Este trabalho apresenta um procedimento de avaliação para a determinação da Integral J e do CTOD para dutos com trincas circunferenciais em sua superfície externa e interna submetidos à flexão pura para uma ampla faixa de geometrias de trinca e propriedades (encruamento) de material baseados em soluções das componentes plásticas de J e CTOD. Uma descrição da metodologia sobre a qual J e CTOD são determinados estabelece o contexto necessário para a determinação das funções adimensionais h1 e h2 aplicáveis a uma grande faixa de geometrias de trinca e propriedades de material características de aços estruturais para a construção de dutos e vasos de pressão. As extensivas análises numéricas não-lineares 3-D fornecem um conjunto completo de soluções para J e CTOD, os quais entram diretamente em procedimentos avançados para a avaliação de defeitos em dutos e cilindros submetidos à flexão. Este estudo também examina uma comparação exploratória entre os resultados do procedimento proposto e os resultados de análises numéricas por elementos finitos de dutos com trincas superficiais submetidos ao processo de enrolamento. / This work provides an estimation procedure to determine the J-integral and CTOD for pipes with circumferential surface cracks subjected to bending load for a wide range of crack geometries and material (hardening) based upon fully-plastic solutions. A summary of the methodology upon which J and CTOD are derived sets the necessary framework to determine nondimensional functions h1 and h2 applicable to a wide range of crack geometries and material properties characteristic of structural, pressure vessel and pipeline steels. The extensive nonlinear, 3-D numerical analyses provide a definite full set of solutions for J and CTOD which enters directly into fitness-for service (FFS) analyses and defect assessment procedures of cracked pipes and cylinders subjected to bending load. The study also examines an exploratory comparison between the resulting fully-plastic solutions and finite element analyses of circumferentially cracked pipes subjected to reeling.

O trabalho apresenta uma análise do desempenho de vários métodos de extração de fatores de intensidade de tensão a partir de soluções numéricas obtidas com o método dos elementos finitos generalizados (MEFG). A convergência dos fatores de intensidade de tensão é comparada com a da energia de deformação a fim de investigar a superconvergência dos métodos. Para extração dos fatores de intensidade de tensão e o cálculo da taxa de energia disponibilizada para propagação da fissura, implementam-se os métodos da integral de contorno (MIC), da função cutoff (MFC) e da integral-J no contexto do MEFG. Desenvolve-se a formulação dos métodos de extração de forma a obter uma implementação independente da malha utilizada na modelagem do problema. Aplica-se a extração dos fatores de intensidade de tensão, para modos puros e mistos, em problemas clássicos da mecânica da fratura. Verifica-se a convergência dos fatores de intensidade de tensão e da taxa de energia disponibilizada para a propagação da fissura, obtidos com cada método de extração, com o enriquecimento da ordem polinomial da solução do MEFG. Investiga-se a robustez dos métodos com relação ao tamanho dos domínios de extração / The performance of several techniques to extract stress intensity factors (SIF) from numerical solutions computed with the generalized finite element method (GFEM) is investigated. The convergence of the stress intensity factors is compared with the convergence of strain energy with the aim of investigate the superconvergence of the methods. The contour integral (CIM), the cutoff function (CFM) and the J-integral methods are considered to compute stress intensity factors and energy release rate. The proposed implementation of the extraction techniques is completely independent of the discretization used. Several numerical examples demonstrating the convergence of the computed stress intensity factors and the energy release rate, with the increasing of p order of the GFEM solution, are presented

