<div>As the use of fiber-reinforced polymer composites grows in aerospace structures, there is an emerging need to implement damage tolerant approaches. The use of <i>in-situ</i> synchrotron X-ray tomography enables direct observations of progressive damage relative to the microstructural features, which is studied in a T650/5320 laminate composite with varying layup orientations (using 45^o and -45^o plies) in a compact tension specimen geometry. Specifically, the interactions of micromechanical damage mechanisms at the notch tip were analyzed through 3D image processing as the crack grew. First, monotonic tests were conducted where X-ray tomography was acquired incrementally between the unloaded state and maximum load. The analysis of the monotonic tension specimens showed intralaminar cracking was dominant during crack initiation, delamination became prevalent during the later stages of crack progression, and fiber breakage was, in general, largely related to intralaminar cracking. After the monotonic tension analysis, modifications were made to the specimen geometry and the loading assembly, and fatigue tests were conducted, also using <i>in-situ</i> synchrotron X-ray tomography. Specifically, tomography images were acquired after select intervals of cyclic loading to examine the crack growth behavior up to 5802 cycles. The analysis of the fatigue tests showed that intralaminar cracking was also dominant, while localized delamination allowed ply cross-over. A finite element analysis was conducted by comparing the crack profile at varying intervals of loading, and the change in stored energy per cycle, dU/dN, was calculated. The combined experimental and simulation analysis showed that when the per ply values of dU/dN were examined, the intralaminar cracking rate collapsed to one curve regardless of the ply orientation, where direct observations of fiber bridging were characterized and associated with a reduction in crack growth rate for the influenced ply. Overall, this work provides a physical understanding of the micromechanics facilitating intralaminar crack growth in composites, providing engineers the necessary assessments for slow crack growth approaches in structural composite materials.<br></div>

Vid samverkansbroar fästes tvärförband mellan huvudbalkar med funktion att leda laster ut mot huvudbalkarna. Dessa kan fästas via s.k. livavstyvningsplåtar mot huvudbalkens liv samt flänsar. Denna infästning kan ske med svetsförband. Vid ett antal fall har utmattningssprickor uppkommit i svetsanslutningen mellan livavstyvningsplåten samt överfläns på huvudbalk. Tydliga riktlinjer finns ej i dagsläget för vilken typ av svetsförband som bör nyttjas vid uppförande av benämnd konstruktionsanslutning. Här genomförs en jämförande studie av kälsvetsförband mot stumsvetsförband, med samt utan svetsutbredning. Då risk för sprickinitiering till följd av utmattning i kälsvetsförbandet studerades beaktades risk för brott i såväl svetstå som svetsrot. Den aktuella studien ämnade ge svar på huruvida en korrelation mellan geometriska parametrar såsom avstånd mellan huvudbalkar samt konsollängd på farbana kunde kopplas till rekommendation gällande vilket svetsutförande som borde nyttjas vid olika dimensioner av dessa båda geometrier. Vidare ämnade studien utröna om eventuella gränsvärden för val av svetsanslutningar kunde fastställas. För framtagande av data nyttjades BRIGADE PLUS, ett beräkningsprogram som nyttjar FEM-modellering. Här användes ett uppfört projekt, Viadukt Söder, beläget i Östersund, som grundmodell för parameterstudien i BRIGADE PLUS. Detta var projekterat av ELU Konsult, på uppdrag av Trafikverket. Beräkningsmodellen bestod av en begränsad del av den aktuella bron, där utmattningslastfordon 3 i SS EN 1993-2 användes för att via influenslinjer återspegla trafiklast på bron och därmed finna värsta lastpositioner. Dessa positioner nyttjades sedermera för beräkning av påverkan från Utmattningslastfordon 3 på den studerade detaljen i form av spänningsamplitud. Analys av dessa spänningsamplituder omräknades sedermera till ett antal lastcykler till brott som sedan ställdes mot de riktlinjer som återfinns i SS EN 1993-1-9:2005. Här nyttjades de förbandsklasser som enligt nationella normer ses som gällande. Resultatet påvisade en exponentiell minskning av antal lastcykler till brott, med avseende på utmattning, då brogeometrin utökades. Utmärkande här var att risk för brott i livavstyvningsplåten klart översteg risk för brott i överflänsen, som i sin tur näst intill kunde bortses ifrån. Den geometriska parameter som blev styrande var konsollängd på farbana. Tydlig differens i livslängd mätt i antal cykler gick att utläsa för de olika svetsförbanden, där styrande faktor blev de respektive förbandsklasserna vid analys av sprickinitiering. Gränsvärden för då antal cykler till brott understeg gränsvärden enligt SS EN 1993-1-9:2005 kopplat till de geometriska parametrarna, gick att fastställa för respektive svetsförband. Kälsvetsens kapacitet med avseende på utmattning understeg vida stumsvetsens kapacitet. / For composite bridges, transverse bracings are attached between main girders with the function of distributing loads between the main girders. These can be attached via so-called web stiffeners against the main girders web and flanges. This attachment can be done via welded joints. In the event of emergence, fatigue cracks have arisen in the welding connection between the web stiffener and the top flange of the main girder. Clear guidelines do not exist at present for the type of welded joints that should be used in the construction of the termed