Due to the increasing use of cyclically loaded cast aluminum components in automotive and aerospace applications, fatigue and fatigue crack growth characteristics of aluminum castings are of great interest. Despite the extensive research efforts dedicated to this topic, a fundamental, mechanistic understanding of these alloys' behavior when subjected to dynamic loading is still lacking. This fundamental research investigated the mechanisms active at the microstructure level during dynamic loading and failure of conventionally cast and SSM Al-Si-Mg alloys. Five model alloys were cast to isolate the individual contribution of constituent phases on fatigue resistance. The major constituent phases, alpha-Al dendrites, Al/Si eutectic phase, and Mg-Si strengthening precipitates were mechanistically investigated to relate microstructure to near-threshold crack growth (Delta Kth) and crack propagation regimes (Regions II and III) for alloys of different Si composition/morphology, grain size, secondary dendrite arm spacing, heat treatment. A procedure to evaluate the actual fracture toughness from fatigue crack growth data was successfully developed based on a complex Elastic-Plastic-Fracture-Mechanics (EPFM/J-integral) approach. Residual stress-microstructure interactions, commonly overlooked by researches in the field, were also comprehensively defined and accounted for both experimentally and mathematically, and future revisions of ASTM E647 are expected.

Made available in DSpace on 2017-07-21T20:43:45Z (GMT). No. of bitstreams: 1 Luis Otavio Ribas Lima.pdf: 8124964 bytes, checksum: d16bc8c64f9e15d57f770b1b271d6b3b (MD5) Previous issue date: 2014-06-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Aluminum alloys have been the primary material of choice for the aircraft due to their properties such as low density, high mechanical and corrosion resistance. Commercial aircraft apply aluminum alloys for the fuselage, wings and supporting structure due to the extensive knowledge in design and production of aluminum components, and most importantly, aluminum alloys continue to be developed, keeping it highly competitive. A great development happen with the heat-treatable alloys, which allow improvement of the mechanical properties. Among this alloys stand out the Al-Zn-Mg-Cu series, known for high strength, toughness and corrosion resistance. The improvement of those alloys occurs by the precipitation of nanometric particles MgZn2, called η phase. This study’s aim was to promote an interrupted heat treatment T6I4-65 in an AA7050 aluminum alloy, with fatigue crack growth resistance as priority. Interrupted heat treatments’ goal is optimizing the consumption of solute atoms during process of nucleation and growth of precipitates as a finely dispersion. The T6I4-65 condition obtained was analyzed by differential scanning calorimetry, DSC, optical and electronic microscopy, mechanical tests as hardness, tensile and fatigue crack growth. The T6I4-65 treatment results in a microstructure with a fine dispersion of precipitated phase η’, about 75% smaller than those resulting from in current use, T7451. This microstructure resulted in a reduction of up to 24% in fatigue crack growth rate compared to that resulting from T7451 treatment, keeping the ductility of 17% of area reduction and yield strength higher than 400MPa. / Ligas de alumínio são o principal material de uso na indústria aeronáutica devido a suas propriedades como baixa densidade, alta resistência mecânica e a corrosão. Aeronaves comerciais utilizam ligas de alumínio em sua fuselagem, asas e na estrutura de suporte devido ao extenso conhecimento no projeto e produção de componentes em alumínio, e mais importante, as ligas de alumínio continuam a serem desenvolvidas, mantendo-se altamente competitivas. Ocorreu um grande avanço com o desenvolvimento das ligas tratáveis termicamente, que permitiram a otimização das propriedades mecânicas. Entre estas ligas tratáveis, destaca se a família Al-Zn-Mg-Cu, conhecidas pela alta resistência mecânica, tenacidade e resistência a corrosão. O aperfeiçoamento destas ligas ocorre pela precipitação de partículas nanométricas de MgZn2, conhecida como fase η. O objetivo deste trabalho foi obter um tratamento térmico interrompido T6I4-65 em uma liga de alumínio AA7050 com prioridade ao aumento de resistência à propagação de trinca por fadiga. Tratamentos interrompidos tem por objetivo otimizar o consumo de átomos de soluto durante os processos de nucleação e crescimento dos precipitados endurecedores na liga na forma de dispersão finamente dispersa. A condição T6I4-65 obtida foi analisada por meio de calorimetria diferencial de varredura, DSC, microscopia ótica e eletrônica de varredura e transmissão, ensaios mecânicos dureza, tração e propagação de trinca por fadiga. Este tratamento resultou em uma microestrutura com uma dispersão de finos precipitados de fase η’, cerca de 75% menores que os resultantes de tratamentos de uso corrente, T7451. Esta microestrutura promoveu a redução de até 24% na taxa de propagação de trinca por fadiga em comparação à resultante do tratamento T7451, mantendo grande ductilidade, até 17% de redução de área e limite de escoamento superior a 400MPa.

