Les travaux présentés dans ce mémoire concernent le développement de méthodes de pronostic à base de modèles. Le pronostic à base de modèles a pour but d'estimer le temps qu'il reste avant qu'un système ne soit défaillant, à partir d'un modèle physique de la dégradation du système. Ce temps de vie restant est appelé durée de résiduelle (RUL) du système.Le pronostic à base de modèle est composé de deux étapes principales : (i) estimation de l'état actuel de la dégradation et (ii) prédiction de l'état futur de la dégradation. La première étape, qui est une étape de filtrage, est réalisée à partir du modèle et des mesures disponibles. La seconde étape consiste à faire de la propagation d'incertitudes. Le principal enjeu du pronostic concerne la prise en compte des différentes sources d'incertitude pour obtenir une mesure de l'incertitude associée à la RUL prédite. Les principales sources d'incertitude sont les incertitudes de modèle, les incertitudes de mesures et les incertitudes liées aux futures conditions d'opération du système. Afin de gérer ces incertitudes et les intégrer au pronostic, des méthodes probabilistes ainsi que des méthodes ensemblistes ont été développées dans cette thèse.Dans un premier temps, un filtre de Kalman étendu ainsi qu'un filtre particulaire sont appliqués au pronostic de propagation de fissure, en utilisant la loi de Paris et des données synthétiques. Puis, une méthode combinant un filtre particulaire et un algorithme de détection (algorithme des sommes cumulatives) a été développée puis appliquée au pronostic de propagation de fissure dans un matériau composite soumis à un chargement variable. Cette fois, en plus des incertitudes de modèle et de mesures, les incertitudes liées aux futures conditions d'opération du système ont aussi été considérées. De plus, des données réelles ont été utilisées. Ensuite, deux méthodes de pronostic sont développées dans un cadre ensembliste où les erreurs sont considérées comme étant bornées. Elles utilisent notamment des méthodes d'inversion ensembliste et un observateur par intervalles pour des systèmes linéaires à temps discret. Enfin, l'application d'une méthode issue du domaine de l'analyse de fiabilité des systèmes au pronostic à base de modèles est présentée. Il s'agit de la méthode Inverse First-Order Reliability Method (Inverse FORM).Pour chaque méthode développée, des métriques d'évaluation de performance sont calculées dans le but de comparer leur efficacité. Il s'agit de l'exactitude, la précision et l'opportunité. / In this manuscript, contributions to the development of methods for on-line model-based prognosis are presented. Model-based prognosis aims at predicting the time before the monitored system reaches a failure state, using a physics-based model of the degradation. This time before failure is called the remaining useful life (RUL) of the system.Model-based prognosis is divided in two main steps: (i) current degradation state estimation and (ii) future degradation state prediction to predict the RUL. The first step, which consists in estimating the current degradation state using the measurements, is performed with filtering techniques. The second step is realized with uncertainty propagation methods. The main challenge in prognosis is to take the different uncertainty sources into account in order to obtain a measure of the RUL uncertainty. There are mainly model uncertainty, measurement uncertainty and future uncertainty (loading, operating conditions, etc.). Thus, probabilistic and set-membership methods for model-based prognosis are investigated in this thesis to tackle these uncertainties.The ability of an extended Kalman filter and a particle filter to perform RUL prognosis in presence of model and measurement uncertainty is first studied using a nonlinear fatigue crack growth model based on the Paris' law and synthetic data. Then, the particle filter combined to a detection algorithm (cumulative sum algorithm) is applied to a more realistic case study, which is fatigue crack growth prognosis in composite materials under variable amplitude loading. This time, model uncertainty, measurement uncertainty and future loading uncertainty are taken into account, and real data are used. Then, two set-membership model-based prognosis methods based on constraint satisfaction and unknown input interval observer for linear discete-time systems are presented. Finally, an extension of a reliability analysis method to model-based prognosis, namely the inverse first-order reliability method (Inverse FORM), is presented.In each case study, performance evaluation metrics (accuracy, precision and timeliness) are calculated in order to make a comparison between the proposed methods.