design connection. Here, a comparative study is carried out between fillet welded joints and butt welded joints, with flat and inclined welds. When the risk of crack initiation as a result of fatigue in the fillet weld was studied, the risk of breakage in both toe and root was considered. The current study intended to provide answers as to whether a correlation between geometric parameters such as distance between main girders and cantilever length of the deck slab could be linked to recommendation regarding which welding design should be used at different dimensions of these two properties. Furthermore, the study intended to determine whether any limit values for the selection of welding connections could be determined. For the production of data, BRIGADE PLUS, a calculation program that utilizes FEM modeling, was used. Here, a constructed project, Viadukt Söder, situated in Östersund, was used as the basic model for the parameter study in BRIGADE PLUS. This was designed by ELU Konsult, on behalf of the Swedish Transport Administration. The calculation model consisted of a limited part of the current bridge, where Fatigue Load Vehicle 3 in SS EN 1993-2 was used to reflect traffic loads on the bridge via influenza lines and thereby find the worst load positions. These positions were subsequently used for calculating the influence of Fatigue Load Vehicle 3 on the studied part in the form of stress amplitude. Analysis of these stress amplitudes was subsequently recalculated to a number of load cycles to offenses that were then set against the guidelines found in SS EN 1993-1-9: 2005. Here, the fatigue resistance values were used which according to national standards are regarded as valid. The result showed an exponential decrease in the number of load cycles to fracture, with respect to fatigue, as the bridge geometry was increased. The characteristic feature here was that the risk of breakage in the web stiffener clearly exceeded the risk of breakage in the upper flange, which in turn could almost be disregarded. The geometric parameter that became guiding was cantilever length on the deck. Clear difference in service life measured in number of cycles could be read out for the different welded joints, where the controlling factor became the respective fatigue resistance values when analyzing crack initiation. Limit values for when the number of cycles to break below the limit values according to SS EN 1993-1-9:2005 linked to the geometric parameters, could be determined for each welded joint. The capacity of the fillet weld with respect to fatigue is far below the capacity of the butt weld.

[pt] A grande maioria das estruturas que trabalham sob cargas alternadas precisa ser dimensionada para evitar a iniciação de trincas por fadiga, o principal mecanismo de dano mecânico nesses casos. Os vários parâmetros dos modelos de previsão de dano à fadiga usados nesses projetos devem ser preferencialmente medidos a partir do ajuste otimizado de suas equações a dados experimentais medidos de forma adequada. Na realidade, a precisão das previsões baseadas nesses modelos depende diretamente da qualidade dos ajustes utilizados para obtenção desses parâmetros. Sendo assim, o objetivo principal deste trabalho é estudar a melhor maneira de se obter os parâmetros dos principais modelos de previsão da iniciação de trincas por fadiga através de ajustes de dados experimentais baseados no algoritmo de LevenbergMarquardt. Primeiro, foram realizados diversos ensaios εN em uma liga de alumínio 6351-T6 para averiguar o desempenho do ajuste proposto para asequações de Coffin-Manson e de Ramberg-Osgood. Em seguida, foram usados dados da literatura de outros oito materiais para ajustar modelos deformaçãovida clássicos, assim como com o expoente de Walker, para assim avaliar o efeito de cargas médias não-nulas em testes εN. Por fim, foi estudado o ajuste de um modelo SN com expoente de Walker que considera limites de fadiga e efeitos de carga média. Esse estudo também inclui considerações estatísticas para quantificar o fator de confiabilidade a partir de diferentes hipóteses de funções densidade de probabilidade, baseadas em dez conjuntos de dados da literatura. / [en] Most structures working under alternate loadings must be dimensioned to prevent fatigue crack initiation, the main mechanism of mechanical damage in these cases. The various parameters from the fatigue damage prediction models used in these projects should preferably be measured by optimally fitting their equations to well-measured experimental data. In fact, the accuracy of the predictions based on these models depends directly on the quality of the adjustments used to obtain these parameters. As a result, the main purpose of this work is to study the best way to obtain the parameters of the leading prediction models of fatigue crack initiation through experimental data fittings based on the Levenberg-Marquardt algorithm. First, several εN tests were performed on a 6351-T6 aluminum alloy to verify the performance of the proposed fit for the Coffin-Manson and Ramberg-Osgood equations. Then, data from the literature of eight other materials were used to fit classic strainlife models, as well as models based on the Walker exponent, to evaluate the effect of non-zero mean loads in εN tests. Finally, the fitting of an SN model including the Walker exponent was studied, which considers fatigue limits and mean load effects. This study includes as well statistical considerations to quantify the reliability factor from different probability density function assumptions, based on ten data sets from the literature.

