[pt] A resistência a fadiga dos elementos estruturais pode ser limitada pela presença de trincas curtas, as quais podem passar despercebidas em inspeções não-destrutivas tradicionais. Para modelar o comportamento dessas trincas pode-se utilizar o tamanho característico das trincas curtas ao, proposto por El Haddad, Topper e Smith (ETS), que permite ajustar adequadamente os dados experimentais do diagrama de Kitagawa-Takahashi. Partindo do modelo ETS, neste trabalho se apresenta o modelo do Gradiente de Tensão (GT), desenvolvido para prever o efeito das trincas curtas que nascem em pontas de entalhes. Este modelo reconhece que trincas podem ser facilmente geradas por fadiga em entalhes afiados, que introduzem efeitos de concentração de tensão elevados nas suas pontas. Mas devido ao alto gradiente de tensão que atua em torno das pontas desses entalhes, as trincas curtas que deles emanam também podem parar de crescer por fadiga após terem se propagado por uma pequena distância, tornando-se assim trincas não-propagantes que podem ser toleradas em serviço. Corpos de prova tipo C(T) modificados foram projetados especificamente para estudar a geração e o crescimento inicial dessas trincas em ensaios de fadiga, e usados para verificar experimentalmente as previsões do modelo proposto. / [en] The fatigue strength of structural elements may be limited by the presence of short cracks, which can not be detected with traditional nondestructive inspections. The behavior of these cracks can be modeled using the characteristic size of short cracks a0, proposed by El Haddad, Topper and Smith (ETS), which allows one to properly adjust experimental data from the Kitagawa-Takahashi diagram. Based on the ETS model, this work presents the Stress Gradient (SG) model, developed to predict the effect of short cracks that grow from the notch tips. This model considers that cracks are easily generated due to fatigue in sharp notches, which introduce high stress concentration effects at their tips. Because of the high stress gradient acting at these notch tips, the short cracks can also stop to grow by fatigue after having propagated through a small distance, thereby becoming non-propagating cracks that can be tolerated in service. C(T) modified specimens were specifically designed to study the generation and initial growth of these cracks in fatigue tests, and used to experimentally verify the predictions of the proposed model.

Structural concrete is the most widely used material in the construction of bridges, pave-ments, runways, dams and other infrastructures which are subjected to uctuating loads during its service period. Concrete contains internal aws in the form of micro-cracks as an inherent property. When subjected to fatigue loading, distributed micro-cracks are formed at the sites of pre-existing aws, which subsequently, localize to form a major crack and propagates. The crack growth curve of a structural component when subjected to fatigue loading depicts a sigmoidal pattern. This curve is divided into three distinct regions namely sub-threshold crack propagation (short crack), stable crack propagation (long crack) and unstable crack propagation depending on the crack propagation rate. Most of the fatigue life is spent in the sub-critical stage (small crack) before the for-mation of long cracks. Hence, from the view of estimating the fatigue life, the crack initiation and early crack propagation (short crack stage) phase are the most important and correct concepts need to be developed. Hence, in this work, the behavior of propa-gation and non-propagationof short cracks in concrete when subjected to fatigue loading is addressed. Small non-propagating cracks are usually found at notch roots when the nominal stress range is below certain limits that depend on the notch sensitivity. Analysis is performed on geometrically similar three-point bend beams of three di erent sizes and subjected to fatigue loading in order to determine the important factors that a ect the notch sensitivity and to determine the minimum stress range required for the initiation and propagation of short cracks. A criterion for crack initiation and propagation is proposed based on linear elastic fracture mechanics. Using this criterion, the maximum length of non-propagating crack that can be formed from fatigue loading alone and the minimum stress range required to propagate a crack without arrest are computed. It is observed that the notch sensitivity increases with increase in beam size, decrease in notch-tip aspect ratio and increase in the fatigue limit of the material. Since the probability of formation of a non-propagating crack at a notch tip decreases with increase in notch sensitivity, and since it is desirable not to have a non-propagating crack in experimental investigations, it is essential to design a specimen with higher notch sensitivity. A crack spends a considerable amount of time in the short crack regime. The short cracks are found to propagate at higher rates than the long cracks at the same nominal stress intensity factor which is known as the short crack anomaly. It is important to consider this anomaly in the prediction of the residual life of damaged concrete structures. Hence, in the present work, an analytical model is developed using the principles of dimensional analysis and self-similarity in order to estimate the rate of short crack growth in concrete. The important parameters such as load range, threshold value of stress intensity factor range, modulus of elasticity, tensile strength, fracture energy, stress ratio, crack size and the maximum aggregate size are considered in the development of the short crack growth model. The model is calibrated and validated using the experimental results that are available in the literature. A probabilistic analysis is carried out to determine the sensitivity of each of the di erent parameters that has been considered on the crack growth rate using the coe cient of variation method. It is found that the crack length is the most sensitive parameter to short crack growth rate followed by the load range. A term called `characteristic fatigue life of short crack' is de ned as the number of fatigue cycles that can be applied such that not more than ve percent of the short cracks is expected to proceed to the long crack regime. Furthermore, the fatigue life of a crack spent in the short crack regime is determined through a reliability based study using the Monte Carlo technique. It is found that the smaller sized specimens have larger fatigue life in the short crack regime than the larger specimens.