Ce mémoire présente une méthode mise au point pour caractériser et analyser des fissures de fatigue présentant un fort caractère tridimensionnel dans des matériaux métalliques opaques. L'analyse consiste à déterminer avec précision la position du front de la fissure étudiée et à mesurer des valeurs de facteurs d'intensité des contraintes le long du front par projection sur les séries de Williams du champ de déplacement issu de la corrélation numérique d'images 3D obtenues par tomographie aux rayons X. La corrélation d'images 3D numériques est utilisée afin de mesurer le champ de déplacement en volume lors de la mise sous chargement d'une éprouvette fissurée fatiguée. La corrélation d'images nécessitant un mouchetis, le matériau retenu pour les expériences est la fonte à graphite sphéroïdal car il présente un mouchetis 3D naturel (les nodules de graphites) parfaitement imagé par tomographie aux rayons X. Le cyclage est appliqué à l'aide d'une machine de fatigue in situ permettant d'alterner des phases de propagation de la fissure avec des acquisitions tomographiques sous différentes charges. L'introduction d'un défaut artificiel (une entaille obtenue par usinage laser) permet de maîtriser l'amorçage et la propagation de la fissure in situ. La méthode de corrélation d'images 3D numériques employée dans ces travaux étant basée sur des éléments finis, nous avons cherché à tirer profit de différents outils développés dans le cadre de cette méthode. Les surfaces libres sont spécifiées afin de bien conditionner le maillage et un enrichissement dans l'esprit des X-FEM permet de renseigner la fissure dont la position est repérée grâce à la trace laissée dans le résidu de corrélation entre l'image avant cyclage et la dernière image acquise. Une régularisation mécanique est également introduite dans le calcul sous forme d'un filtre de longueur d'onde choisie. Le champ de déplacement mesuré avec précision est ensuite projeté sur les séries de Williams augmentées des termes correctifs de Leblond et Torlai qui prennent en compte la courbure du front de la fissure. L'annulation du terme super-singulier d'ordre -1 des séries de Williams est utilisée pour détecter la position du front de la fissure. Une procédure itérative a été mise en place afin de concilier l'enrichissement et la courbure du front avec la projection sur les séries de Williams. Une fois la position du front 3D de la fissure déterminée et les valeurs des facteurs d'intensité des contraintes associées calculées, les résultats obtenus sont confrontés à la littérature. / This manuscript describes a methodology used to compute Stress Intensity Factor values along the curved front of a fatigue crack inside a nodular cast iron. An artificial defect is introduced at the surface of a small sample. The initiation and growth of a fatigue crack from this defect during constant amplitude cycling is monitored in situ by laboratory x-ray tomography. The method for processing the 3D images in order to compute SIF values is described in detail. The results obtained show variations of the stress intensity factor values along the crack front.

Ultrafeinkörnige metallische Werkstoffe haben verstärkt wissenschaftliche Bedeutung erlangt. Um dieser neuartigen Werkstoffklasse über die grundlagenorientierte Forschung hinaus einen Einsatz in technischen Anwendungen zu ermöglichen, ist es notwendig, deren Verhalten unter verschiedenen einsatzrelevanten Belastungsbedingungen vorhersagen zu können. In der vorliegenden Arbeit wird das Schädigungsverhalten einer ultrafeinkörnigen Aluminiumlegierung in den Bereichen der hochzyklischen (HCF) und niedrigzyklischen (LCF) Ermüdung sowie des Rissfortschritts untersucht. Im Mittelpunkt steht dabei die Identifikation der mikrostrukturell wirksamen Mechanismen bei der Entstehung und Ausbreitung von Ermüdungsrissen. Es werden ein homogen ultrafeinkörniger und ein bimodaler Zustand sowie verschiedene duktilitätsoptimierte Zustände betrachtet und systematisch der Einfluss der Korngröße, der Korngrößenverteilung, der Ausscheidungscharakteristik sowie der Festigkeit und Duktilität auf das Ermüdungs- und Rissfortschrittsverhalten ermittelt. Die Untersuchungen zeigen, dass das Schädigungsverhalten der ultrafeinkörnigen Aluminiumlegierung insbesondere durch die Korngröße und Korngrößenverteilung sowie den Kohärenzgrad der festigkeitssteigernden Ausscheidungen beeinflusst wird.

