[pt] Para garantir que um componente estrutural resistirá ao longo de sua campanha operacional às trincas que podem não ter sido detectadas durante a última inspeção, é preciso estudar a tolerância aos defeitos nos componentes estruturais. As trincas longas podem ser modeladas por conceitos tradicionais da Mecânica da Fratura, mas as trincas curtas, em especial aquelas que partem de entalhes, não podem. O comportamento destas trincas curtas é modelado a partir do conceito do seu tamanho característico a0, proposto por El Haddad, Topper e Smith, que concilia o limite de iniciação de uma trinca por fadiga com o limiar de propagação das trincas longas. Para obtenção deste parâmetro, o limite de fadiga SL da liga de Al 6351-T6 é estimado por termografia e verificado extrapolando sua curva eN medida por procedimentos normalizados para uma vida útil muito longa. O limiar de propagação das trincas longas DeltaKth é medido através de ensaios padronizados. Por último, tamanhos de trincas em corpos de prova de geometrias diferentes são previstos por aproximações analíticas a partir dos campos de tensões à frente dos entalhes Sigma y(x)/Sigma n por Inglis e Creager e Paris. / [en] To guarantee the structural integrity of a component during its operational life, it is necessary to study the tolerances to defects. Long cracks may be modeled by traditional concepts of Fracture Mechanics, but short cracks, especially those that start from notches, cannot. The behavior of these short cracks is modeled on the concept of characteristic size a0, presented by El Haddad, Topper and Smith, which reconciles the initiation limit of a fatigue crack with the propagation threshold of the long crack. To obtain this parameter, the fatigue limit SL is estimated by thermography, and thereafter, the result of the Al 6351-T6 alloy, presented in this work, is verified by extrapolating its eN curve measured by standard procedures for a very long service life. The propagation threshold of long cracks Kth is measured by the standard test. Finally, crack sizes in specimens for different geometries are predicted by analytical approximations from the stress fields ahead of the notches by Inglis and Creager and Paris.

Foram estudadas as propriedades de fadiga em dois grupos de soldas de alta resistência e baixa liga com diferentes composições microestruturais. As soldas do grupo A apresentaram microestruturas compostas de ferrita acicular, ferrita alotriomórfica e ferrita de Widmanstätten, com limite de escoamento de aproximadamente 460 MPa, enquanto que as soldas do grupo B apresentaram microestruturas compostas de martensita de baixo carbono, bainita e ferrita acicular, com limite de escoamento de aproximadamente 850 MPa. A partir do ensaio de trincas longas, foi obtida a taxa de crescimento por ciclos de carregamento, da/dN, de da/dN=1,18·10-12·DeltaK2,91 e da/dN=1,34·10-11·DeltaK2,64, respectivamente para as soldas dos grupos A e B. Como pode ser observado a partir destas equações, a taxa de crescimento foi mais alta para o grupo B. Da análise do fechamento da trinca pode ser concluído que o principal fator determinante de uma menor taxa de propagação para as soldas do grupo A foi a plasticidade desenvolvida pela estrutura. Dos ensaios de trincas curtas foi observado que no caso das soldas do grupo A, uma vez nucleada a trinca, esta se propagava até o colapso do corpo de prova. Para as soldas do grupo B foi observado que não bastava a existência de uma trinca para que esta se propagasse até a fratura total do corpo de prova e que o fator controlador foi a granulomentria associada a uma determinada composição microestrutural. / The fatigue properties of two groups of high strength low alloy steel weld metals with different microstructural composition were studied. Weld metals from group A presented microstructures composed of acicular ferrite, Widmanstätten ferrite and allotriomorphic ferrite, with yield strength of 460 MPa. Weld metals from group B exhibited a microstructural composition of low carbon martensite, bainite and acicular ferrite, with a yield strength of 850 MPa. The fatigue crack growth per cycle of loading, da/dN, for weld metals from groups A and B is obtained from the relationships, da/dN=1,18·10-12·DeltaK2,91 and da/dN=1,34·10-11·DeltaK2,64, respectively. As can be seen from these equations, the crack growth rate was higher for group B. From the crack growth closure analysis, it may be concluded that the lower crack growth rate obtained for weld metals from group A was mainly due to the higher crack tip plasticity developed in this type of microstructure. From the short crack fatigue tests, it was observed for weld metals from group A, that once a crack was nucleated, it propagated until the testpiece plastic collapsed. For weld metals from group B, it was observed that the existence of a crack was not sufficient to cause the complete testpiece failure, and the association of the grain size with the local microstructure was the main factor controlling the failure process.