The presented master’s thesis deals with description of short fatigue cracks and can be divided to the several parts. In the first part, theoretical background of fatigue of materials and fracture mechanics parameters which can describe fatigue cracks is presented. Following part describes how to determine fracture mechanics parameters by finite elements method. Due to the shape of propagated fatigue crack, numerical model was established as a three-dimensional. Results obtained based on this model, was compared with literature with very good agreement. Than real shape of propagated short crack was used for description of the experimental data. It was shown, that plastic part of J-integral is suitable parameter for description of the short cracks.

The main goal of this diploma thesis is the examination of the influence of structure directionality on fatigue properties of formed aluminium alloy 6082/T6. The main attention is focused on the study of the influence of structure directionality on kinetics of short fatigue cracks growth. The measurement of short fatigue cracks growth was performed on cylindrical samples. The samples were made in two different directions; one parallel with the forming direction and second perpendicular to the forming direction. Servo hydraulic machine MTS 880 was used for the cyclic loading. The samples were cycled at two different constant stress amplitudes. Cyclic loading was systematically interrupted in order to measure the length of short cracks by a light microscope. Tensile tests, measuring of cycling hardening-softening curves, observation of microstructure, observation of surface relief, measuring of microhardness and fractographical analysis of fracture surfaces were used for further examination of the influence of the structure directionality. Some of these measured characteristics did not show any influence of the structure directionality (microhardness, fatigue life curve, Young modulus). In other cases is this influence measurable, however insignificant (yield stress, ultimate stress, cyclic hardening-softening curves and kinetics of short fatigue cracks growth). It can be summarised that the material, though the directionality of its microstructure is apparent, shows relatively isotropic mechanical behaviour.

La tomographie en contraste de diffraction est une nouvelle technique non destructive d'imagerie synchrotron qui caractérise la microstructure et l'orientation des grains dans les matériaux polycristallins en trois dimensions (3D). En la combinant avec la tomographe par contraste de phase. Il est pour la première fois possible d'observer in situ la propagation 3D des fissures de fatigue courtes au sein d'un ensemble de grains entièrement caractérisé (orientation et forme). L'approche combinée, appelée « tomographie tri-dimensionnelle par rayons X des fissures courtes et de la microstructure »(T3DXFM), a été développée sur l’alliage de titane métastable "Beta21S". Une grande partie de ce travail porte sur le développement de la méthodologie T3DXFM. Dans le jeu de données combinées, chaque point de la surface de rupture 3D peut être associé à une structure de données multidimensionnelle contenant des variables décrivant l'orientation des grains, l'orientation locale de la surface de rupture ainsi que l'histoire de la propagation. La méthode utilise un maillage de surface composé de triangles qui décrit la fissure (en d'autres termes: la surface de rupture) dans l'état de propagation mesuré au dernier cycle de fatigue réalisé. Les orientations des grains, les différents fronts de la fissure, les vitesses de croissance locales ainsi que les joints de grains peuvent être visualisés en attribuant des couleurs à ce maillage. Des outils d'extraction des figures de pôle ont été créés et mis en œuvre. Un algorithme a été développé qui est capable de mesurer la vitesse de propagation locale 30 d'une fissure contenant des branchements. / X-Ray Diffraction Contrast Tomography (DCT) is a recently developed, non-destructive synchrotron imaging technique which characterizes microstructure and grain orientation in polycrystalline materials in three dimensions (3D). By combining it with propagation based phase contrast tomography (PCT) it is for the first lime possible to observe in situ the 3D propagation behavior of short fatigue cracks (SFCs) within a set of fully characterized grains (orientation and shape). The combined approach, termed 3D X-ray Tomography of short cracks and Microstructure (3DXTSM), has been developed on the metastable beta titanium alloy "Beta21S". A large part of this work deals with the development of the 3DXTSM methodology. In the combined dataset, each point on the 3D fracture surface can be associated with a multidimensional data structure containing variables describing the grain orientation, the local fracture surface normal and the propagation history. The method uses a surface mesh composed of triangles that describes the crack (in other words: the fracture surface) in the last propagation state measured. Grain orientations, crack fronts, local growth rates and grain boundaries can be visualized by assigning colors to this mesh. The data structure can be interrogated in a number of different ways. Tools for extracting pole figures and pole density distribution functions have been implemented. An algorithm was developed that is capable of measuring the 3D local growth rate of a crack containing branches. The accuracy of the grain boundaries as reconstructed with OCT was evaluated and the elastic constants of Beta21S were determined.