Este trabalho visa o refinamento do procedimento para estimativa dos parâmetros elasto-plásticos de tenacidade à fratura, integral J e CTOD, incorporando o efeito de dissimilaridade mecânica devido à introdução de juntas soldadas utilizando a metodologia eta, tal efeito não é previsto na formulação das atuais normas de avaliação de tenacidade à fratura, porém a dissimilaridade mecânica afeta fortemente a relação entre o carregamento global do espécime e as forças motrizes na ponta da trinca. Para o desenvolvimento das análises foi empregada a geometria normalizada C(T), compacta, pois esta pode apresentar potencias vantagens sobre a geometria SE(B), flexão três pontos, como menor consumo de material para a confecção dos espécimes, menor capacidade do aparato experimental e fácil manipulação na prática dos testes laboratoriais, porém carece de fatores eta quando comparados ao tradicional espécime SE(B). Os principais objetivos deste trabalho são gerar um compêndio de fatores eta e propor uma formulação robusta que incorpore os efeitos de dissimilaridade mecânica para o cálculo de integral J e CTOD. Para tal intento a matriz de análise deste trabalho abrange diferentes comprimentos de trinca, níveis de dissimilaridade mecânica e larguras de cordão de solda, 0.45a/W0.6 e 1M y 1.3, 10 mm2h20 mm respectivamente. As análises numéricas foram realizadas nas condições de estado plano de deformação (2D) e tridimensional (incluindo o efeito acoplado entre os campos de tensões e deformações no plano e fora do plano), os resultados fornecem um bom suporte ao uso da geometria C(T) com trinca central no cordão de solda para avaliação de tenacidade à fratura em juntas soldadas de materiais comumente aplicados na construção de dutos e vasos de pressão. / This work focuses on the evaluation procedure to determine the elastic-plastic J integral and CTOD fracture toughness based upon the eta-method for C(T) fracture specimens including overmatched weldments. Since fracture toughness test protocols do not address weld strength mismatch effect, this effect strongly alters the relationship between global loads and crack driving forces. The objectives of this investigation are to enlarge plastic eta-factor data base for C(T) specimen and to develop a robust formulation to address weld strength mismatch. The present analyses enable the introduction of a larger set of plastic eta-factors for a wide range of crack sizes (as measured by the a/W-ratio) and material properties, including different levels of weld strength mismatch, applicable to structural, pipeline and pressure vessel steels. Very detailed non-linear finite element analyses for plane-strain and full 3D models of standard C(T) fracture specimens provide the evolution of load with increased crack mouth opening displacement (and LLD) required for the estimation procedure. The results provide a strong support to use the plastic eta-factor in J integral and CTOD estimation procedures for center notch welded C(T) fracture specimen.

Este trabalho apresenta um procedimento de avaliação para a determinação da Integral J e do CTOD para dutos com trincas circunferenciais em sua superfície externa e interna submetidos à flexão pura para uma ampla faixa de geometrias de trinca e propriedades (encruamento) de material baseados em soluções das componentes plásticas de J e CTOD. Uma descrição da metodologia sobre a qual J e CTOD são determinados estabelece o contexto necessário para a determinação das funções adimensionais h1 e h2 aplicáveis a uma grande faixa de geometrias de trinca e propriedades de material características de aços estruturais para a construção de dutos e vasos de pressão. As extensivas análises numéricas não-lineares 3-D fornecem um conjunto completo de soluções para J e CTOD, os quais entram diretamente em procedimentos avançados para a avaliação de defeitos em dutos e cilindros submetidos à flexão. Este estudo também examina uma comparação exploratória entre os resultados do procedimento proposto e os resultados de análises numéricas por elementos finitos de dutos com trincas superficiais submetidos ao processo de enrolamento. / This work provides an estimation procedure to determine the J-integral and CTOD for pipes with circumferential surface cracks subjected to bending load for a wide range of crack geometries and material (hardening) based upon fully-plastic solutions. A summary of the methodology upon which J and CTOD are derived sets the necessary framework to determine nondimensional functions h1 and h2 applicable to a wide range of crack geometries and material properties characteristic of structural, pressure vessel and pipeline steels. The extensive nonlinear, 3-D numerical analyses provide a definite full set of solutions for J and CTOD which enters directly into fitness-for service (FFS) analyses and defect assessment procedures of cracked pipes and cylinders subjected to bending load. The study also examines an exploratory comparison between the resulting fully-plastic solutions and finite element analyses of circumferentially cracked pipes subjected to reeling.

