Nenhuma / A tenacidade à fratura avalia a resistência à propagação de uma trinca e tornou-se uma importante propriedade a ser considerada em metodologias para avaliação de integridade estrutural de componentes mecânicos em geral. A principal metodologia para avaliação dos efeitos da perda de restrição à plasticidade (Teoria J-Q) representa um grande passo para a inclusão dos efeitos geométricos nos estudos da fratura. Alguns avanços têm sido propostos para a obtenção de um parâmetro para transferência de valores de tenacidade obtidos em laboratório para o componente estrutural real. Assim, neste trabalho teórico de pesquisa foram realizadas diversas análises numéricas 3D, com o objetivo de compreender os efeitos da perda de restrição à plasticidade sobre os valores de tenacidade à fratura. Parâmetros como tamanho de trinca e geometria do corpo-de-prova foram analisados para fornecer informações mais detalhadas sobre a perda de restrição à plasticidade. Esta análise revelou uma variação da integral J e do parâmetro Q com a espessura de cada corpo-de-prova. Novas curvas J-QA foram traçadas para a descrição do nível de restrição à plasticidade e para um ajuste dos valores mais realísticos de tenacidade à fratura. Também foram comparados os resultados com o código ASME, onde foi possível ver como o mesmo tem um conceito extremamente conservador. / The fracture toughness is used to evaluate the resistance to the propagation of a crack and became an important property to be considered in methodologies for structural integrity evolution of mechanical components in general. The main methodology for assessing the crack-tip constraint (JQ Theory) represents a major step towards the inclusion of geometrical effects in studies of fracture. Some advances have been proposed for a parameter to transfer values of toughness obtained in laboratory to real structural components. Thus, theoretical work in this research consisted of several 3D numerical analysis with the aim of understanding the constraint effects on the values of fracture toughness. Several parameters such as crack size and specimens geometry were analyzed to provide detailed information about constraint effects. This analysis revealed a variation of J integral and the parameter Q with the thickness of each specimen. New J-Q curves were drawn to describe the level constraint of plasticity and a more realistic set of values of fracture toughness. The results were compared with the ASME code, where it was possible to see that the code criteria are very conservative.

A indústria aeronáutica tem buscado melhorias no conceito de integridade estrutural, a partir do desenvolvimento de projetos mais otimizados com a produção de aeronaves mais leves e seguras. Tais projetos garantem aeronaves operacionalmente mais viáveis e redução no consumo de combustível, beneficiando o fabricante, os operadores e a população em geral, pois aplica o conceito de aeronave verde. Estruturas aeronáuticas em operação recebem solicitações de cargas típicas de vôo, como pressurização, sustentação, que por sua vez, geram esforços dos mais variados tipos e suas combinações, como tração, compressão, fadiga, torção, flexão, flambagem, cargas aeroelásticas, vibrações e flutter, associados a ambientes críticos. O conhecimento sobre o comportamento do material estrutural perante ambientes corrosivo ou de baixa temperatura, é importante para avaliação da vida útil das aeronaves. Neste contexto, o objetivo deste trabalho foi avaliar o comportamento da liga AA2050-T84 sob ponto de vista de corrosão-fadiga e tenacidade a fratura em criogenia e, correlacionar com a microestrutura e fractografia através de ensaios mecânicos e de tenacidade a fratura em temperatura ambiente e criogênica. As condições de ensaios foram determinadas próximas a de serviço a que o material será inserido sendo, para criogenia -54 ºC e para os ensaios de propagação de trinca por fadiga em atmosfera ambiente e névoa salina com concentração de solução de 3,5% e 5% NaCl, frequência de 15Hz e razões de carga R = 0,1 e 0,5. Os resultados em criogenia mostraram que há melhora nas propriedades trativas e estabilidade na tenacidade, pois o material retém dutilidade com o decréscimo da temperatura. Os ensaios de propagação de trinca por fadiga foram executados com ΔK decrescente e os parâmetros para geração de névoa salina foram determinados experimentalmente. As curvas de crescimento de trinca e determinação do fator limite foram comparadas quanto a razão de carga e atmosfera de ensaio. Observou-se que para os ensaios de propagação de trinca por fadiga a presença da névoa salina acelera a taxa de propagação e resultam em um fator limite menor. / The aviation industry has sought improvements with the concept of structural integrity, from the development