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Finite element analyses are frequently used to model growing fatigue cracks and the associated plasticity-induced crack closure. Two-dimensional, elastic-perfectly plastic finite element analyses of middle-crack tension (M(T)), bend (SEB), and compact tension (C(T)) geometries were conducted to study fatigue crack closure and to calculate the crack opening values under plane-strain and plane-stress conditions. The loading was selected to give the same maximum stress intensity factor in both geometries, and thus similar initial forward plastic zone sizes. Mesh refinement studies were performed on all geometries with various element types. For the C(T) geometry, negligible crack opening loads under plane-strain conditions were observed. In contrast, for the M(T) specimen, the plane-strain crack opening stresses were found to be significantly larger. This difference was shown to be a consequence of in-plane constraint. Under plane-stress conditions, it was found that the in-plane constraint has negligible effect, such that the opening values are approximately the same for the C(T), SEB, and M(T) specimens. Next, the crack opening values of the C(T), SEB and M(T) specimens were compared under various stress levels and load ratios. The effect of a highly refined mesh on crack opening values was noted and significantly lower crack opening values than those reported in literature were found. A new methodology is presented to calculate crack opening values in planar geometries using the crack surface nodal force distribution under minimum loading as determined from finite element analyses. The calculated crack opening values are compared with values obtained using finite element analysis and more conventional crack opening assessment methodologies. It is shown that the new method is independent of loading increment, integration method (normal and reduced integration), and crack opening assessment location. The compared opening values were in good agreement with strip-yield models.

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No description available.