This work presents a fracture mechanics analysis of the cathodic delamination problem for the polyurethane/titanium and polyurea/steel interfaces. The nonlinear behavior of both polymers was investigated. The recent Marlow model was used to define the strain energy function of the polymers. Viscoelastic effects of the polyurea were also studied. The Marlow model was associated with a nine-term Prony series. This model was seen to represent experimental data relatively well for a wide range of strain rates both in tension and compression. The driving force for delamination, the strain energy release rate G, is presented for both interfaces. Cathodic delamination data for several temperatures are presented as crack growth rate as a function of crack driving force. The approach recognizes that both temperature and stress can be used as accelerated life testing parameters. / text

Le problème du rendement de la distribution des eaux potables a récemment fait l’objet de nombreux travaux de recherche. En effet, les ruptures des canalisations et les fuites sont des phénomènes assez fréquents en milieu urbain. Afin de réduire au maximum les risques de fuite à long terme, près de 60 % des réseaux d’eau potable sont construits ou renouvelés avec des conduites en polyéthylène de troisième génération, PE100. De par ses caractéristiques, c’est un matériau de choix pour les réseaux d’adduction d’eau. Mais la présence d’un défaut superficiel peut générer la rupture de la conduite sous l’effet d’écoulement transitoire. Afin d’étudier ce problème, notre étude est décomposée en deux parties. La première est consacrée à l’étude de l’effet dynamique du comportement viscoélastique du matériau sur l’écoulement transitoire à l’aide d’un modèle mathématique que nous avons développé dans cette thèse. Nous avons démontré que le comportement viscoélastique du PE100 joue un rôle primordial dans l’amortissement du phénomène du coup de bélier et de résonance. En cas de présence de couplage de jonction, l’étude de l’interaction fluide-structure est nécessaire pour définir correctement les fréquences propres d’un système de conduites. Ensuite, dans la seconde partie, nous avons étudié le comportement à la fissuration des conduites en PE100 présentant un défaut. A l’aide d’essais expérimentaux et de modélisations par éléments finis, nous avons démontré que le concept de la mécanique élasto-plastique de rupture, l’intégrale J, peut définir avec une précision acceptable le comportement à la fissuration d’une conduite en PE100. Nous avons cherché à déterminer l’intégrale J à l’aide d’un modèle semi-empirique afin de définir une relation entre la pression d’amorçage de fissure, la taille de défaut (fissure semi-elliptique) et la géométrie de la conduite / The efficiency of potable water distribution systems has been recently the subject of much research. Leakages or a ruptures, occurring in pipes, are quite a frequent phenomenon in urban areas. In order to minimize long-term risks of leakage, about 60% of potable water networks are built or renewed with the third generation of polyethylene pipe, PE100. It is a material with various features, which makes it a widely used material in the water supply networks. However, under transient conditions and with a surficial defect in the pipe, a failure occurs. To investigate this issue, our study is divided into two main parts. The first part is studying the dynamic effect of the viscoelastic material under transient flow conditions using a developed mathematical model. We have demonstrated that the viscoelastic behavior of PE100 plays a primordial role in the damping of water hammer and resonance phenomenon. In case of presence of coupling junction, a study of the fluid structure interaction is mandatory to correctly define the natural frequencies of a piping system. In the second part, we have investigated the crack behavior of PE100 pipes with defects. Using the experimental tests and finite elements results, we have demonstrated that the concept of elastic-plastic fracture mechanics, the J-Integral, define with reasonable accuracy the behavior of cracked PE100-pipe. At the end, we sought to determine the J-Integral with a semi-empirical model in order to define a relationship between the crack initiation pressure, the dimension of semi-elliptical surface cracks and the geometry of the pipe

