A cumulative damage theory for fatigue crack initiation and propagation

A method for evaluating the cumulative damage resulting from the application of cyclic stress (or strain) sequences of varying amplitude is presented. Both the crack initiation and propagation stages of the fatigue failure process are included. The development is based on the concept of plastic strain energy dissipation as a function of cyclic life. The damage accumulated at any stage is evaluated from a knowledge of the fatigue limit in the initiation phase and an ‘apparent’ limit obtained through fracture mechanics for the propagation phase. The proposed damage theory is compared with two-level strain cycle test data of thin-walled specimens, and is found to be in fairly good agreement.     

A model for fatigue crack propagation

A model for fatigue crack propagation is presented which incorporates low cycle fatigue, mechanical properties and a microstructurally-associated process zone. Comparison of the model to published date for 4340 (hard and soft), a series of TRIP steels, Ti-6A1-4V, 2024-T6 and 300 grade maraging steel shows good agreement.     

A fatigue crack propagation model

A model for fatigue crack propagation has been developed which incorporates mechanical, cyclic and fatigue properties as well as a length parameter. The latter can be associated with the microstructure of the material. The fatigue failure criterion is based on a measure of the dissipated plastic strain energy. This model predicts crack propagation at low and intermediate ΔK values, i.e. stage I crack growth rate as well as that of the stage II. A number of crack growth rate models proposed earlier, are shown to be particular cases of the one developed herein. Predictions of the model are in good agreement with the experimental data. The required data for predicting the crack growth rate, can be found in standard material handbooks where fatigue properties are listed.     

A low-cycle fatigue approach to fatigue crack propagation

The damage accumulation hypothesis is used to derive a fatigue crack growth rate equation. The fatigue life of a volume element inside the plastic zone is evaluated by using low-cycle fatigue concepts. Crack growth rate is expressed as a function of cyclic material parameters and plastic zone characteristics. For a given material, crack growth increment, is predicted to be a fraction of the plastic zone size which can be expressed in terms of fracture mechanics parameters,K andJ. Hence, the proposed growth rate equation has a predictive capacity and is not limited to linear elastic conditions.     

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.

     

Mechanisms for corrosion fatigue crack propagation

ABSTRACT The corrosion fatigue crack growth (FCG) behaviour, the effect of applied potential on corrosion FCG rates, and the fracture surfaces were studied for high‐strength low‐alloy steels, titanium alloys, and magnesium alloys. During investigation of the effect of applied potential on corrosion FCG rates, polarization was switched on for a time period in which it was possible to register the change in the crack growth rate corresponding to the open‐circuit potential and to measure the crack growth rate under polarization. Due to the higher resolution of the crack extension measurement technique, the time rarely exceeded 300 s. This approach made possible the observation of a non‐single mode effect of cathodic polarization on corrosion FCG rates. Cathodic polarization accelerated crack growth when the maximum stress intensity (K_max) exceeded a certain well‐defined critical value characteristic for a given material‐solution combination. When K_max was lower than the critical value, the same cathodic polarization, with all other conditions (specimen, solution, pH, loading frequency, stress ratio, temperature, etc.) being equal, retarded or had no influence on crack growth. The results and fractographic observations suggested that the acceleration in crack growth under cathodic polarization was due to hydrogen‐induced cracking (HIC). Therefore, critical values of K_max, as well as the stress intensity range (ΔK) were regarded as corresponding to the onset of corrosion FCG according to the HIC mechanism and designated as K_HIC and ΔK_HIC. HIC was the main mechanism of corrosion FCG at K_max > K_HIC (ΔK > ΔK_HIC). For most of the material‐solution combinations investigated, stress‐assisted dissolution played a dominant role in the corrosion fatigue crack propagation at K_max < K_HIC (ΔK < ΔK_HIC).     

A fatigue crack propagation model for strain hardening materials

In this paper a crack propagation model based on Tomkins concept (dl/dN ∝ Δε_p · ω) has been developed using the theoretically developed cyclic plastic zone sizes. The crack propagation rates are found to be functions of stress intensity factor, Elber's effective stress range ratio, cyclic yield strength of material, crack length, specimen width and cyclic strain hardening exponent. Suitably grouped to give the crack growth rate in terms of five constants termed as Loading Constant, Material constant, Crack size constant, specimen Width Constant and Stress Intensity Exponent. The crack growth rates found by theory are compared with the experimental results available in literature and a good agreement is found.     

