Cette thèse est consacrée au développement d’un outil de pré-dimensionnement par éléments finis pour l’estimation de l’endommagement par fatigue polycyclique de structures linéaires sous chargements multiaxiaux et stationnaires gaussiens. L’état de contraintes atteint dans ces structures étant aléatoire, il devient nécessaire de raisonner en terme de statistique et l’approche spectrale s’avère particulièrement adaptée pour cette situation. Dans ce travail, les méthodes spectrales sont améliorées par la prise en compte des largeurs de bande des spectres de réponses des structures soumises à des chargements nonproportionnels et de moyennes non nulles. Le critère d’endommagement de Sines est retenu. L’étude numérique de la distribution de l’endommagement résultant des incertitudes sur les paramètres matériaux et des applications dans le domaine de l’optimisation des structures sont également abordées. / This dissertation is devoted to the development of a finite element pre-designing tool for the estimation of high cycle fatigue damage for linear structure subject to multiaxial and Gaussian stationary loads. Given the random nature of the stress state, it becomes necessary to look at this problem from a statistical point of view and spectral methods appear to be the best approach. In this work, spectral methods are improved by taking into account the response spectral bandwidths of structures under non proportional and non zero mean loads; the Sines’ damage criterion is employed. The numerical analysis of the fatigue damage distribution resulting from the uncertainties of the material parameters and applications in the field of structural optimisation are also treated.

Les vibrations aléatoires sont les sollicitations les plus représentatives à celles qui se trouvent dans l'environnement réel. Elles sont souvent rencontrées dans l'environnement de fonctionnement automobile, aéronautique, spatial, ferroviaire et d'autres. La particularité des vibrations aléatoires est l'utilisation de son analyse par fatigue. Grâce aux propriétés statistiques des signaux aléatoires que les méthodes spectrales permettent d'estimer la moyenne du dommage d'une façon efficace et économique mais avec certaines limitations. Une étude numérique sur un système électronique embarqué accompagnée des essais expérimentaux ont été mis en place dans cette thèse pour présenter une démarche complète d'une analyse spectrale des vibrations aléatoires. Une modélisation par éléments finis a été réalisée ainsi qu'une technique du 'zoom structural' en analyse spectrale des vibrations aléatoires a été proposée dans ce travail avec la présentation des équations de cette technique. Une application numérique a montré la validité de la technique proposée en appliquant une étude de l'endommagement par fatigue par l'approche temporelle et par l'approche spectrale. Les résultats numériques de cette application mènent à une estimation d'un temps à l'initiation de la fissure très proche du temps de défaillance observé dans les résultats des essais expérimentaux. Cette technique montre la performance et l'efficacité des méthodes spectrales dans l'estimation du dommage par fatigue aléatoire. Une étude de l'optimisation d'un système soumis aux sollicitations aléatoires a été développée. L'objectif de cette étude est de rechercher la conception optimale du système soumis aux vibrations aléatoires en posant des limitations sur le dommage qui en résulte. Ce dommage estimé par les méthodes spectrales de Dirlik et de Single Moment ne doit pas dépasser un dommage cible pour assurer la fiabilité du système étudié. / Random vibrations are the most representative excitations that can be found in the real environment. They are often encountered in the automotive, aeronautical, space, railway and other operating environments. The special feature of the random vibrations is their important role in damage fatigue analysis. The spectral methods allow to estimate efficiently and economically the mean of the damage using the statistical properties of the random signals. A numerical study on an embedded electronic system with experimental tests was set up in this thesis to present a complete spectral analysis of random vibrations methodology. A finite element model was performed as well as submodelling technique in spectral analysis of random vibrations with associated equations was proposed in this work. A numerical application has shown the validity of the proposed technique by applying the fatigue damage study using the time-domain approach and the spectral approach. The numerical results of this application lead to the estimation of a crack initiation time very close to the failure time observed in the experimental tests. This technique shows the performance and efficiency of spectral methods in the estimation of random fatigue damage. The optimization of a system subjected to random excitations has been developed in this work. The objective of this study is to retrieve the optimal design of the system subjected to random vibrations with limitations on the resulting damage. This damage estimated by Dirlik and Single Moment spectral methods must not exceed defined target damage in order to insure the reliability of the studied system.

[pt] Este trabalho apresenta um método para calcular a resistência à fadiga de uma torre de perfuração considerando a elevação da superfície do mar, a dinâmica da plataforma na qual a torre está instalada e a dinâmica da própria torre. Modelos de ordem reduzida são utilizados para obter a elevação da superfície do mar e a dinâmica torre, e as incertezas nos parâmetros dos componentes do sistema podem ser incluídas na análise também. As análises podem ser feitas para vários estados de mar, conforme sua distribuição de probabilidade, e nenhuma hipótese sobre a distribuição de probabilidade precisa ser feita inicialmente. O histograma de distribuição de ciclos de tensão para toda vida útil do equipamento é obtido usando um procedimento de contagem de ciclos Rainflow. Os resultados e as incertezas nos mesmos são discutidos. / [en] This work presents a method for evaluation of the fatigue resistance of a drilling tower considering the sea surface elevation, the dynamics of the platform on which the tower is installed and the dynamics of the tower itself. Reduced order models are used for obtaining the sea surface elevation and the dynamics of the tower, and the uncertainties on the parameters of the components of the system can be included in the analysis as well. The analysis can be done for several sea states, according its probability distribution, and no assumption about the probability distribution of the stress ranges has to be made previously. The histogram for the distribution of stress ranges for the entire working life of the equipment is obtained using a Rainflow technique. The results and the uncertainties on them are discussed.