The integrity of nearly all engineering structures are threatened by the presence of cracks. Structural failure occurs if a crack larger than a critical size exists. Although most well designed structures initially contain no critical cracks, subcritical cracks can grow to failure under fatigue loading, called fatigue crack growth (FCG). Because it is impossible or impractical to prevent subcritical crack growth in most applications, a damage tolerant design philosophy was developed for crack sensitive structures. Design engineers have taken advantage of the FCG threshold concept to design for long fatigue lives. FCG threshold (DKth) is a value of DK (crack-tip loading), below which no significant FCG occurs. Cracks are tolerated if DK is less than DKth. However, FCG threshold is not constant. Many variables influence DKth including microstructure, environment, and load ratio. The current research focuses on load ratio effects on DKth and threshold FCG. Two categories of load ratio effects are studied here: extrinsic and intrinsic. Extrinsic load ratio effects operate in the crack wake and include fatigue crack closure mechanisms. Intrinsic load ratio effects operate in the crack-tip process zone and include microcracking and void production. To gain a better understanding of threshold FCG load ratio effects (1) a fatigue crack closure model is developed to consider the most likely closure mechanisms at threshold, simultaneously, and (2) intrinsic load ratio mechanisms are identified and modeled. An analytical fatigue crack closure model is developed that includes the three closure mechanisms considered most important at threshold (PICC, RICC, and OICC). Crack meandering and a limited amount of mixed-mode loading are also considered. The rough crack geometry, approximated as a two-dimensional sawtooth wave, results in a mixed-mode crack-tip stress state. Dislocation and continuum mechanics concepts are used to determine mixed-mode crack face displacements. Plasticity induced crack closure is included by modifying an existing analytical model, and an oxide layer in the crack mouth is modeled as a uniform layer. Finite element results were used to verify the analytical solutions for crack-tip stress intensity factor and crack face displacements. These results indicate that closure for rough cracks can occur at two locations: (1) at the crack-tip, and (2) at the asperity nearest the crack-tip. Both tip contact and asperity contact must be considered for rough cracks. Tip contact is more likely for high Kmax levels, thick oxide layers, and shallow asperity angles, a. Model results indicate that closure mechanisms combine in a synergistic manner. That is, when multiple closure mechanisms are active, the total closure level is greater than the sum of individual mechanisms acting alone. To better understand fatigue crack closure where multiple closure mechanisms are active (i.e. FCG threshold), these interactions must be considered. Model results are well supported by experimental data over a wide range of DK, including FCG threshold. Closure-free load ratio effects were studied for aluminum alloys 2024, 7050, and 8009. Alloys 7050 and 8009 were selected because load ratio effects at FCG threshold are not entirely explained by fatigue crack closure. It is believed that closure-free load ratio mechanisms occur in these alloys. Aluminum alloy 2024 was selected for study because it is relatively well behaved, meandering most load ratio effects are explained by fatigue crack closure. A series of constant Kmax threshold tests on aluminum alloys were conducted to eliminate fatigue crack closure at threshold. Even in the absence of fatigue crack closure load ratio (Kmax) effects persist, and are correlated with increased crack-tip damage (i.e. voids) seen on the fatigue crack surfaces. Accelerated FCG was observed during constant Kmax threshold testing of 8009 aluminum. A distinct transition is seen the FCG data and is correlated with a dramatic increase in void production seen along the crack faces. Void production in 8009 aluminum is limited to the specimen interior (plane-strain conditions), promoting crack tunneling. At higher values of Kmax (+_ 22.0 MPaà m), where plane-stress conditions dominate, a transition to slant cracking occurs at threshold. The transition to slant cracking produces an apparent increase in FCG rate with decreasing DK. This unstable threshold behavior is related to constraint conditions. Finally, a model is developed to predict the accelerated FCG rates, at higher Kmax levels, in terms of crack-tip damage. The effect of humidity (in laboratory air) on threshold FCG was studied to ensure that environmental effects at threshold were separated from load ratio effects. Although changes in humidity were shown to strongly affect threshold FCG rates, this influence was small for ambient humidity levels (relative humidity between 30% and 70%). Transient FCG behavior, following an abrupt change in humidity level, indicated environmental damage accumulated in the crack-tip monotonic plastic zone. Previous research implies that hydrogen (a component of water vapor) is the likely cause of this environmental damage. Analysis suggests that bulk diffusion is not a likely hydrogen transport mechanism in the crack-tip monotonic plastic zone. Rather, dislocation-assisted diffusion is presented as the likely hydrogen transport mechanism. Finally, the (extrinsic) fatigue crack closure model and the (intrinsic) crack-tip damage model are put in the context of a comprehensive threshold model. The ultimate goal of the comprehensive threshold model is to predict fatigue lives of cyclically loaded engineering components from (small) crack nucleation, through FCG, and including failure. The models developed in this dissertation provide a basis for a more complete evaluation of threshold FCG and fatigue life prediction. The research described in this dissertation was performed at NASA-Langley Research Center in Hampton, Virginia. Funding was provided through the NASA GSRP program (Graduate Student Researcher Program, grant number NGT-1-52174). / Ph. D.

