The importance of compressive stresses on fatigue crack propagation rate

This paper is concerned with the importance of compressive stresses on crack propagation rate. In a previous paper, namely ‘Crack Closure Inadequacy at Negative Stress Ratios’, Int. Journal of Fatigue, 26, 2004, pp. 241–252, was demonstrated the inadequacy of the crack closure concept and ΔK_eff, at a negative stress ratio, R=−1, to predict crack propagation rate. It that paper was verified that, at negative stress ratios, crack closure changes with P_max, for the same R ratio. The main conclusion was about plastic properties and mainly cyclic plastic properties, the Bauschinger effect included, on crack propagation when compressive stresses exist. It was then suggested that in the place of the crack closure concept, another concept based on plasticity should be used to explain fatigue crack propagation.In this paper, instead of working with the same negative R ratio (R=−1), a study on the behavior of crack propagation rate as a function of R ratio, from negative to positive stress ratios, is made. Both the effect of P_max and of R ratio is taken into consideration. Measurements of roughness and of crack opening loads are made, in order to verify their influence on crack propagation rate. Different materials, in order to cover different cyclic plastic properties and different sensitivities to roughness are studied (Ck45-cyclic hardening; Ti6Al4V-cyclic softening, and aluminum, Al 7175-cyclically neutral) are studied. Aluminium alloys and titanium alloys are considered to be sensitive to roughness induced crack closure (RICC) while steels are more dependent on plastic properties (PICC).In this study it is emphasized the importance of the compressive part of the cycle, and of cyclic plastic properties, on crack propagation rate. It is reassessed the inadequacy of crack closure concept and ΔK_eff to describe crack propagation rate, at negative stress ratios. It is also verified that models based solely on extrinsic properties of materials, like da/dN−ΔK or da/dN−ΔK (K_max) should also incorporate intrinsic properties of the materials in order to properly correlate fatigue crack growth.     

Significant effect of thermal stresses on fatigue crack propagation properties

Fatigue crack propagation properties of low-alloy ferritic steel were investigated using 50-mm-wide compact-type (CT) specimens and 200-mm-wide center-cracked-type (CCT) specimens at room temperature and 300°C. Most of the stress ratios were nearly equal to zero. Significant differences in fatigue crack propagation rate in the CCT specimen, which was heated to the test temperature only locally near the crack plane, were compared with the rates for the CT specimen which was enclosed completely by a furnace. It was found that the differences were related to the compressive stresses arising from the thermal gradients.

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Résumé On étudie les propriétés de propagation des fissures de fatigue dans un acier ferritique faiblement allié à l'aide d'éprouvettes de traction compactes CT longues de 50 mm et d'éprouvettes de traction à fissure centrale (CCT) longues de 200 mm, à température ambiante et à 300°C. Dans la plupart des cas, les rapports de contraintes R sont égaux à zéro. On constate et on compose des différences importantes de vitesses de propagation en fatigue sur les éprouvettes CCT où le chauffage jusqu'à température d'essai est appliqué localement au voisinage du plan de la fissure, par rapport aux vitesses de propagation constatées sur les éprouvettes CT complètement insérées dans un four. On trouve que ces différences sont liées aux contraintes de compression associées aux gradiants thermiques.

     

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.     

Elastic–plastic finite element analysis of the effect of compressive loading on crack tip parameters and its impact on fatigue crack propagation rate

The effects of applied compressive stress on the crack tip parameters and their implications on fatigue crack growth have been studied. Four center-cracked panel specimens with different crack lengths are analysed using finite element method. The results show that under tension–compression loading the local crack tip parameters are determined by two loading parameters. The two loading parameters are the maximum stress intensity and the maximum compressive stress in the applied stress cycle. Predictions of fatigue crack propagation behaviour based on the maximum stress intensity and maximum compressive stress agree well with experimental observations.     