of more optimized designs with production aircraft with low weight and secure. These projects ensure an aircraft more operationally doable and reduced fuel consumption, benefiting the manufacturer, operators and the people, applying the concept of green aircraft. Aerospace structures in operation receive requests loads typical of flight, how pressurization support and lift that produce several types and combinations of requests, such as tensile, compression, fatigue, torsion, bending, buckling , aeroelastic loads, vibration and flutter associated with critical environments. Knowledge about the behavior of the structural material into corrosive environments or cryogenic temperature, it is important for evaluation to the lifetime of the aircraft. Accordingly , the aim of this study was to estimate the behavior of AA2050 - T84 alloy, about corrosion-fatigue and fracture toughness at cryogenic situations and correlate with microstructure and fractography, by mechanical tests and fracture toughness at room temperature and cryogenic. The test conditions has been determined near of the service that the material will be inserted, for cryogenic temperature -54 ºC and testing of fatigue crack propagation in air and salt spray with concentration of 3.5% and 5% NaCl, frequency 15Hz and load ratios R = 0.1 and 0.5. The cryogenic results showed that there improvement in tensile properties and stability in toughness due the restraint of ductility with decreasing temperature. Tests of fatigue crack propagation were carried out with ΔK decreasing and the parameters to obtain salt spray were determined experimentally. The crack growth curves and determination of the threshold were compared the according to load ratio and test atmosphere. In the fatigue crack propagation it was observed that presence of salt spray accelerates the rate of propagation and result in a lower threshold.

Lors du chargement cyclique d’une pièce métallique fissurée, un champ de température hétérogène est créé à la pointe de la fissure. Ce champ de température est dû à trois types de sources de chaleur : (i) la première source est une source de couplage thermoélastique liée à la partie hydrostatique du tenseur des contraintes résultant de la sollicitation mécanique cyclique. Elle fluctue périodiquement dans le temps et l’énergie qui lui est associée est nulle à la fin de chaque cycle de chargement ; (ii) la deuxième source de chaleur est une source dissipative et intrinsèque au comportement du matériau. Elle est reliée au phénomène de l’auto-échauffement dû à la microplasticité dissipée en chaleur dans le matériau à l’échelle microscopique. Elle est positive et s’accumule dans le temps ; (iii) enfin, la troisième source de chaleur a les mêmes origines et propriétés que la deuxième source, mais elle est associée à la plasticité, à l’échelle macroscopique, qui se dissipe en chaleur dans la zone de plasticité cyclique à la pointe de la fissure. En présence de ces trois sources de chaleur, le champ de température résultant génère un champ de contrainte dû au phénomène de la dilatation thermique. Ce nouveau champ des contraintes s’ajoute au champ des contraintes dû au chargement mécanique cyclique, et donc l’état des contraintes sur la fissure est modifié. En conséquence, le facteur d’intensité des contraintes, qui est un paramètre clé dans la modélisation de la propagation des fissures, est modifié. D’où l’objectif de cette thèse qui vise à quantifier les conséquences de ces trois sources de chaleur sur le facteur d’intensité des contraintes, et ce dans le cas d’une fissure longue de fatigue. / By subjecting a cracked specimen to a cyclic loading, thermal effects take place and create a heterogeneous temperature field around the crack tip. Those thermal effects are associated with coupling and dissipative heat sources, namely: (i) the heat source due to thermoelastic coupling generated by the hydrostatic part of the stress tensor related to cyclic mechanical loading; (ii) the heat source due to intrinsic dissipation associated with the self-heating phenomena originating from plasticity at the microscopic scale; (iii) and the heat source due to cyclic plasticity, at the macroscopic scale, which occurs in the reverse cyclic plastic zone ahead of the crack tip, and dissipates into heat. The overall heterogeneous temperature field resulting from the heat sources induces a heterogeneous stress field due to thermal expansion phenomena. As a consequence, the stress state over the crack is modified and leads to modify the stress intensity factor, which is a key parameter in modeling fatigue crack growth. Therefore, the aim of this PhD thesis is to quantify the consequences of the heat sources on the stress intensity factor, in the case of a long propagating fatigue crack.

