Ce travail porte sur l’étude du risque d’amorçage de fissure en fretting/fatigue du contact aubes/disque de soufflante en alliage de titane Ti-6Al-4V d’un turboréacteur civil. De part les vibrations du moteur et le passage du flux d’air, le contact aube/disque est sujet à de microdéplacements: le fretting. Ce problème complexe concerne des zones en contact de faibles dimensions subissant des pressions de contact importantes et des micro-déplacements associées à des structures soumises à des chargements eux-mêmes complexes. Des essais de fretting simple, fretting précontraint et fretting fatigue sont réalisés en vue d’identifier les conditions d’amorçage de fissure pour plusieurs géométries présentant des gradients de contraintes différents. Les résultats expérimentaux mettent en évidence l’effet du gradient de contrainte sur l’amorçage. Ainsi, via des essais présentant une gamme étendue de gradient, il a été confirmé que les gradients de contraintes retardent l’initiation de fissure. Une approche non-locale couplée à un critère de fatigue multiaxiale et identifiée sur une unique condition expérimentale de fretting simple a permis la prédiction de l’ensemble des résultats expérimentaux. Ainsi, une méthodologie prédictive des durées de vie à amorçage a été proposée. Cette approche numérique intègre la multiaxialité du chargement, l’effet du gradient des contraintes, la réponse élastoplastique de l’interface et les limites de fatigue en traction/compression et torsion alternée du matériau. L’interface aube/disque grenaillée du moteur subit une alternance de sollicitations de faibles amplitudes générant l’amorçage de fissure, et de grandes amplitudes favorisant l’usure des zones en contact. Le phénomène de compétition usure/fissure a alors été étudié via les courbes en cloches (durée de vie en fonction de l’amplitude de déplacement) ainsi que l’influence des contraintes résiduelles de grenaillage. Une première conclusion sur l’effet bénéfique de l’usure a pu être apportée dans le cas d’un matériau sans traitement de surface. Si les contraintes résiduelles de grenaillage permettent d’apporter un gain notable sur les durées de vie pour des sollicitations de glissement partiel, à l’inverse, il a été observé que le matériau avec le traitement de surface de grenaillage présente des durées de vie plus faibles pour des sollicitations favorisant l’usure. À travers d’essais inédits avec un dispositif expérimental à trois vérins, le chargement complexe de l’interface aube/disque du moteur a pu être reproduit à l’échelle du laboratoire. Ainsi, la durabilité globale du contact représentatif de l’interface aube/disque de soufflante a été étudiée. Une synergie des sollicitations oligocycliques et polycycliques à l’interface a été constatée provoquant des phénomènes de réorganisation de contraintes résiduelles et l’accélération des cinétiques d’usure. Cette étude a montré l’importance de prendre en compte les sollicitations polycycliques dans le dimensionnement des structures aubes/disque. Ces sollicitations couplent les aspects de fatigue « fissuration » aux phénomènes de cumul de dommage et de cinétique d’usure des interfaces. / This work aims at studying the crack initiation risk of a blade/disk contact under fretting/fatigue loading. The fan stage of a civil engine is studied and the material used is a titanium alloy: Ti-6Al-4V. This complex issue concerns small contacts which are subjected to high contact pressures and micro-displacements. Thus, a complex multiaxial loading occurs on the structure. Fretting, static stressed fretting and fretting fatigue testing are performed in order to quantify the crack nucleation thresholds. In addition, several geometries which present different stress gradient values are used. The experimental results show a stress gradient effect on the crack initiation. Thus, using a wide range of stress gradient, it has been confirmed that stress gradient delays crack nucleation. A multiaxial fatigue criterion is used to determine the equivalent stress field under the contact. Then, a non-local approach, identified thanks to one fretting experimental condition, is employed in order to consider the stress gradient effect. This approach provides the prediction of the whole experimental results. In this way, a predictive method of the initiation fatigue life has been introduced. This numerical approach takes into account the multiaxial loading, the stress gradient effect, the plastic-elastic behavior of the interface and the fatigue strength limits of the material. The blade/disk contacts of the engine are shot-peened. During the flight, interfaces are subjected to low displacement amplitudes leading to crack initiation. On the other hand, during landing and take-off, contacts are submitted to high displacement amplitudes leading to the interface wear. As a consequence, competition between wear kinetic and nucleation one is studied and “bell curves” are plotted (i.e. fatigue life time versus displacement amplitude).Moreover, the effect of the shot-peening residual stresses on fatigue life time is observed. In case of un-treated material, a beneficial impact on the fatigue life time is observed due to wear process. Compressive residual stresses of shot-peening increase the fatigue life when fretting/fatigue on partial slip regime occurs. Nevertheless, a decrease of the fatigue life time is observed when wear process is activated by the gross slip condition. Finally, the complex loading of the engine blade/disk contact has been reproduced in the laboratory. To achieve this, a new testing, using an experimental machine composed of three hydraulic actuators is developed. Thus, the global life time of the representative interface of the fan stage is studied. Oligocyclic (low frequency) and polycyclic (high frequency) solicitations interact themselves and lead, firstly, to a rearrangement of the residual stresses, and secondly, to an increase of the wear kinetics. This research work highlights the interest to consider the polycyclic loadings to design the blade/disk structure. These solicitations reproduce the “cracking” fatigue phenomenon, the cumulative damages and the wear kinetics of the interface.

