of the delaying effects of overloads on fatigue crack propagation

A simple theoretical model valid for generalized plane stress conditions is described which is able to predict the effects of overloads on crack tip deformation and fatigue crack propagation rates. The model is based upon a method of superimposing crack problems in an attempt to represent the effect of residual stresses in the plastic zones. An expression for the crack opening displacement is derived which is valid whilst the crack tip is propagating through the overload plastic zone. Crack tip closure is predicted during stress cycling and, following tradition, this is regarded as reducing the effect of the stress range intensity factor on crack propagation rate thus causing retardation. The model also predicts that, whenever a simple condition involving applied stress ratios is satisfied, crack arrest will take place. In keeping with experimental observations the model predicts that during its propagation through the overload plastic zone the crack growth rate first declines to a minimum and then increases to the appropriate value which would result if the overload had not been applied. In certain circumstances the model also predicts some acceleration effects and delayed retardation.It is shown how to construct delay maps characterizing the effect of applied stress ratios on growth rate, independent of specimen geometry whenever small scale yielding conditions prevail. Such delay maps, when used in conjunction with uniform amplitude fatigue crack growth data, offer a very convenient method of predicting delay for practical situations.

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Résumé On décrit un modèle théorique simple valable pour les conditions généralisées d'état plan de tension et à même de prédire les effets de surcharge sur la déformation d'une extrémité d'une fissure ainsi que sur les vitesses de propagation d'une fissure de fatigue. Le modèle est basé sur une méthode de superposition de problèmes de fissure en vue de représenter l'effet de contrainte résiduelle dans les zônes plastiques. Une expression du COD est dérivée, valable au cours de la propagation de l'extrémité de la fissure au travers de la zône de déformation plastique correspondant à la surcharge. La fermeture de l'extrémité de la fissure est prédite au cours d'un cyclage de la contrainte et, conformément à la tradition, ceci est considéré comme un effet réducteur du facteur d'intensité de contrainte sur la vitesse de propagation de la fissure, causant ainsi un retard de propagation. Le modèle prédit également que, pour autant qu'une condition simple impliquant les rapports des contraintes soit satisfaite, il se produira un arrêt de la fissure. En considérant les observations expérimentales, le modèle prédit qu'au cours de la propagation au travers de la zône de déformation plastique correspondant à la surcharge, la vitesse de croissance de la fissure passe d'abord par un minimum et s'accroit ensuite jusqu'à une valeur adéquate qui correspondrait aux conditions où ne se produirait pas de surcharge. Sous certaines circonstances, le modèle prédit également quelques effets d'accélération ainsi que des ralentissements différés. On montre la manière de construire des cartes de retard caractérisant l'effet des rapports des contraintes appliquées sur la vitesse de croissance et ce indépendamment de la géométrie de l'éprouvette, pour autant que prévallent des conditions d'écoulement plastique à faible échelle. De telles cartes de retard, lorsqu'elles sont utilisées en complément de données sur la croissance de fissures de fatigue sous amplitude uniforme, constituent une méthode très commode pour prédire les délais qui peuvent se produire dans des situations pratiques.

     

Mode III fatigue crack propagation rates in 6061-T6 aluminium

Fatigue crack growth rates were studied in type 6061-T6 aluminium alloy. Unlike the preponderance of previous studies, the present observations were carried out on cracks driven by a Mode III, or antiplane shear, type of loading. The observed crack growth rates were precisely correlated with the Mode III stress intensity factor range, ΔK_III. A simple power growth rate law, similar to that which predicts the growth rates of the more common Mode I driven crack, relates the incremental extension of the fatigue crack per cycle of loading to the stress intensity factor range. Fractographic examination of the fatigue crack surfaces indicated that the cracks propagated transgranularly, and did not seek out principal tensile stress planes, or Mode I growth habits.     

Corrosion fatigue crack propagation of an aluminum alloy under periodic overloads

Periodic tensile overloads superposed on constant amplitude cycles were used on compact tension fracture mechanics specimens of an aluminum (Al–Cu–Mg) alloy. The delayed retardation of corrosion fatigue crack propagation in the low part of the Paris regime was investigated in a 3.5% NaCl environment. The aluminum alloy exhibits the intensive retardation effect of crack propagation under overload ratios from 1.3 to 2.0 and overload intervals from 10² to 10⁴ cycles. The crack propagation under the periodic overloads can be treated as the base constant amplitude crack propagation, i.e. . The periodic overloads decrease the crack propagation resistance coefficient of B_cf, but have less effect on the threshold value of obtained by best fitting of this model.     