Fretting fatigue is a damage process that may arise in engineering applications where small cyclic relative displacements develop inside contacts leading to detrimental effects on the material fatigue properties. Fretting is located in regions not easily accessible, which makes it a dangerous phenomenon. It is therefore important to be able to make reliable predictions of the fretting fatigue lives. The work presented in this thesis has its focus on different aspects related to fretting fatigue in the titanium alloy Ti-17. A fretting experiment was developed which allowed for separate control of the three main fretting loads. Initially, the evolution of the coefficient of friction inside the slip region was investigated experimentally and analytically. Subsequently, 28 fretting tests were performed in which large fatigue cracks developed. The fretting tests were firstly evaluated with respect to fatigue crack initiation through five multiaxial fatigue criteria. The criteria predicted a too high fretting fatigue limit. A possible clue to the discrepancy was found in the fretting induced surface roughness with the asperity-pit interactions. The fatigue growth of the large fretting cracks was numerically modelled through a parametric crack growth procedure. The predicted lives were compared to the experimental outcome. The numerical simulations showed that linear elastic fracture mechanics was an appropriate tool for the prediction of fretting fatigue propagation lives in the long crack regime. Fatigue cracks spend most of their propagation life in the small crack regime. The possibility of modelling the small crack behaviour is therefore very important from the engineering point of view. The fatigue growth of through thickness short cracks was studied experimentally and numerically in the four-point bend configuration. It was found that linear elastic fracture mechanics and closure-free material growth data furnished conservative estimates for cracks longer than 50 μm. One method to improve fretting fatigue life is to shot peen the contact surfaces. Experimental results on fretting life with or without shot peening were simulated. The fatigue life enhancement in shot peened specimens could be explained by slower crack growth in the surface material layer with residual compressive stresses. / QC 20100827

In der vorliegenden Arbeit wurden Untersuchungen zum Initiierungs- und Ausbreitungsverhalten kurzer Ermüdungsrisse in einem austenitischen sowie einem austenitisch-ferritischen Edelstahl durchgeführt. Dazu erfolgten zyklische Verformungsexperimente sowohl ex situ als auch in situ im Rasterelektronenmikroskop. Die Auswertung der Experimente erfolgte im Rasterelektronenmikroskop sowohl abbildend in verschiedenen Modi als auch über Rückstreuelektronenbeugungsmessungen. Bezüglich der Rissinitiierung wurde eine Häufigkeitsverteilung der Rissinitiierungsorte für beide Stähle erstellt. Die dabei ermittelte stark unterschiedliche Häufigkeit für die transkristalline Rissinitiierung in der austenitischen Phase konnte mit der unterschiedlichen Textur und Mikrostruktur der beiden Stähle in Zusammenwirken mit den elastischen Eigenschaften der beiden Phasen erklärt werden. Für die Rissausbreitung wurde gezeigt, dass eine Korrelation zwischen der Risslänge und der Rissausbreitungsrate besteht, aus der hervorgeht, dass die Übergangsrisslänge zwischen den Bereichen der mikrostrukturell und mechanisch kurzen Risse etwa einen Korndurchmesser beträgt. Anhand der in situ Messung der (plastischen) Rissöffnung und -scherung wurden die Unterschiede im Rissausbreitungsverhalten in den verschiedenen Phasen herausgearbeitet. Für die austenitische Phase ergibt sich dabei ein öffnungsdominierter und für die ferritische Phase ein scherungsdominierter Mechanismus. Die im Ferrit auftretenden zwei unterschiedlichen Ausprägungen der Oberflächenrisspfade („rau“ und „glatt“) konnten mit der Orientierung der jeweils risstragenden Körner korreliert werden. In Zusammenwirken mit der beobachteten Systematik der Anordnung der Gleitspuren um kurze Risse im Ferrit sowie einer Analyse der Spannungsverteilung um die Rissspitze wurde ein Modell des Rissausbreitungsmechanismus\' erstellt sowie die bisher in der Literatur vorherrschende These des Einfachgleitens widerlegt. Schließlich konnte die Barrierenwirkung von Korn- und Phasengrenzen sowohl anhand der Messung der Rissausbreitungsrate als auch der plastischen Rissöffnung bzw. -scherung gezeigt und daraus Rückschlüsse auf die Ausdehnung der plastischen Zone vor der Rissspitze gezogen werden. Gleichzeitig wurde dabei die Korrelation zwischen Rissausbreitungsrate und plastischer Rissöffnung bzw. -scherung nachgewiesen.

