Doctor of Philosophy / Department of Industrial & Manufacturing Systems Engineering / Zhijian Pei / Poor machinability of hard-to-machine materials (such as advanced ceramics and titanium) limits their applications in industries. Ultrasonic-vibration-assisted grinding (UVAG), a hybrid machining process combining material-removal mechanisms of diamond grinding and ultrasonic machining, is one cost-effective machining method for these materials. Compared to ultrasonic machining, UVAG has much higher material removal rate while maintaining lower cutting pressure and torque, reduced edge chipping and surface damage, improved accuracy, and lower tool wear rate. However, physics-based models to predict cutting force in UVAG have not been reported to date. Furthermore, edge chipping is one of the technical challenges in UVAG of brittle materials. There is no report related to effects of cutting tool design on edge chipping in UVAG of brittle materials. The goal of this research is to provide new knowledge of machining these hard-to-machine materials with UVAG for further improvements in machining cost and surface quality. First, a thorough literature review is given to show what has been done in this field. Then, a physics-based predictive cutting force model and a mechanistic cutting force model are developed for UVAG of ductile and brittle materials, respectively. Effects of input variables (diamond grain number, diamond grain diameter, vibration amplitude, vibration frequency, spindle speed, and federate) on cutting force are studied based on the developed models. Interaction effects of input variables on cutting force are also studied. In addition, an FEA model is developed to study effects of cutting tool design and input variables on edge chipping. Furthermore, some trends predicted from the developed models are verified through experiments. The results in this dissertation could provide guidance for choosing reasonable process variables and designing diamond tools for UVAG.

Este trabalho apresenta o estudo da Retificação de Ultraprecisão de ligas de carbeto de tungstênio-cobalto (WC-Co) com diferentes microestruturas. A motivação para este estudo foi o grande potencial desta liga para a fabricação de componentes que requerem materiais de alta dureza e resistência à fratura. Devido à combinação dessas características, esses materiais vêm sendo usados na fabricação de moldes para injeção de lentes ópticas de dispositivos eletrônicos e ópticos. Assim, amostras de carbeto de tungstênio-cobalto foram submetidas a vários testes para determinação da correlação entre os parâmetros de corte e parâmetros estruturais (tamanho de grão e teor de cobalto) com o regime de remoção de material. As amostras foram polidas e posteriormente microendentadas com cargas variadas para pré-avaliar a ocorrência de formação de microtrincas. Testes de usinagem foram conduzidos em uma retificadora de ultraprecisão, usando rebolos de diamante e posteriormente a rugosidade e os danos da superfície (microtrincas e crateras) foram avaliados. Para melhor entendimento da influência dos parâmetros estruturais e dos parâmetros de corte sobre os resultados de rugosidade foi realizado um teste ANOVA. As forças de usinagem foram medidas durante os ensaios usando um microdinamômetro piezelétrico com objetivo de estimar a temperatura na zona de retificação. Os resultados obtidos indicam que tanto os parâmetros estruturais como os parâmetros de corte influenciam na rugosidade, microdureza e temperatura na zona de retificação das ligas de carbeto de tungstênio-cobalto. Amostras com maior tamanho de grãos apresentam as menores rugosidades e altas temperaturas na zona de retificação. A velocidade de avanço (Vf) mostrou-se mais influente que a profundidade de corte (ap). Menores velocidades de avanço aumentam a temperatura na zona de retificação e a microdureza na camada superficial. Entretanto, verificou-se que as maiores temperaturas obtidas nos ensaios não foram suficientes para promover alteração metalúrgica no material. Algumas condições de corte combinadas com parâmetros estruturais levam a remoção de material em regime dúctil, resultando em superfícies com qualidade óptica. A porcentagem de cobalto e a velocidade de avanço (Vf) têm forte influência na alteração da microdureza da camada superficial das amostras retificadas. A diminuição da velocidade de avanço tende a aumentar a microdureza na camada. Há aumento de microdureza de até 200 kgf/mm2, sugerindo a ocorrência de encruamento por tensões compressivas. Com base nestes resultados, acredita-se que a retificação de ultraprecisão apresenta-se como uma opção viável para a manufatura de componentes de carbeto de tungstênio com acabamento submicrométrico, possibilitando a eliminação dos processos tradicionais de manufatura óptica, tais como a lapidação e o polimento. / The ultraprecision grinding of different tungsten carbide-cobalt