As ligas de alumínio são aplicadas em cerca de 70% dos componentes estruturais dos aviões e o processo de fadiga e o modo de falha predominante em estruturas aeronáuticas, para a maioria das quais a presença de concentradores de tensão e inevitável. O comportamento em fadiga e as propriedades mecânicas das ligas de alumínio endurecíveis por precipitação são fortemente influenciadas por parâmetros como tamanho, espaçamento e densidade dos precipitados endurecedores. Neste contexto, pesquisas anteriores tem mostrado que o envelhecimento interrompido (T6I4) pode proporcionar melhores combinações de propriedades mecânicas para estas ligas. O presente trabalho tem como objetivo o estudo das propriedades mecânicas e do comportamento em fadiga de alto ciclo das ligas de alumínio AA6351 e AA7050 nas condições de tratamento térmico convencionais (T6 e T7451, respectivamente) e na condição T6I4, bem como da influência das características microestruturais e do tratamento térmico sobre estas propriedades. Dentro deste contexto, analises de Microscopia Eletrônica de Transmissão (MET) da liga AA6351 mostraram que a condição T6I4 resultou em uma maior densidade de precipitados endurecedores com tamanho heterogêneo, quando comparada com a condição T6. Para esta liga, a condição T6I4 também resultou em menores valores de tensão limite de escoamento, resistência a tração, resistência a fadiga e sensibilidade ao entalhe, com maior ductilidade e tenacidade. Para a liga AA7050, as análises de MET mostraram que a condição T6I4 resulta em uma maior densidade de precipitados endurecedores com menor tamanho, promovendo um melhor impedimento ao movimento de discordâncias durante a deformação por fadiga, quando comparada com a condição T7451. Esta alteração microestrutural proporcionou a condição T6I4 valores de resistência ao escoamento e resistência a tração similares a condição T7451, com maior ductilidade e tenacidade. A resistência a fadiga da condição T6I4 foi similar a condição T7451, entretanto o envelhecimento interrompido resultou em um melhor comportamento em sensibilidade ao entalhe. / Aluminum alloys are applied in approximately 70% of the aircraft structural components and the fatigue process is the dominant failure mode in aeronautical structures, for the most of which, the presence of stress concentrators is unavoidable. The fatigue behavior and the mechanical properties of the age hardenable aluminum alloys are strongly influenced by parameters including the size, spacing and density of strengthening precipitates. Within this context, previous researches have shown that the interrupted ageing (T6I4) could provide an improved combination of mechanical properties for these alloys. This work aims to study the mechanical properties and the high cycle fatigue behavior of AA6351 and AA7050 aluminum alloys in the conventional heat treatment conditions (T6 and T7451, respectively) and in the T6I4 condition, as well as the influence of the microstructural characteristics and of the heat treatment on these properties. Within this context, Transmission Electron Microscopy (TEM) analyzes of the AA6351 alloy showed that T6I4 condition resulted in higher density of hardening precipitates with heterogeneous size compared to T6 condition. For this alloy, the T6I4 condition resulted in lower values of yield stress, ultimate tensile strength, fatigue strength and notch sensitivity, with higher ductility and toughness. For the AA7050 alloy, TEM analyses showed that T6I4 condition presented a higher density of strengthening precipitates with smaller size promoting an improved dislocation pinning effect during the fatigue deformation compared to T7451 condition. This microstructural change provided to T6I4 condition yield stress and ultimate tensile strength similar to T7451, with higher ductility and toughness. The fatigue strength of T6I4 condition was also similar to T7451, however the interrupted ageing provided a better notch sensitivity behavior.

