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During this thesis, a Boundary Element Method (BEM) has been developed for the solution of static linear elastic problems with microstructural effects in two (2D) and three dimensions (3D).The second simplified form of Mindlin's Generalized Gradient Elasticity Theory (Mindlin's Form II)has been employed. The fundamental solution of the 4th order partial differential equation, that describes the aforementioned theory, has been derived and the integral equations that govern Mindlin's Form II Gradient Elasticity Theory have been obtained. Furthermore, a BEM formulation has been developed and specific Boundary Value Problems (BVPs) were solved numerically and compared with the corresponding analytical solutions to verify the correctness of the formulation and demonstrate its accuracy. Moreover, two new partially discontinuous boundary elements with variable order of singularity, a line and a quadrilateral element, have been developed for the solution of fracture mechanics problems. The calculation of the unknown fields near the crack tip (or front) demanded the use of elements that could interpolate abruptly varying fields. The new elements were created in a way that their interpolation functions were no longer quadratic but their behavior depended on the order of singularity of each field. Finally, the Stress Intensity Factor (SIF) of the crack has been calculated with high accuracy, based on the element's nodal traction values. Static fracture mechanics problems for Mode I and Mixed Mode (I & II) cracks, have been solved in 2D and 3D and the corresponding SIFs have been obtained, in the context of both classical and Form II Gradient Elasticity theories. / Κατά τη διάρκεια της παρούσας διδακτορικής διατριβής, αναπτύχθηκε Μέθοδος Συνοριακών Στοιχείων (ΜΣΣ) για την επίλυση στατικών προβλημάτων ελαστικότητας με επιδράσεις μικροδομής σε δύο και τρεις διαστάσεις. Η θεωρία στην οποία εφαρμόστηκε η ΜΣΣ είναι η δεύτερη απλοποιημένη μορφή της γενικευμένης θεωρίας ελαστικότητας του Mindlin. Για τη συγκεκριμένη θεωρία ευρέθη η θεμελιώδης της μερικής διαφορικής εξίσωσης 4ης τάξης που περιγράφει τη συμπεριφορά των συγκεκριμένων υλικών και κατασκευών. Επίσης διατυπώθηκε η ολοκληρωτική εξίσωση των αντίστοιχων προβλημάτων και έγινε η αριθμητική εφαρμογή μέσω της ΜΣΣ. Επιλύθηκα αριθμητικά συγκεκριμένα προβλήματα συνοριακών τιμών και έγινε σύγκριση των αποτελεσμάτων με τα αντίστοιχα θεωρητικά. Στη συνέχεια αναπτύχθηκαν δύο νέα ασυνεχή στοιχεία μεταβλητής τάξης ιδιομορφίας με σκοπό την επίλυση προβλημάτων θραυστομηχανικής, ένα για δισδιάστατα και ένα για τρισδιάστατα προβλήματα. Συγκεκριμένα, επειδή τα πεδία των τάσεων απειρίζονται στην κορυφή μιας ρωγμής και περιέχουν συγκεκριμένων τύπων ιδιομορφίες δεν ήταν δυνατός ο ακριβής υπολογισμός των πεδίων αυτών κοντά στη ρωγμή με τα συνήθη τετραγωνικά συνοριακά στοιχεία. Ως εκ τούτου τα νέα στοιχεία κατασκευάστηκαν με τέτοιο τρόπο ώστε οι συναρτήσεις παρεμβολής τους να μην είναι τετραγωνικες, αλλά να εξαρτώνται από τον τύπο ιδιομορφίας του κάθε πεδίου. Έπειτα, έγινε ακριβής υπολογισμός του συντελεστή έντασης τάσης της ρωγμής με βάση τις τιμές του πεδίου των τάσεων κοντά σε αυτή. Τέλος επιλύθηκαν στατικά προβλήματα θραυστομηχανικής σε δύο και τρεις διαστάσεις και υπολογίστηκαν οι συντελεστές έντασης τάσης για ρωγμές σε υλικά με επίδραση μικροδομής.