microstructures (WC-Co) were investigated. The motivation for this study is the materials high hardness and potential application for micromolds. These materials have been used as optical inserts in glass injection molding processes for optical and electric devices, due to their excellent combination of high hardness, ductility and fracture toughness. Tungsten carbide samples were subjected to tests to determine the correlation between cutting parameters and microstructures to achieve the ductile regime of material removal. Polished surfaces of carbide samples were indented using varying loads to evaluate the microcracks formation. The machining tests were conducted using an ultraprecision grinding and A V-shaped metal-bond was used. Surface roughness was investigated as functions of the grinding conditions by means Analysis of Variance (ANOVA). The tangential force was measured using a piezoelectric dynamometer to estimate the grinding zone temperature. The results indicate that structural parameters (grain size and cobalt content) and cutting parameters have a significant influence on surface roughness, micro-hardness and grinding zone temperature for tungsten carbide-cobalt alloys.Tungsten carbide-cobalt samples with the larger grain size presented lower surface finish results and high grinding temperatures. The feed rate (Vf) showed greater influence that the in-feed (ap). The grinding zone temperature and the hardness are increased when speed rate is reduced. However, it was found that the highest temperature achieved did not reach a critical temperature for phase transformation. Some cutting parameters combined with structural parameters lead to ductile mode grinding mechanism, and as consequence, high optical quality surfaces are obtained. The micro-hardness of layer is extremely influenced by cobalt content and speed rate. Lower feed rate tends to increase the micro-hardness up to 200 kgf/mm2, suggesting that the compressive stress occurs. Considering the results presented it is believed that the Ultraprecision grinding showed to be a viable option for the fabrication of components made of tungsten carbide-cobalt with nanometer surface finish possibly eliminating traditional optical manufacturing processes such as lapping and polishing.

L’indentation instrumentée est largement utilisée pour la détermination des propriétés mécaniques des matériaux, principalement la dureté et le module d’élasticité. Pour obtenir des données fiables, plusieurs corrections comme la prise en compte du défaut de pointe et la complaisance de l’instrument doivent être apportées dans la méthodologie d’analyse des données de l’essai. Malgré tout, ces corrections ne suffisent plus pour la caractérisation de matériaux fragiles et poreux, qu’ils soient sous une forme massive ou de revêtement. En effet, d’autres sources d’erreurs peuvent provenir de la fragilité de ces matériaux, mais aussi de la représentativité des mesures locales dans le cas des matériaux hétérogènes, ou de l'influence du substrat dans le cas des revêtements. Pour limiter ces effets, l’indenteur Knoop semble être un bon candidat car, à charge équivalente, sa surface de contact est plus grande et la profondeur d’indentation plus faible. Toutefois, par rapport aux indenteurs habituels, le retour élastique du matériau au voisinage de l'empreinte Knoop, qui doit être pris en compte dans les calculs des propriétés, n’est pas bien connu. Ceci constitue donc un frein à son utilisation. C’est pourquoi, nous proposons d’adapter la méthodologie conventionnelle proposée par Oliver et Pharr pour obtenir des résultats fiables par indentation Knoop. Pour atteindre cet objectif, nous analysons d’abord des résultats obtenus par indentation de différents matériaux céramiques denses en comparant les indentations Knoop et Vickers, ce dernier étant utilisé comme référence. Tout d’abord, nous analysons le retour élastique en indentation Knoop et nous montrons qu’il est possible de retrouver les mêmes valeurs qu’en indentation Vickers en intégrant un facteur correctif lié simplement à des grandeurs géométriques de l’empreinte. Cette approche est valable qu’il s’agisse de la détermination du module d’élasticité ou de la dureté. Toutefois, pour cette dernière propriété, il est nécessaire de bien préciser la définition utilisée pour son calcul. Nous en justifions le choix. Ensuite nous appliquons la méthodologie d’analyse ainsi établie pour l’étude de la réponse mécanique des matériaux poreux sous forme massive et de revêtement où non seulement le paramètre de porosité joue un rôle important sur la réponse du matériau, mais aussi son hétérogénéité, sa rugosité et son épaisseur. De manière générale, nous montrons que l’indenteur Knoop présente un intérêt certain par rapport aux indenteurs habituels, tout au moins dans le cas des céramiques. / Instrumented indentation is widely used for the assessment of mechanical properties, mainly