The accurate description of the nonlinear structural behaviour is an important issue in engineering science. Usually, classic nonlinear theories, such as fracture and damage mechanics, applied to finite element programmes are used to fulfil that purpose. Classic fracture mechanics describes the structural deterioration process by a few discrete cracks. This theory presents good precision for structures with simple geometries, few cracks and homogeneous materials. Classic damage mechanics measures the deterioration process by an internal variable called damage. This theory has been successful in the description of several deterioration mechanisms in continuum media. Despite their accuracy, classic fracture and damage mechanics present some drawbacks. Firstly, regarding civil engineering problems, both theories are not suitable for some practical applications. Secondly, fracture mechanics demands the consideration of initial cracks to begin the analysis. Lastly, classic damage models may present an issue known as localisation, what essentially leads to ill-posed problems and mesh-dependent numerical algorithms. Alternatively, a recent theory, called lumped damage mechanics, was proposed in order to achieve good accuracy in actual engineering problems. Such theory applies key concepts from fracture and damage mechanics in plastic hinges. In the light of the foregoing, the main goal of this thesis is the extension of the lumped damage mechanics framework to analyse different engineering problems. So far, lumped damage mechanics was characterised as a simplified methodology to analyse reinforced concrete frames under seismic and monotonic loadings; even with a few contributions on the analysis of local buckling in metallic structures. Therefore, this work extends the lumped damage mechanics framework to analyse reinforced concrete arches, unreinforced concrete structures, high cycle fatigue and continuum problems. The application examples show the accuracy of the proposed methodologies. / A descrição acurada do comportamento não linear de estruturas é um problema importante na engenharia. Usualmente, teorias não lineares clássicas, tais como as mecânicas da fratura e do dano, aplicadas a programas de elementos finitos são utilizadas a fim de cumprir aquele propósito. A mecânica da fratura clássica descreve o processo de deterioração estrutural por meio de um pequeno número de fissuras discretas. Esta teoria apresenta boa precisão para estruturas com geometrias simples, poucas fissuras e materiais homogêneos. A mecânica do dano clássica tem sido exitosa na descrição de diversos mecanismos de deterioração em meios contínuos. Apesar de precisas, as abordagens clássicas em fratura e dano apresentam alguns entraves. Primeiramente, tratando-se de problemas da engenharia civil, ambas teorias não são adequadas para aplicações práticas. Em segundo lugar, os modelos clássicos de fratura demandam a consideração de fissuras iniciais para iniciar a análise. Por fim, os modelos clássicos de dano podem apresentar um problema conhecido como localização, o que essencialmente implica em problemas mal colocados e algoritmos com dependência de malha. Alternativamente, uma teoria recente, chamada teoria do dano concentrado, foi proposta a fim de obter boa precisão em problemas reais de engenharia. Tal teoria aplica conceitos-chave das mecânicas da fratura e do dano em rótulas plásticas. À luz do exposto, o principal objetivo desta tese é a extensão da teoria do dano concentrado para analisar diferente problemas da engenharia. Até então, a teoria do dano concentrado era caracterizada como uma metodologia simplificada para analisar pórticos de concreto armado sob solicitações monotônicas ou sísmicas; mesmo com algumas poucas contribuições na análise de instabilidade local em estruturas metálicas. Desta forma, este trabalho estende a teoria do dano concentrado a fim de analisar arcos de concreto armado, estruturas de concreto simples, fadiga de alto ciclo e problemas contínuos. Os exemplos de aplicação mostram a acurácia das metodologias propostas.