High cycle fatigue tests were carried out on a medium strength continuous casting AA 5754 Al alloy, and new generation high strength AA 2026 and AA 2099 Al alloys. The effect of texture on fatigue properties and short crack behavior were studied. The strengthening mechanisms were also thoroughly investigated for the two high strength alloys.Texture played an important role in the anisotropy of fatigue strength for the AA 5754 Al alloy. Being a solution strengthened alloy, it had a fatigue strength of 120% σy. High strength Al alloys had a strong tendency for planar slip due to the high density of coherent and shearable precipitates in the alloys. Texture was a key factor controlling the crack initiation and propagation. The crack path and the possible minimum twist angles were measured using EBSD and calculated theoretically by a crystallographic model. Based on the micro-texture measured by EBSD, the crack paths were predicted for the AA 2099 alloy and confirmed by the observed values.The excellent balance of superior fatigue properties and high tensile strength of AA 2026 and AA 2099 was attributed to the reduced population of Fe-containing particles, homogeneously distributed precipitates and dislocations. The addition of Zr coupled with the optimized thermo-mechanical treatment strongly restrained the recrystallization, refined the grain structure and promoted the homogenization of the precipitates. Moreover, the retainment of the deformation texture developed during the hot extrusion provided significant orientation strengthening in the high strength Al alloys.Fatigue cracks tended to initiate at coarse second phase particles on sample surfaces and the crack population varied markedly with the applied stresses in the high strength Al alloys. The relationship between of the crack population and the applied stress level was studied and quantified by a Weibull distribution function. Since the measured cracknumbers were associated with the crack initiate sites (i.e., the weakest links) in an alloy, the fatigue weakest-link density, which is defined as the crack population per unit area when stress close to the ultimate tensile stress, and the weakest-link strength distribution can all be calculated and regarded as a property of the studied materials.

abstract: A full understanding of material behavior is important for the prediction of residual useful life of aerospace structures via computational modeling. In particular, the influence of rolling-induced anisotropy on fatigue properties has not been studied extensively and it is likely to have a meaningful effect. In this work, fatigue behavior of a wrought Al alloy (2024-T351) is studied using notched uniaxial samples with load axes along either the longitudinal or transverse direction, and center notched biaxial samples (cruciforms) with a uniaxial stress state of equivalent amplitude about the bore. Local composition and crystallography were quantified before testing using Energy Dispersive Spectroscopy and Electron Backscattering Diffraction. Interrupted fatigue testing at stresses close to yielding was performed on the samples to nucleate and propagate short cracks and nucleation sites were located and characterized using standard optical and Scanning Electron Microscopy. Results show that crack nucleation occurred due to fractured particles for longitudinal dogbone/cruciform samples; while transverse samples nucleated cracks by debonded and fractured particles. Change in crack nucleation mechanism is attributed to dimensional change of particles with respect to the material axes caused by global anisotropy. Crack nucleation from debonding reduced life till matrix fracture because debonded particles are sharper and generate matrix cracks sooner than their fractured counterparts. Longitudinal samples experienced multisite crack initiation because of reduced cross sectional areas of particles parallel to the loading direction. Conversely the favorable orientation of particles in transverse samples reduced instances of particle fracture eliminating multisite cracking and leading to increased fatigue life. Cyclic tests of cruciform samples showed that crack growth favors longitudinal and transverse directions with few instances of crack growth 45 degrees (diagonal) to the rolling direction. The diagonal crack growth is attributed to stronger influences of local anisotropy on crack nucleation. It was observed that majority of the time crack nucleation is governed by the mixed influences of global and local anisotropies. Measurements of crystal directions parallel to the load on main crack paths revealed directions clustered near the {110} planes and high index directions. This trend is attributed to environmental effects as a result of cyclic testing in air. / Dissertation/Thesis / M.S. Mechanical Engineering 2011