hardness and elastic modulus. In order to obtain reliable results, analysis methodology has to refer several corrections, such as tip defect and frame compliance. However, these corrections are insufficient for the characterization of brittle and porous materials, whether bulk or coatings. Not only brittleness but also local surrounding in the case of heterogeneous materials and substrate influence in the case of coatings raise error concerns. To limit these unwanted effects, the Knoop indenter appears to be a favorable candidate because of the larger contact area and lower indentation depth at equivalent loads. However, compared to other commonly used indenters, radial elastic recovery near Knoop indent that has to be taken into account in the analysis methodology, is not well known. This constitutes therefore an obstacle for its use. Thereof, we propose to adapt the conventional methodology proposed by Oliver and Pharr to obtain reliable results with Knoop indentation. To achieve this purpose, we analyze the indentation data of different dense ceramic materials by comparing Knoop and Vickers indentations, this latter being used as a reference. First, we analyze the elastic recovery using Knoop indenter. We show that correlation to Vickers indentation results is possible using a geometric correction factor. This approach is valid for the determination of elastic modulus and hardness. However, for the latter property, it is necessary to specify the definition used for its calculation. The established analysis methodology was applied for studying the mechanical response of porous bulk materials and coatings, with respect to material porosity, roughness and thickness. It was confirmed that Knoop indenter may be favorable compared to the commonly used indenters, at least in the case of ceramics.

Este trabalho apresenta o estudo da Retificação de Ultraprecisão de ligas de carbeto de tungstênio-cobalto (WC-Co) com diferentes microestruturas. A motivação para este estudo foi o grande potencial desta liga para a fabricação de componentes que requerem materiais de alta dureza e resistência à fratura. Devido à combinação dessas características, esses materiais vêm sendo usados na fabricação de moldes para injeção de lentes ópticas de dispositivos eletrônicos e ópticos. Assim, amostras de carbeto de tungstênio-cobalto foram submetidas a vários testes para determinação da correlação entre os parâmetros de corte e parâmetros estruturais (tamanho de grão e teor de cobalto) com o regime de remoção de material. As amostras foram polidas e posteriormente microendentadas com cargas variadas para pré-avaliar a ocorrência de formação de microtrincas. Testes de usinagem foram conduzidos em uma retificadora de ultraprecisão, usando rebolos de diamante e posteriormente a rugosidade e os danos da superfície (microtrincas e crateras) foram avaliados. Para melhor entendimento da influência dos parâmetros estruturais e dos parâmetros de corte sobre os resultados de rugosidade foi realizado um teste ANOVA. As forças de usinagem foram medidas durante os ensaios usando um microdinamômetro piezelétrico com objetivo de estimar a temperatura na zona de retificação. Os resultados obtidos indicam que tanto os parâmetros estruturais como os parâmetros de corte influenciam na rugosidade, microdureza e temperatura na zona de retificação das ligas de carbeto de tungstênio-cobalto. Amostras com maior tamanho de grãos apresentam as menores rugosidades e altas temperaturas na zona de retificação. A velocidade de avanço (Vf) mostrou-se mais influente que a profundidade de corte (ap). Menores velocidades de avanço aumentam a temperatura na zona de retificação e a microdureza na camada superficial. Entretanto, verificou-se que as maiores temperaturas obtidas nos ensaios não foram suficientes para promover alteração metalúrgica no material. Algumas condições de corte combinadas com parâmetros estruturais levam a remoção de material em regime dúctil, resultando em superfícies com qualidade óptica. A porcentagem de cobalto e a velocidade de avanço (Vf) têm forte influência na alteração da microdureza da camada superficial das amostras retificadas. A diminuição da velocidade de avanço tende a aumentar a microdureza na camada. Há aumento de microdureza de até 200 kgf/mm2, sugerindo a ocorrência de encruamento por tensões compressivas. Com base nestes resultados, acredita-se que a retificação de ultraprecisão apresenta-se como uma opção viável para a manufatura de componentes de carbeto de tungstênio com acabamento submicrométrico, possibilitando a eliminação dos processos tradicionais de manufatura óptica, tais como a lapidação e o polimento. / The ultraprecision grinding of different tungsten carbide-cobalt microstructures (WC-Co) were investigated. The motivation for this study is the materials high hardness and potential application for micromolds. These materials have been used as