This dissertation aims to study the benefit of rail grinding on service life of railroad rails, focusing on failures due to rolling contact fatigue (RCF) at the rail head. Assuming a tangent rail with one-point contact at the running surface, a finite element analysis of a full-scale wheel-rail rolling contact with a nonlinear isotropic kinematic hardening material model is performed to simulate the accumulation of residual stresses and strains in the rail head. Using rolling stress and strain results from the sixth loading cycle, in which residual stresses and strains are at their steady-state, as input, two critical plane fatigue criteria are proposed for fatigue analyses. The first fatigue criterion is the stress-based approach—namely the Findley fatigue criterion. It suggests an important role of tensile residual stresses on subsurface crack nucleation and early growth in the rail head, but applications of the criterion to the near-running-surface region are limited because of plastic deformation from wheel-rail contact. The second fatigue criterion is the strain-based approach—namely the Fatemi-Socie fatigue criterion. Contributed mainly from shear strain amplitudes and factorized by normal stress components, the criterion also predicts fatigue crack nucleation at the subsurface as a possible failure mode as well as fatigue crack nucleation at the near-surface, while maintaining its validity in both regions. A collection of fatigue test data of various types of rail steel from literature is analyzed to determine a relationship between fatigue damages and number of cycles to failure. Considering a set of wheel loads with their corresponding number of rolling passage as a loading unit (LU), optimizations of grinding schedules with genetic algorithm (GA) show that fatigue life of rail increases by varying amount when compared against that from the no-grinding case. Results show that the proposed grinding schedules, optimized with the exploratory and local-search genetic algorithms, can increase fatigue life of rail by 240 percent. The optimization framework is designed to be able to determine a set of optimal grinding schedules for different types of rail steel and different contact configurations, i.e. two-point contact occurred when cornering.

L’optimisation du dimensionnement des structures passe par une meilleure connaissance de leur mode d’endommagement. Cette étude se focalise donc sur la caractérisation de l’endommagement du contact aube/disque des moteurs aéronautique. Cet assemblage mécanique est soumis a une combinaison d’un effort normal (force centrifuge) et tangentiel (dynamique de l’aube). La portée du disque en Ti-6Al-4V subi donc un chargement complexe de type fretting fatigue. Ce type de sollicitation entraine, entre autre dégradation, de la fissuration dont la modélisation expérimentale et numérique est rendue difficile par les limitations des moyens et des connaissances actuelles. Le premier objectif de ce travail de thèse est de développer un moyen d’essai et une instrumentation associée afin d’étudier de façon qualitative et quantitative la fissuration d’un contact Ti-6Al-4V/Ti-6Al-4V. Le second but est d’utiliser les données issues de ce moyen expérimental afin de proposer un modèle de prédiction des durées de vie de cet assemblage. Un montage inédit de fretting fatigue double vérin mono-contact a été mis en place avec une instrumentation nouvelle pour ce type d’essai : suivi de fissuration par suivi de potentiel et par émission acoustique. Une attention particulière a été apportée aux calibrations et aux méthodologies expérimentales. Ce banc d’essai permet notamment de simuler des efforts de fretting applique en phase ou alors de telle manière a simuler un vrai cycle de vol. Cet outil a permis de décrire quantitativement les premières courbes de Wohler en fretting à amorçage (Effort de fretting vs Nombre de cycles à amorçage) pour deux configurations de contact (cylindre/plan et plan/plan). Les impacts des différents paramètres de fretting sur l’amorcage ont pu être quantifies. Les paramètres influant sont : la configuration du contact, les niveaux des efforts appliques et leur mode de combinaison (cycles en phase ou cycles de type vol). De plus des courbes de cinétique de propagation des fissures ont pu être extraites des différents essais, montrant un fort impact du fretting sur les vitesses de propagation des fissures. Une analyse qualitative via l’émission acoustique a montré un mécanisme d’amorçage et de propagation en 3 étapes suivant la perte d’influence du contact. Un modèle de prédiction de l’amorçage et de simulation de la propagation des fissures a été mis en place. Bien que limite dans la prise en compte des effets gradients (approches non locales), ce modèle se montre très performant surtout dans sa capacité à utiliser les données expérimentales dans l’identification des lois d’amorçage ou de propagation. Ce travail a donc permis d’importantes avancées dans la compréhension des mécanismes de fissuration et dans leur modélisation ouvrant ainsi la porte vers une prédiction fiable de l’endommagement des contacts aube/disque. / Optimization of structures design requires a better understanding of their damage process. This study focuses on the characterisation of the blade/disk contact damaging process on aircraft engines. That mechanical structure is subjected to a normal load (centrifugal forces) combined with a tangential force (blade dynamic). Thus the Ti-6Al-4V disk seat sees a complex fretting fatigue loading. This type of solicitation can generate a series of degradations like cracking. Experimental and