Acoustic emission monitoring of corrosion fatigue crack growth in offshore steel

A research and development programme has been carried out to establish relationships between corrosion fatigue crack growth in offshore steel qualities and acoustic emission. Laboratory experiments on small-scale specimens and wide plates have shown that when a certain combination of crack size and crack surface corrosion deposit thickness has been reached, high acoustic emission event rates, in the range of 10–40 events per fatigue cycle, are recorded. The main activity is recorded on rising load, generated from crack surface activity, eg secondary emission. On the basis of the results from this programme general AE equipment can now be modified for offshore applications, and a research and development strategy to implement these modifications is presented,     

A study of stochastic fatigue crack growth modeling through experimental data

To capture the statistical nature of fatigue crack growth, many stochastic models have been proposed in the literature. These models may have been verified by only one data set, and therefore not appreciated by other fellow researchers. Part of the reason is the difficulty and time-consuming in obtaining the statistically meaningful fatigue crack growth data. In the present study, experimental work is carried out to obtain the fatigue crack growth data of a batch of 2024-T351 aluminum alloy specimens. A rather universal stochastic fatigue crack growth model proposed by Yang and Manning is employed to analyze the data. The solution of the stochastic differential equation associated with the stochastic model gives us the crack exceedance probability as well as the probability of random time to reach a specified crack size. Through comparison between the analytical and experimental results, it is found the model with a minor modification can fit the experimental data rather well. Once the appropriate stochastic model is established, it can be used for the fatigue reliability prediction of structures made of the tested material. In the present study, in particular, it can be used for the reliability assessment of aging aircraft made of 2024-T351 aluminum alloy.     

A fatigue crack growth theory

The fatigue crack growth model proposed by Frost and Dixon, based on the different crack tip geometries of a loaded and unloaded crack, is restated and extended using the stress intensity factor concept. The resulting crack growth predictions agree reasonably well both with experimental fatigue crack growth data, and data on the threshold stress necessary for fatigue crack growth.

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Zusammenfassung Das von Frost und Dixon vorgeschlagene Modell der Fortpflanzung von Ermüdungsrissen, welches auf den Unterschieden in der Geometrie einer belasteten und einer nicht belasteten Probe beruht, wird unter Hinzuziehen des Begriffs des Spannungsintensitätsfaktors neu formuliert und erweitert.Die sich aus dieser neuen Formulierung ergebenden Voraussagen stehen in guter Übereinstimmung mit den experimentellen Werten, welche für das Fortschreiten von Ermüdungsrissen und die für die Fortpflanzung des Risses erforderliche kritische Belastung ermittelt wurden.

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Résumé Le modèle de propagation des fissures de fatigue proposé par Frost et Dixon, qui repose sur les différences de géométrie de l'extrémité d'une fissure selon que celle-ci est sous contrainte ou déchargée, est reformulé et étendu, en utilisant le concept de facteur d'intensité de contrainte.Les prédictions de propagation de fissure qui résultent de cette nouvelle expression sont en bon accord avec les données expérimentales de propagation des fissures en fatigue, ainsi qu'avec la valeur critique de la contrainte, nécessaire pour que cette propagation ait lieu.

     

Stage II fatigue crack growth

The linear part of the fatigue crack growth diagram is found to be divided into Stages IIa and IIb by the point O whose coordinates K^* and A are dependent on the physical and structural characteristics of the material. In Stage IIa K_eff remains constant as the microcrack advances in increments corresponding to the dislocation cell structure size, λ, pausing for (dN−1) cycles to accumulate the elastic energy required for the crack opening. During Stage IIb K_op remains constant and the microcrack opens during each cycle and advances irrespective of the substructure but in accordance with an increasing value of K_eff. The effects of temperature and vacuum on K^* are considered; the A values correspond to those of λ and are independent of the above effects.     