Οι κατασκευές των περισσοτέρων τεχνολογικών εφαρμογών υπόκεινται σε σύνθετες θερμικές καταπονήσεις. Παράλληλα, η επεξεργασία σύγχρονων υλικών συνήθως συνδέεται με ειδικές θερμικές κατεργασίες. Η πολυπλοκότητα στη γεωμετρία των κατασκευών αυτών σε συνδυασμό με τις απότομες μεταβολές της θερμοκρασίας και γενικότερα της επιβαλλόμενης θερμικής καταπόνησης, συχνά οδηγεί στη λύση της συνέχειας των υλικών μέσω της δημιουργίας ρωγμών η οποία μειώνει τα επίπεδα αξιοπιστίας και παράλληλα αυξάνει δραματικά το κόστος συντήρησης και παραγωγής τους. Οι θερμικές φορτίσεις των ρηγματωμένων κατασκευών οι οποίες συνδέονται σχεδόν πάντα με απορρόφηση θερμότητας και επομένως ταυτόχρονη διαστολή των υλικών, οδηγούν στο λεγόμενο «κλείσιμο» της ρωγμής κατά το οποίο οι επιφάνειες της ρωγμής έρχονται τμηματικά ή και εξολοκλήρου σε επαφή δηλαδή συμβάλλουν. Εξαιτίας της πολυπλοκότητας και της μη γραμμικής φύσης του προβλήματος της επαφής, o χαρακτηρισμός της θερμικής θραύσης, υπό την παρουσία φαινομένων συμβολής των επιφανειών της, δεν έχει διερευνηθεί διεξοδικά στη βιβλιογραφία. Η επικρατούσα παραδοχή, ότι δηλαδή η ρωγμή παραμένει εντελώς ανοιχτή κατά τη θερμική φόρτιση, οδηγεί σε εσφαλμένα αποτελέσματα και επομένως δεν έχει πρακτική αξία στον κατασκευαστικό σχεδιασμό. Για το λόγο αυτό, η ανάπτυξη ενός αξιόπιστου και οικονομικού από απόψεως υπολογιστικής ισχύος αριθμητικού εργαλείου για την αντιμετώπιση τέτοιων προβλημάτων είναι αναγκαία. Η αριθμητική προσομοίωση και ο χαρακτηρισμός, μέσω της μεθόδου των συνοριακών στοιχείων, της θερμικής θραύσης η οποία επηρεάζεται από το φαινόμενο της επαφής των επιφανειών της ρωγμής είναι ο σκοπός της παρούσας διατριβής. / The structures of most technological applications are subject to complicate thermal loadings. Additionally, the processing of modern materials is usually related with special thermal treatments. The complex geometry of these structures in combination with the rabid changes of the temperature and generally with the imposed thermal load, often leads to the dissolution of continuity of the materials via the creation of cracks, fact that decreases the reliability standards and simultaneously increases dramatically the maintenance and manufacturing cost. The thermal loadings of the cracked structures which are associated with heat absorption and consequently simultaneous dilation of materials, lead to the well known crack closure phenomenon in which the surfaces of the crack come partially or even entirely into contact i.e. they interfering. Due to the complexity and non linear nature of the contact problem, the fracture characterization under crack closure phenomena has not been investigated thoroughly in the literature. The prevalent assumption, that the crack remains completely open during thermal loading, leads to inaccurate results and thus is not of practical importance in structural design. Therefore, the development of a reliable numerical tool offering low computational cost is required for the treatment of such problems. The numerical simulation and characterization, through the boundary element method, of thermal fracture that is influenced by crack closure phenomenon is the aim of the present thesis.

Este trabalho trata da análise de problemas da Mecânica da Fratura Elástica Linear (MFEL) utilizando o Método dos Elementos de Contorno (MEC). Esse método constitui uma poderosa e precisa técnica de análise numérica. A necessidade da discretização somente do contorno do modelo é um dos grandes atrativos do MEC. Na Mecânica da Fratura, o MEC é adequado pela própria natureza de sua formulação, a qual está baseada em soluções fundamentais. Dentre os parâmetros da MFEL, destaca-se o Fator de Intensidade de Tensão (FIT). No presente desenvolvimento, esse parâmetro é analisado numericamente pela técnica da correlação dos deslocamentos e por uma técnica alternativa a qual emprega o campo de tensões presente na extremidade da trinca. A direção do crescimento da trinca é analisada por meio do critério da Máxima Tensão Circunferencial. Os resultados obtidos são comparados à solução analítica e a outros resultados encontrados na literatura. / This work deals with the analysis of Linear Elastic Fracture Mechanics (LEFM) problems using the Boundary Element Method (BEM). This method is a powerful and accurate technique of numerical analysis. The need of discretization only of the boundary of the model is one of the major advantageous features of the BEM. In Fracture Mechanics, the BEM is adequate due to its intrinsic formulation, which is based on fundamental solutions. In the LEFM, the Stress Intensity Factors (SIF) is one of the most important parameters. In the present study, this parameter is numerically analyzed by the correlation displacement technique and by an alternative technique which considers the stress field at the crack tip. The direction of the crack growth is analyzed using the criterion of Maximum Circumferential Stress. The results are compared to the analytical solution and to other results of literature.

Neste trabalho, apresenta-se a formulação do método dos elementos de contorno dual (MECD) aplicada a análise de problemas da Mecânica da Fratura Elástica Linear (MFEL). O objetivo da pesquisa consiste em avaliar o fator de intensidade de tensão (FIT) de sólidos bidimensionais fraturados, por meio de três técnicas distintas, quais são: a técnica da correlação dos deslocamentos, a técnica com base no estado de tensão na extremidade da fratura e a técnica da integral. As análises são realizadas utilizando o código computacional desenvolvido durante a pesquisa, que incorpora as formulações diretas em deslocamento e em força de superfície, do método dos elementos de contorno (MEC), com destaque para a utilização dos elementos de contorno curvos de ordem qualquer. No MECD as equações integrais singulares do tipo O(\'R POT.-1\') e O(\'R POT.-2\') são avaliadas satisfatoriamente com o Método da Subtração de Singularidade (MSS). Dessas integrais resultam termos analíticos, os quais são avaliados por meio do Valor Principal de Cauchy (VPC) e da Parte Finita de Hadamard (PFH). Compara-se o código desenvolvido com as soluções analíticas encontradas na literatura inclusive na análise de sólidos com fraturas predefinidas e para a avaliação do FIT, que produziram bons resultados. / This work presents the dual boundary element formulation applied to linear crack problem. The goal of this research is the evaluation of stress intensity factor for two-dimensional crack problem using three different techniques, which are: the technique of correlation of displacements, the technique based on the state of tension at the crack tip and J integral. The analysis is performed using the computational code developed during the research, which incorporates the direct formulations related to displacement and traction boundary element equation. A greater emphasis is given to the use of curved boundary element of any order. In the dual boundary element method the singular integral equations with singular others O(\'R POT.-1\') and O(\'R POT.-2\') are assessed satisfactorily with the application of the singularity subtraction method. The results of these singular integrals are evaluated by the Cauchy Principal Value and the Hadamard Finite Part. The code developed is compared with the analytical solutions found in the literature including the analysis of solids with fractures default and evaluation of stress intensity factor, which produced good results.