O presente trabalho consiste no desenvolvimento de uma ferramenta computacional para análises de fratura e fadiga de componentes tridimensionais a partir de modelos geométricos de Desenho Assistido por Computador (CAD, acrônimo do inglês). Modelos de propagação de fissuras associados a leis empíricas de fadiga permitem a determinação da vida útil de peças mecânico-estruturais. Tais análises são de vital importância para garantir a segurança estrutural em diversos projetos de engenharia tais como os de pontes, plataformas off-shore e aeronaves. No entanto, a criação de modelos de análise a partir de modelos geométricos de CAD envolve diversas etapas intermediárias que visam a obtenção de malhas volumétricas adequadas. A grande maioria dos modelos de CAD trabalha com a representação de sólidos a partir de seu contorno utilizando superfícies paramétricas, dentre as quais se destacam as superfícies B-Splines Racionais Não Uniformes (NURBS, acrônimo do inglês). Para gerar malhas volumétricas é necessário que o conjunto de superfícies NURBS que descrevem o objeto seja \"estanque\", ou seja, sem lacunas e/ou superposições nas conexões das superfícies, o que não é possível garantir na grande maioria dos modelos constituídos por NURBS. As contribuições propostas no presente trabalho são aplicáveis a modelos baseados no Método dos Elementos de Contorno dual (MEC dual), os quais exigem apenas a discretização das superfícies do problema, ou seja, contorno mais fissuras. No intuito de criar os modelos de análise de maneira eficiente a partir dos modelos geométricos de CAD, desenvolveu-se uma estratégia de colocação que permite discretizar de maneira independente cada uma das superfícies NURBS que compõem os modelos geométricos sólidos. Com a estratégia proposta evitam-se as dificuldades no tratamento das conexões entre as superfícies sendo possível analisar modelos geométricos \"não estanques\". A implementação abrange superfícies NURBS, aparadas ou não, de ordens polinomiais quaisquer e elementos de contorno triangulares e quadrilaterais de aproximação linear. As equações integrais de deslocamentos e de forças de superfície são regularizadas e as integrais singulares e hipersingulares são tratadas pelo Método de Guiggiani. Fissuras de borda são inseridas nos modelos de análise a partir de um algoritmo de remalhamento simples baseado em tolerâncias dimensionais. O mesmo algoritmo é utilizado para as análises incrementais de propagação. Três técnicas de extração dos Fatores de Intensidade de Tensão (FIT) foram implementadas para os modelos baseados na Mecânica da Fratura Elástica Linear (MFEL), a saber, as técnicas de correlação, de extrapolação e de ajuste de deslocamentos. A extensão dessa última técnica para problemas tridimensionais é outra contribuição do presente trabalho. Os critérios da máxima taxa de liberação de energia e de Schöllmann foram utilizados para determinar o FIT equivalente e o caminho de propagação das fissuras. O ângulo de deflexão é determinado por um algoritmo de otimização e o ângulo de torção, definido para o critério de Schöllmann, é imposto no vetor de propagação a partir de uma formulação variacional unidimensional, definida sobre a linha de frente da fissura. Nos modelos de fadiga adota-se a MFEL e a equação de Paris-Erdogan para determinar a vida útil à propagação de defeitos preexistentes. Um procedimento iterativo foi desenvolvido para evitar a interpenetração da matéria após o contato das faces da fissura, permitindo análises de fadiga com carregamentos alternados. Como proposta para a continuidade da pesquisa propõe-se desenvolver formulações isogeométricas de elementos de contorno para analisar problemas de fratura e fadiga diretamente dos modelos geométricos de CAD, sem a necessidade de gerar as malhas de superfície. Um estudo numérico preliminar envolvendo uma versão isogeométrica do MEC dual baseada em NURBS e a versão convencional utilizando polinômios de Lagrange lineares e quadráticos foi realizado. A partir do estudo foi possível apontar as vantagens e desvantagens de cada formulação e sugerir melhorias para ambas. / The present work consists in the development of a computational tool for fracture and fatigue analysis of three-dimensional components obtained from geometrical models of Computer-Aided Design (CAD). Crack propagation models associated with empirical fatigue laws allow the determination of residual life for structural-mechanical pieces. These analyses are vital to ensure the structural safety in several engineering projects such as in bridges, offshore platforms and aircraft. However, the creation of the analysis models from geometrical CAD models requires several intermediary steps in order to obtain suitable volumetric meshes