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[pt] Na análise da predição de vida de estruturas a presença de defeitos por trincas é de fundamental importância. Estudos iniciais utilizando a Mecânica da Fratura Linear Elástica mostram que o Fator de Intensidade de Tensão controla o crescimento de trinca por fadiga. Contudo, sobrecargas podem induzir efeitos de memória no material ao reduzir, parar ou acelerar taxas de propagação, comportamento não previsto considerando-se um único parâmetro elástico. Devido às hipóteses consideradas, as soluções fornecidas pelos métodos analíticos não verificam condições importantes de equilíbrio e compatibilidade, especialmente quando são usados campos singulares idealizados de tensão e de deformação na região da ponta da trinca. Neste trabalho uma extensa revisão dos resultados analíticos recentemente publicados para materiais nos regimes elástico e elastoplástico são apresentadas: Williams e HRR com campo de distribuição singular das tensões e Creager-Paris com campo não-singular das tensões com o material elástico. Neste estudo, estas soluções são comparadas com resultados da análise numérica utilizando a discretização por elementos finitos tridimensionais elastoplásticos com o critério de escoamento do material de von Mises na representação do cegamento da ponta da trinca e importantes conclusões são apresentadas com referência aos limites de aplicação dos modelos teóricos bem como a extensão dos requerimentos para o modelo numérico. Além de carregamentos monotonicamente crescentes, o descarregamento foi também considerado na análise numérica, apesar desta condição não estar presente nas referências consideradas para as soluções analíticas. Para as simulações numéricas consideradas algoritmos de elastoplasticidade foram implementados em um framework com arquitetura baseada em plugins. / [en] In structure life prediction analysis the occurrence of crack defects are of paramount importance to be considered. Basic studies using Linear Elastic Fracture Mechanics approach shows that the Stress Intensity Factor (SIF) parameter controls Fatigue crack growth (FCG). However, overloads may induce material memory effects that delay, arrest or accelerate the FCG rate, a behavior that is not described by considering a single elastic parameter. To account for service variable amplitude loadings, the use of a prescribed stress-strain distribution has been proposed in recent research studies, as the driving force of FCG, using the critical damage approach. Due to the assumptions considered in the analytical derivations, important equilibrium and compatibility conditions are violated in the obtained solutions, since an idealized singular stress-strain field at the crack front region is used. In this work a comprehensive review of the recently published analytical results for solutions under the elastic and elastoplastic material behavior regimens are presented: Williams and HRR with singular stress distribution field and Creager-Paris with a non singular stress field, but with the material elastic approach. These solutions are compared, throughout the study, to results obtained from the numerical analysis using a 3D finite element discretization with elastoplastic von Mises yielding criteria employed for the modeling of the crack tip blunt and some comprehensive conclusions are derived regarding application limits of the theoretical models as well as the required extent of the numerical model representation. In addition to monotonic increasing applied loads, unloading conditions were also considered in the numerical analysis, although no reference to this condition is available in the literature, considering the analytical approach. For the numerical simulations presented elastoplastic algorithms were implemented in a plugin based framework.

The ability to predict fatigue crack growth rates is essential in safety critical systems. The discovery of fatigue crack closure in 1970 caused a flourish of research in attempts to simulate this behaviour, which crucially affects crack growth rates. Historically, crack tip plasticity models have been based on one-dimensional rays of plasticity emanating from the crack tip, either co-linear with the crack (for the case of plane stress), or at a chosen angle in the plane of analysis (for plane strain). In this thesis, one such model for plane stress, developed to predict fatigue crack closure, has been refined. It is applied to a study of the relationship between the apparent stress intensity range (easily calculated using linear elastic fracture mechanics), and the true stress intensity range, which includes the effects of plasticity induced fatigue crack closure. Results are presented for all load cases for a finite crack in an infinite plane, and a method is demonstrated which allows the calculation of the true stress intensity range for a growing crack, based only on the apparent stress intensity range for a static crack. Although the yield criterion is satisfied along the plastic ray, these one-dimensional plasticity models violate the yield criterion in the area immediately surrounding the plasticity ray. An area plasticity model is therefore required in order to model the plasticity more accurately. This thesis develops such a model by distributing dislocations over an area. Use of the model reveals that current methods for incremental plasticity algorithms using distributed dislocations produce an over-constrained system, due to misleading assumptions concerning the normality condition. A method is presented which allows the system an extra degree of freedom; this requires the introduction of a parameter, derived using the Prandtl-Reuss flow rule, which relates the magnitude of slip on complementary shear planes. The method is applied to two problems, confirming its validity.