Neste trabalho apresenta-se a formulação do problema de múltiplas fissuras baseada numa abordagem de superposição utilizada pelo Método da Partição (Splitting Method). Um dos objetivos principais deste trabalho refere-se à aferição da capacidade deste método na obtenção de fatores de intensidade de tensão, tendo em vista o seu desenvolvimento recente e a ausência de outras fontes de pesquisa além daquelas oriundas dos seus próprios autores. Segundo a abordagem do Método da Partição, os fatores de intensidade de tensão finais de uma estrutura podem ser encontrados a partir da sobreposição de três subproblemas. Deste modo, o problema é resolvido mediante imposição de que nas faces das fissuras as tensões que resultam da sobreposição sejam nulas. Sendo assim, apresenta-se a formulação do Método da Partição para uma ou mais fissuras e diversas análises numéricas que contemplam interação entre fissuras submetidas aos modos I e II de abertura. Outra etapa do trabalho refere-se à aplicação do Método dos Elementos Finitos Generalizados (MEFG) num dos subproblemas, dito local, ao invés do emprego do Método dos Elementos Finitos (MEF), que em sua forma convencional pode requerer um refinamento excessivo da malha, particularmente junto à ponta da fissura, aumentando o custo computacional da análise. Exemplos de simulação numérica são apresentados no sentido de comprovar que a utilização do MEFG viabiliza a obtenção de resultados com boa aproximação mesmo com malhas pouco refinadas, reduzindo significativamente o custo computacional de toda a análise. Além disto, é apresentada a formulação do Método da Partição para casos que contemplam também fissuras internas, uma vez que a formulação atual admite somente fissuras de borda. / This work presents the formulation of the problem of multiple cracks based on an superposition approach used by the Splitting Method. The main goal of this work concerns the verification of the ability of this method of obtaining stress intensity factors, in view of its recent development and the absence of other research sources beyond those derived from their own authors. According to the approach of Splitting Method, the final stress intensity factors of a structure can be found from the superposition of three subproblems. Thus, the problem is solved by superposition and then imposing the nullity of the stresses on the faces of cracks. Thus, the formulation of the Splitting Method is presented to one or more cracks and also several numerical simulations that consider the interaction between cracks subjected to opening mode I and II. Another part of this work concerns the application of the Generalized Finite Element Method (GFEM) in the local subproblem instead of the use of Finite Element Method (FEM), which in its conventional form may require an excessive mesh refinement, particularly near the tip the crack, increasing the computational cost of analysis. Examples of numerical simulation are presented in order to show that the use of GFEM enables to obtain results with good approximation even with little refined meshes, thus significantly reducing the computational cost of the entire analysis. Moreover, the formulation of the Splitting Method is presented for cases which also have internal cracks due to the current formulation admits only boundary cracks.

No presente trabalho foi estudado o comportamento de um aço inoxidável austenítico do sistema Fe-Cr-Mn-N, nas condições como recebido, solubilizado e sensitizado, quando submetidos à meios contendo cloretos. Para analisar a suscetibilidade à corrosão sob tensão foram utilizados corpos de prova dos tipos DCB (\"Double Cantilever Beam\") e C(T) (\"Compact- Tension\"), pré-trincados em fadiga, com entalhes laterais e carregados com cunhas. Os meios empregados foram as soluções aquosas 45% em peso de MgCl2 na temperatura de ebulição de 154°C, água do mar sintética na temperatura ambiente e de ebulição de 100°C e 3,5% em peso de NaCI na temperatura ambiente. A suscetibilidade à corrosão sob tensão foi avaliada em termos do fator limite de intensidade de tensão, KISCC, e foram caracterizados os aspectos fractográficos dos corpos de prova em que ocorreram propagação de trinca por corrosão sob tensão. Foi verificado que apenas os corpos de prova do aço E3949 nas condições como recebido e sensitizado, foram suscetíveis à corrosão sob tensão em solução aquosa de 45% em peso de MgCl2 na temperatura de ebulição. Também foi determinado o comportamento eletroquímico do material nas condições citadas acima com relação aos meios empregados. Os resultados das curvas de polarização obtidas mostraram que o material apresenta baixa resistência à corrosão, principalmente em meios de MgCl2. / The present work studies the stress corrosion cracking behavior in austenitic Fe-Cr-Mn-N stainless steel, in as received, solubilized and sensitized conditions, when submited to several chlorides environments. To evalued the stress corrosion cracking susceptibility, DCB (\"Double Cantilcver Beam\") and C(T) (\"Compact- Tension\") specimens, fatigue precracked, side grooved and wedge loaded were used. The environments employed were boiling solution of 45 wt% of MgCl2 at 154ºC, synthetic sea water at room and 100°C temperatures, and a solution with 3,5 wt% of NaCI at room temperature. The susceptibility to stress corrosion cracking has been evaluated in terms of the threshold stress intensity factor, KISCC, and the fracture surface appearance of those specimens whose the crack propagation took place was characterized. The results showed that only the specimens in the as received and sensitized conditions, were suceptible to the stress corrosion cracking effect in the solution with 45 wt% of MgCl2 at the boilling temperature. Also, it has been verified the electrochemical behavior of this steel when submited in the above environments. The results of polarization curves showed that the material presents low corrosion strength, mainly in MgCl2 environments.