of the problems. The majority of CAD models represent solids with parametric surfaces to describe its boundaries, which is known as the Boundary representation (B-representation). The most common parametric surfaces are Non-Uniform Rational B-Splines (NURBS). To generate a volumetric mesh it is required that the set of surfaces that describe the object must be watertight, i.e., without gaps or superposition at the surfaces connections, which is not possible to unsure using NURBS. The contributions proposed at the present thesis are applicable to models based on the Dual Boundary Element Method (DBEM), which require only the discretization of the surfaces of the problems, i.e., boundary and cracks. A special collocation strategy was developed in order to create the analysis models efficiently from the geometrical CAD models. The collocation strategy allows discretizing independently each one of the NURBS surfaces that compose the geometrical solid models. Therefore, the difficulties in the treatment of the surface connections are avoided and it becomes possible to create analysis models from non-watertight geometrical models. The implementation covers trimmed and non-trimmed NURBS surfaces of any polynomial orders and also triangular and quadrilateral boundary elements of linear order. The displacement and traction boundary integral equations are regularized and the strong and hypersingular integrals are treated with the Guiggiani\'s method. Edge cracks are inserted in the models by a simple remeshing procedure based on dimensional tolerances. The same remeshing approach is adopted for the incremental crack propagation analysis. Three techniques were adopted to extract the Stress Intensity Factors (SIF) in the context of Linear Elastic Fracture Mechanics (LEFM), i.e., the displacement correlation, extrapolation and fitting techniques. The extension of this last technique to three-dimensional problems is another contribution of the present work. Both the general maximum energy realise rate and the Schöllmann\'s criteria were adopted to determine the equivalent SIF and the crack propagation path. The deflection angle is obtained by an optimization algorithm and the torsion angle, defined for the Schöllmann\'s criterion, is imposed in the propagation vector through a one-dimensional variational formulation defined over the crack front line. The concepts of LEFM are adopted together with the Paris-Erdogan equation in order to determine the fatigue life of pre-existing defects. An iterative procedure was developed to avoid the self-intersection of the crack surfaces allowing fatigue analysis with alternate loadings. Finally, as suggestion for future researches, it was started the study of isogeometric boundary element formulations in order to perform fracture and fatigue analysis directly from CAD geometries, without surface mesh generation. A preliminary numerical study involving an isogeometric version of the DBEM using NURBS and the conventional DBEM using linear and quadratic Lagrange elements was presented. From the study it was possible to point out the advantages and disadvantages of each approach and suggest improvements for both.

Le caoutchouc naturel présente une très bonne résistance à la propagation de fissure. Cette particularité est généralement attribuée dans la littérature à sa capacité à cristalliser sous déformation. A ce jour, l'essentiel des travaux dans ce domaine porte sur des échantillons réticulés par une vulcanisation dite efficace, c’est-à-dire dont les noeuds de réticulation sont principalement composés de ponts monosulfures. Pour certaines applications, et parce qu’elle est réputée conduire à de meilleure propriétés en fatigue, il est intéressant d'utiliser une vulcanisation dite conventionnelle. Le matériau est alors composé majoritairement de ponts polysulfures. Le phénomène de cristallisation sous déformation, exacerbée en pointe de fissure en raison d'une amplification du champ de déformation, semble être l'un des mécanismes responsables de l'accroissement de la durée de vie en fatigue du matériau vulcanisé de manière efficace. Cependant, sur matériaux vulcanisés de manière conventionnelle et thermo-oxydés (77°C), cette corrélation doit être confirmée en raison d’une évolution importante de l'architecture du réseau élastomère pendant son vieillissement pouvant en effet avoir un impact important sur la capacité du matériau à cristalliser sous déformation. Cette étude se propose donc de caractériser l’évolution de réseaux élastomères vulcanisés de manières conventionnelles pendant leur vieillissement thermo-oxydant, puis d’évaluer leur résistance à la propagation de fissure à différents niveaux de déformation macroscopique. Des analyses in situ WAXS sous rayonnement synchrotron en fond de fissure permettent alors de relier ces résultats à l'évolution de l’aptitude de ces matériaux à cristalliser sous déformation. / Natural rubber (NR) is largely used in the tire industry due to its excellent mechanical properties, e.g. its very good resistance to fatigue crack growth at high strain. It is generally accepted that this outstanding behavior is related to its ability to crystallize under strain. Such phenomenon, so called SIC, strongly depends on parameters like temperature, strain rate as well as the architecture of the rubber network. The microstructure of this network is formed during the crosslinking process and depends on the vulcanization system, i.e. “Efficient” or “Conventional”. The former vulcanization recipe consists in the formation of short or monosulfide bridges in the elastomer network whereas the latter (necessary to ensure a good adhesion between metallic and rubber parts in a tire) will mainly create longer polysulfide bridges. During its life, the tire will be submitted to a slow aerobic ageing which will cause structural modifications of the initial network and therefore an evolution of the rubber ability to crystallize under strain and to resist against crack propagation. In general, the structural modifications are caused by complex chemical mechanisms, highly sensitive to temperature, leading to chain scission and chain crosslinking. They can also involve sulfur bridge reorganization when NR is conventionally vulcanized. Nevertheless, most of the literature on NR ageing has been performed on efficiently cross-linked NR, and in thermal conditions which are much too severe to be representative of the material ageing in tire applications. Within this frame, our objective is to study this material when it is aged at 77 °C in air. Such parameters have been identified as capable of reproducing more realistically and over a reasonable duration, the ageing of rubber in some use conditions. After characterization of the evolution of the aged materials microstructure, their crack propagation resistance will be studied at 0.01 Hz for different values of macroscopic deformations. Time resolved Wide Angle X-ray scattering (WAXS) measure-ments, carried out at room temperature, will then provide information on the crystallization process around the crack tip. Based on these results, the relation between the network evolution during ageing, the fatigue properties and the ability to strain crystal-lize in such conditions will be established in this work.

Favorable properties of Balsa wood make it an interesting alternative in a number of applications including thermal insulation or as a lightweight core material in sandwich composites. Increasing use in construction necessitates a better understanding of its mechanical and failure properties. In the present work, mode I and mode II fracture toughness for different types of balsa wood and a sandwich structure (balsa as core and fiber glass as skin layer) are studied experimentally by using load-displacement diagrams and visually acquired crack growth data. / Graduation date: 2013

During the earthquake in Japan and California in the 1990s, some weld beam-to-column connections had some cracks in heavy rigid frame steel building. Consequently it is required to assess the performance of the welded connection in term of rotation capacity and crack propagation strength. Some experimental tests have been performed. The weld connections were submitted to cyclic loading with increasing amplitude until macro crack event. However the crack phenomenon depends on many parameters: the geometry, the material, the welding process. For this reason, it is interesting to develop a finite element modeling of this connection to complete these experiments and perform a parametric study. The welded connection is modeled by three dimensional mixed solid elements. The constitutive law is elastoplastic with isotropic hardening identified for the base metal and the weld metal. The crack propagation is modeled by cohesive zone model. The parameters of the cohesive zone model have been identified by inverse method with the modeling of three point bend tests of a pre-cracked sample performed on the base and weld metal. The fatigue damage generated by the cyclic loading is computed by the fatigue continuum damage model of Lemaitre and Chaboche and it is coupled with the cohesive zone model. The damage and the crack propagation depend on the residual stresses generated by the welding process. They have been computed by a simulation of this process with a thermo mechanical finite element analysis. This thesis presents the used models and the results compared with the experimental tests.