An experimental method was further developed to quantify the anisotropy of multi-site fatigue crack initiation behaviors in high strength Al alloys by four-point bend fatigue testing under stress control. In this method, fatigue crack initiation sites (fatigue weak-links, FWLs) were measured on the sample surface at different cyclic stress levels. The FWL density in an alloy could be best described using a three-parameter Weibull function of stress, though other types of sigmoidal functions might also be used to quantify the relationship between FWL density and stress. The strength distribution of the FWLs was derived from the Weibull function determined by fitting the FWLs vs. stress curve experimentally obtained. As materials properties, the FWL density and strength distribution could be used to evaluate the fatigue crack nucleation behaviors of engineering alloys quantitatively and the alloy quality in terms of FWL density and strength distribution. In this work, the effects of environment, types of microstructural heterogeneities and loading direction on FWLs were all studied in detail in AA7075-T651, AA2026-T3511, and A713 Al alloys, etc. It was also found that FWLs should be quantified as a Weibull-type function of strain instead of stress, when the applied maximum cyclic stress exceeded the yield strength of the tested alloys. In this work, four-point bend fatigue tests were conducted on the L-T (Rolling-Transverse), L-S (Rolling-Short transverse) and T-S planes of an AA7075-T651 alloy plate, respectively, at room temperature, 20 Hz, R=0.1, in air. The FWL populations, measured on these surfaces, were a Weibull-type function of the applied maximum cyclic stress, from which FWL density and strength distribution could be determined. The alloy showed a significant anisotropy of FWLs with the weak-link density being 11 mm-2, 15 mm-2 and 4 mm-2 on the L-T, L-S and T-S planes, respectively. Fatigue cracks were predominantly initiated at Fe-containing particles on the L-T and L-S planes, but only at Si-bearing particles on the T-S plane, profoundly demonstrating that the pre-fractured Fe-containing particles were responsible for crack initiation on the L-T and L-S planes, since the pre-fracture of these particles due to extensive deformation in the L direction during the prior rolling operation could only promote crack initiation when the sample was cyclically stressed in the L direction on both the L-T and L-S planes. The fatigue strengths of the L-T, L-S and T-S planes of the AA7075 alloy were measured to be 243.6, 273.0 and 280.6 MPa, respectively. The differences in grain and particle structures between these planes were responsible for the anisotropy of fatigue strength and FWLs on these planes. Three types of fatigue cracks from particles, type-I: the micro-cracks in the particles could not propagate into the matrix, i.e., type-II: the micro-cracks were fully arrested soon after they propagated into the matrix, and type-III: the micro-cracks became long cracks, were observed in the AA7075-T651 alloy after fatigue testing. By cross-sectioning these three-types of particles using Focused Ion Beam (FIB), it was found that the thickness of the particles was the dominant factor controlling fatigue crack initiation at the particles, namely, the thicker a pre-fractured Fe-containing particle, the easier it became a type-III crack on the L-T and L-S planes. On the T-S plane, there were only types-I and III Si-bearing particles at which crack were initiated. The type-I particles were less than 6.5 μm in thickness and type-III particles were thicker than 8.3 μm. Cross-sectioning of these particles using FIB revealed that these particles all contained gas pores which promoted crack initiation at the particles because of higher stress concentration at the pores in connection with the particles. It was also found that fatigue cracks did not always follow the any specific crystallographic planes within each grain, based on the Electron Backscatter Diffraction (EBSD) measurement. Also, the grain orientation did not show a strong influence on crack initiation at particles which were located within the grains. The topography measurements with an Atomic Force Microscope (AFM) revealed that Fe-containing particles were protruded on the mechanically polished surface, while the Si-bearing particles were intruded on the surface, which was consistent with hardness measurements showing that Si-bearing particles were softer (4.030.92 GPa) than Fe-containing ones (8.9 0.87 GPa) in the alloy. To verify the 3-D effects of the pre-fractured particles on fatigue crack initiation in high strength Al alloys, rectangular micro-notches of three different types of dimensions were fabricated using FIB in the selected grains on the T-S planes of both AA2024-T351 and AA7075-T651 Al alloys, to mimic the three types of pre-fractured particles found in these alloys. Fatigue testing on these samples with the micro-notches verified that the wider and deeper the micro-notches, the easier fatigue cracks could be initiated at the notches. In the AA2024-T351 samples, cracks preferred to propagate along the {111} slip plane with the smallest twist angle and relatively large Schmid factor. These experimental data obtained in this work could pave a way to building a 3-D quantitative model for quantification of fatigue crack initiation behaviors by taking into account the driving force and resistance to short crack growth at the particles in the surface of these alloys.