De nombreuses structures aéronautiques telles que les contacts aube/disque, rivet/tôle, assemblages frettés ou boulonnés subissent des endommagements de fretting fatigue dus à des sollicitations vibratoires. Ces sollicitations, qui combinent des chargements de contact de fretting (micro déplacements alternés) et de fatigue, peuvent induire des phénomènes de fissuration. L’objectif de cette thèse est d’identifier les mécanismes de propagation et d’arrêt de fissuration pour différentes configurations, impliquant des chargements de fretting et de fatigue. Différents aspects seront étudiés : - Les essais de fretting simple, fretting fatigue et fatigue seront corrélés de manière à mesurer certaines propriétés mécaniques de matériaux. Dans cette démarche, une méthode inverse permettant l’identification du seuil d’arrêt de propagation des fissures longues et courtes en fatigue à partir d’essais de fretting simple et fretting fatigue est introduite. - L’effet du rapport de charge est pris en compte afin de quantifier la fermeture de fissure pour les essais de fretting et fretting fatigue. Un nouveau modèle de fermeture sera proposé. - L’effet d’échelle est étudié grâce au développement d’une nouvelle machine de fretting fatigue permettant le suivi in situ des propagations de fissures sur des éprouvettes millimétriques. Le comportement des fissures courtes en fretting pendant un essai de fretting fatigue a été observé pour la première fois. L’idée principale de ce travail est de considérer que lors d’un essai en fretting simple, une condition d’arrêt de propagation est systématiquement atteinte. Les facteurs d’intensités de contraintes seuils en fatigue peuvent ainsi être extraits par une méthode inverse à partir des essais de fretting. La méthodologie adoptée consiste à mesurer la longueur de fissure maximale obtenue lors d’un essai de fretting correspondant à une condition d’arrêt de propagation. En jouant sur les chargements de fretting, les domaine des fissures courtes et longues sont étudiés. Pour chaque condition d’arrêt, le facteur d’intensité de contraintes seuil correspondant est calculé. Enfin, en traçant l’évolution de ce dernier en fonction de la longueur de fissure, une description complète des seuils d’arrêt de fissuration en fatigue peut être obtenue. Cette méthodologie est appliquée sur plusieurs configurations de fretting simple et est étendue aux essais de fretting fatigue. Ainsi une large gamme de rapports de charge peut être étudiée. Des essais conventionnels de fatigue propagation sur éprouvettes C(T) ont été réalisés de manière à valider complètement la démarche d’identification inverse des conditions d’arrêt de fissuration. Le manuscrit est divisé en six chapitres adoptant une évolution linéaire. Le chapitre 1 traite d’une revue bibliographique concernant la propagation des fissures courtes et longues en fatigue dans les matériaux métalliques, introduisant les phénomènes de fermeture. L’analyse est étendue à la propagation des fissures en fretting et fretting fatigue. Le chapitre 2 présente l’ensemble des techniques et méthodes expérimentales utilisées au cours de ce travail. Une analyse numérique et la méthode inverse d’identification des conditions d’arrêt de propagation sont introduites dans le chapitre 3. Les chapitres suivants traitent les différents résultats obtenus. Le chapitre 4 présente les essais de fretting simples menés sur différents matériaux métalliques. Une corrélation entre les conditions d’arrêt de fretting simple avec celles de fissures longues en fatigue est obtenue pour rapports de charge négatifs. Cette analyse est étendue aux rapports de charge positifs au chapitre 5 en couplant les essais de fretting simple, fretting précontraints et essais de fatigue C(T). Enfin, les effets d’échelle et la cinétique de propagation des fissures de fretting fatigue sont étudiés au chapitre 6. / Aircraft structures such as blade/disk, rivet/sheet and fretted or bolted assembly contacts are subjected to fatigue fretting damage caused by vibratory loads. These loads combining fretting (alternating micro displacements) and fatigue contact loading can induce cracks. The objective of this thesis is to identify the propagation and crack arrest mechanisms for different configurations involving fretting and fatigue loads. Various aspects will be studied : - Simple fretting, fatigue fretting