No presente trabalho foi realizado um estudo comparativo entre as ligas AA7050- T7451 e AA2050-T84, bem como entre as direções L-T e T-L para analisar o comportamento das ligas, quando submetidos à temperatura ambiente e criogênica. Para realizar a análise comparativa entre as ligas e entre as direções, foram utilizados corpos de prova tipo C(T) (Compacto Tension), pré-trincados em fadiga. A análise comportamental das ligas foram avaliadas através dos ensaios de tenacidade à fratura, KIC, Curva KR, fadiga, da/dN. A microestrutura foi caracterizada através da microscopia ótica, microscopia eletrônica de varredura e microscopia eletrônica de transmissão. Foi observado que na direção L-T há uma maior resistência à propagação da trinca em relação à direção T-L, no que diz respeito à Curva KR, tanto para temperatura ambiente quanto para temperatura criogênica. Quando comparou-se as duas ligas na direção L-T em temperatura ambiente, ambas apresentaram um fator de intensidade de tensão similar. Os resultados dos ensaios de fadiga mostraram que a direção T-L é mais sensível à razão de carga. Analisando os resultados entre as direções L-T e T-L, observou-se que as duas ligas apresentaram comportamento anisotrópico. / A comparative study was made of the AA7050-T7451 and AA2050-T84 alloys and of the L-T and T-L directions to analyze the behavior of the alloys when subjected to room and cryogenic temperatures. The comparative analyses of the alloys and directions were performed using fatigue-precracked compact tension (CT) test specimens. The behavior of the alloys was analyzed based on fracture toughness, KIC, KR curve, fatigue, and da/dN tests. Their microstructure was characterized by optical microscopy, scanning electron microscopy and transmission electron microscopy. The KR curve indicated that resistance to crack propagation was higher in the L-T direction than in the T-L direction at both room and cryogenic temperatures. In a comparison of the two alloys in the L-T direction at room temperature, they were found to present a similar stress intensity factor. The results of the fatigue tests demonstrated that the T-L direction is more sensitive to the load ratio. An analysis of the results in the L-T and T-L directions indicated that the two alloys exhibited anisotropic behavior.

No presente trabalho foi realizado um estudo comparativo entre as ligas AA7050- T7451 e AA2050-T84, bem como entre as direções L-T e T-L para analisar o comportamento das ligas, quando submetidos à temperatura ambiente e criogênica. Para realizar a análise comparativa entre as ligas e entre as direções, foram utilizados corpos de prova tipo C(T) (Compacto Tension), pré-trincados em fadiga. A análise comportamental das ligas foram avaliadas através dos ensaios de tenacidade à fratura, KIC, Curva KR, fadiga, da/dN. A microestrutura foi caracterizada através da microscopia ótica, microscopia eletrônica de varredura e microscopia eletrônica de transmissão. Foi observado que na direção L-T há uma maior resistência à propagação da trinca em relação à direção T-L, no que diz respeito à Curva KR, tanto para temperatura ambiente quanto para temperatura criogênica. Quando comparou-se as duas ligas na direção L-T em temperatura ambiente, ambas apresentaram um fator de intensidade de tensão similar. Os resultados dos ensaios de fadiga mostraram que a direção T-L é mais sensível à razão de carga. Analisando os resultados entre as direções L-T e T-L, observou-se que as duas ligas apresentaram comportamento anisotrópico. / A comparative study was made of the AA7050-T7451 and AA2050-T84 alloys and of the L-T and T-L directions to analyze the behavior of the alloys when subjected to room and cryogenic temperatures. The comparative analyses of the alloys and directions were performed using fatigue-precracked compact tension (CT) test specimens. The behavior of the alloys was analyzed based on fracture toughness, KIC, KR curve, fatigue, and da/dN tests. Their microstructure was characterized by optical microscopy, scanning electron microscopy and transmission electron microscopy. The KR curve indicated that resistance to crack propagation was higher in the L-T direction than in the T-L direction at both room and cryogenic temperatures. In a comparison of the two alloys in the L-T direction at room temperature, they were found to present a similar stress intensity factor. The results of the fatigue tests demonstrated that the T-L direction is more sensitive to the load ratio. An analysis of the results in the L-T and T-L directions indicated that the two alloys exhibited anisotropic behavior.