Zyklische Kohäsivzonenmodelle beschreiben irreversibles Separationsverhalten und Schädigungsakkumulation unter zyklischer Belastung. In der vorliegenden Arbeit wird die Formulierung zyklischer Kohäsivzonenmodelle systematisiert und ihr Potenzial zur Simulation von Ermüdungsvorgängen analysiert. Die Kohäsivspannungs-Separations-Beziehungen werden auf Basis etablierter thermodynamischer Konzepte der Schädigungsmechanik aufgestellt. Zyklische Schädigungsakkumulation wird über die Entwicklungsgleichung der Schädigungsvariablen unter Berücksichtigung einer zustandsabhängigen Dauerfestigkeit beschrieben. Das Kohäsivzonenmodell wird erfolgreich für die Simulation von Werkstoffermüdung angewandt. Numerisch mithilfe der Methode der finiten Elemente erzeugte Rissfortschrittskurven bilden das experimentell beobachtete Ermüdungsrisswachstumsverhalten in allen Bereichen ab. Über Parameterstudien wird der Einfluss der einzelnen Modellparameter ermittelt. Darüber hinaus wird die Anwendung des zyklischen Kohäsivzonenmodells auf die Simulation von Wöhler-Versuchen vorgestellt und der Probengrößeneffekt auf das Ermüdungsverhalten untersucht. Der Zusammenhang zwischen den lokalen Beanspruchungszuständen in der Kohäsivzone und dem vorhergesagten globalen Versagensverhalten wird aufgeklärt. Die gewonnenen Erkenntnisse bilden die Grundlage für ein Konzept zur Identifikation der Kohäsivparameter, das auf der Auswertung von Wöhler- und Rissfortschrittskurven beruht. / Cyclic cohesive zone models describe irreversible separation behaviour and damage accumulation under cyclic loading. In the present thesis, the formulation of cyclic cohesive zone models is systemised and their potential to simulate fatigue processes is analysed. The relation between traction and separation is described based on established thermodynamical concepts of damage mechanics. Cyclic damage accumulation is controlled by a damage evolution equation taking into account a state-dependent endurance limit. The cohesive zone model is applied successfully to the simulation of material fatigue. Fatigue crack growth rate curves, which were obtained numerically by means of the finite element method, reproduce the experimentally observed behaviour in all stages. The influences of the particular parameters of the model are determined by parametric studies. In addition, simulations of uniaxial fatigue tests using the cyclic cohesive zone model are presented. Furthermore, the size effect on the fatigue behaviour is investigated. The relation between the local states within the cohesive zone and the predicted global failure modes is explained. These findings form the foundation for a concept of parameter identification which bases on the evaluation of Wöhler-curves and fatigue crack growth rate curves.

This thesis presents a novel hybrid prognostic methodology, integrating physics-based and data-driven prognostic models, to enhance the prognostic accuracy, robustness, and applicability. The presented prognostic methodology integrates the short-term predictions of a physics-based model with the longer term projection of a similarity-based data-driven model, to obtain remaining useful life estimations. The hybrid prognostic methodology has been applied on specific components of two different engineering systems, one which represents accelerated, and the other a nominal degradation process. Clogged filter and fatigue crack propagation failure cases are selected as case studies. An experimental rig has been developed to investigate the accelerated clogging phenomena whereas the publicly available Virkler fatigue crack propagation dataset is chosen after an extensive literature search and dataset analysis. The filter clogging experimental rig is designed to obtain reproducible filter clogging data under different operational profiles. This data is thought to be a good benchmark dataset for prognostic models. The performance of the presented methodology has been evaluated by comparing remaining useful life estimations obtained from both hybrid and individual prognostic models. This comparison has been based on the most recent prognostic evaluation metrics. The results show that the presented methodology improves accuracy, robustness and applicability. The work contained herein is therefore expected to contribute to scientific knowledge as well as industrial technology development.