Stochastic loading and material inhomogeneity in fatigue crack propagation

The Gaussian stationary stochastic load process is considered to cause fatigue crack growth in randomly inhomogeneous materials. The Paris-Erdogan model is applied and the time when the crack length reaches a critical value (lifetime) is determined as a random variable. It is shown that random variations of the lifetime are not significantly affected by stochastic fluctuations of loading and material inhomogeneity. These fluctuations, however, affect significantly the mean value of the lifetime. An example is carried out to show quantitatively the influence of the load and material randomness on the structural lifetime.     

A stochastic model of fatigue crack propagation under variable-amplitude loading

This paper presents a stochastic model of fatigue crack propagation in ductile alloys that are commonly encountered in mechanical structures and machine components of complex systems (e.g. aircraft, spacecraft, ships and submarines, and power plants). The stochastic model is built upon a deterministic state-space model of fatigue crack propagation under variable-amplitude loading. The (non-stationary) statistic of the crack growth process for center-cracked specimens is obtained as a closed form solution of the stochastic differential equations. Model predictions are in agreement with experimental data for specimens fabricated from 2024-T3 and 7075-T6 aluminum alloys and Ti-6Al-4 V alloy subjected to constant-amplitude and variable-amplitude loading, respectively. The stochastic model of crack propagation can be executed in real time on an inexpensive platform such as a Pentium processor.     

Effect of tensile overloads on fatigue crack growth of high strength steel wires

Fatigue of the tensile armor wires is the main failure mode of flexible risers. Techniques to increase the life of these components are required to improve the processes safety on oil exploration. This work evaluates the crack growth retardation of high strength steel wires used in flexible pipelines. Fracture toughness tests were performed to establish the level of stress intensity factor wherein the wires present significant plastic deformation at the crack tip. The effect of tensile overload on fatigue behavior was assessed by fatigue crack growth testing under constant ΔK control and different overload ratios with two different load ratios. The outcomes show that the application of controlled overloads provides crack retardation and increases the fatigue life of the wires more than 31%. This behavior is also evident at stress ratio of 0.5, in spite of the crack closure effect being minimized by increasing the applied mean stress.     

Can pure mode III fatigue loading contribute to crack propagation in metallic materials?

The possibility of pure mode III crack growth is analysed on the background of theoretical and experimental results obtained in the last 20 years. Unlike for modes I and II, there is no plausible micromechanistic model explaining a pure mode III crack growth in ductile metals. In order to realize 'plain' mode III fracture surface, we propose the propagation of a series of pure mode II cracks along the crack front. Fractographical observations on crack initiation and propagation in a low alloy steel under cyclic torsion support such a model. The authors have not seen any clear indication of a pure mode III crack growth micromechanism in metals until now.     

A mathematical model of fatigue crack propagation under variable amplitude loading

A mathematical model of fatigue crack propagation based on the crack closure concept is proposed. It allows prediction of fatigue crack growth under complex loading sequences on the basis of data obtained under constant amplitude and simple Low-High, High-Low loading sequences. The model explains the influence of single and multiple positive overloads and the interaction of positive and negative overloads. An algorithm for cycle-by-cycle calculation of crack growth is proposed.     

A regression model of fatigue crack propagation under flight simulation loading

A multi-variable regression analysis is made of crack propagation data under flight simulation loading for the 2024-T3 and 7075-T6 alloys. The study is made using an effective stress range concept based on cracl closure considerations. A two-variable regression model of the equivalent stress range is suggested. The model is used to calculate fatigue crack propagation lives. Predictions using the proposed model are compared with empirical results. It is shown that the model accounts for the influence of maximum, minimum and mean stress levels of the load spectrum.     

The effects of overloads in fatigue crack growth

Several theories have been proposed to explain the transient fatigue crack growth decelerations and accelerations which follow overloads. The mechanisms that have been proposed to explain retardation after a tensile overload, for example, include residual stress, crack deflection, crack closure, strain hardening, and plastic blunting/resharpening. These mechanisms are reviewed in the light of recent experimental results, and implications with regard to their applicability are examined. It is suggested that no single mechanism can be expected to represent observed effects over the entire range of da/dN versus ΔK; eg, behaviour ranging from the near threshold region to the Paris region.     