This thesis is on fatigue crack growth experiments and assessments of fatigue crack growth rates. Both constant and variable amplitude loads in two different materials are considered; a nickel based super-alloy Inconel 718 and a stainless steel 316L. The considered load levels extend from small scale yielding (SSY) to large scale yielding (LSY) for both materials. The effect of different load schemes on the fatigue crack growth rates is investigated on Inconel 718 and compact tension specimens in Paper A. It is concluded that load decreasing schemes give a to high Paris law exponent compared to constant or increasing load amplitude schemes. Inconel 718 is further analyzed in Paper B where growth rates at variable amplitude loading in notched tensile specimens are assessed. The predictions are based on the fatigue crack growth parameters obtained in Paper A. The crack closure levels are taken into consideration and it is concluded that linear elastic fracture mechanics is incapable of predicting the growth rates in notches that experience large plastic cyclic strains. Even if crack closure free fatigue parameters are used and residual stresses due to plasticity are included. It is also concluded that crack closure free and nominal fatigue crack growth data predict the growth rates equally well. However, if the crack closure free parameters are used, then it is possible to make a statement in advance on the prediction in relation to the experimental outcome. This is not possible with nominal fatigue crack growth parameters. The last three papers consider fatigue crack growth in stainless steel 316L. Here the load is defined as the crack tip opening displacement parameter. Paper C constitutes an investigation on the effect of plastic deformation on the potential drop and consequently the measured crack length. It is concluded that the nominal calibration equation obtained in the undeformed geometry can be used at large plastic deformations. However, two conditions must be met: the reference potential must be taken in the deformed geometry and the reference potential needs to be adjusted at every major change of plastic deformation. The potential drop technique is further used in Paper D and Paper E for crack length measurements at monotonic LSY. Constant amplitude loads are considered in Paper D and two different variable amplitude block loads are investigated in Paper E. The crack tip opening displacement is concluded in Paper D to be an objective parameter able to characterize the load state in two different geometries and at the present load levels. Furthermore, if the crack tip opening displacement is controlled in an experiment and the local load ratio set to zero, then only monotonic LSY will appear due to extensive isotropic hardening, i.e. elastic shake-down. This is also the reason why the linear elastic stress-intensity factor successfully could merge all growth rates, extending from SSY to monotonic LSY along a single line in a Paris law type of diagram, even though the generally accepted criteria for SSY is never fulfilled. For the variable amplitude loads investigated in Paper E, the effect of plastic deformation on measured potential drop is more pronounced. However, also here both the crack tip opening displacement parameter and the linear elastic stress-intensity factor successfully characterized the load state. / <p>QC 20130108</p>

La nitruration gazeuse est utilisée par les fabricants d’engrenages pour traiter la surface des dentures. En effet, l’augmentation de la dureté et l’introduction de contraintes résiduelles de compression contribuent à retarder voire inhiber l’initiation et la propagation des fissures superficielles de fatigue de contact. Cependant la majorité des aciers alliés présentent des réseaux de précipités de carbures dans la couche nitrurée. Ceux-ci ont la particularité de se retrouver aux joints de grains relativement parallèles à la surface, ce qui leurs ont attribué les surnoms de «liserés de carbures». Associés à une phase dure et fragile, ces carbures constituent des zones d’hétérogénéités. Par ailleurs, la norme pour la qualité des matériaux d’engrenages autorise une large gamme de tailles de grains, conduisant à diverses microstructures pour les couches nitrurées des aciers alliés. En effet, la morphologie des réseaux de carbures après nitruration dépend entre autres de la taille de grain de l’acier. De par le manque de travaux sur l’impact réel de ces précipités sur la fatigue de contact, la présente étude propose des analyses d’essais. Les essais consistent à reproduire de l’écaillage initié en surface sur des éprouvettes dont les