Résumé : Cette étude a pour objectif de mieux comprendre les mécanismes précurseurs de l'amorçage de fissures dans le cas de métaux ductiles monophasés, comme le cuivre pur, sollicités à des amplitudes de contrainte inférieures à la limite de fatigue conventionnelle et jusqu'à des nombres de cycles atteignant le domaine de la fatigue gigacyclique (Very High Cycle Fatigue, VHCF). Les essais ont été réalisés sur une machine de fatigue ultrasonique à une fréquence de sollicitation de 20 kHz. Les mécanismes précurseurs de l'amorçage des fissures se manifestent (1) sous forme de bandes de glissement qui apparaissent sur la surface de l'éprouvette et (2) par un auto-échauffement du matériau dû à la dissipation intrinsèque. Les cartographies de température de la surface des éprouvettes nous ont permis d'estimer des dissipations d'énergie moyennes et de caractériser leur évolution avec le nombre de cycles et l'amplitude de contraintes. En parallèle, l'évolution du relief de la surface, initialement lisse et sans contrainte résiduelle, a été analysée à partir d'observations en microcopie optique, électronique à balayage et à force atomique. Nous avons établi que l'amplitude de contrainte nécessaire pour faire apparaître les premières bandes décroit en fonction du nombre de cycles. Des analyses EBSD, couplées à des calculs éléments finis intégrant l'anisotropie élastique des grains, ont révélé le rôle clé (1) des joints de macles et (2) du glissement dévié dans l'amorçage de bandes de glissement intenses.Mots clés : Fatigue gigacyclique, Bandes de glissement, Microplasticité cyclique, Dissipation, Anisotropie élastique, Simulation multicristalline, Thermographique infrarouge. / Abstract : This work aims to better understanding mechanisms leading to crack initiation in ductile single phase metals such as pure copper, loaded stress amplitudes lower than the conventional fatigue threshold and after about 109 cycles, the so-called Very High Cycle Fatigue regime. Tests were conducted using an ultrasonic technique at loafing frequency of 20 kHz. The mechanisms leading to crack initiation express (1) via slip bands at the specimen surface and (2) via self-heating due to intrinsic dissipation. Thermal maps were used to estimate the mean dissipation and its change with number of cycles and stress amplitudes. At the same time, the surface relief changes were characterized using optical, scanning electronic and atomic force microscopes. The stress amplitude required to observe the slip bands was found to decrease as a function of number of cycles. EBSD investigations combined with finites elements simulations accounting for elastic anisotropy of copper revealed the key role of (1) twin boundaries and (2) cross slip in slip band initiation.Keywords : Very High Cycle Fatigue, Slip bands, Cyclic microplasticity, Dissipation, Elastic anisotropy, Multicrystals simulation, Infrared thermography.

Cette étude fait partie du projet ANR DEFISURF, avec pour objectif d'identifier et de modéliser les divers effets de la surface sur la tenue en fatigue de composants forgés. Deux composants sont étudiés: une éprouvette extrudée à froid et une bielle estampée à chaud et nettoyée de sa calamine par grenaillage (shot-blasting). Pour chaque composant, différents lots sont étudiés afin de quantifier l'effet des procédés sur les caractéristiques mécaniques et sur le comportement en fatigue. Deux taux de corroyage différents sont utilisés pour l'extrusion à froid. Pour les bielles, différents grenaillages sont réalisés pour obtenir divers états de surface.Les différents lots sont caractérisés de façon approfondie et des essais de fatigue sont effectués. Des essais de fatigue en traction, torsion et flexion plane sont réalisés sur les éprouvettes extrudées. Des éprouvettes de fatigue sont prélevées dans l'âme des bielles et sollicitées en flexion plane.En extrusion à froid, les aspects les plus influents en fatigue sont la prédéformation subie lors de la mise en forme (taux de corroyage) et les contraintes résiduelles. En forgeage à chaud, ce sont les défauts de forgeage en surface et les contraintes résiduelles introduites par le grenaillage qui ont le plus d'influence.Une modélisation en fatigue est proposée pour chaque composant. Pour l'extrusion, un critère de fatigue multiaxial permet de prendre en compte les différents types de chargement ainsi que l'effet des contraintes résiduelles. Pour les bielles deux approches sont utilisées. La première est une analyse de la géométrie des défauts qui utilise un demi-ellipsoïde pour approximer leur forme. La deuxième approche est une simulation numérique par éléments finis des défauts critiques. Les contraintes résiduelles sont intégrées dans les simulations avec un critère multiaxial. Les simulations permettent de retrouver les résultats expérimentaux avec une erreur d'environ 15%. / This study is part of the DEFISURF project, with the goal of analysing and modelling the various effects of the surface on the fatigue strength of forged components. Two components are studied: a cold-extruded specimen and a connecting rod which is hot-forged and then cleaned by shot-blasting. For each component, different batches are studied in order to quantify the effects of the process on the mechanical characteristics and the fatigue behaviour. Two different reduction of sections are used for the cold-extruded specimens and shot-peening is used to obtain various surface states for the connecting rods.The various batches are thoroughly characterised and fatigue tests are performed. Traction, torsion and plane-bending tests are conducted on the cold-extruded specimens. Fatigue specimens are machined from the central part of the connecting rods and loaded in plane-bending.For cold-extrusion, the parameters with the most influence in fatigue are the prestrain induced during forging and the residual stresses. In hot-forging, the surface defects produced during forging and the residual stresses induced by the shot-blasting have the most influence.For each component, a fatigue model is suggested. For the cold-extruded specimens, a multiaxial fatigue criterion is used to take into account the various fatigue loadings and the effect of the residual stresses. Two approaches are used for the connecting rods. The first is a geometrical analysis of the defect which approximates them with an ellipsoid. The second approach uses finite element simulations of the critical defects. The shot-peening residual stresses are integrated in the simulations with a multiaxial criterion. These simulations predict the fatigue limit of the specimens with an error of around 15%.

