Fatigue crack paths for inclined cracks and surface flaws under biaxial loading

Two approaches are developed for geometrical modeling of crack growth trajectories for the inclined through thickness central cracks and the part-through surface flaw respectively. The principal feature of such modeling is the determination of crack growth direction and the definition of crack length increment in this direction. The damage process zone size concept is employed for calculations of mixed-mode crack growth trajectories and surface flaw shape and positions. Crack front behavior for a straight-fronted edge crack in an elastic bar of circular cross-section is studied through experiments and computations under axial tension loading. The elaborated theoretical model is applied for fatigue crack shape simulation of part-through cracks in a hollow thick- and thin-walled cylinders under different biaxial loading conditions. Suggested approach of crack paths modeling is used for an analysis and prevention of operation failures of existing in-service aircraft gas-turbine engine rotating components.     

On crack paths

Crack paths are discussed from several different points of view. The remarkable reproducibility of crack paths, especially the frequent occurrence of straight cracks, is considered. The general dominance of mode I growth at mixed mode loading (via kinking or tilting of the crack edge) is examined, and it is shown that mode I growth can be suppressed by superposition of a high pressure. Mode I growth is scarcely combineable with mode II or III, because of different micromechanisms, whereas a mixture of modes II and III growth appears to be possible. Directional stability of straight crack paths is also analysed with special reference to the importance of a meaningful definition of the concept itself. Finally crack branching is briefly discussed.     

Fatigue crack closure

A loading stage for the scanning electron microscope has been used in conjunction with the stereoimaging technique to study fatigue crack closure for a center notched specimen of an aluminum alloy. The results are compared to similar measurements from single edge notched specimens of the same alloy and other materials. The magnitudes of closure loads were found to be different for these two specimen designs, but the dependence on stress intensity factor (ΔK) is the same. Comparison of experiments is made with a finite element model simulation of crack opening, a simple model is developed which simulates the observed opening behavior, and a method is given for estimating threshold ΔK from materials parameters and crack opening behavior in the near threshold region.     

Fatigue crack paths in AA2024-T3 when loaded with constant amplitude and simple underload spectra

It is well known that variable amplitude fatigue loading produces progression marks on fatigue crack surfaces that are related to the loading sequence. These marks are generally a local change in the crack path. The same pattern of loading can produce a pattern of progression marks that have differences from material-to-material or from heat treatment-to-heat treatment, yet the crack path changes that produce these markings are not considered in the prediction of the crack growth behaviour. These path changes can be used to: investigate how the crack grows, aid crack growth measurement and shed light on the mechanism that forms striations. Consequently, an understanding of these path changes and their fundamental cause in structurally significant alloys is important to the explanation of how fatigue cracks grow and how their life can be predicted.In this paper, a number of simple loading sequences were used to investigate the influence that underloads have on the crack path, to develop a better understanding of the formation of fatigue striations and the coarser crack path changes associated with loading changes. The material chosen was aluminium alloy (AA)2024-T3. The results from the tests reported here were compared to previously investigated AA7050-T7451 specimens that were loaded in a similar manner. It is shown that the fatigue crack surfaces that were produced here were the direct consequence of the applied loading interacting with the crystal structure of the material. By changing the loading, via the addition of underloads it was possible to produce fatigue crack surfaces that where composed of not only striations but ridges, depressions and fissures. These features give an indication of the crack growth mechanism. Although, AA2024-T3 and AA7050-T7451 have different chemical compositions, mechanical properties and micro-structures, it was shown that both materials share essentially similar fracture features corresponding to crack propagation at the cycle-by-cycle level. It also appears that despite the above noted differences, similar failure mechanisms may take place.     