couches nitrurées, issues d’un seul traitement thermochimique, présentent les mêmes propriétés mécaniques (dureté et contraintes résiduelles) mais différentes propriétés microstructurales (tailles de grains et morphologies de carbures). Les analyses ont permis de proposer des mécanismes d’initiation de micro-fissures induites en proche surface sous les conditions d’essai appliquées. Les sites d’initiation dépendent de la taille de grain de l’acier et peuvent en particulier s’établir au niveau des carbures intergranulaires. L’étude des réseaux de fissures couplée à l’analyse des contraintes résiduelles a permis d’établir des scénarii de propagation des fissures dans les couches nitrurées. Sous les conditions de contact appliquées, l’apparition de déformation plastique entraîne, par accommodation des variations de volume, la relaxation des contraintes résiduelles compressives initialement présentes dans le matériau, aux profondeurs les moins sollicitées. Ces contraintes étant moins compressives, elles libèrent les micro-fissures déjà présentes en proche surface. Dès lors, la propagation au travers des carbures qui s’apparentent à des sites privilégiés pour la croissance des fissures en cours de fatigue est possible. En particulier, ces précipités entraînent les fissures vers le cœur lorsqu’ils sont en forte densité dans les couches nitrurées, tandis que l’endommagement reste superficiel lorsque l’éloignement entre les précipités est trop important. Enfin, la continuité et la longueur des carbures augmentent localement la vitesse de propagation des fissures. Ceci se traduit par l’apparition plus rapide de l’écaillage initié en surface pour les couches nitrurées de microstructures grossières. / Gas nitriding is a thermochemical surface treatment widely used by gear manufacturers to improve the rolling contact fatigue endurance of their components. Indeed, increasing the hardness and introducing compressive residual stresses to the geartooth surfaces inhibit or delay crack initiation and propagation. However, most of the alloyed steel nitrided layers show the presence of intergranular carbide networks. The precipitation of these carbides specifically occurs at parallel grain boundaries during the treatment and, being a carbon-rich phase, they are associated to tough and fragile heterogeneities. Besides, standards for gear material quality recommend a broad range of steel grain sizes which lead to various possible microstructures on gear components after nitriding. Indeed, the intergranular carbide network morphology depends on the steel grain size. Since there is no evidence regarding the real effect of the carbides on rolling contact fatigue, this work presents experimental investigations carried out on a twin-disc machine. The tests consist in reproducing surface-initiated pitting on specimens whose nitrided layers, obtained by a unique thermochemical surface treatment, display similar mechanical properties (hardness and compressive residual stresses) but different microstructures (grain sizes and carbide network morphologies). The first analysis resulted in suggesting the micro-crack nucleation mechanisms. In this study, the test conditions were chosen to induce these micro-cracks near the disc surfaces. For a given contact stress field, nucleation sites depend on the steel grain size and can take place at intergranular carbides. Investigations of crack networks led on cross sections and 3D observations by means of high energy X-ray computed tomography, coupled with compressive residual stress evolution analysis, help the authors proposing the rolling contact fatigue crack propagation scenarios in nitrided layers. When contact shear stresses locally exceed the material micro-yield shear stress limit, micro-deformations arise and add compressive residual stresses to the treated layers. To accommodate these volume variations the compressive residual stresses, initially induced by nitriding, release at depths where contact stresses are lower. The pre-existing residual stresses being less compressive, micro-cracks near the surface can propagate through the carbides that act as preferential crack growth sites. When the nitrided layers display high carbide density, the intergranular precipitates drag the cracks toward the core, whereas rolling contact fatigue failures are limited to the near surface when the distance between the precipitates is too important. Finally, the length and the continuity of the carbides, linked to the steel grain size, locally increase the crack propagation speed. This gives rise to a lower endurance to surface-initiated pitting in coarse microstructures.