Il existe actuellement une demande croissante pour le développement de méthodes expérimentales rapides et fiables permettant d'estimer la résistance à la fatigue dans le domaine de la fatigue à grands nombres de cycles. En ce sens, la fatigue ultrasonique apparue dans les années cinquante est très intéressante pour les industriels. En effet, la fréquence typique de ces essais est de 20 kHz ce qui permet d'atteindre le domaine des très grandes durées de vie en des temps d'essais raisonnables (109 cycles sont atteints en 14 h). Cependant ces essais posent le problème de l'effet de la fréquence et plus généralement de la validité des résultats obtenus pour estimer la durée de vie de structures chargées à des fréquences très inférieures à 20 kHz. L'objectif de ce travail est d'évaluer l'effet de la fréquence du chargement sur les mécanismes précurseurs de l'initiation de fissures et plus précisément sur les mécanismes de microplasticité à l'échelle du grain. Ce travail de thèse s’intéresse au cas du cuivre pur polycristallin sollicité en traction-compression alternée et symétrique. Pour mettre en évidence un effet de la fréquence, les courbes de Wöhler ont été construites à différentes fréquences. L’étude s’est ensuite focalisée sur les mécanismes de microplasticité précurseurs de l’initiation de fissures et plusieurs critères ont été examinés : les morphologies des bandes de glissement et leurs positions en lien avec la microstructure, les seuils d’apparition des bandes de glissement, le développement de ces bandes avec le nombre de cycles, la répartition de la microplasticité dans les grains, les valeurs d’énergie dissipée au cours d’un cycle. Le glissement dévié et la production-diffusion de lacunes sont deux mécanismes qui interviennent dans la formation des bandes de glissement et des extrusions en surface. Leurs rôles respectifs sur les effets de fréquence observés sont discutés. / Nowadays there is a growing demand for the development of fast and robust fatigue life prediction methods in the very high cycle fatigue domain. In this way, ultrasonic fatigue technique which appeared in 1950 is very interesting for manufacturers. Because the typical frequency of these tests is 20 kHz, this technique is efficient to perform tests up to a very high number of cycles in a reasonable time (109 cycles are reached in 14 h). However, the frequency domain of these fatigue tests facilities raises the issue of the effect of frequency and more generally the validity of the obtained results for estimating fatigue life of structures loaded at frequencies three or four order of magnitude below ultrasonic frequencies. The objective of this work is to evaluate the effect of the loading frequency on the precursors of fatigue damage, namely the microplasticity at the grain scale. This thesis work deals with the case of polycrystalline pure copper loaded in fully reversed tensioncompression. To show the effect of frequency, the Wöhler or S-N curves were constructed at different frequencies. Then, the study focused on the mechanisms of microplasticity preceding crack initiation and several criteria were investigated: the morphologies of the slip bands and their locations in the microstructure, the thresholds of appearance of the slip bands, the evolution of the slip bands amount with the number of cycles, the distribution of the microplasticity in the grains, the dissipated energy during a fatigue cycle. Cross slip and vacancies production and diffusion are two mechanisms which play a part in the formation of slip bands and extrusions in surface. Their respective roles on the effects of frequency observed are discussed

Malgré plusieurs décennies d'études expérimentales et numériques sur la tenue en fatigue d'assemblages soudés, cette problématique demeure une préoccupation principale de l'industrie automobile. En effet, de nombreux composants aux géométries complexes (e.g. berceaux) sont obtenus à partir de pièces soudées et constituent des éléments de sécurité pour lesquels aucune défaillance ne peut être acceptée. Malgré les progrès en modélisation numérique, des essais sont toujours nécessaires afin de fournir des données sur éprouvettes « simples » afin d'alimenter les modèles numériques, mais aussi de démontrer le bon dimensionnement des structures. Les procédures classiques d'essais de fatigue sont coûteuses en temps et nécessitent la destruction de plusieurs pièces. La méthode dite d'auto-échauffement permet de réduire significativement le temps d'essai et propose une approche non destructive. Cette méthode consiste à mesurer l'évolution de température en surface de la structure étudiée au cours du chargement cyclique. Cette approche permet de tirer avantage du signal thermique macroscopique afin de mettre en