Cette thèse s’inscrit dans le cadre général de l’étude de la tolérance au dommage des pièces tournantes dans les turbomachines d’hélicoptères et porte sur la résistance à la propagation de fissures courtes 2D.Pour mener à bien cette étude, l’effet de la température est d’abord étudié sur les seuils de propagation de fissures longues à R=0,1 sur deux alliages TA6V et Ti6242 de microstructure bimodale (20°C et 400°C pour le TA6V et 20°C, 200°C et 500°C pour le Ti6242). Au voisinage du seuil, le comportement effectif(après correction de la fermeture) est sensiblement identique pour les deux alliages aux températures testées. La fermeture est principalement induite par l’oxyde à haute température et par la rugosité des surfaces de rupture à température ambiante.L’évolution du seuil de propagation en fonction de la longueur de fissure a ensuite été étudiée à R=0,1. Un outil de détermination automatique du niveau de fermeture a été mis en place afin d’améliorer la mesure pour des fissures très courtes (80 μm). La fermeture mesurée pour différentes longueurs de fissure obtenues par usinage progressif du sillage plastique est comparable à celle obtenue au cours de la propagation d’une fissure courte 2D au seuil, sauf pour les hautes températures où la fermeture induite par l’oxyde se développe rapidement. Les différences de comportement entre fissure longue et fissure courte sont expliquées par une contribution réduite de la fermeture lorsque le sillage de la fissure est réduit.Un critère de non-propagation s’inspirant du formalisme initialement proposé par Kitagawa et une loi de propagation adaptée permettent de mieux prédire la résistance à la propagation des fissures physiquement courtes. / Damage tolerance analyses of rotating parts, containing 2D-short crack, in turbomachines of helicopters is the main focus of this thesis.Fatigue crack propagation tests were performed at R=0.1 on two bimodal Titanium alloys at different temperatures (20°C and 400°C for TA6V and 20°C, 200°C and 500°C for Ti6242). Near-threshold effective behaviors (after crack closure correction) were approximately the same for the two alloys attested temperatures. Crack closure was principally due to oxide layer at high temperatures and to fracture surface roughness at ambient temperature.Then the variations of the crack propagation threshold with crack length was studied at R=0.1 and different temperatures. A numerical tool was developed to automatically detect crack closure level more precisely for, as short as, 80μm cracks. Crack closure levels measured at different crack lengths obtained from progressive machining of the plastic wake were quite similar to the ones obtained during propagation of 2D-short cracks near the threshold, except at high temperatures where oxide-induced crack closure developed rapidly. Differences in behavior of long cracks and short cracks were explained by a reduction of crack closure level when crack wake was not fully developed.A non-propagation criterion based on formalism initially proposed by Kitagawa and a modified-Paris propagation law allow to give a better description of physically 2D-short crack propagation resistance.

Foram estudadas as propriedades de fadiga em dois grupos de soldas de alta resistência e baixa liga com diferentes composições microestruturais. As soldas do grupo A apresentaram microestruturas compostas de ferrita acicular, ferrita alotriomórfica e ferrita de Widmanstätten, com limite de escoamento de aproximadamente 460 MPa, enquanto que as soldas do grupo B apresentaram microestruturas compostas de martensita de baixo carbono, bainita e ferrita acicular, com limite de escoamento de aproximadamente 850 MPa. A partir do ensaio de trincas longas, foi obtida a taxa de crescimento por ciclos de carregamento, da/dN, de da/dN=1,18·10-12·DeltaK2,91 e da/dN=1,34·10-11·DeltaK2,64, respectivamente para as soldas dos grupos A e B. Como pode ser observado a partir destas equações, a taxa de crescimento foi mais alta para o grupo B. Da análise do fechamento da trinca pode ser concluído que o principal fator determinante de uma menor taxa de propagação para as soldas do grupo A foi a plasticidade desenvolvida pela estrutura. Dos ensaios de trincas curtas foi observado que no caso das soldas do grupo A, uma vez nucleada a trinca, esta se propagava até o colapso do corpo de prova. Para as soldas do grupo B foi observado que não bastava a existência de uma trinca para que esta se propagasse até a fratura total do corpo de prova e que o fator controlador foi a granulomentria associada a uma determinada composição microestrutural. / The fatigue properties of two groups of high strength low alloy steel weld metals with different microstructural composition were studied. Weld metals from group A presented microstructures composed of acicular ferrite, Widmanstätten ferrite and allotriomorphic ferrite, with yield strength of 460 MPa. Weld metals from group B exhibited a microstructural composition of low carbon martensite, bainite and acicular ferrite, with a yield strength of 850 MPa. The fatigue crack growth per cycle of loading, da/dN, for weld metals from groups A and B is obtained from the relationships, da/dN=1,18·10-12·DeltaK2,91 and da/dN=1,34·10-11·DeltaK2,64, respectively. As can be seen from these equations, the crack growth rate was higher for group B. From the crack growth closure analysis, it may be concluded that the lower crack growth rate obtained for weld metals from group A was mainly due to the higher crack tip plasticity developed in this type of microstructure. From the short crack fatigue tests, it was observed for weld metals from group A, that once a crack was nucleated, it propagated until the testpiece plastic collapsed. For weld metals from group B, it was observed that the existence of a crack was not sufficient to cause the complete testpiece failure, and the association of the grain size with the local microstructure was the main factor controlling the failure process.