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.

     

Resonance controlled fatigue crack propagation

Fatigue crack growth in resonating structural members is studied. The crack propagation rate is related to the stress intensity factor range by way of the well known power law. The depth of the crack determines the local flexibility due to crack which in turn influences the dynamic response of the system under an external force with constant amplitude and frequency. The propagating crack introduces additional flexibility to the system which results in gradual shift away from the resonance with smaller loading of the cracked section. This slows down the crack growth rate.It was shown that this mechanism can guide the system to a value of the crack growth rate below a conventional threshold rate which can be interpreted as dynamic crack arrest. It was found that material damping is the decisive factor determining the crack growth rate in a resonant system where the material damping is the dominant damping mechanism of the system.     

A model of fatigue crack propagation in metals

A model of the formation and evolution of a local plastic deformation zone at the crack tip is proposed based on the analysis of the main physical processes taking place in a metallic material under the action of cyclic loads. An equation of fatigue crack growth rate curves, which explicitly accounts for the loading frequency, was derived. The equation applies to the whole range of crack lengths from short cracks to macroscopic ones. __________ Translated from Problemy Prochnosti, No. 1, pp. 35–43, January–February, 2009.     

A plastic flow-induced fracture theory for fatigue crack growth

A plastic flow-induced fracture theory for fatigue crack growth is presented. A new formulae for the fatigue stress intensity threshold and the fatigue crack growth rate law are derived by applying the principle of energy conservation in considering the fatigue crack growth process in the presence of local plastic flow ahead of the crack-tip. The present theory predicts not only the fatigue crack growth rate being just proportional to the rate of creation of dislocation at the crack-tip, but also the fatigue stress intensity threshold, which can be determined according to the applied fatigue stress amplitude and the characteristic size of microstructural fracture process ahead of the crack-tip, and can account for the fatigue crack growth characteristics at both low and high levels of applied fatigue stress intensity amplitude. All the results are universal and agree with the existing empirical results and experimental observations.     

Kinetic theory approach to fatigue crack propagation in terms of dislocation dynamics

International Journal of Fracture -     

Transient effects in fatigue crack propagation

The transient fatigue crack propagation resulting from the sudden change of the stress intensity factor amplitude or from the change of the stress cycle asymmetry or from the application of the single overload cycle was measured on carbon steel specimens. To simplify the conditions and to increase the accuracy the shape of the specimens was chosen in such a way, that the stress intensity factor was independent of the crack length. It was shown that the transient effects can be qualitatively understood and quantitatively in the first approximation described solely on the basis of the steady state fatigue crack propagation data, provided that the threshold conditions of non-propagation are taken into account.     

First-passage solutions in fatigue crack propagation

The statistical characteristics of the time required by the crack size to reach a specified length are sought. This time is treated as the random variable time-to-failure and the analysis is cast into a first-passage time problem. The fatigue crack propagation growth equation is randomized by employing the pulse train stochastic process model. The resulting equation is stochastically averaged so that the crack size can be approximately modelled as Markov process. Choosing the appropriate transition density function for this process and setting the proper initial and boundary conditions it becomes possible to solve the associated forward Kolmogorov equation expressing the solution in the form of an infinite series. Next, the survival probability of a component, the cumulative distribution function and the probability density function of the first-passage time are determined in a series form as well. Corresponding expressions are also derived for its mean and mean square. Verification of the theoretical results is attempted through comparisons with actual experimental data and numerical simulation studies.     

Some aspects of fatigue crack propagation

The models of fatigue crack propagation proposed by Forman et al. and Roberts and Erdogan were studied in this paper. By applying these models to existing data in the literature for thin 2024-T3 and 7075-T6 aluminum plates subjected to fluctuating tensile loads, it was found that both models gave comparable results when one considered just a gross correlation of the experimental data. By modifying Forman's model to incorporate the ideas of Roberts and Erdogan, a model was produced which appeared to be a more rational basis for studying the problem of fatigue crack propagation in thin plates and shells subjected to tensile loads, bending loads, or a combination of both. This fact was demonstrated for the case of thin plates subjected to fluctuating bending loads and for the case of thin cylindrical shells subjected to fluctuating internal pressure.     