It has been known for decades that fatigue crack propagation in elastic-plastic media is very sensitive to load history since the nonlinear behavior of the material can have a great influence on propagation rates. However, the raw computation of millions of fatigue cycles with nonlinear material behavior on tridimensional structures would lead to prohibitive calculation times. In this respect, we propose a global model reduction strategy, mixing both the a posteriori and a priori approaches in order to drastically decrease the computational cost of these types of problems. First, the small scale yielding hypothesis is assumed, and an a posteriori model reduction of the plastic behavior of the cracked structure is performed. This reduced model provides incrementally the plastic state in the vicinity of the crack front, from which the instantaneous crack growth rate is inferred. Then an additional a priori model reduction technique is used to accelerate even more the time to solution of the whole problem. This a priori approach consists in building incrementally and without any previous calculations a reduced basis specific to the considered test-case, by extracting information from the evolving displacement field of the structure. Then the displacement solutions of the updated crack geometries are sought as linear combinations of those few basis vectors. The numerical method chosen for this work is the finite element method. Hence, during the propagation the spatial discretization of the model has to be updated to be consistent with the evolving crack front. For this purpose, a specific mesh morphing technique is used, that enables to discretize the evolving model geometry with meshes of the same topology. This morphing method appears to be a key component of the model reduction strategy. Finally, the whole strategy introduced above is embedded inside an adaptive approach, in order to ensure the quality of the results with respect to a given accuracy. The accuracy and the efficiency of this global strategy have been shown through several examples; either in bidimensional and tridimensional cases for model crack propagation, including the industrial example of a helicopter structure.

La fatigue de contact est un des modes de défaillance prédominants des composants tels que les engrenages ou les roulements. Les mécanismes d’initiation de fissures associés à ce mode de défaillance sont fortement liés à la microstructure du matériau. Cependant, la plupart des modèles utilisés pour prédire la durée de vie se situent à l’échelle macroscopique. Un modèle basé sur une représentation de type Voronoi des grains (échelle mésoscopique) est développé afin d’analyser les mécanismes d’initiation. Le concept d’endommagement est appliqué aux joints de grain modélisés par la méthode des zones cohésives. L’objectif de ce modèle est (i) de contribuer à une meilleure compréhension de l’influence de paramètres tels que ceux liés aux conditions de contact (rugosité, lubrification) ou aux matériaux (présence d’inclusions ou gradients de propriétés et contraintes résiduelles générés par les traitements de surface…) sur les mécanismes d’initiation et (ii) de fournir une estimation de la durée de vie jusqu’à cette initiation. Un premier modèle 2D isotrope a permis de mettre en place l’approche proposée et d’analyser le comportement numérique des éléments cohésifs : influence de la valeur des raideurs cohésives et apparition de singularités aux jonctions triples. Cette singularité semble inévitable, mais l’approche consistant à considérer le joint de grain comme une unique entité, et donc à utiliser des valeurs moyennes le long du joint de grain permet de s’affranchir de cette singularité. La représentativité du modèle a ensuite été améliorée par la modélisation de l’anisotropie cristalline. Un modèle de type élasticité cubique a été utilisé pour modéliser le comportement des grains. Enfin, une analyse approfondie de l’application du concept d’endommagement aux joints de grains a permis de proposer une nouvelle formulation entraînant une influence plus réaliste de cet endommagement sur le cisaillement intergranulaire et conduisant à une durée de vie estimée (apparition des premières micro-fissures) d’un ordre de grandeur comparable à celles données par l’expérience. / Contact fatigue is the predominant mode of failure of components subjected to a repeated contact pressure, like rolling element bearings or gears. This phenomenon is known as rolling contact fatigue (RCF). A large number of models have been developed to predict RCF, but there is today no complete predictive life model, and understanding RCF failure mechanism remains a significant challenge. RCF failure mechanisms are known to be very sensitive to a large number of parameters linked to contact conditions (roughness, lubrication) or materials (inclusions, gradients properties, residual stresses…). To improve knowledge about the influence of these parameters on failure mechanisms and life, a numerical model is developed to simulate the progressive damage of a component subject to rolling contact fatigue. Mechanisms associated with the initiation stage of failure process are located at a scale lower than the macroscopic scale. The proposed approach is to develop a grain level model (mesoscopic scale) in order to focus on initiation mechanisms. A Voronoi tessellation is used to represent the material microstructure. The progressive deterioration is simulated by applying the concept of damage mechanics at grain boundaries represented by cohesive elements. This approach has been first applied to a 2D isotropic model. The numerical behaviour of cohesive elements has been investigated: the influence of cohesive stiffness has been analysed and singularities at the triple junctions has been highlighted. The representativeness of the original model was improved by modelling crystal anisotropy. A cubic elasticity model was used to represent the behaviour of grains. Finally, a thorough analysis of the application of the damage concept at grain boundaries highlighted that the initial formulation results in a very low influence of the damage on the intergranular shear stress. A new formulation leading to a direct influence of the damage on the intergranular shear stress has been proposed. This new formulation has resulted in (i) a change in the distribution of micro-cracks, with coalescence between the different micro-cracks, and (ii) a large increase in the RCF life estimated by the model. The order of magnitude of the number of cycles corresponding to the first micro-cracks is comparable to that given by experiments.

