On the statistical characteristics of fatigue crack propagation

In order to investigate the governing factor which causes the statistical fluctuation in the fatigue crack growth process, various experimental and simulated results obtained based on the Paris-Erdogan equation of fatigue crack growth rate were surveyed. Then, the governing factors for the randomness in microscopic fatigue fracture process being reflected on the phenomenological crack growth characteristics were examined. As a result, the distribution of the resisting strength of material to crack propagation with a certain unit size US is considered to be important. Also, the significance of the restriction of crack plane, that it can not rotate remarkably around the crack growth direction axis, is also indicated.     

A computer simulation study of Hertzian cone crack growth

A general method for simulating on a computer the growth of the cone-shaped fracture that forms under Hertzian contact loading is outlined. The program involves an incrementing procedure in which both contact circle and cone crack are grown in piecewise manner, according to suitable rate equations. The contact circle expands at a rate determined by the mode of indenter loading, and thereby sets up a time-varying stress field. Appropriate fracture-mechanics criteria are then invoked to calculate the response of the growing crack to the contact stresses. Effects of loading mode, specimen environment and temperature, size and location of the initial flaw from which the cone crack nucleates, are investigated systematically. The computer predictions compare favourably with available experimental data. The results are discussed in the light of previous theoretical treatments of the Hertzian fracture problem, and some new features in the crack-growth characteristics are pointed out. Calculations are made specifically for normal contact loading on glass, but ready extension of the program to other loading situations and materials in envisaged.     

On statistical moments of fatigue crack propagation

A new statistical theory is proposed for the analysis of fatigue crack propagation, based on the concepts of fracture mechanics and random processes. Focus is centered on conceivably more useful information of the random time at which the crack size grows to any specific value. Given an initial crack size, recursive relationship is obtained for the statistical moments of this random time for a rather general class of material behaviors, and examples are given for the case where the crack propagation rate is governed by a power law. A procedure to estimate the parameters in the power-law model is also illustrated, using the experimental data of some 7475-T7351 aluminum fastener hole specimens subjected to the excitation of a certain bomber load spectrum.     

Environmentally-controlled non-equilibrium crack propagation in ceramics

A general framework is developed for environmentally-controlled non-equilibrium crack propagation and applied to ceramic materials that exhibit microstructurally-controlled fracture resistance variations. Increasing fracture resistance with crack length, arising from frictional interlocking of predominantly intergranular fracture surfaces, is modelled by the influence of a localized line force behind the crack tip. An indentation fracture mechanics analysis incorporates the fracture resistance variation to describe the inert strength of ceramic materials as a function of dominant flaw size. Non-equilibrium fracture is modelled as the competition between thermally-activated bond-rupture and bond-healing processes, in which the activation barriers are modified by the net mechanical energy release rate acting on a crack. The resulting dependence of crack velocity on mechanical energy release rate is used to describe the strength of ceramic materials as a function of applied stressing rate in a reactive environment. The deconvoluted crack velocity behavior allows both the macroscopic reactive environment fracture resistance and the atomistic lattice traps for fracture to be determined. An implication is that fracture resistance variations are more important in determining observed fracture behavior in reactive environments than in inert environments.     

Quantifying the parameters in fatigue crack propagation

Fatigue crack growth data in the region of stage II(a) and stage II(b) have been attempted. It has been observed that the stage II(a) and the stage II(b) crack growth rate vs ΔK relations have their own pivot points. The dependence of the threshold stress intensity factor on the stress ratio and temperature has been obtained in terms of the pivot point co-ordinates. The predicted values of the threshold ΔK compare well with the experimental data.     

On the mechanism of fatigue crack propagation in ductile metallic materials

An overview of our research performed during the last 15 years is presented to improve the understanding of fatigue crack propagation mechanisms. The focus is devoted to ductile metals and the material separation process at low and intermedial crack propagation rates. The effect of environment, short cracks, small‐scale yielding as well as large‐scale yielding are considered. It will be shown that the dominant intrinsic propagation mechanism in ductile metallic materials is the formation of new surface due to blunting and the re‐sharpening during unloading. This process is affected by the environment, however, not by the length of the crack and it is independent of large‐ or small‐scale yielding.     

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.     

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 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.     

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.     

Microstructural aspects of crack propagation in ceramics

X-ray microradiographic examination supported by optical and SEM observations was used to study crack propagation in various ceramics, including glasses and cubic and noncubic polycrystalline bodies of different grain sizes. The nature of crack propagation in ceramics was often extremely complex. While cracks in glassy materials were generally simple, as would be expected, in cubic and non-cubic polycrystalline specimens both wandering and branching of cracks was observed. In cubic materials, wandering and branching occurred on the scale of the grain size, while in fine grain, non-cubic materials these were on a multi-grain scale. Results are consistent with the grain size dependence of fracture energy. Elastic anisotropy and thermal expansion anisotropy were suggested as major factors in crack wandering and branching.     

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.     

Modelling fatigue crack propagation in CT specimens

Although there are a great number of numerical studies focused on the numerical simulation of crack shape evolution, a deeper understanding is required concerning the numerical parameters and the mathematical modelling. Therefore, the objectives of the paper are the study of the influence of numerical parameters, particularly the radial size of crack front elements and the magnitude of individual crack extensions, the mathematical modelling of crack propagation regimes, and the linking of crack shape changes with K distribution. A relatively simple through-crack geometry, the CT specimen, was studied and the numerical model was validated with experimental results with a good agreement. The K distribution along crack front was found to be the driving force for shape variations. Shape variations were found to be one order of magnitude lower than K variations.     

Early stage crack propagation in fretting fatigue

A stress model of the fretting fatigue damage mechanism is developed on the basis of microscopic observations of the fatigue failure process in fretting. According to the model the state of stress in the element in the region of fretting pads defines the fatigue strength of the fretting assembly. Areas where the first fatigue crack initiates and the direction of its early stage propagation can be well explained by the elastic strain energy in the specimen near the fretting pads. The main fatigue crack initiates in the cyclically loaded member from the edge of the fretting pad, grows at the beginning and then stops, becoming a non-propagating crack, when the member is loaded below the fretting fatigue limit.     

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.