This thesis is concerned with the evaluation, in-situ, of the elastic strain energy release rate of cracks. This can define the criteria for crack propagation, and it is usually necessary to obtain this via calculation from the geometry and applied load. A new method is proposed, based on the conjoint use of digital image correlation to measure full-field displacements and finite element to extract the strain energy release rate of surface cracks. It has been extended to 3-D datasets with the use of digital volume correlation and tomographic imaging. A finite element model with imported full-field displacements measured by DIC/DVC acting as boundary conditions is solved and the J-integral is calculated. For linear elastic materials, modal contributions can be separated via the interaction integral. The method has been benchmarked using synthetic datasets to assess its sensitivity to noise and experimental uncertainties. It is very robust to experimental noise and can be used without knowledge of the specimen geometry and applied loads. The application of the method in 2-D is demonstrated in an analysis of experimental data for a mode I fatigue crack, introduced to an aluminium alloy compact tension specimen. Analysis of mixed-mode cracks in 2-D is shown on a PMMA sample with the Arcan geometry. In 3-D, static loading of a fatigue crack in nodular graphite cast iron is studied and the results from the method are compared with those obtained via a field-fitting approach. Diffraction analysis of polycrystalline materials can determine the full tensor of the elastic strains within them. Maps of elastic strains can thus be obtained typically using synchrotron X-rays or neutrons. A method is presented to calculate the elastic strain energy release rate of a crack from 2-D diffraction strain maps. The diffraction data is processed via a finite element approach to obtain the parameters required to calculate the $J$-integral. A validation is presented using a synthetic dataset from a finite element model. Its experimental application is demonstrated in an analysis of synchrotron X-ray diffraction strain maps of a propagating fatigue crack in a bainitic steel, before and after an overload. Finally, a complex case study of stable fracture propagation in polygranular isotropic nuclear graphite is presented. Synchrotron X-ray tomography and strain mapping by diffraction were combined with DVC and image analysis to extract the full-field displacements and elastic crystal strains. The displacement fields have been analysed using the developed methods to extract the critical strain energy release rate for crack propagation. Non-linear properties described the effect of microcracking on the elastic modulus in the fracture process zone. The analysis was verified by comparison of the predicted and measured elastic strain fields.

Le stress hydrique menacera plus que 40% de la population mondiale en 2050. Plus de 240 millions de personnes seront dépourvues d’accès à une source d’eau améliorée. En effet, pour assurer une gestion durable de cette ressource, la minimisation des ruptures dans les réseaux d'adduction d'eau potable est primordiale. La rupture des canalisations, phénomène assez fréquent en milieu urbain, s’amorce sur un défaut et sous l’effet des contraintes engendrées par un chargement inhabituel : coup de bélier, un phénomène de surpression. Depuis les années 80, le polyéthylène prend une part de plus en plus importante dans la fabrication des canalisations d'eau potable. Les jonctions sont les zones les plus dangereuses dans les réseaux. D'où l'importance d'étudier la résistance à la rupture des conduites coudées en PEHD. Pour résoudre ce problème, une étude est abordée par une approche expérimentale et une approche numérique par éléments finis pour caractériserle comportement à la fissuration des conduites coudées en PE100. Deux méthodologies sont proposées pour déterminer la ténacité du PEHD : la méthode de l'intégrale J et la méthode du déplacement d'ouverture en pointe de fissure ''CTOD''.La combinaison de ces outils permet de choisir la valeur critique de l'intégrale J comme valeur de la ténacité du PEHD.Ensuite, nous proposons une formule simplifiée basée sur la détermination de l'intégrale J en fonction de la pression dans les réseaux d'adduction d'eau potable en présence d'un défaut superficiel. Enfin, nous étudions le phénomène de coup de bélier pour déterminer la surpression avec un modèle mathématique développé dans cette thèse. Nous démontrons l'importance de l'interaction fluide-structure pour définir la pression au niveau des coudes / Water scarcity will be threatening more than 40% of the world population by 2050, more than 240 million people will not have a source of improved water. In fact, to ensure a sustainable management of this resource, the minimization of the leakages in drinking-water supply network is vital. Pipe rupture, a frequent phenomenon in urban zones, starts with a defect, under the effect of constraints caused by an unusual over pressure: Water Hammer. Since the 80s, polyethylene is being widely considered in manufacturing the pipelines water supply networks. Nevertheless, junctions are the most dangerous zones in the networks. As a result, it is vital to study the tear resistance of the angled conducts in PEHD. To solve this problem, a study is approached with an experimental investigation and a digital approach by fine elements in order to characterize the behavior in the fissuring of pipe bends PE100. Two methodologies are proposed to determine the tenacity of the PEHD: the method of the J-integral and the method of the sharp's movement opening of crack "CTOD ". The combination of these tools permits to choose the critical value of the integral J as a value of the tenacity of the HDPE. In addition, a simplified formula was proposed based on the calculation of the J-integral as a function of the pressure in water supply networks in the presence of a superficial defect. Finally, the water hammer phenomenon was investigated in order to determine the overpressure with a mathematical model which was developed in this thesis. The fluid-structure interaction was found to be important in defining the pressure at elbow pipe