numerical simulation of this damaging is very difficult considering the present state of arts. The first aim of this work is to develop a new experimental set-up with the appropriate instrumentation in order to conduct a qualitative and a quantitative analysis of the cracking in a Ti-6Al-4V/Ti6-Al-4V contact. The second goal is to build a life prediction numerical model that would be able to use the data obtain with the new experimental tests. The new dual-actuator fretting-fatigue set-up is now operational. It allows to run single contact test under different loading combinations: fretting and fatigue loads can be applied in phase or in a way to simulate the real ‘in flight’ conditions. New instrumentations have been added in order to follow the crack initiation and propagation: potential-drop technique and acoustic emission. Thanks to this new test procedure, the first fretting Wöhler curve to crack nucleation have been described (fretting load vs number of cycles to crack nucleation) for two contact geometries (cylinder on flat and flat on flat). The separate influences of fatigue and fretting parameters have been determined. The mains parameters are: the contact characteristics, the stress level and the force combination modes (‘in phase’ cycles or ‘in-flight’ cycles). Moreover, the very first crack propagation kinetics have been drowned. Also, a major influence of the fretting on the crack propagation has been exposed. The qualitative analysis conducted with the acoustic emission has revealed a three steps crack propagation process. The crack propagation process evolves with the decrease of the contact influence. A model has been developed in order to predict crack initiation and propagation lives. Even if the model suffers from a major limitation due to the difficult considerations of the stress gradient effects, it has shown very good results through its ability to directly include experimental data. This work has led to major breakthroughs in the understanding of the cracking mechanisms and their simulation. This forms solid foundations for future predictions of the blade/disk interface durability.

[pt] Esta dissertação revisita quatro modelos multiaxiais de dano por fadiga (SWTD, SWT, Findley e Crossland) e discute a sua aplicação na previsão do risco de nucleação de trinca sob solicitações de fadiga por fretting segundo as abordagens local e não-local. As previsões do risco de nucleação de trinca obtidas através dos modelos estudados foram confrontadas com dados experimentais disponíveis na literatura para o contato cilindro/plano em aços AISI 52100 e AISI 1034 respectivamente. As melhores previsões foram obtidas através da versão desviadora SWTD. Segundo a abordagem local, o modelo SWTD fez previsões menos conservativas que os demais, sendo estas com erros conservativos inferiores a 15 porcento. Segundo a abordagem não-local, os quatro modelos geram previsões com erros inferiores a 15 porcento se os mesmos forem calibrados de forma independente. É importante mencionar que as melhores previsões obtidas através da abordagem não-local (que requer a calibração de um parâmetro adicional) são similares àquelas obtidas por SWTD local. Especificamente para os testes de fadiga por fretting com carga remota, o modelo SWTD não-local gerou previsões com 100 porcento de acertos (13 testes). Segundo a abordagem não-local, foi verificado que, para o conjunto de testes estudado, a precisão nas previsões é mais influenciada pela dimensão característica (que deve ser calibrada) que pelo modelo de fadiga multiaxial ou método de integração considerado. Por fim, verificou-se que previsões não conservativas podem ser obtidas ao se considerar uma dimensão característica assumida como parâmetro material (sem calibração) tal qual a distância crítica proposta por Taylor, definida em termos do método do ponto. / [en] This work presents and discusses four multiaxial fatigue damage models (SWTD, SWT, Findley and Crossland) applied to crack nucleation prediction under fretting fatigue loadings according to the local and the non-local approaches. The predictions have been compared with experimental data available in the literature for the cylinder on flat configuration made of 52100 and 1034 AISI steel s respectively. In particular, for the data set analyzed, SWTD parameter (deviatoric version of SWT model) predictions were less conservative than the ones made by the other three models and have better correlated the experimental results. Considering the local approach, the error observed on the SWTD predictions was lower than 15 percent. On the other hand, for the non-local approach, it has been demonstrated that the four multiaxial fatigue models can provide crack nucleation predictions with similar level of accuracy (error lower than 15 percent) if the characteristic dimension is calibrated model-by-model. Note that this same level of accuracy was obtained with SWTD parameter defined in terms of the local approach, which requires one less parameter to be calibrated (characteristic dimension). In particular, considering only the fretting fatigue tests with bulk stresses, SWTD non-local (area method) prediction accuracy was 100 percent (13 tests). For the material studied, it has also been concluded that the non-local predictions accuracy depends more on the calibrated characteristic dimension than on the multiaxial model or integration method considered. Moreover, it has been verified that non-conservative predictions can be made if the characteristic dimension is assumed as a material property as proposed by Taylor on the critical distances theory (point method).