The application of polynomial reproducing methods has been explored in the context of linear and non linear problems. Of specific interest is the application of a recently developed reproducing scheme, referred to as the error reproducing kernel method (ERKM), which uses non-uniform rational B-splines (NURBS) to construct the basis functions, an aspect that potentially helps bring in locall support, convex approximation and variation diminishing properties in the functional approximation. Polynomial reproducing methods have been applied to solve problems coming under the class of a simplified theory called Cosserat theory. Structures such as a rod which have special geometric properties can be modeled with the aid of such simplified theories. It has been observed that the application of mesh-free methods to solve the aforementioned problems has the advantage that large deformations and exact cross-sectional deformations in a rod could be captured exactly by modeling the rod just in one dimension without the problem of distortion of elements or element locking which would have had some effect if the problem were to be solved using mesh based methods. Polynomial reproducing methods have been applied to problems in fracture mechanics to study the propagation of crack in a structure. As it is often desirable to limit the use of the polynomial reproducing methods to some parts of the domain where their unique advantages such as fast convergence, good accuracy, smooth derivatives, and trivial adaptivity are beneficial, a coupling procedure has been adopted with the objective of using the advantages of both FEM and polynomial reproducing methods. Exploration of SMW (Sherman-Morrison-Woodbury) in the context of polynomial reproducing methods has been done which would assist in calculating the inverse of a perturbed matrix (stiffness matrix in our case). This would to a great extent reduce the cost of computation. In this thesis, as a first step attempts have been made to apply Mesh free cosserat theory to one dimensional problems. The idea was to bring out the advantages and limitations of mesh free cosserat theory and then extend it to 2D problems.

No description available.

Functionally graded materials (FGMs) are composites that have continuously varying material properties, which eliminate undesirable stress concentrations that might otherwise occur in layered composites. The concept of inhomogeneously varying properties is observed in nature; examples include bones, teeth, shells and timber. Modern engineering applications of FGMs include thermal barrier coatings, wear-resistant coatings, biomedical implants and MEMS devices. Syntactic foams, particle filled nano-composites are examples of inhomogeneous materials of current interest. Analyses and experiments available in the literature have focused on characterizing the inhomogeneous material modulus and density variations. Common techniques employed are nano-indentation and wave propagation studies. There are a few fracture mechanics analyses and experiments available in the literature; most of which are devoted to measuring the fracture toughness of graded materials. A few fracture analyses of graded materials are devoted to deriving asymptotic stress, strain and displacement fields around stationary and steadily growing cracks in inhomogeneous materials. Only a few studies exist that deal with understanding the effect of material property inhomogeneity on the spontaneous crack propagation. In the present thesis the effect of material property inhomogeneity on the dynamic fracture mechanics of cracks in FGMs is described. Numerical analysis of the elastodynamic initial boundary value problem is performed using a spectral scheme. Spectral scheme is a special numerical technique developed to simulate spontaneous, planar crack propagation in a variety of materials. The method is numerically efficient as it can be implemented on parallel machines with ease. The numerical scheme is versatile and can handle any state-and rate-dependent traction-separation laws (cohesive zone models) or frictional laws. Spectral scheme has successfully been used in simulating intersonic crack propagation, earthquake slip dynamics and also direct silicon wafer bonding process used in realizing 3D MEMS structures. In the present work, the spectral formulation accounts for the inhomogeneous variation in the material wave speeds in the medium. The effect of inhomogeneity on spontaneous crack propagation due to in-plane mixed-mode loading is also addressed here. A parametric study has been performed by varying the inhomogeneity length scales independently in the top and bottom half-spaces. The effect of inhomogeneity in shear wave speed on the dynamic stress intensity factors (SIFs) of a crack propagating in a quasi-steady-state along the interface between the two functionally graded half-spaces is studied. A symmetric hardening FGM offers the maximum fracture resistance, while the fracture resistance is minimum for a symmetric softening FGM. Our simulation shows that increasing the inhomogeneity in the wave speed leads to eliminate the overshoot in the dynamic stress intensity factor. The magnitude of the steady-state (long-time) SIF increases indicating an increase in the fracture resistance. The effect of the inhomogeneous wave speed on the mode-3 crack propagation characteristics is demonstrated by taking snapshots of the crack opening at a time interval. The magnitude of the crack sliding displacement is found to increase with increase in the inhomogeneity. The effect of the material property inhomogeneity on the mode-1 crack propagation is simulated to track the crack opening displacements. The inhomogeneity is assumed to be symmetric about the weak-plane. Our spectral scheme developed here for functionally graded material with exponential variation in the material properties is capable of simulating independent bimaterial combinations. When the graded material becomes progressively stiffer and denser (hardening), the crack opening displacement in reduced, indicating an increase in the fracture resistance. On the other hand, for the softening FGMs the crack opening displacement increases indicating a reduction in fracture toughness. It is noted that the cohesive fracture resistance on the weak-plane remains same in all the FGMs.