The effect of single overloads in tension and compression on the fatigue crack propagation behaviour of short cracks

The crack propagation behaviour in cast quenched and tempered steel after one overload cycle in tension as well as in compression on short cracks is investigated in deep notched specimens. The overload cycle exhibits a significant influence on the fatigue life endurance, due to the formation of an overload plastic zones in front of the crack tip. The crack propagation after overload cycles is investigated by inspection of the fatigue threshold R-curve and fatigue crack propagation rate. Tension overload increased the long crack threshold and reduced the R-curve effect, whereas overloads in compression reduced the crack growth resistance and shifted the threshold value to larger crack extension. A simple FE simulation was also performed to investigate the variation in the contribution of plasticity induced crack closure during crack propagation after the overload. Macroscopic mechanistic and dislocation models are introduced to explain the results obtained.     

Micro-mechanical modelling of mode III fatigue crack growth in rotor steels

A study has been made of fatigue crack propagation in mode III (anti-plane shear) for A469 and A470 commercial rotor steels (tensile strength 621 and 764 MN/m² respectively) using torsionally-loaded circumferentially-notched cylindrical specimens. For crack growth under both small-and large-scale yielding conditions, radial mode III crack propagation rates are observed to be similar in both steels and to be uniquely related to the plastic intensity range 163-1 per cycle, provided friction, abrasion and interlocking between sliding crack faces is minimized by the application of a small tensile mean load. Over the range studied (i.e., 10^-6 to 10^-1 mm/cycle), mode III growth rates (dc/dN)_III are found to be independent of load ratio (for R=–1.0 and –0.5) and to be a power law function of 163-1 or the mode III cyclic crack tip displacement. When compared to mode I crack growth at equivalent cyclic crack tip displacements, however, crack propagation rates in mode III are seen to be two orders of magnitude smaller than in mode I. Based on fractographic evidence of elongated voids, parallel to the crack front, at the tip of the fatigue crack, several models for mode III crack growth are proposed utilizing the concept that mode III crack advance occurs by the initiation and coalescence of voids formed at inclusions directly ahead of the crack tip. By considering the linkage of these voids to take place by mode II shear parallel to the main crack front, expressions for the mode III crack propagation rate are developed based either on considerations of the local mode II crack tip displacementsor the mode II accumulated crack tip strain (computed from the Coffin-Manson damage relationship). Whereas both types of models predict mode III growth rates to be a small fraction of the cyclic crack tip displacements per cycle, the damage accumulation model in particular is found to provide excellent agreement with experimentally measured growth rates in the present rotor steels.

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Résumé On a procédé à une étude de la propagation en mode III (cisaillement antiplanaire) des fissures de fatigue dans les aciers commerciaux pour rotors des nuances A 469 (UTS 621 MN/m²) et A 47 à (UTS 764 MN/m²) à l'aide d'éprouvettes cylindriques à entaille circonférentielle soumises à tension.Pour des croissances de fissures demeurant sous les conditions d'écoulement plastique à petite ou à grande échelle, on observe que les vitesses de propagation d'une fissure radiale en mode III sont similaires dans les deux aciers. Si on minimise les frottements, l'abrasion et les couplages mécaniques entre les faces de la fissure en appliquant une légère contrainte de traction, on observe également que ces vitesses sont en seule relation avec l'étendue de la déformation plastique III par cycle. Dans la gamme étudiée (F de 10^-6 à 10^-1 mm/cycle) on trouve que la vitesse de croissance de la fissure en mode III est indépendante de R (pour R=–1 et –0,5) et est une fonction parabolique de III ou du déplacement d'extrémité de la fissure. Toutefois, si on compare les vitesses de croissance en mode III à celles obtenues en mode I sous les mêmes déplacements d'extrémités de fissure, on constate que les premières sont inférieures aux secondes de deux ordres de grandeur. On propose divers modèles pour la croissance de fissure en mode III, en se basant sur l'observation fractographique de la présence de lacunes allongées parallèles sur front de fissuration.Ces modèles recourent au concept de préfissuration par coalescences des lacunes formées sur des inclusions en amont de la fissure. En considérant que ces lacunes se réunissent par un cisaillement de mode II parallèle au front de fissuration principale, on a développé des expressions pour la vitesse de propagation suivant le mode III, qui reposent soit sur les déplacements locaux de l'extrémité de la fissure suivant un mode II, soit sur la déformation de mode II accumulée à l'extrémité de la fissure et calculée par la relation de dommages cumulés de Coffin-Manson.Si les deux types de modèle prédisent que les taux de croissance selon le mode II ne sont qu'une faible fraction des déplacements par cycle, le modèle recourant au concept de dommages cummulés se montre quant à lui en excellent accord avec les vitesses de propagation mesurées expérimentalement sur lesdits aciers pour rotors.