Simulation of simplified zigzag crack paths emerging during fatigue crack growth

When subjected to fatigue loading, microstructurally short cracks form zigzag shapes in single shear mechanisms due to nucleation, glide and annihilation of dislocations. Such crack progression is geometrically complicated and computationally expensive to model. This paper investigates the possibilities of efficiently modelling such growth behaviour by geometrical simplifications of the zigzag path. The crack path and the emerging plasticity was modelled by two different dislocation formulations and it was found that, irrespective of dislocation modelling technique, a valid geometrical approximation was to disregard the surface roughness except for the zigzag section closest to the crack tip.     

Transient crack propagation in asymmetric cruciform paths

Summary The problem of two cracks emanating from the same origin and propagating asymmetrically at different velocities in an elastic and isotropic solid is treated in this paper. An unbounded and otherwise undisturbed medium and a constant anti-plane loading at infinity were assumed. Techniques of self-similar elastodynamics were utilized in conjunction with analytic-function theory. Since a closed-form solution of such a problem is impossible we relied in the last steps of the procedure upon numerical analysis.With 4 Figures     

Fatigue crack closure after overload

The fatigue crack closure after overload was measured by small foil strain gages. The effect of overload on crack closure stress and crack propagation rate was observed to extend over a range several times larger than the overload plastic zone. Analysis of experimental data showed that the extra amount of plastic deformation introduced by the overload was the controlling factor. A relationshp between crack closure stress and crack length in the affected zone was found, and the amount of plastic deformation by the overload was estimated. This estimate was further confirmed by analysis of the crack closure pictures.     

Fatigue crack propagation in steels

From previous investigations of the mechanisms of both fracture and fatigue crack propagation, the static fracture model proposed by Lal and Weiss may be thought as reasonable for describing fatigue crack propagation in metals at both low and intermediate stress intensity factor ranges $\text{ΔK}$. Recent progress in fatigue crack propagation indicates that it is not only possible, but also necessary, to modify this static fracture model. Based on the modified static fracture model, the effective stress intensity factor range $\text{ΔK}{}_{\mathrm{eff}}$, which is defined as the difference between $\text{ΔK}$ and the fatigue crack propagation threshold value $\text{Δ}{}_{\mathrm{th}}$, is taken as the governing parameter for fatigue crack propagation. Utilising the estimates of the theoretical strengths of metals employed in industry, a new expression for fatigue crack propagation, which may be predicted from the tensile properties of the metals, has been derived. The correlation between the fatigue crack propagation rate and the tensile properties is thus revealed. The new expression fits the test results of fatigue crack propagation of steels below 10^?3 mm/cycle and indicates well the effect of stress ratio on the fatigue crack propagation rate.     

Fatigue crack growth in polymers

A number of fatigue crack propagation laws applied in the study of polymers is described. Consideration of the stress field distribution at the crack tip leads to the application of fracture mechanics. It is shown that a simplified relationship of the form da/dN =F , where is a function ofK _IC,K _max,K _min andK _TH appears to be a convenient expression for cyclic crack growth. The effect of mean stress is more complicated than that in the field of metals, the compressive component of cyclic stress may delay the crack growth. Cyclic tests in tension performed on PMMA and PVC are dependent on K and its mean value,K _m . The threshold value,K _TH, is also influenced byK _m but a more complicated behaviour due to strain rate effects may be observed. Other differences, such as the position of upper and lower transition points and growth rate changes with frequence, are noted. The effect of biaxial cyclic loading of PMMA and PVC plates is compared and some differences highlighted. The results available so far indicate little effect of the crack curving on its growth. However, it is shown that, while the increasing biaxiality can substantially retard the crack growth in PMMA, no such effect was recorded in PVC. Finally, it is shown that at very high stress levels (region III), the cyclic crack growth consists of two propagation modes, namely, a pure cyclic propagation, together with slow growth. At lower stress levels, slow growth disappears and the crack propagates in pure fatigue (region II). In region I, the propagation is very slow, without the usual correspondence between cycles and striations. The results recently obtained on glass reinforced plastics (GRP) are also presented and differences highlighted.