Les divers composants d'un réacteur d'avion sont soumis à des chargements de fatigue mécaniques et thermiques fortement variables. Afin de prédire au mieux leurs durées de vie, il est alors nécessaire de prendre en compte l'ensemble de ces variations. Pour ce faire, un modèle représentant de façon incrémentale l'évolution de la plasticité en pointe de fissure a été développé. Celui-ci permet de prédire la vitesse de propagation d'une fissure tout en prenant en compte les effets d'histoire provenant de la plasticité produite lors de surcharges ou de sous-charges. Dans cette étude, ce modèle condensé de plasticité a été exprimé plus simplement à partir du facteur d'intensité des contraintes et l'identification automatisée de ses divers paramètres a été redéveloppée. Dans ce but, un essai de fissuration stable a été conçu pour déterminer simplement le seuil de non-propagation du matériau. Par ailleurs, les éventuelles fissures se propageant dans un composant sont en général amorcées en surface à partir de chocs ou de rayures. Ces fissures passent la majeure partie de leur vie dans un régime de propagation de fissure courte, différant de celui d'une fissure longue. En effet, à facteur d'intensité des contraintes équivalent, une fissure courte se propagera plus rapidement qu'une fissure longue. La prise en compte de ce comportement dans la prédiction de durée de vie est donc primordiale. En outre, il a été observé qu'une fissure longue subissant une contrainte T négative se propage de façon analogue à une fissure courte. Il a donc été choisi de développer un nouveau modèle adapté aux fissures courtes en prenant en compte l'influence de la contrainte T sur la vitesse de propagation. Enfin, à partir des essais de fissuration stable, un protocole a été développé pour réaliser des éprouvettes comportant fissure courte. Une campagne d'essais multiaxiaux pour différentes valeurs de contrainte T a été menée en régime permanent et transitoire afin d'étudier les similitudes entre effet de fissure courte et influence de la contrainte T. / The various components of an aircraft engine undergo strong changes in mechanical and thermal fatigue loadings. All these variations must be taken into account in order to anticipate the components' total fatigue life to the best. An incremental model showing the changes in plasticity at the crack tip has therefore been developed. It allows us to foresee the crack growth rate with history effects by modelling the plastic behaviour produced when overloads or underloads occur. In this study, the plasticity condensed model has been represented in an easier way, using the stress intensity factor and the automated identification of its parameters has been redeveloped. A stable crack growth test has been designed to determine easily the fatigue crack growth threshold of the material. Cracks usually grow from scratches or impacts on the surface of the component. These cracks spend much of their fatigue life growing with a short crack behaviour, differing from the long crack one. As a matter of fact, a short crack grows faster than a long crack for a same stress intensity factor. This behaviour must therefore be taken into account while modelling the crack growth to accurately predict the total fatigue life of the component. It appeared furthermore that a long crack undergoing a negative T-stress grows the same way as a short crack. It has consequently been chosen to develop a short crack growth model using the influence of T-stress on the crack growth rate. Finally, using the stable crack growth specimens, an experimental protocol has been designed to produce new specimens containing a short crack. A multiaxial tests campaign was carried out for various values of T-stress in permanent and transitional regimes in order to compare short crack and T-stress effects.

X-Ray Diffraction Contrast Tomography (DCT) is a recently developed, non-destructive synchrotron imaging technique which characterizes microstructure and grain orientation in polycrystalline materials in three dimensions (3D). By combining it with propagation based phase contrast tomography (PCT) it is for the first lime possible to observe in situ the 3D propagation behavior of short fatigue cracks (SFCs) within a set of fully characterized grains (orientation and shape). The combined approach, termed 3D X-ray Tomography of short cracks and Microstructure (3DXTSM), has been developed on the metastable beta titanium alloy "Beta21S". A large part of this work deals with the development of the 3DXTSM methodology. In the combined dataset, each point on the 3D fracture surface can be associated with a multidimensional data structure containing variables describing the grain orientation, the local fracture surface normal and the propagation history. The method uses a surface mesh composed of triangles that describes the crack (in other words: the fracture surface) in the last propagation state measured. Grain orientations, crack fronts, local growth rates and grain boundaries can be visualized by assigning colors to this mesh. The data structure can be interrogated in a number of different ways. Tools for extracting pole figures and pole density distribution functions have been implemented. An algorithm was developed that is capable of measuring the 3D local growth rate of a crack containing branches. The accuracy of the grain boundaries as reconstructed with OCT was evaluated and the elastic constants of Beta21S were determined.