[pt] Corrosão sob tensão (SCC), que consiste na iniciação e propagação de trincas devido ao efeito combinado de tensões mecânicas e o ambiente corrosivo, é um dano potencial para estruturas e componentes. Além do mais, SCC pode ser explicado por diferentes mecanismos dependendo do par material ambiente corrosivo considerado, o que dificulta o uso de um modelo geral para predizer o comportamento de trincas em SCC. Sendo assim, projetos frequentemente utilizam um critério conservativo que desqualifica materiais susceptíveis à SCC sem analisar de maneira apropriada a influência dos campos de tensão que a induzem. O objetivo deste trabalho é avaliar o efeito de tensões elastoplásticas na corrosão sob tensão. Esta abordagem mecânica considera que todos os efeitos corrosivos envolvidos na corrosão sob tensão podem ser apropriadamente quantificados pelas tradicionais resistências do material à iniciação e propagação de trincas para um ambiente corrosivo específico. Corpos de prova de flexão em Alumínio fragilizados por Gálio líquido serão utilizados para prever o efeito de tensões residuais induzidas por deformações plásticas na iniciação de trincas por corrosão sob tensão. Além disso, uma análise quantitativa baseada no comportamento de trincas não propagantes a partir de entalhes será usada para estimar a tensão necessária para iniciar e propagar trincas em corpos de prova entalhados em aço AISI 4140 sujeitos à corrosão por sulfeto de hidrogênio em ambiente aquoso. O comportamento de trincas curtas e a carga máxima suportada pelos corpos de prova entalhados são analisadas considerando campos de tensões lineares elástico e elastoplásticos através do modelo proposto que será validado através de dados experimentais. / [en] Stress Corrosion Cracking (SCC), which consist in the initiation and propagation of cracks due to the combined attack of mechanical stresses and a corrosive environment is a potential danger for structures and components. Moreover, SCC can be explained by different mechanisms depending on the metal environmental pair, what makes difficult to create a generalized analytical approach to predict the crack behavior in SCC. Therefore, projects often use an over-conservative design criteria that disqualify a material susceptible to SCC without properly evaluate the influence of the stress fields that drive them. The aim of this work is to evaluate the effect of elastic-plastic stress in SCC. This mechanical approach assumes that all chemical effects involved in SCC problems can be appositely described and quantified by traditional material resistances to crack initiation and propagation at under specific environment. Aluminum bending specimens in Gallium environment are used to predict the effect of the residual stress induced by plastic deformation in the crack initiation under SCC conditions. Furthermore, a quantitative analysis based on the non-propagating crack behavior departing from notch tips are used to calculate the necessary stress to initiate and propagate SCC in AISI 4140 steel notched specimens under aqueous hydrogen sulfide environment. The non-propagating crack behavior and the maximum load supported by notched specimens are analyzed under linear elastic and elastic-plastic stress field through the proposed model that will be validated by experimental data.