     

Effect on fatigue crack growth of interactions between overloads

ABSTRACT Various types of interactions between overloads were studied in a 0.38% C low carbon steel. The retarding effect due to consecutive overloads is found to increase with the number of overloads, until it reaches a maximum. Similarly, it is found that a critical distance between overloads ensures the highest retarding effect, while shorter or longer spacing are less efficient for retarding crack growth. These effects are successfully explained using FEM calculations of the effective stress intensity factor. The kinematic hardening of the alloy, which is very efficient in ferritic–pearlitic steels, is shown to be mostly responsible for those effects. Taking into account the amplitude of kinematic hardening allows qualitative explanation of the observed effects. The order of application of the cycles during variable amplitude fatigue is thus important and should be taken into account for predicting fatigue lives.     

Effect of load sequences on crack propagation under random and program loading

Crack propagation was studied in 2024-T3 Alclad sheet specimens under two types of random loading and under program loading with a very short period (40 cycles) and program loading with a longer period (40,000 cycles). In the program tests Lo-Hi, Lo-Hi-Lo and Hi-Lo sequences were employed. The loads were based on a gust spectrum. The crack rates were about the same under random loading and program loading with the short period. Under program loading with the longer period the crack rates were 2.5 times slower on the average, while a significant sequence effect was observed in these tests. Fractographic observations indicated different cracking mechanisms for the random tests and program tests with a short period on the one hand and the program tests with the longer period on the other hand. Implications for fatigue tests in practice are discussed.     

Influence of material microvoids and heterogeneities on fatigue crack propagation

The evaluation of crack initiation, short-crack growth as well as crack path at microscopic scale is a crucial issue for the safety assessment of macroscopically fracture-free structural components. In the present paper, the crack propagation at the material microscale is modeled by taking into account the spatial variability of mechanical characteristics of the material as well as the local multiaxial stress field disturbance induced by inhomogeneities (inclusions or voids). By adopting some crack extension criteria under mixed mode, the short-crack path is determined. A microstructure dependence of the crack path arises in the short-crack regime, while the microstructure of the material does not influence the crack propagation for sufficiently long cracks. A mean weighted equivalent stress-intensity factor (SIF) is computed for kinked short cracks, where the range of such a SIF can be used as a key parameter dictating their fatigue crack growth rate.     

Effects of tensile overloads on crack closure and crack propagation rates in 7050 aluminum

It has been suggested that the crack closure concept can account for the retardation in crack growth rate following removal of tensile overloads. To test this possibility measurements of effective stress were made on center notched cracked specimens during tests in which tensile overloads were applied. A comparison of the changes in crack growth rate and in effective stress following removal of the overload indicates that the crack growth rate reaches a minimum value before the effective stress does indicating that the closure concept cannot account for the decrease in crack growth rate. Additional evidence for the inability of crack closure to account for the retardation in crack growth rate is provided by specimens run at a high mean stress and then overloaded. No crack closure is observed when there is a high mean stress present, yet the crack growth rate does decrease by an amount about the same as that observed at low mean stresses where crack closure is present. Measurements of closure stress and effective stress were obtained from load-displacement curves recorded using an extensometer mounted across the crack on the specimen centerline. This procedure also enabled us to measure the distance over which the crack faces were in contact when the stress was at its minimum value in the stress cycle. The length of crack closed reached a minimum value later than did either the crack growth rate or the effective stress. It occurred when the crack tip had propagated nearly across the plastic zone created by the application of the overload.     

Near-threshold fatigue crack propagation of welded joint under varying loading

The influence of varying loading on the fatigue crack propagation properties of HT80 steel welded joint and base metal was investigated by using center cracked specimens under two-step programmed test. The higher stress intensity range was slightly above the threshold level obtained by constant amplitude test and the lower one was 70% of the higher one. The fatigue crack propagated below the threshold level for the base metal at the stress ratio of 0 and 0.4. However, the fatigue crack did not propagate below the threshold level either for the base metal at the stress ratio of 0.9 or for the welded joint at the stress ratio of 0. These results mean that the use of the threshold level obtained under the constant amplitude test would be dangerous for assessing the fatigue performance of the base metal under varying loading. The use of the threshold level obtained for the center cracked welded joint specimens would be conservative even under the varying loading.