Cette thèse fait partie d’un programme de recherche international (IRG Cognac). Lancé par le motoriste SNECMA (groupe SAFRAN), ce projet regroupe l’ENS Cachan, UnB, ENSMA, CNRS, Snecma, Turbomeca et Messier Bugatti Dowti, et se concentre sur l’effet du gradient des contraintes sur endommagement par fretting fatigue. Le fretting-fatigue se réfère au processus d’endommagement localisés en bord de fuite entre deux corps en contact soumis à un chargement de fatigue. La maitrise de ce phénomène est d’une importance cruciale dans la détermination des durées de vie des disques de turbine. En bord de contact, le champ de contrainte hérité des forces de contact est maximal à la surface mais présente un fort gradient en s’éloignant du contact.Il a été montré dans cette thèse que pour l’alliage Ti-6AL-4V, les approches locales, basés sur le niveau de contrainte au points critiques ne sont pas applicable dans ces conditions. Une approche non locale, s’appuyant sur la théorie de la distance critique a donc été utilisée. En effet, des fissures courtes initiées au point critique peuvent propager jusqu’à rupture ou peuvent s’arrêter si la diminution des contraintes est suffisamment sévère. Une seconde difficulté réside dans la nature multiaxial et localement non proportionnel du chargement. Le fretting fatigue est généralement créé par la superposition d’un chargement de fatigue cyclique, d’une force normale à la surface souvent considérée constante, et d’une force cyclique tangentiel à la surface mais dont la fréquence peut être différente de celle de la fatigue.Les résultats des essais réalisés ont mis en évidence l’effet du gradient des contraintes sur la fissuration et ont étaient utilisés pour évaluer le potentiel de diffèrent critères pour le dimensionnement en fatigue des structures. La simulation du phénomène a en effet été réalisé en utilisant différente approches. La première s’appuie sur la Théorie de la distance critique et utilise un critère multiaxial. La seconde utilise l’amplitude du facteur d’intensité des contraintes, ΔK, pour prédire l’arrêt des fissures courtes. Finalement un récent modèle construit comme un critère de plasticité en pointe de fissure a été appliqué au problème de fretting fatigue. Ce critère a pour particularité de prendre en compte la contrainte T dans le développement asymptotique en pointe de fissure. / This thesis is part of an international research program (IRG Cognac) initiated by the engine manufacturer SNECMA (SAFRAN group) involving ENS Cachan, UnB, ENSMA, CNRS, Snecma, Turbomeca et Messier Bugatti Dowty. The thesis focuses on the effect of a stress gradient in fretting fatigue. Fretting-fatigue refers to the damage process localized at the frontier of the contact between two contacting bodies subjected to fatigue loadings. The prediction of this phenomenon is of major importance in determining, for instance, the lifetime of fan's disc. In the vicinity of the contact front, the stress field inherited from the contact loads is maximal at the surface and displays a strong gradient from the surface. It was shown in this thesis, for a Ti-6AL-4V alloy, that local approaches, based on local stresses at the most critical point, are not appropriate to predict fretting fatigue lives. As a matter of fact, short cracks initiated at the most critical point may stop if the stress decay from the surface is strong enough or may continue their growth, up to the failure of the component, if the stress gradient from the surface is not string enough. A second difficulty is the multiaxial and non-proportional nature of the loading conditions. Fatigue-fretting stems from the combination of loads that have neither the same spatial distribution nor the same time-dependency. In fretting-fatigue tests, three loading components are considered, the fatigue loading of the component (cyclic), the normal part (assumed to be constant) and the in-plane part (cyclic) of the loads between the two contacting components. To quantify the effect of the stress gradient, tests were carried out on a fatigue testing contact bench developed at the University of Brasilia, with experimental conditions ensuring different stress gradient while keeping the maximal stress the same. Damage mechanisms were studied using post-mortem analysis and optical microscopy on the contact elements tested. The prediction of the fretting fatigue life was done using different approaches. The first one is based on the Critical Distance Method and a fatigue criterion. The second is based on a K-based short crack arrest method. Finally, a new criterion was proposed. This method considers a generalized von Mises yield criterion for the crack tip region and accounts for the T-stresses in the asymptotic LEFM development.

The fatigue life and the kinetics of short crack growth in specimen of austenitic-ferritic duplex steel cycled with constant stress amplitude and different mean stresses is studied. Fatigue life was determined on smooth cylindrical specimens. Strain amplitude and mean strain were recorded. Short crack growth was studied in cylindrical specimens with a shallow notch. Cyclic straining was interrupted and crack length was measured using an optical microscope mounted on the testing machine. Crack length and crack growth rates were evaluated. The effect of the mean stress on the rate of short cracks and fatigue life were discussed.