évidence la micro-plasticité responsable de la rupture par fatigue. Les objectifs du travail présenté sont de déterminer si un lien peut être réalisé entre les mesures de température et la tenue en fatigue d'assemblages soudés, puis d'étudier l'influence de paramètres sur la tenue en fatigue grâce à la méthode proposée. Un protocole expérimental est d'abord proposé afin de mesurer l'évolution de température des mini-structures soudées sous sollicitation cyclique. Une première analyse de la réponse thermique de simples tôles d'acier sous chargement cyclique de faible amplitude est proposée afin de valider un modèle déterministe de champ de source à la fois pour des sollicitations de traction et de flexion. Ces essais permettent par la suite de décrire correctement le comportement thermique de la matière de base des éprouvettes soudées hors du cordon de soudure. Le modèle est alors étendu à l'étude d'éprouvettes soudées, avec la prise en compte de la dissipation de la zone soudée. Une fois le champ de source identifié à partir du modèle, son évolution en fonction de l'amplitude du chargement appliqué mène à une courbe d'auto-échauffement. L'analyse de cette courbe permet une bonne estimation de la limite en fatigue de l'éprouvette soudée après seulement quelques heures d'essais. La méthode est alors appliquée à d'autres configurations de mini-structures soudées afin d'étudier l'influence du grenaillage et d'un gradient de contrainte en zone critique sur la tenue en fatigue. Finalement, la procédure d'essai est appliquée afin de déterminer la tenue en fatigue d'une pièce industrielle, un triangle de suspension mécano-soudé. À cause des mauvaises conditions aux limites thermiques sur une telle structure, une autre méthode est proposée afin de déduire une première estimation du champ de source sur toute la surface observée à partir des mesures thermiques. Cette estimation mène à l'identification de la zone critique en fatigue de la structure et à une première bonne estimation de sa limite en fatigue. / Fatigue design of weld assemblies still remains of prior concern in the automotive industry, despite several decades of experimental, theoretical and numerical body of work. Actually, many complex components (e.g. front and rear axles) are embedded thanks to welding process. Such welded assemblies are expected to be designed as high-safety parts, for which any fatigue failure is supposed to be prevented. Despite numerical modelling is more and more effective, experimental tests are still necessary in order to provide basic design data and at last to prove the design reliability. Standard fatigue tests procedures are sensibly time consuming, are usually destructive and need for several specimens in order to manage reliable results. Conversely, the so-called self-heating tests offer the opportunity to dramatically shorten the test duration and save specimens because it is a non-destructive method. It consists in measuring the temperature evolution of the structure surface during cyclic loading. Such an approach allows to take advantage of the macroscopic thermal signature of microscopic plasticity processes responsible for fatigue damage. The purpose of the present work is the determination of a correlation between thermal measurement and fatigue properties of welded structures, and then studying the influence of parameters on fatigue properties with the developed method. An experimental protocol is first proposed to measure the temperature of the tested specimen under cyclic loading. A first analysis of the thermal response of standard steel sheet specimen under low load amplitude is proposed in order to validate a deterministic heat source model for both tensile and bending tests. These tests allow us to correctly describe the thermal behavior of the base material of welded specimen away from the joint. Then, the model is extended to welded specimen in order to take into account the dissipation of the welded area. Once the dissipative heat source is identified thanks to the model, its evolution with the applied loading leads to a self-heating curve allowing an estimation of the fatigue limit of the welded specimen after only few hours of test. The method is then applied to other configurations of welded specimens in order to study the effects of shot peening and stress gradient on fatigue properties. Finally, the testing procedure is applied for the determination of an industrial component fatigue properties, a welded car wishbone. Due to the bad heat boundary condition, another analysis is proposed to estimate the heat source along the entire component. This estimation leads to the determination of the weakest area of the structure concerned by fatigue and a first good estimation of its fatigue limit.