Effect of mechanical properties of material on rate of fatigue crack propagation

Many experimental and analytical equations on a rate of a fatigue crack propagation have been proposed. However, it seems that they can not fully express its complex behavior. There are still many problems remaining to be solved in order to clarify its mechanism. One of them is to clarify the relation between the rate of the crack propagation and the mechanical properties of material. In this paper, the rate of the crack propagation is analysed to clarify this problem. This analysis is based on the observation results of the fatigue crack propagation behavior previously by the authors. The analytical result is compared with the experimental one to make sure that they agree with each other. The conclusion obtained is; the rate of fatigue crack propagation is expressed by using the stress intensity factors as

$\text{dl}\text{dN}\text{= {}\text{c}\text{[Y}{}^2\text{F}{}^{\mathrm{a}}\text{E}{}^{\mathrm{a(1?n)}}\text{]}\text{} (K}{}_{\max }\text{)}{}^2\text{(K}{}_{\mathrm{a}}\text{)}{}^{\mathrm{a(2?n)}}$

. where C is a constant; E, Young's modulus; F, plastic coefficient; Y, yield stress; K_max and K_a, maximum and amplitude of the stress intensity factor, and α and n, exponents of the Manson-Coffin's law and work-hardening.     

Mechanical loading and cyclic heating phase shift effect on fatigue crack propagation rate. Part 2. Fatigue crack propagation rate prediction

Using the relation between plastic zone size in the crack tip vicinity, loading cycle parameters, and material properties, which has been derived in Part 1, we have elaborated fatigue crack propagation rate prediction for low-cycle mechanical loading combined with cyclic heating with account of the phase shift effect. The data for governing equation were obtained from simple tests. Application of the proposed method yields a good fit of calculated and experimental results.     

The influence of crack depth on the fatigue crack propagation rate for a marine steel in seawater

It has been shown that, for QIN steel specimens tested in seawater at a zero-tension cyclic frequency of 30 cycles per hour, crack growth rates are influenced by crack depth at low values of the stress intensity range (K). Crack growth rates are faster for shallow cracks in the crack depth range 0.5 to 2.0 mm when K is less than about 30 MN m^–3/2. For deeper cracks at low stress intensity ranges and for all crack depths at high stress intensity ranges, crack depth does not exert a significant influence on crack growth rate. The implications of such factors in relation to the provision of corrosion fatigue crack growth rate data for use in engineering design are discussed.     

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.

     

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 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.     

Analysis of crack propagation during tooth interior fatigue fracture

Tooth interior fatigue fracture is a failure mode that is initiated as a fatigue crack in the interior of the tooth of a gear. TIFF cracks have been observed in case hardened idler gears. A fracture mechanical analysis of a TIFF crack is performed utilising FEA. A 3D TIFF crack is modelled at a position in the tooth that corresponds with an observed crack surface. The different material properties in the case and the core, determined by mechanical testing, are considered, as well as the residual state of stress due to case hardening. Various crack lengths are analysed to estimate crack propagation both into the core and into the case. The following results have been found:

• A TIFF crack initiated slightly under the case layer will propagate into the case layer where it stops.

• The main crack propagation will take place in the core.

• The crack propagation is only a small portion of the total life (order of 10⁵ cycles).

• After reaching the case layer the TIFF crack eventually deflects toward the tooth root and the upper part of the tooth falls off. The crack deflection is due to redistribution of contact loading. Several gear teeth pairs are simultaneously in contact and the cracked tooth is loaded less than the uncracked during this stage of life.