The work is concerned with the development of a multi-stage corrosion fatigue lifetime model, with emphasis on pitting as a precursor to cracking. The model is based upon the quantitative evaluation of damage during the overall corrosion fatigue process. The fatigue response of as-received API 5L X65 linepipe steel has been investigated in terms of the evolution of damage during pit development, pit-to-crack transition and crack propagation. Micro-potentiostatic polarisation was conducted to evaluate role of stress on pit development. Crack growth rate measurements were conducted on pre-pitted specimens, which were tested in air and brine, to evaluate the initiation and propagation behaviour of cracks emanating from artificial pits. Finite element analysis was undertaken to evaluate the stress and strain distribution associated with the pits. A cellular automata finite element model was also developed for predicting corrosion fatigue damage. Pit growth rate was enhanced under stress. It was considered that the strain localisation effect of the pit facilitated strain-assisted dissolution. In air, cracks initiated predominantly from the pit mouth. FEA results indicated that this was due to localisation of strain towards the pit mouth. In corrosion fatigue, cracks tended to initiate at the pit base at low stress and at the pit mouth at higher stresses. Crack initiation lifetimes were shorter in the aggressive environment compared to air and the effect of the environment on crack initiation lifetime was lower at higher stress levels. Crack initiation lifetime for double pits generally decreased with decreasing pit-to-pit separation distance. The microstructure was observed to influence crack growth behaviour in air particularly in the early stages when cracks were short. The acceleration and retardation in crack growth were attributed to the resistance of grain boundaries to crack advance. Cracks sometimes arrested at these barriers and became non-propagating. Introduction of the environment for a short period appear to eliminate the resistance of the microstructural barriers thus promoting re-propagation of the previously arrested crack. The continued crack propagation after the removal of the environment suggests that the influence of the environment is more important in the early stages of crack growth. Crack growth rates were higher in the aggressive environment than in air. The degree of environmental enhancement of crack growth was found to be greater at lower stress levels and at short crack lengths. Oxide-induced crack closure and crack coalescence were two mechanisms that also affected crack growth behaviour.2-D cellular automata finite element simulation results, with and without stress, show good agreement agreed with experiments i.e. pit depth and pit aspect ratio increase with time. Results from 3-D cellular automata simulations of pits are also consistent with experiments. Fatigue lifetimes were significantly shorter (i) in the brine environment than in air and (ii) for specimens with double pits compared to single pits of similar depth. Fatigue strength in air was found to decrease with increasing pit depth. Corrosion fatigue lifetimes predicted based upon the developed model showed good agreement with the experimental lifetimes.

In der vorliegenden Arbeit wurden Untersuchungen zum Initiierungs- und Ausbreitungsverhalten kurzer Ermüdungsrisse in einem austenitischen sowie einem austenitisch-ferritischen Edelstahl durchgeführt. Dazu erfolgten zyklische Verformungsexperimente sowohl ex situ als auch in situ im Rasterelektronenmikroskop. Die Auswertung der Experimente erfolgte im Rasterelektronenmikroskop sowohl abbildend in verschiedenen Modi als auch über Rückstreuelektronenbeugungsmessungen. Bezüglich der Rissinitiierung wurde eine Häufigkeitsverteilung der Rissinitiierungsorte für beide Stähle erstellt. Die dabei ermittelte stark unterschiedliche Häufigkeit für die transkristalline Rissinitiierung in der austenitischen Phase konnte mit der unterschiedlichen Textur und Mikrostruktur der beiden Stähle in Zusammenwirken mit den elastischen Eigenschaften der beiden Phasen erklärt werden. Für die Rissausbreitung wurde gezeigt, dass eine Korrelation zwischen der Risslänge und der Rissausbreitungsrate besteht, aus der hervorgeht, dass die Übergangsrisslänge zwischen den Bereichen der mikrostrukturell und mechanisch kurzen Risse etwa einen Korndurchmesser beträgt. Anhand der in situ Messung der (plastischen) Rissöffnung und -scherung wurden die Unterschiede im Rissausbreitungsverhalten in den verschiedenen Phasen herausgearbeitet. Für die austenitische Phase ergibt sich dabei ein öffnungsdominierter und für die ferritische Phase ein scherungsdominierter Mechanismus. Die im Ferrit auftretenden zwei unterschiedlichen Ausprägungen der Oberflächenrisspfade („rau“ und „glatt“) konnten mit der Orientierung der jeweils risstragenden Körner korreliert werden. In Zusammenwirken mit der beobachteten Systematik der Anordnung der Gleitspuren um kurze Risse im Ferrit sowie einer Analyse der Spannungsverteilung um die Rissspitze wurde ein Modell des Rissausbreitungsmechanismus\' erstellt sowie die bisher in der Literatur vorherrschende These des Einfachgleitens widerlegt. Schließlich konnte die Barrierenwirkung von Korn- und Phasengrenzen sowohl anhand der Messung der Rissausbreitungsrate als auch der plastischen Rissöffnung bzw. -scherung gezeigt und daraus Rückschlüsse auf die Ausdehnung der plastischen Zone vor der Rissspitze gezogen werden. Gleichzeitig wurde dabei die Korrelation zwischen Rissausbreitungsrate und plastischer Rissöffnung bzw. -scherung nachgewiesen.