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Résumé On décrit les diverses lois de propagation des fissures de fatigue appliquées a l'étude des polymères. En considérant la distribution de champs de contrainte a 1'extremité de la fissure, on est conduit á appliquer la mécanique de la rupture. On montre qu'une relation simplifiée de la forme da/dN =F ^a, où est une fonction deK _IC,K _max,K _min etKTH apparait être une expression convenable pour la croissance cyclique d'une fissure. L'effet de la contrainte moyenne est plus complexe que dans le domaine des métaux et la composante de compression du cycle de contraintes pent différer la croissance de la fissure. Des essais cycliques en traction exécutés sur du PMMA et du PVC dépendent de K et de la valeur moyenneK _m . La valeur de seuilK _TH est également influencée parK _m mais un comportement plus complexe associé aux effets de vitesses de déformation peut être observé aux effets de vitesees de déformation peut être observé. D'autres differénces, telles que la position des points de transition supérieurs et inférieurs ainsi que les changements de vitesse de croissance avec la fréquence ont été notées. L'effet d'une mise en charge cyclique biaxiale d'un PMMA ou d'un PVC sous forme de plaque est comparé et on met en avant certaines des différences observées. Les résultats disponibles jusqu'ici indiquent un effet modéré de la courbure de la fissure sur sa propagation. Cependant, on montre que si une biaxialité croissante pent retarder d'une manière substancielle la croissance d'une fissure dans du PMMA, aucun effet de ce genre n a été enregistré dans le cas d'un PVC. Enfin, on montre que pour des niveaux de contrainte très élevés (région III) la croissance cyclique d'une fissure consiste en deux modes de propagation, à savoir une propagation purement cyclique accompagnée d'une croissance lente. A des niveaux de contrainte plus faible, la phase de croissance lente disparait et la propagation de la fissure s'effectue en fatigue pure (région II). Dans la région I, la propagation est très lente sans que se présente la correspondance usuelle entre les cycles et les striures. Les résultats récemment obtenus sur des plastiques renforcés de verre (GRP) sont également présentés et les differences en sont mises en évidence.

     

Fatigue crack propagation in polyacetal

The fatigue crack propagation characteristics of a typical commercial homopolymer and copolymer polyacetal were determined. These materials were found to be the most fatigue resistant plastics examined to date, thus confirming the generally high fatigue resistance of all crystalline polymers. A discontinuous fatigue cracking process was identified at all test frequencies in the acetal copolymer and at high frequencies in the homopolymer, while continuous crack propagation occurred at low test frequencies in the homopolymer. The discrete advance increments of the crack in the discontinuous mode were equal to the dimension of the prevailing crack-tip plastic zone. On a more local scale, the crack path is seen to be mainly trans-spherulitic in nature.     

Fatigue analysis for crack initiation

For the prediction of life leading to fatigue crack initiation, a method for performing a cycle-by-cycle local stress analysis at the stress concentration area of a structural component was developed. Elastoplastic stress-strain values along the hysteresis loop are traced for each load reversal in making the life prediction calculations. In this manner, the load sequence effect and the residual stress due to local yielding are inherently included. Neuber's rule and a linear rule were used with this method and compared. The results of life prediction were compared with test results. The use of the linear rule provided more accurate predictions than using other alternatives, including Miner's rule.     

Simulation of crack paths in functionally graded materials

One of the main interests of fracture mechanics in functionally graded materials is the influence of such an inhomogeneity on crack propagation processes. Using the Griffith’ energy principle, the change of energy has to be calculated, if the crack starts to propagate. In homogeneous linear-elastic structures (asymptotically precise) formulas for the energy release rate are known, but a direct transfer of these methods to functionally graded materials can lead to very inaccurate results. Moreover, the influence of the inhomogeneity on the crack path cannot be seen. Here, a simple model for functionally graded materials is introduced. For this model, a formula for the change of potential energy is derived, giving detailed information on the effect of the gradation on crack propagation.