and fatigue tests will be correlated in a way to measure some material mechanical properties. A reverse approach allowing to identify the long and short fatigue crack propagation thresholds from simple fretting and fretting fatigue will be introduced. - A new closure model taking into account the effect of loading ratio on crack closure in fretting and fretting fatigue tests will be proposed. - The scaling effect will be studied thanks to the development of a new fretting fatigue machine allowing for in-situ monitoring of the propagation of small scale cracks. The behavior of fretting short cracks has been observed for the first time in a fretting fatigue test. The main idea behind the current work is the consideration that for a simple fretting test, the crack will always lead to a crack propagation arrest condition. Threshold stress intensity factors can thus be extracted from fretting tests using a reverse method. The methodology used consists in measuring the longest fretting crack corresponding to a crack propagation arrest condition. Short and long crack regimes are studied by varying fretting loads and geometries. The corresponding threshold stress intensity factor is calculated for each arrest condition. A complete description of fatigue crack arrest thresholds can be obtained from a plot depicting the evolution of the stress intensity factor range as a function of crack length. This methodology has been applied on multiple simple fretting configurations and was extended to fretting fatigue tests allowing to study a large range of loading ratios. Conventional fatigue crack propagation tests were carried out on C(T) specimens in order to validate the reverse method used for crack arrest conditions. The present thesis is divided into six main chapters. Chapter 1 provides a complete literature review on short and long crack propagation in metallic materials introducing crack closure. It provides a treatment for both fretting and fretting fatigue including a comparative analysis. Chapter 2 provides an overview of the different techniques and methodologies used as part of this research project. The reverse method used for the identification of crack propagation arrest conditions as well as a numerical analysis are presented in Chapter 3. The following Chapters provide a treatment of the various results obtained. Chapter 4 focuses on simple fretting tests carried out on different metallic materials. A correlation between simple fretting and long fatigue crack arrest conditions was obtained for negative loading ratios. This analysis is extended to positive loading ratios in Chapter 5 combining simple fretting, prestressed fretting and C(T) fatigue tests. Finally, scaling effects and fretting fatigue crack propagation kinetics are studied in Chapter 6.

Wind power, especially offshore, is considered to be one of the most promising sources of ‘clean’ energy towards meeting the EU targets for 2020 and 2050. However, its popularity has always fluctuated with the price of fossil fuels since nowadays wind electricity production cannot compete with nuclear or coal electricity production. Support structures are thought to be one of the main drivers for reducing costs in order to make the wind industry more economically efficient. Foundations and towers should be fit for purpose, extending their effective service life but avoiding costs of oversizing. An exhaustive review of the background and state of the art of the Fatigue-Life assessment approaches has been carried out, combining analysis of the gathered experimental data and the development of Finite Element models based on contemporary 3D solid models with diverse Regression Analyses, in order to identify their weakness and evaluate their accuracy. This research shows that the guides and practices currently employed in the design and during the operation of the offshore wind turbine support structures are obsolete and not useful for optimisation, which generally leads to conservationism and an unnecessary increase in costs. The basis for a comprehensive update of the Girth Weld and Tubular Joint S-N curves and the Stress Concentration Factors of Tubular Joints has been set out. Furthermore, a reliable methodology for deriving the Stress Intensity Factor at the deepest point of a semi-elliptical surface saddle crack in a tubular welded T-joint has been proposed.