[pt] Este trabalho teve como objetivo o estudo do comportamento à fratura do aço estrutural DIN 42CrMo4 através da determinação experimental de curvas de resistência (curvas R) à propagação estável de trincas. Inicialmente, conduziram-se ensaios de tração para a determinação das propriedades mecânicas do material. Os ensaios de tenacidade à fratura foram realizados em espécimes do tipo SE(B) entalhados, submetidos à flexão e com 3 geometrias distintas. Os corpos de prova foram pré-trincados por fadiga de maneira a atender a relação a/W equivalente a 0,5. Nos ensaios de propagação de trinca, adotou-se a técnica de corpo de prova único com a utilização do método das descargas parciais (Unloading Compliance Method) para a obtenção das curvas carga (P) versus deslocamento da boca do entalhe (CMOD - Crack Mouth Opening Displacement). A cada ponto de descarregamento, relacionando a inclinação da linha de carga com as medidas da flexibilidade elástica do corpo de prova, pôde-se calcular o comprimento da trinca e, consequentemente, valores do parâmetro elasto-plástico J. Em sequência, com base nos valores de J e propagação de trinca, foram levantadas as curvas R do material. Os resultados experimentais mostraram que a geometria dos corpos de prova influenciou a estabilidade da propagação das trincas durante o ensaio, sendo possível a obtenção de curvas R somente para os corpos de prova com geometria mais robusta. Além disso, percebeu-se que os valores de propagação de trinca calculados pelo método Compliance foram superestimados. / [en] This work aimed the study of the fracture behavior of the structural steel DIN 42CrMo4 through the experimental determination of resistance curves (R curves) to the stable spread of cracks. Traction tests were initially conducted to determine the mechanical properties of the material. The fracture tenacity tests were carried out in specimens of the type SE(B) notched, subjected to flexion and with 3 distinct geometries. The samples were precracked by fatigue in order to meet the a/W ratio equivalent to 0.5. In the crack propagation tests, the single specimen technique was adopted with the use of the partial discharge method for obtaining the curves load (P) versus displacement of the notch mouth (CMODCrack mouth Opening Displacement). At each point of unloading, relating the inclination of the load line with the measurements of the elastic flexibility of the sample, it was possible to calculate the length of the crack and consequently the values of the elasto-plastic parameter J. In sequence, based in the values of J and crack propagation, the R curves of the material were raised. The experimental results showed that the geometry of the specimens influenced the stability of crack propagation during the test, and it was possible to obtain R curves only for the most robust specimens. In addition, it was noticed that the crack propagation values calculated by the compliance method were overestimated.

O trabalho apresenta uma análise do desempenho de vários métodos de extração de fatores de intensidade de tensão a partir de soluções numéricas obtidas com o método dos elementos finitos generalizados (MEFG). A convergência dos fatores de intensidade de tensão é comparada com a da energia de deformação a fim de investigar a superconvergência dos métodos. Para extração dos fatores de intensidade de tensão e o cálculo da taxa de energia disponibilizada para propagação da fissura, implementam-se os métodos da integral de contorno (MIC), da função cutoff (MFC) e da integral-J no contexto do MEFG. Desenvolve-se a formulação dos métodos de extração de forma a obter uma implementação independente da malha utilizada na modelagem do problema. Aplica-se a extração dos fatores de intensidade de tensão, para modos puros e mistos, em problemas clássicos da mecânica da fratura. Verifica-se a convergência dos fatores de intensidade de tensão e da taxa de energia disponibilizada para a propagação da fissura, obtidos com cada método de extração, com o enriquecimento da ordem polinomial da solução do MEFG. Investiga-se a robustez dos métodos com relação ao tamanho dos domínios de extração / The performance of several techniques to extract stress intensity factors (SIF) from numerical solutions computed with the generalized finite element method (GFEM) is investigated. The convergence of the stress intensity factors is compared with the convergence of strain energy with the aim of investigate the superconvergence of the methods. The contour integral (CIM), the cutoff function (CFM) and the J-integral methods are considered to compute stress intensity factors and energy release rate. The proposed implementation of the extraction techniques is completely independent of the discretization used. Several numerical examples demonstrating the convergence of the computed stress intensity factors and the energy release rate, with the increasing of p order of the GFEM solution, are presented