Mechanical fatigue is a failure phenomenon that occurs due to repeated application of mechanical loads. Very High Cycle Fatigue (VHCF) is considered as the domain of fatigue life greater than 10 million load cycles. Increasing numbers of structural components have service life in the VHCF regime, for instance in automotive and high speed train transportation, gas turbine disks, and components of paper production machinery. Safe and reliable operation of these components depends on the knowledge of their VHCF properties. In this thesis both experimental tools and theoretical modelling were utilized to develop better understanding of the VHCF phenomena. In the experimental part, ultrasonic fatigue testing at 20 kHz of cold rolled and hot rolled stainless steel grades was conducted and fatigue strengths in the VHCF regime were obtained. The mechanisms for fatigue crack initiation and short crack growth were investigated using electron microscopes. For the cold rolled stainless steels crack initiation and early growth occurred through the formation of the Fine Granular Area (FGA) observed on the fracture surface and in TEM observations of cross-sections. The crack growth in the FGA seems to control more than 90% of the total fatigue life. For the hot rolled duplex stainless steels fatigue crack initiation occurred due to accumulation of plastic fatigue damage at the external surface, and early crack growth proceeded through a crystallographic growth mechanism. Theoretical modelling of complex cracks involving kinks and branches in an elastic half-plane under static loading was carried out by using the Distributed Dislocation Dipole Technique (DDDT). The technique was implemented for 2D crack problems. Both fully open and partially closed crack cases were analyzed. The main aim of the development of the DDDT was to compute the stress intensity factors. Accuracy of 2% in the computations was attainable compared to the solutions obtained by the Finite Element Method. / Very High Cycle Fatigue (VHCF) is considered as the domain of fatigue life greater than 10 million load cycles. Structural components that have service life in the VHCF regime include wheels and axles of high speed trains, gas turbine disks, and components of paper production machinery. Safe and reliable design, and the longevity, of these components depends on the knowledge of their VHCF properties. The overall aim of the experimental portion of this thesis was to gain in-depth knowledge of the VHCF properties of stainless steels. Fatigue test data in the VHCF regime was generated for different stainless steel grades using ultrasonic fatigue testing. The mechanisms for fatigue crack initiation and short crack growth were investigated using electron microscopes. Theoretical modelling of complex crack geometries involving kinks and branches was carried out by using the Distributed Dislocation Dipole Technique (DDDT). The main aim of this development was to compute the stress intensity factors and to analyse the stress state around the cracks. The results showed that accuracy of 2% was attainable compared to the solutions obtained by Finite Element Method (FEM). / <p>Artikel 4 publicerad i avhandlingen som manuskript</p>

Fatigue analysis is a critical stage in the design of any structural component. Typically fatigue is analysed during post-processing, but as the size of the analysed component increases, the amount of data stored for the analysis increases simultaneously. This increases the computational and memory requirements of the system, intensifying the work load on the engineer. A continuum mechanics approach namely ’Continuous time fatigue model’, for fatigue analysis is available in a prior study which reduces the computational requirements by simultaneously computing fatigue along with the stress. This model implements a moving endurance surface in the stress space along with the damage evolution equation to compute high-cycle fatigue. In this thesis the continuous time fatigue model is compared with conventional model (ie.Cycle counting) to study its feasibility. The thesis also aims to investigate the continuous time fatigue model and an evolved version of the model is developed for non-proportional load cases to identify its limitations and benefits.