Delay in fatigue crack growth

The importance of delay, or retardation in the rate of fatigue crack growth, produced by load interactions in variable amplitude loading on the accurate prediction of fatigue lives of engineering structures has been well recognized for some time. Heretofore, only a few simple loading combinations or spectra have been examined systematically. In this investigation the effects of a broad range of loading variables on delay in fatigue crack growth at room temperature are examined for a mill annealed Ti-6A1-4V alloy. The results are used to estimate crack growth behavior under programmed loads.

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Zusammenfassung Die Wichtigkeit des Einflusses des Aufschiebung oder Verspätung der Ausdehnungsgeschwindigkeit eines Müdigkeitrisses, unter Belastung mit wechselnder Amplitude, durch gegenseitige Beeinflussung der Lasten, auf die genaue Voraussagung der Müdigkeitslebensdauer von Bauelementen ist seit einer gewissen Zeit gut bekannt.Bis jetzt wurden nur einige einfachen Belastungsfälle oder Kollektive systematisch untersucht. In diesem Bericht wird der Einfluss von einer grossen Anzahl Belastungsveränderlichen auf die Verspätung der Ausdehnungsge-schwindigkeit eines Müdigkeitrisses bei Zimmertemperatur untersucht, für einen geglühten Ti-6A1-4V legierten Stahl. Die Ergebnisse werden gebraucht um die Rissausdehnung unter einem Belastungskollektiv vorauszusagen.

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Résumé On a reconnu depuis quelque temps l'importance que revêt, pour une prédiction fiable de l'endurance en fatigue des éléments de construction, le ralentissement dans la vitesse de propagation des fissures de fatigue, résultant d'interaction des charges lorsque celles-ci sont d'amplitudes variables.Jusqu'à présent, seul un petit nombre de combinaisons de charges ou de spectres ont fait l'objet d'un examen systématique. Dans la présente étude, on a étudié les effets d'une gamme étendue de variations de la charge sur le retard à la propagation des fissures de fatigue à température ambiante, dans le cas d'un alliage Ti-6A1-4V recuit.Les résultats de cette étude sont appliqués à l'estimation de l'extension des fissures de fatigue sous des programmes collectifs de charges.

     

A theory of fatigue crack growth

Existing experimental data on fatigue crack growth are summarized. A fatigue crack growth model is proposed, based on the different crack tip geometries of a loaded and unloaded crack; the model leads to predictions of the rates of growth of fatigue cracks, in certain materials, comparable to those determined experimentally.

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Zusammenfassung Bestehende, experimentelle Angaben über die Ermüdungsrissvergrösserung werden zusammengefasst. Ein auf die verscheidenen mit dem beanspruchten und nicht beanspruchten Riss verbundenen Rissspitzformen gegründetes Modell der Ermüdungsrissvergrösserung wird vorgeschlagen; es ermöglicht Vorhersagen von Ermüdungsrissvergrösserungsgeschwindigkéiten, die sich den aus gewisse Werkstoffe experimentell festgestellten gut zuordnen.

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Résumé Les données expérimentales disponsibles sur la fissuration progressive sous chargement cyclique sont résumées. Un schéma de la fissuration progressive sous chargement cyclique est propesé, qui se base sur les differéntes formes adoptées par l'extrémité d'une fissure selon que celle-ci est sollicitée ou non; ce schéma permet une prédiction des vitesses de fissuration progressive sous chargement cyclique qui se rapproche de celles établies par détermination expérimentale.

     

Acoustic emissions of fatigue crack growth

Acoustic emissions of fatigue crack growth have been monitored and quantitatively correlated with growth rate and the applied range of stress intensity for high cycle fatigue of 2024-T851 aluminum alloy. The data suggest a more cogent relationship for acoustic emissions and the applied range of stress intensity rather than between acoustic emissions and the average crack growth rate. Since nearly all crack growth is expected during the maximum load portion of the fatigue cycles, only the emissions from the acoustic events in the vicinity of the peak load were incorporated in correlations with $\text{d}\text{a/}\text{d}\text{n}$ and $\text{ΔK}$. Large amplitude emissions in the proximity of the minimum cyclic load were also detected. Because of their characteristics, these emissions are attributed to crack surface interference and, consequently, were not included in the correlation analyses.     