Fatigue in concrete is a complex phenomenon involving formation of microcracks, their coalescence into major crack and simultaneous formation of the fracture process zone ahead of the crack tip. Complex phenomena are best dealt through an energy approach and hence it is reasonable to use the theory of thermodynamics. Fracture mechanics and damage mechanics are two theories that are based on physically sound principles and are used to describe failure processes in materials. The former deals with the study of macroscopic cracks, whereas the latter defines the state of microcracking. In this study, the concepts from these theories are utilized to improve our understanding and modeling of fatigue process in concrete. In this thesis, a closed form expression for the thermodynamic function entropy is proposed and examined for its size independency and its use as a material property to characterize failure of concrete under fatigue. In the thermodynamic formalism, dissipative phenomena are described by a dissipation potential or its dual, from which evolution laws for internal variables could be defined. In this work, closed form expressions for dual of dissipation potential are derived using concepts of dimensional analysis and self-similarity within the framework of fracture mechanics and damage mechanics. Consequently, a fatigue crack propagation law and a fatigue damage evolution law are proposed respectively. A method is proposed in this study to correlate fracture mechanics and damage mechanics theories by equating the potentials obtained in each theory. Through this equivalence, a crack could be transformed into an equivalent damage zone and vice versa. Also, damage state corresponding to a given crack in a member can be quantified in terms of a damage index. An analytical way of computing size independent S-N curves is proposed, using a nonlocal damage theory by including aggregate size and specimen size in the formulation. It is realized from this study that fracture mechanics and damage mechanics theories should be used in a unified manner in order to accurately model the process of fatigue in concrete. Furthermore, based on the models developed in this study, several damage indicators for fatigue of concrete are proposed. The advantages and limitations of each of these indices are presented such that, the relevant damage index could be used, based on available parameters. Additionally, deterministic sensitivity studies are carried out to determine the most important parameters influencing fatigue life of a concrete member.

This thesis focuses on the development of a health monitoring system for gearbox transmissions. This was accomplished by developing and understanding a two-stage gearbox computer model that emulates an actual gearbox test rig. The computer model contains actual gearbox geometry, flexible shafts, bearings, gear contact forces, input motor torque, output brake torque, and realistic gearbox imbalance. The gear contact force of each gear stage and the input bearing translational acceleration were the main outputs compared between a healthy gearbox and damaged gearbox computer model. The damage of focus was a fatigue crack on the input pinion gear. A sideband energy ratio comparison yielded the computer simulation accurately modeled the difference between a healthy and damaged gearbox. The next step in this study involved the development of a repeatable procedure to initiate and propagate a fatigue crack at the tooth root in an actual spur gear. A damaged spur gear allows for a future comparison of an actual healthy and damaged gearbox system in the lab. A custom fatigue fixture was designed and manufactured for a Martin S1224BS 1 spur gear. The fatigue crack was initiated by position control fatigue testing which deflects the gear tooth a set amplitude for a number of cycles. Over the length of the test, the load that the tooth can withstand in bending decreases as damage begins to occur. Once the max load on the gear has dropped by a significant percentage (5-15%) a crack has initiated and begun to propagate across the tooth face. The use of a scanning electron microscope confirmed the presence a fatigue crack.

This diploma thesis deals with FEM analysis and optimization of carriage for top drive system of drilling rig Bentec 350 AC and it is defined as a development contract for company MND Drilling & Services a.s. Intensive drilling leads to damages and repeated occurrence of fatigue cracks on carriage especially along edges of welded ribs in their heat-affected zone. The aim of this thesis is to draft construction improvements of carriage which leads to elimination of damages. Realization of this modifications depends on correct definition of boundary conditions, analysis of damage occurrence as well as verification of carriage drafts with finite element method.

This master's thesis deals with data processing for an electrodynamic test bench. The thesis presents a theoretical overview of signal distribution, determination of fatigue damage from random vibrations and a description of test benches. The next part deals with setting up the test time reduction in GlyphWorks software. The aim of this thesis is to process and create a procedure for an accelerated fatigue test from data measured during an operational test on a polygon. The data are then verified on an electrodynamic test rig using a Skoda Auto dynamic test room. The final part of the thesis contains data evaluation and a guide explaining how to easily create a test in the relevant software.