L'objet de ce travail est de proposer une approche multi-échelle de la fatigue fondée sur l'énergie, et susceptible d'estimer les durées de vie associées à des chargements multidimensionnels variables. Le fondement de la démarche consiste à supposer que l'énergie dissipée à petite échelle régit le comportement à la fatigue. À chaque point matériel, est associée une distribution stochastique de points faibles qui sont susceptibles de plastifier et de contribuer à la dissipation d'énergie sans affecter des contraintes macroscopiques globales. Ceci revient à adopter le paradigme de Dang Van en fatigue polycyclique. La structure est supposée élastique (ou adaptée) à l'échelle macroscopique. De plus, on adopte à l'échelle mésoscopique un comportement élastoplastique avec une dépendance de la fonction de charge plastique non seulement de la partie déviatorique des contraintes, mais aussi de la partie hydrostatique. On considère également un écrouissage cinématique linéaire sous l'hypothèse d'une plasticité associée. Au lieu d'utiliser le nombre de cycles comme variable incrémentale, le concept d'évolution temporelle du chargement est adopté pour un suivi précis de l'historique du chargement réel. L'effet de la contrainte moyenne est pris en compte dans la fonction de charge mésoscopique ; une loi de cumul non linéaire de dommage est également considérée dans le modèle. La durée de vie à la fatigue est ensuite déterminée à l'aide d'une loi de phénoménologique fondée sur la dissipation d'énergie mésoscopique issue du cycle d'accommodation plastique. La première partie du travail a porté sur une proposition d'un modèle de fatigie à gradient de mise en oeuvre plus simple que les précédents modèles. / The aim of this work is to propose a multi-scale approach to energy-based fatigue, which can estimate lifetimes associated with variable multidimensional loading. The foundation of the approach is to assume that the energy dissipated on a small scale governs the fatigue behavior. Each material point is associated to a stochastic distribution of weak points that are likely to plasticize and contribute to the dissipation of energy without affecting global macroscopic stresses. This amounts to adopting Dang Van's paradigm of high cycle fatigue. The structure is supposed to be elastic (or adapted) on a macroscopic scale. In addition, we adopt on the mesoscopic scale an elastoplastic behavior with a dependence of the plastic load function not only of the deviatoric part of the stresses, but also of the hydrostatic part. Linear kinematic hardening is also considered under the assumption of an associated plasticity. Instead of using the number of cycles as an incremental variable, the concept of temporal evolution of the load is adopted for a precise follow-up of the history of the actual loading. The effect of mean stress is taken into account in the mesoscopic yield function; a law of nonlinear accumulation of damage is also considered in the model. Fatigue life is then determined using a phenomenological law based on mesoscopic energy dissipation from the plastic accommodative cycle. The first part of the work focused on a proposal for a fatigue model with a simpler implementation gradient than the previous models.

Classical fatigue models teach that there is an intrinsic fatigue limit for steels, representing a level of stress that is too low for regular crack growth where every cyclic load propagates a fatigue crack through the material. Modern application with extreme lifetimes has shown that fatigue will still take place in steels with stress levels well below the expected fatigue limit. This relatively new area of study has been named Very High Cycle Fatigue, or VHCF, and describes fatigue failures with a number of load cycles exceeding 107. Fractography of steels that has suffered VHCF tends to reveal an especially rough crack surface adjacent to where the fatigue crack originates, which is typically some form of defect in the bulk of the steel. This area is believed to be critical for VHCF and has been referred to in a number of ways by different studies, but will herein be called Fine Granular Area, or FGA. The aim of this study is to try and get a better understanding of VHCF. This was done by fractography analysis of test specimens of high strength tool steel that suffered fatigue failure at lifetimes ranging from about 106 cycles to 1,9x109 cycles. The lower lifetimes were achieved using hydraulic testing equipment, while the specimens in the VHCF range suffered fatigue failure in ultrasonic testing equipment allowing the application of a cyclic stress at a rate of 20 000 Hz. The resulting fracture surfaces were then investigated using a scanning electron microscope, or SEM, taking special note of the fatigue initiating defects and, in the case of VHCF, the rough area found adjacent to it. In combination with the SEM an elemental analysis of the fatigue initiating defects as