Im Rahmen des Forschungsprojekts ”TMF-Rissverlaufsberechnung für ATL-Heißteile“ des FVV e.V. wurden Untersuchungen zur Entwicklung eines Rissfortschrittsgesetzes unter thermomechanischer Wechselbeanspruchung (thermo-mechanical fatigue, TMF) für das austenitische Gusseisen Ni-Resist D-5S durchgeführt. Ziel der experimentellen Arbeiten war es, mit einseitig gekerbten Proben (SENT) eine Datenbasis für Risswachstum unter TMF-Belastung zu schaffen. Das Werkstoffverhalten des betrachteten austenitischen Gusseisens Ni-Resist D-5S wurde mithilfe eines validierten viskoplastischen, temperaturabhängigen Materialmodells modelliert, das zur Berücksichtigung großer Verzerrungen und Rotationen am Riss auf große Deformationen erweitert wurde. Zur Beurteilung des Rissfortschritts unter TMF wurde die zyklische Rissspitzenöffnungsverschiebung (ΔCTOD) als geeigneter Beanspruchungsparameter verwendet. Für die Simulation der Rissausbreitung wurde ein automatischer FEM-Algorithmus mit inkrementeller, adaptiver Neuvernetzung entwickelt. Dabei wurden Verformungen und inelastische Zustandsvariablen auf das neue Netz übertragen. Der Einfluss verschiedener Parameter innerhalb der Simulationsstruktur wurde analysiert. Ein verbesserter Mapping-Algorithmus zur Übertragung der Zustandsvariablen wurde entwickelt. Mithilfe begleitender 2D FEM-Simulationen wurden die Rissfortschrittskurven des Werkstoffs basierend auf den experimentellen Daten ermittelt und unter Anwendung des ΔCTOD Konzepts in parametrisierter Form dargestellt. Zusätzlich wurden Rissfortschrittsgesetze durch den Einsatz von Machine-Learning-Konzepten bestimmt. Dies ermöglicht erstmals eine quantitative Vorhersage der Rissentwicklung unter Beanspruchungsbedingungen mit Großbereichsfließen unter Berücksichtigung von TMF. / As part of the research project ”TMF crack propagation calculation for ATL hot parts“ of the FVV e.V., an investigation was carried out to develop a crack propagation law under thermomechanical fatigue (TMF) for the austenitic cast iron Ni-Resist D-5S. The aim of the experimental work was to create a database for crack growth under TMF loading with single edge notch tension specimens (SENT). The material behavior of the austenitic cast iron under consideration, Ni-Resist D-5S, was modeled using a validated viscoplastic temperature dependent material model, which was extended to large deformations to account for large distortions and rotations in the crack. The cyclic crack opening displacement (ΔCTOD) was used as a suitable loading parameter to assess crack propagation under TMF. An automatic FEM algorithm with incremental adaptive remeshing was developed for the simulation of crack propagation. In the process, the deformations and inelastic state variables were transferred to the new mesh. The influence of different parameters within the simulation structure was analyzed. An ideal mapping algorithm for the transfer of state variables was developed. With the help of accompanying 2D FEM simulations, the crack propagation curves of the material were determined on the basis of the experimental data and presented in parameterized form using the concept ΔCTOD. Furthermore, crack propagation laws were determined using machine learning concepts. This allows for the first time a quantitative prediction of crack development under loading conditions with large scale yielding taking TMF into account.

Thermomechanical fatigue is a fatigue failure caused by combined thermal and mechanical loading cycles where both stresses and temperature can vary with time. A cohesive zone model simulates material failure within the finite element method by describing material behaviour and damage evolution through a traction-separation relation. In this work, a viscoplastic cohesive zone model is developed in order to describe the fatigue and fracture behaviour of high performance superalloys undergoing thermomechanical fatigue loading. A micromechanically motivated cohesive potential, incorporating fatigue and creep damage variables, is proposed and its thermodynamic consistency is established. The characteristic behaviour of the cohesive law during cyclic loading is described in terms of both traction and energy. The developed cohesive zone model is applied to simulate the lifetime behaviour in a smooth specimen. The effect of loading parameters such as temperature, dwell period, and strain rate on isothermal, in-phase and out-of-phase thermomechanical fatigue is successfully demonstrated. Using crack growth simulations in a boundary layer model, the relation between the local behaviour of the cohesive zone and fracture parameters like stress intensity factor, J-integral and crack tip opening displacement is established. The three stages of fatigue crack growth rate curves that are experimentally observed were obtained through simulations. Crack growth in a corner crack specimen is simulated under cyclic stress-controlled loading to obtain the experimentally observed crack profiles. Material parameters for the Nickel based superalloy MAR-M247 are identified using experimental data from the literature.

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 ΔKth 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 (ΔK) 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 ΔKth 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 (ΔK) 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.

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.