Microstructural effects on crack closure and propagation thresholds of small fatigue cracks

The crack closure behaviour of microstructurally small fatigue cracks was numerically simulated by combining the crack-tip slip band model with the plasticity-induced crack closure model. A Stage II crack started to propagate from an initiated Stage I crack. When the plastic zone was constrained by the grain boundary or the adjacent grain with higher yield stresses, the crack opening stress increased with crack extension, and the effective component of the stress range decreased. The crack-tip opening displacement range (Δ CTOD ), first decreased with crack extension due to the development of the residual stretch, then increased until the tip of the plastic zone reached the neighbouring grain boundary. When the plastic zone was blocked by the grain boundary, Δ CTOD began to decrease. The arrest condition of cracks was given by the threshold value of Δ CTOD . At the fatigue limit, the arrest of small cracks takes place just after the Stage II crack crosses the grain boundary when the grain boundary does not act as a barrier. Only when the grain boundary has a blocking strength and the yield stress of adjacent grains is not so high, the arrest of Stage II cracks takes place before the crack reaches the grain boundary. The fatigue limit decreases with the mean stress. The predicted relation between the fatigue limit and the mean stress is close to the modified Goodman relation.     

Numerical simulation of fatigue crack propagation in compressive residual stress fields of notched round bars

In this paper, the influence of the residual compressive stresses induced by roller burnishing on fatigue crack propagation in the fillet of notched round bar is investigated. A 3D finite element simulation model of rolling has allowed to introduce a residual stress profile as an initial condition. After the rolling process, fatigue loading has been applied to three‐point bending specimens in which an initial crack has been introduced. A numerical predictive method of crack propagation in roller burnished specimens has also been implemented. It is based on a step‐by‐step process of stress intensity factor calculations by elastic finite element analyses. These stress intensity factor results are combined with the Paris law to estimate the fatigue crack growth rate. In the case of roller burnished specimens, a numerical modification concerning experimental crack closure has to be considered. This method is applied to three specimens: without roller burnishing, and with two levels of roller burnishing (type A and type B). In all these cases, the computational finite element predictions of fatigue crack growth rate agree well with the experimental measurements. The developed model can be easily extended to crankshafts in real operating conditions.     

The effects of the plastic wake zone on the conditions for fatigue crack propagation

Closure is investigated with an optical interference technique which measures the transverse displacement associated with a propagating fatigue crack. The results of this study require that closure be devided into two phenomena, each of which affects the propagating mechanism differently. The plastic region is partitioned into the plastic wake zone behind the crack front and the active plastic zone ahead of the crack. The work to be presented deals with the effects of the plastic wake zone on fatigue crack propagation. It is found that the contact length between the crack faces can be several times the specimen thickness dimensions and that contact occurs only in the plane stress region of the specimen. It is concluded that the contact forces between the crack faces act like some external tensile load, modifying the K _Imin of the loading cycles with low R-ratios. But, contact between the fracture faces (and the plastic wake zone) cannot account for any overload effects. The occurence of contact in the plane stress region of the specimen explains the observed thickness dependence of fatigue crack growth rates.

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Résumé La fermeture d'une fissure est étudiée à l'aide d'une technique d'interférence optique qui mesure le déplacement transversal associé à la propagation d'une fissure de fatigue. Les résultats de cette étude implique que la fermeture soit divisée en deux phénomènes dont chacun affecte le mécanisme de propagation de manière différente. La région plastique est divisée en une zône plastique de sillage qui suit le front de fissure et une zône plastique active en amont de la fissure. Le travail présenté est relatif aux effets de la zone plastique de sillage sur la propagation d'une fissure de fatigue. On trouve que la longueur de contact entre les faces de la fissure peut être plusieurs fois plus importante que l'épaisseur de l'éprouvette et que le contact se produit seulement dans la zône d'état plan de tension de l'éprouvette. On en conclut que les forces de contact entre les faces de la fissure agissent à la manière d'une contrainte de traction extérieure qui modifie le K _Imin du cycle de sollicitation pour des faibles valeurs de rapport R. Néanmoins, le contact entre les faces de rupture et la zône de sillage plastique ne peut rendre compte de tous les effets de surcharge. L'apparition d'un contact dans la zône d'état plan de tension d'une éprouvette explique la dépendance de l'épaisseur qui a été observée dans les vitesses de croissance d'une fissure de fatigue.