Energy considerations in fatigue crack propagation

The concept of Griffith fracture theory was extended to fatigue crack propagation problems by defining the Gibbs free energy of solids under cyclic loading.As a result, the rate of fatigue crack propagation, dc/dN, was obtained as % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbqfgBHr% xAU9gimLMBVrxEWvgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvA% Tv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9% vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea% 0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabe% aadaabauaaaOqaamaalaaabaGaciizaiaadogaaeaaciGGKbGaamOt% aaaacqGH9aqpcaGGOaGaaGOmaiaac6cacaaIZaGaciiEaiaaigdaca% aIWaWaaWbaaSqabeaacaGGTaGaaGOmaaaakiaacMcadaWcaaqaaiab% eQ7aRjaacIcacqGHuoarcaWGlbGaaiykamaaCaaaleqabaGaaGinaa% aaaOqaaiabeY7aTjabeo8aZnaaCaaaleqabaGaaGOmaaaaiqGakiaa% -vfaaaaaaa!547A!\[\frac{{\operatorname{d} c}}{{\operatorname{d} N}} = (2.3\operatorname{x} 10^{ - 2} )\frac{{\kappa (\Delta K)^4 }}{{\mu \sigma ^2 U}}\] where is a proportionality constant (01), K is the stress intensity amplitude, is the shear modulus, is an appropriate strength parameter for fatigue failure of the alloy and U is the energy to make a unit fatigue surface.

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Résumé Le concept de la théorie de rupture de Griffith a été étendu aux problèmes de propagation des fissures de fatigue en définissant l'énergie libre de Gibbs pour les solides soumis à sollicitations cyclique.Le résultat de cette approche est la détermination de la vitesse de propagation d'une fissure de fatigue dc/dN par la formule suivante: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbqfgBHr% xAU9gimLMBVrxEWvgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvA% Tv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9% vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea% 0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabe% aadaabauaaaOqaamaalaaabaGaciizaiaadogaaeaaciGGKbGaamOt% aaaacqGH9aqpcaGGOaGaaGOmaiaac6cacaaIZaGaciiEaiaaigdaca% aIWaWaaWbaaSqabeaacaGGTaGaaGOmaaaakiaacMcadaWcaaqaaiab% eQ7aRjaacIcacqGHuoarcaWGlbGaaiykamaaCaaaleqabaGaaGinaa% aaaOqaaiabeY7aTjabeo8aZnaaCaaaleqabaGaaGOmaaaaiqGakiaa% -vfaaaaaaa!547A!\[\frac{{\operatorname{d} c}}{{\operatorname{d} N}} = (2.3\operatorname{x} 10^{ - 2} )\frac{{\kappa (\Delta K)^4 }}{{\mu \sigma ^2 U}}\] où est une constante de proportionnalité, K est l'amplitude de l'intensité de contrainte, est le module de cisaillement, est un paramètre de résistance approprié à la rupture par fatigue de l'alliage considéré, et U est l'énergie nécessaire à la création d'une surface de fatigue unitaire.

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This research was supported by the Air Force Office of Scientific Research, Grant No. AF-AFOSR-76-2892A, and partially supported under the NSF-MRL program through the Materials Research Center of Northwestern University (Grant DMR 76-80847).     

A new method of analysing fatigue crack propagation data

A new method of assessing the validity of fatigue crack propagation laws is described. The method is illustrated by correlating experimental data collected using compact tension specimens for several steels and several testing environments. At no stage in the analysis is it necessary to estimate crack growth rates from the crack length-cycles data, a procedure which is extremely difficult to carry out accurately in practice. Six different fatigue crack growth laws are considered and it is shown that a simple law derived from a damage accumulation theory consistently offers the best correlation for the limited sets of data so far tested. This fatigue crack growth law when used in conjunction with compact tension specimens could provide a very useful method of assessing by comparison the fatigue crack growth properties of metals and it could therefore be a valuable tool for use in materials selection procedures.