well as the bulk of the material was done using energy-dispersive X-ray spectroscopy, or EDS. This was done to find out what the defects consisted of; confirming that they were slags and checking that the composition of the material of the bulk of the specimen matches what was expected. Using light optical microscopy in combination with acid etching of the surface of samples cut out of the test specimens the structure of the steel was investigated. Calculating the local stresses at the location of the fatigue initiating defect was done using FEM in combination with displacement amplitude gathered from the ultrasonic testing equipment. The data gathered was then measured and compared to that of previous studies, using models of prediction and seeing how they match the experimental results. The results suggest that the stress intensity factor at the internal slags is critical for VHCF and that with lower stress intensity factors one can expect longer lifetimes. Another observation is a relatively consistent stress intensity factor at the edge of the FGA combined with the original defect, likely signifying the transition from the creation of FGA to traditional crack propagation. There also seems to be a connection between the size of the FGA and the number of cycles to failure, with larger FGA with increasing lifetimes. The most glaring shortcoming of this study is the amount satisfactory tests conducted, and thus amount of data points, is very low due to the majority of specimens suffered failure at the threading used to connect them to the ultrasonic testing equipment at lifetimes far too low to be relevant. / Klassiska utmattningsmodeller lär ut att det finns en utmattningsgräns för stål, vilket representerar en spänningsnivå som är för låg för regelbunden sprickväxt där varje cyklisk belastning sprider en utmattningsspricka genom materialet. Moderna applikation med extrema livstider har visat att utmattning fortfarande äger rum i stål med spänningsnivåer långt under den förväntade utmattningsgränsen. Detta relativt nya studieområde har fått namnet Very High Cycle Fatigue, eller VHCF, och beskriver utmattningsfall med ett antal belastningscykler som överstiger 107. Fraktografi av stål som har drabbats av VHCF tenderar att ha en särskilt gropig sprickyta som ligger intill där utmattningssprickan har sitt ursprung, vilket typiskt är någon form av defekt i stålets bulk. Detta område tros vara kritiskt för VHCF och har hänvisats till på ett antal sätt av olika studier, men kommer här att kallas Fine Granular Area eller FGA. Syftet med denna studie är att försöka få en bättre förståelse för VHCF. Detta gjordes genom fraktografianalys av testprover av verktygsstål med hög hållfasthet som drabbades av utmattningsbrott vid livstider från cirka 106 cykler till 1,9x109 cykler. De lägre livslängderna uppnåddes med hjälp av hydraulisk testutrustning, medan proverna i VHCF-området drabbades av utmattningsbrott i ultraljudstestutrustning som klarar att applicera en cyklisk stress med en frekvens på 20 kHz. De resulterande sprickytorna undersöktes sedan med hjälp av ett svepelektronmikroskop, eller SEM, med särskild fokus på utmattningsinitierande defekter och, i fallet med VHCF, det grova området som hittades intill det, FGA. I kombination med SEM utfördes en elementanalys av utmattningsinitierande defekter liksom huvuddelen av materialet med energidispersiv röntgenspektroskopi, eller EDS. Detta gjordes för att ta reda på vad inneslutningarna bestod av för att bekräfta att de var slagg samt kontrollera att sammansättningen av materialet i huvuddelen av provet matchar det som förväntades. Med användning av optisk ljusmikroskopi i kombination med syraetsning av ytan på prover som skars ut ur testproverna undersöktes stålets struktur. Beräkning av de lokala spänningarna på platsen för den utmattningsinitierande defekten gjordes med hjälp av FEM i kombination med förskjutningsamplituden som samlats från ultraljudsutrustningen. De insamlade uppgifterna mättes sedan och jämfördes med tidigare studier genom att använda diverse modeller och se hur de matchar de experimentella resultaten. Resultaten antyder att stressintensitetsfaktorn vid inneslutningarna är kritisk för VHCF och att man med lägre stressintensitetsfaktorer kan förvänta sig längre livstid. En annan observation är en relativt konsekvent stressintensitetsfaktor vid kanten av FGA, vilket sannolikt markerar övergången från skapandet eller utbredning av FGA till traditionell sprickutbredning. Det verkar också finnas en koppling mellan storleken på FGA och antalet cykler till fel, med större FGA med ökande livslängd. Den mest uppenbara bristen i denna studie är mängden tillfredsställande tester som genomförts. Därmed är mängden datapunkter mycket låg, detta på grund av att majoriteten av proverna misslyckades vid gängningen som användes för att ansluta dem till ultraljudstestutrustningen vid livstider alltför låga för att vara relevanta.