Ces travaux ont pour objectif l'identification et la compréhension de l'effet de la corrosion aqueuse sur la durée de vie en fatigue à grand nombre de cycles (HCF) d'un acier inoxydable martensitique utilisé dans des applications aéronautiques. Tout d'abord, l'effet géométrique des défauts de corrosion sur la limite de fatigue à 10^7 cycles à l'air a été étudié avec quatre tailles différentes de piqûres de corrosion. A partir de ces résultats, une nouvelle approche volumique non locale de modélisation numérique a été proposée pour prendre en compte une géométrie réelle d'un défaut de corrosion issu des analyses en microtomographie X. Ensuite, les phénomènes de couplage chargement cyclique/corrosion ont été identifiés par des essais de fatigue à grande durée de vie (entre 10^5 et 10^7 cycles) dans une solution aqueuse à 0,1 M NaCl (à pH = 6) pour deux rapports de charge (R = -1 et 0,1). Le comportement électrochimique du film passif a été étudié in situ au cours des essais de fatigue-corrosion par le suivi du potentiel libre de corrosion et des mesures d'impédance électrochimique. Les observations des mécanismes d'amorçage de fissures et des mesures électrochimiques in-situ ont permis d'identifier un scénario d'amorçage de fissures de fatigue. Ce scénario implique des processus de rupture locale du film passif (induite par le chargement cyclique) et de corrosion assistée par le chargement cyclique. Finalement un modèle analytiquede prévision de la durée de vie en fatigue dans un milieu aqueux corrosif a été proposé à partir des résultats expérimentaux. / This study addresses the effects of corrosion on the high cycle fatigue (HCF)strength of a martensitic stainless steel used in aeronautic applications. First, the geometry of corrosion pits on the fatigue strength in air at 10^7 cycles were studied with four different pit sizes. A new non-local fatigue criterion was proposed to simulate real shapes of pits as identified by X-ray microtomography. Corrosion fatigue synergy phenomena was studied by HCF tests (between 10^5 and 10^7 cycles) in a 0.1 M NaCl aqueous solution (pH = 6) with two load ratios (R = -1 and 0.1). Next, the electrochemical behavior of the passive film was investigated during in situ corrosion fatigue tests by free potential measurements and electrochemical impedance spectroscopy (EIS). Based on fractography analysis and electrochemical test results, corrosion fatigue crack initiation mechanisms were investigated. A scenario of fatigue crack initiation was proposed based on physical evidence. This scenario implied combined processes of local passive film rupture (induced by the cyclic loading), stress-assisted corrosion and enhanced pitting development. Local passive film ruptures were the main cause of the corrosion fatigue crack initiation. Finally, a analytical model for corrosion fatigue crack initiation was proposed based.

Main extrinsic and intrinsic modifiers factors of crack growth rate in AA7050-T7451 were assessed in order to provide tools for aeronautical structures designers. These tools cover most necessary information to project aircraft\'s structures using the studied alloy, under damage tolerance philosophy. The experimental methodology consisted of use CT specimens, on TL and LT rolling direction to test its behavior under different conditions of stress ratio, force waveform, and the environment. The stress ratio values were 0.1 and 0.5, the force waveform used were sine and trapezoidal or Dwell under normal air laboratory conditions and salt fog 3.5%NaCl weight in order to simulate the marine environment. In Dwell tests, results were checked with the electrical potential drop technique (DCPD) in addition to the crack opening displacement (COD) method. Using the Walker coefficients, calculated on the present research, could be projected accurately the crack propagation behavior on Paris region and do fatigue life predictions using da/dN and S-N diagrams for different stress ratio values. The corrosion environment increases both crack growth rate and &Delta;Kth due to oxides formation on the crack path that generates a crack closure effect. Dwell carrying makes decrease the crack growth rate by decreasing the slope of the Paris line on log (da/dN) versus log (&Delta;K) curve, instead of shifting down the line as occurs on titanium alloys. Rolling direction change from LT to TL increase the FCG rate in both threshold and Paris region, where the rate change use to be small. / Os principais fatores modificadores extrínsecos e intrínsecos da taxa de propagação de trincas na liga AA7050-T7451 foram avaliados para fornecer subsídios para projetistas de estruturas aeronáuticas, com base na filosofía de tolerância ao dano. A metodologia experimental consistiu em ensaiar corpos de prova do tipo compact tension (CT) da liga nas direções de laminação TL e LT, para verificar seu comportamento sob diferentes razões de tensões, forma de onda e condição ambiente. Os valores de razão de tensão estudados foram 0,1 e 0,5, as formas de onda foram senoidal e trapezoidal ou de Dwell, em condições normais de laboratório, ao ar, e névoa salina 3,5% NaCl, em massa, para simular um ambiente marinho. No caso dos ensaios Dwell, os resultados foram conferidos pelo método de queda de potencial eléctrico (QPE), além do método de flexibilidade elástica. Usando os coeficientes de Walker calculados a partir dos resultados obtidos, pôde-se projetar com precisão o comportamento da propagação de trinca na região de Paris e prever a vida em fadiga usando os diagramas da/dN e S-N para diferentes valores da razão de tensões. O ambiente corrosivo aumenta tanto a taxa de propagação de trinca, quanto o valor de &Delta;Kth por causa da formação de óxidos na trajetória da trinca, que geram um efeito de fechamento sobre a mesma. Quanto à forma de onda, verificou-se que o carregamento Dwell diminui a taxa de propagação de trinca, diminuindo a inclinação das curvas log (da/dN) versus log (&Delta;K) na região de Paris, ao invés de deslocá-la paralelamente como ocorre com ligas de titânio. A mudança da direção de laminação de LT para TL aumenta a taxa de propagação de trinca por fadiga (PTF) tanto na região de threshold, quanto na região de Paris, onde a mudança de taxa é pequena.