Approximate calculation of fatigue crack growth

For small scale yielding and plane strain conditions a method for calculating the propagation rate of fatigue cracks in work-hardening materials is described. It is assumed that a characteristic plastic displacement near the crack tip is equal to the crack propagation during each load cycle. The calculation is carried out for crack opening mode III, and the result is then transformed to crack opening mode I. The comparison of the calculated crack rates with measured values yields encouraging agreement. In most cases the measured crack rates are higher than the calculated ones. The reasons for this behaviour are discussed.

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Zusammenfassung Es wird eine Methode zur Berechnung der Ausbreitungsgeschwindigkeit von Ermüdungsrissen in Werkstoffen mit Verfestigung für Kleinbereichsfließen und ebene Dehnung beschrieben. Dabei wird angenommen, daß eine charakteristische plastische Verschiebung an der Rißspitze gleich dem Rißfortschritt je Lastwechsel ist. Die Rechnung wird für den Rißöffnungsmodus III durchgeführt und das Resultat auf Modus I übertragen. Der Vergleich der berechneten Rißgeschwindigkeiten mit den Meßwerten ergibt eine gute Übereinstimmung, wobei die tatsächlichen Rißgeschwindigkeiten im allgemeinen höher als die berechneten liegen. Die Gründe für dieses Verhalten werden diskutiert.

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Résumé On décrit une méthode de calcul de la vitesse de propagations des fissures de fatigue dans des matériaux sensibles à l'écrouissage, pour des conditions d'état plan de déformation et des déformations plastiques réduites. On suppose l'éxistence d'un déplacement caractéristique dans le domaine plastique au voisinage de l'extrémité de la fissure, égal à la propagation de la fissure lors de chaque cycle de charge. On procède au calcul pour le mode III d'ouverture de fissure, et les résultats sont ensuite transposé au mode I.Un accord encourageant a été constaté entre les calculs de vitesses de propagation et les résultats de mesures expérimentales.Dans la plupart des cas, ces dernières donnent cependant des vitesses de propagation plus élevées, et les raisons d'un tel comportement font l'objet d'une discussion.

     

Parameter representation of fatigue crack growth

From the study of the crack propagation data in fatigue, a parameter in the form P = mlogδK + C has been suggested, where the slope m and the intercept C are functions of the variables like stress ratio R, frequency w, and temperature T. Case studies where data are available for various stress ratios have been made and a Master Curve connecting the crack propagation rate da/dN and the parameter P has been obtained. Experimental data for various values of δK and R have been found to agree well with the theoretical prediction.     

Numerical simulation of fatigue crack growth

A numerical simulation of fatigue crack growth which uses currently available crack tip stress and strain fields is described. The essential features of the numerical model are the concepts of damage accumulation cycle by cycle and repeated re-initiation at the tip of the growing crack. The failure criteria employed are a combination of a failure condition and a critical distance over which this condition must be achieved. This critical distance, the material size parameter, has a magnitude which depends on the failure mechanism.

The use of the model to illustrate the effects of stress ratio and environmental effects is described and the ability of the model to predict the onset of bursts of crack growth due to static failure mechanisms is demonstrated. The phenomenon of self-arresting cracks is also displayed.

Material characteristics are included in the model and comparisons with experimental data are presented for a C-Mn steel used in the fabrication of offshore structures.     

AE load-cycle dependence applied to monitoring fatigue crack growth under complex loading conditions

Acoustic emission (AE) has been used to continuously monitor fatigue critical zones in a Mirage aircraft undergoing full-scale fatigue testing, in order to establish the feasibility of detecting AE due to crack growth during flight. The major problem was to distinguish crack growth from the many spurious AE sources. Thus, to discriminate between AE due to different sources, the activity in each zone was analysed in terms of its load-cycle dependence. Regions on the load cycle where AE due to fatigue crack growth was most likely to occur were identified, and a correlation was found between crack growth and relatively high AE activity in this region. Active cracks deeper than 0.3–0.6 mm were detected, although the size of the AE indication was not proportional to the cracking activity and zoning calibration studies had to be taken into account. No significant cracks were missed.     