Les simulations numériques des fissures fragiles par les modèles d’endommagement à gradient deviennent main- tenant très répandues. Les résultats théoriques et numériques montrent que dans le cadre de l’existence d’une pre-fissure la propagation suit le critère de Griffith. Alors que pour le problème à une dimension la nucléation de la fissure se fait à la contrainte critique, cette dernière propriété dimensionne le paramètre de longueur interne.Dans ce travail, on s’attarde sur le phénomène de nucléation de fissures pour les géométries communément rencontrées et qui ne présentent pas de solutions analytiques. On montre que pour une entaille en U- et V- l’initiation de la fissure varie continument entre la solution prédite par la contrainte critique et celle par la ténacité du matériau. Une série de vérifications et de validations sur diffèrent matériaux est réalisée pour les deux géométries considérées. On s’intéresse ensuite à un défaut elliptique dans un domaine infini ou très élancé pour illustrer la capacité du modèle à prendre en compte les effets d’échelles des matériaux et des structures.Dans un deuxième temps, ce modèle est étendu à la fracturation hydraulique. Une première phase de vérification du modèle est effectuée en stimulant une pré-fissure seule par l’injection d’une quantité donnée de fluide. Ensuite on étudie la simulation d’un réseau parallèle de fissures. Les résultats obtenus montrent qu’il a qu’une seule fissure qui se propage et que ce type de configuration minimise mieux l’énergie la propagation d’un réseau de fractures. Le dernier exemple se concentre sur la stabilité des fissures dans le cadre d’une expérience d’éclatement à pression imposée pour l’industrie pétrolière. Cette expérience d’éclatement de la roche est réalisée en laboratoire afin de simuler les conditions de confinement retrouvées lors des forages.La dernière partie de ce travail se concentre sur la rupture ductile en couplant le modèle à champ de phase avec les modèles de plasticité parfaite. Grâce à l’approche variationnelle du problème on décrit l’implantation numérique retenue pour le calcul parallèle. Les simulations réalisées montrent que pour une géométrie légèrement entaillée la phénoménologie des fissures ductiles comme par exemple la nucléation et la propagation sont en concordances avec ceux reportées dans la littérature. / Phase-field models, sometimes referred to as gradient damage, are widely used methods for the numerical simulation of crack propagation in brittle materials. Theoretical results and numerical evidences show that they can predict the propagation of a pre-existing crack according to Griffith’s criterion. For a one- dimensional problem, it has been shown that they can predict nucleation upon a critical stress, provided that the regularization parameter is identified with the material’s internal characteristic length.In this work, we draw on numerical simulations to study crack nucleation in commonly encountered geometries for which closed-form solutions are not available. We use U- and V-notches to show that the nucleation load varies smoothly from the one predicted by a strength criterion to the one of a toughness criterion when the strength of the stress concentration or singularity varies. We present validation and verification of numerical simulations for both types of geometries. We consider the problem of an elliptic cavity in an infinite or elongated domain to show that variational phase field models properly account for structural and material size effects.In a second movement, this model is extended to hydraulic fracturing. We present a validation of the model by simulating a single fracture in a large domain subject to a control amount of fluid. Then we study an infinite network of pressurized parallel cracks. Results show that the stimulation of a single fracture is the best energy minimizer compared to multi-fracking case. The last example focuses on fracturing stability regimes using linear elastic fracture mechanics for pressure driven fractures in an experimental geometry used in petroleum industry which replicates a situation encountered downhole with a borehole called burst experiment.The last part of this work focuses on ductile fracture by coupling phase-field models with perfect plasticity. Based on the variational structure of the problem we give a numerical implementation of the coupled model for parallel computing. Simulation results of a mild notch specimens are in agreement with the phenomenology of ductile fracture such that nucleation and propagation commonly reported in the literature.