En raison de la gravité des accidents liés au phénomène de fatigue-propagation de fissure, les préoccupations de l’industrie aéronautique à assurer l’intégrité des structures soumises à ce mode de sollicitation revêtent un caractère tout à fait essentiel. Les travaux de thèse présentés dans ce mémoire visent à appréhender le problème de sûreté des structures aéronautiques dimensionnées en tolérance aux dommages sous l’angle probabiliste. La formulation et l’application d’une approche fiabiliste menant à des processus de conception et de maintenance fiables des structures aéronautiques en contexte industriel nécessitent cependant de lever un nombre important de verrous scientifiques. Les efforts ont été concentrés au niveau de trois domaines dans ce travail. Une méthodologie a tout d’abord été développée afin de capturer et de retranscrire fidèlement l’aléa du chargement de fatigue à partir de séquences de chargement observées sur des structures en service et monitorées, ce qui constitue une réelle avancée scientifique. Un deuxième axe de recherche a porté sur la sélection d’un modèle mécanique apte à prédire l’évolution de fissure sous chargement d’amplitude variable à coût de calcul modéré. Les travaux se sont ainsi appuyés sur le modèle PREFFAS pour lequel des évolutions ont également été proposées afin de lever l’hypothèse restrictive de périodicité de chargement. Enfin, les analyses probabilistes, produits du couplage entre le modèle mécanique et les modélisations stochastiques préalablement établies, ont entre autre permis de conclure que le chargement est un paramètre qui influe notablement sur la dispersion du phénomène de propagation de fissure. Le dernier objectif de ces travaux a ainsi porté sur la formulation et la résolution du problème de fiabilité en tolérance aux dommages à partir des modèles stochastiques retenus pour le chargement, constituant un réel enjeu scientifique. Une méthode de résolution spécifique du problème de fiabilité a été mise en place afin de répondre aux objectifs fixés et appliquée à des structures jugées représentatives de problèmes réels. / Ensuring the integrity of structural components subjected to fatigue loads remains an increasing concern in the aerospace industry due to the detrimental accidents that might result from fatigue and fracture processes. The research works presented here aim at addressing the question of aircraft safety in the framework of probabilistic fracture mechanics. It should be noticed that a large number of scientific challenges requires to be solved before performing comprehensive probabilistic analyses and assessing the mechanical reliability of components or structures in an industrial context. The contributions made during the PhD are reported here. Efforts are provided on each step of the global probabilistic methodology. The modeling of random fatigue load sequences based on real measured loads, which represents a key and original step in stochastic damage tolerance, is first addressed. The second task consists in choosing a model able to predict the crack growth under variable amplitude loads, i.e. which accounts for load interactions and retardation/acceleration effects, at a moderate computational cost. The PREFFAS crack closure model is selected for this purpose. Modifications are brought in order to circumvent the restrictive assumption of stationary load sequences. Finally, probabilistic analyses resulting from the coupling between the PREFFAS model and the stochastic modeling are carried out. The following conclusion can especially be drawn. Scatter in fatigue loads considerably affects the dispersion of the crack growth phenomenon. Then, it must be taken into account in reliability analyses. The last part of this work focuses on phrasing and solving the reliability problem in damage tolerance according to the selected stochastic loading models, which is a scientific challenge. A dedicated method is established to meet the required objectives and applied to structures representative of real problems.

In the flow past bluff bodies for a certain range of velocity a periodical vortex shedding emerges which is known as von Kármán vortex street. This phenomenon causes the periodical alteration of pressure field which affects the body. Should the vortex shedding frequency be similar to the body natural frequency, the amplitude of vibration significantly increases which can lead to fatigue cracking. In the case of water turbines, this phenomenon often affects the stay vanes. Both the vortex shedding frequency and the lift force amplitude can be influenced by the modification of the trailing edge geometry. The aim of this thesis is to use CFD computation in order to find the optimal geometry of the stay vane trailing edge for the specific Francis turbine unit.