Multiple-cracked fatigue crack growth by BEM

The dual boundary element method is applied for the two-dimensional linear elastic analysis of fatigue problem of multiple-cracked body. The traction integral equation is applied on ones of surfaces of cracks while the usual displacement integral equation simultaneously on the others. General multiple crack growth problem is solved in a single-region formulation. All crack surfaces are discretized with discontinuous quadratic boundary elements. J-integral technique is used to evaluate stress intensity factors. The real extension path of cracks is simulated by a linear incremental crack extension, based on the maximum principal stress criterion. For each increment analysis of the cracks, crack extension is conveniently modelled with new boundary elements. Remeshing is no longer necessary. Fatigue life analysis is carried out with Paris' formulae. Several numerical examples show high efficiency of present method.     

Flight-by-flight fatigue crack growth life assessment

Conventionally, fatigue crack growth in aircraft structures under flight spectrum loading is often analysed and predicted based on crack growth rates obtained from constant-amplitude crack growth testing with cycle-by-cycle life prediction methods or models. Because the mechanism of fatigue crack growth under spectrum loading is yet to be fully understood, no matter how closely the models are able to account for the load interaction effects, the predictions generally have to be subjected to the validation by fatigue crack growth tests using either representative specimens or real structures under the representative flight spectrum. In view of this fact, it is not difficult to deduce that the predictions should be much more reliable if the predictions are made directly based on the flight spectrum crack growth data. Therefore, a new approach to fatigue crack growth life assessment has been proposed in this paper based on the analysis of flight-by-flight fatigue crack growth data measured by quantitative fractography for several common aircraft structural materials under various fighter aircraft flight spectra. Quantitative fractography was successfully used for titanium coupons to generate crack growth curves under flight spectrum loading. The crack growths were also shown to be exponential. As a demonstration, the flight-by-flight approach was used to determine fatigue crack growth lives of aircraft aft fuselage frames under a fighter aircraft usage.     

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.     

Mixed mode fatigue crack growth predictions

This work is aimed at developing a predictive capability for the quantitative assessment of crack growth under fatigue loadings. The crack growth rate relation, $\text{Δa}\text{ΔN}$, may involve all three stress intensity factors k₁-k₃ such that the direction of crack growth may not be known in advance and must be predicted from a preassumed criterion. In principle, both the stress amplitude and the mean stress level should be included in the original expression for $\text{Δa}\text{ΔN}$.The strain energy density factor range, ΔS, is found to be a convenient parameter for predicting fatigue crack growth and can be applied expediently to examine the combined influence of crack geometry, complex loadings and material properties. Assumed is the accumulation of energy, $\text{ΔW}\text{ΔV}$, stored in an element ahead of the crack which triggers subcritical crack growth upon reaching a number of loading cycle, say ΔN. The proposed $\text{δa}\text{ΔN}$ relationship includes both the stress amplitude and mean stress effects.     

考虑裂纹表面摩擦阻尼的振动疲劳裂纹扩展分析

以含表面裂纹悬臂梁为研究对象,研究了裂纹面摩擦效应对裂纹疲劳扩展的影响。分析时,用双线性弹簧描述裂纹呼吸行为,用Galerkin方法把呼吸裂纹梁简化为单自由度系统,基于Coulomb摩擦模型和能量耗散理论推导了摩擦阻尼损耗因子,运用广义的Forman方程模拟疲劳裂纹扩展,通过振动分析与裂纹扩展计算同步进行的方法考虑振动与疲劳的耦合效应,探讨了摩擦阻尼对裂纹梁疲劳裂纹扩展寿命的影响。结论表明,摩擦阻尼损耗因子随裂纹扩展呈单调递增趋势,摩擦阻尼对振动疲劳裂纹扩展的影响不容忽视     

A crack opening stress equation for fatigue crack growth

International Journal of Fracture -