Il est connu depuis des décennies que la propagation des fissures de fatigue dans les matériaux élastoplastiques est très sensible à l’histoire du chargement car le comportement non-linéaire du matériau peut avoir une grande influence sur les vitesses de propagation. Cependant, le calcul brut de millions de cycles de fatigue avec des comportements matériaux non-linéaires sur des structures tridimensionnelles réalistes conduirait à des temps de calcul prohibitifs. Ainsi, nous proposons de coupler deux approches de réduction de modèle a priori et a posteriori, afin de diminuer considérablement le coût de calcul de ce type de problèmes. Tout d’abord, considérant l’hypothèse de plasticité confinée, une stratégie de réduction de modèle a posteriori du comportement plastique de la structure fissurée est proposée. Le modèle réduit ainsi obtenu fournit incrémentalement l’état plastique autour du front de fissure, duquel est déduite la vitesse instantanée de la fissure. De plus, une seconde approche de réduction de modèle, a priori cette fois, est aussi mise en place afin d’accélérer encore plus les temps de résolution du problème global. Cette approche a priori consiste à construire incrémentalement —et sans calculs préalables— une base réduite spécifique à chaque cas-test, en extrayant de l’information des champs de déplacement de la structure au cours du temps et pendant la propagation éventuelle de la fissure. Ainsi, les champs de déplacement solutions de la géométrie fissurée réactualisée sont vus comme une combinaison linéaire de cette base réduite de vecteurs. La méthode numérique considérée ici est la méthode des éléments finis. De fait, pendant la propagation de la fissure, la discrétisation spatiale du modèle doit être réactualisée afin d’être conforme avec le front de la fissure. Dans ce but, une technique spécifique de déformation de maillage est utilisée, et permet de discrétiser la géométrie variable du modèle avec des maillages de même topologie. Cette technique de déformation de maillage apparaît comme une étape clé de la stratégie de réduction de modèle. Finalement, une approche adaptative est construite autour de cette stratégie. Elle permet de garantir la qualité des résultats obtenus par rapport à un critère de précision donné. La précision et l’efficacité de cette stratégie globale sont démontrées à travers de nombreux exemples bidimensionnels et tridimensionnels dans le cadre de propagation de fissure en model, de même que pour un exemple industriel d’une pièce fissurée d’hélicoptère. / It has been known for decades that fatigue crack propagation in elastic-plastic media is very sensitive to load history since the nonlinear behavior of the material can have a great influence on propagation rates. However, the raw computation of millions of fatigue cycles with nonlinear material behavior on tridimensional structures would lead to prohibitive calculation times. In this respect, we propose a global model reduction strategy, mixing both the a posteriori and a priori approaches in order to drastically decrease the computational cost of these types of problems. First, the small scale yielding hypothesis is assumed, and an a posteriori model reduction of the plastic behavior of the cracked structure is performed. This reduced model provides incrementally the plastic state in the vicinity of the crack front, from which the instantaneous crack growth rate is inferred. Then an additional a priori model reduction technique is used to accelerate even more the time to solution of the whole problem. This a priori approach consists in building incrementally and without any previous calculations a reduced basis specific to the considered test-case, by extracting information from the evolving displacement field of the structure. Then the displacement solutions of the updated crack geometries are sought as linear combinations of those few basis vectors. The numerical method chosen for this work is the finite element method. Hence, during the propagation the spatial discretization of the model has to be updated to be consistent with the evolving crack front. For this purpose, a specific mesh morphing technique is used, that enables to discretize the evolving model geometry with meshes of the same topology. This morphing method appears to be a key component of the model reduction strategy. Finally, the whole strategy introduced above is embedded inside an adaptive approach, in order to ensure the quality of the results with respect to a given accuracy. The accuracy and the efficiency of this global strategy have been shown through several examples; either in bidimensional and tridimensional cases for model crack propagation, including the industrial example of a helicopter structure.