optical inserts in glass injection molding processes for optical and electric devices, due to their excellent combination of high hardness, ductility and fracture toughness. Tungsten carbide samples were subjected to tests to determine the correlation between cutting parameters and microstructures to achieve the ductile regime of material removal. Polished surfaces of carbide samples were indented using varying loads to evaluate the microcracks formation. The machining tests were conducted using an ultraprecision grinding and A V-shaped metal-bond was used. Surface roughness was investigated as functions of the grinding conditions by means Analysis of Variance (ANOVA). The tangential force was measured using a piezoelectric dynamometer to estimate the grinding zone temperature. The results indicate that structural parameters (grain size and cobalt content) and cutting parameters have a significant influence on surface roughness, micro-hardness and grinding zone temperature for tungsten carbide-cobalt alloys.Tungsten carbide-cobalt samples with the larger grain size presented lower surface finish results and high grinding temperatures. The feed rate (Vf) showed greater influence that the in-feed (ap). The grinding zone temperature and the hardness are increased when speed rate is reduced. However, it was found that the highest temperature achieved did not reach a critical temperature for phase transformation. Some cutting parameters combined with structural parameters lead to ductile mode grinding mechanism, and as consequence, high optical quality surfaces are obtained. The micro-hardness of layer is extremely influenced by cobalt content and speed rate. Lower feed rate tends to increase the micro-hardness up to 200 kgf/mm2, suggesting that the compressive stress occurs. Considering the results presented it is believed that the Ultraprecision grinding showed to be a viable option for the fabrication of components made of tungsten carbide-cobalt with nanometer surface finish possibly eliminating traditional optical manufacturing processes such as lapping and polishing.

Impact of rain drops at relatively high velocities, which is known as rain erosion, causes severe damages on various materials. Every material can withstand the rain erosion up to a specific impact velocity. However, this damage is critical for optical windows which are very important components for Electro-Optical (EO) systems such as thermal camera. Even a small scratch may affect the transmission capability of the optical window adversely and leads to some functional problems in the device due to insufficient transmitted data. Since it has a vital effect on the EO systems, the rain erosion is needed to be investigated on the special optical windows, particularly for determining the velocity that a damage initiates. In this study, the rain erosion is investigated on germanium which is a kind of optical window, by means of numerical simulations in LS-DYNA. Damage Threshold Velocity (DTV) is examined for two different water shapes (which are spherical water drop and water jet) within a velocity range between 100 and 250 m/s. Both single and multiple impact cases are considered for both water shapes up to ten consecutive collisions. By using the results, the &ldquo / DTV versus number of impact curves&rdquo / are obtained in order to understand the amount of damage with respect to both single and multiple impacts. Results are compared with both literature and the experimental data within the scope of DTV and shape of the damage. In the numerical simulations, ALE (Arbitrary Lagrangian Eulerian) method is used for modelling water. &ldquo / JOHNSON-HOLMQUIST-CERAMICS (JH-2)&rdquo / which is recommended for both ceramics and glass applications is used as the material model for Germanium. JH-2 is a complete material model which contains damage effects, failure criteria, and Equation of State (EOS) all together. Among the material models available in the library of LS-DYNA, &ldquo / MAT-NULL + EOS-GRUNEISEN&rdquo / is used for water.

Made available in DSpace on 2014-06-11T19:28:35Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-03-21Bitstream added on 2014-06-13T20:37:41Z : No. of bitstreams: 1 rodrigues_ea_me_bauru.pdf: 1602991 bytes, checksum: 7f755b87b5be84900b2d054f02413197 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / No presente trabalho desenvolve-se um modelo constitutivo baseado na mecânica do dano contínuo para representar o comportamento de materiais que apresentam diferentes respostas quando solicitados à tração ou à compreensão. obtem-se uma representação constitutiva através da composição de modelos simples e específicos para tratar cada tipo de solicitação. Este modelo combinado é capaz inclusive de lidar com carregamentos alternados (tração e compreensão), envolvendo fechamento e reabertura de fissuras existentes. Para modelar o comportamento em compreensão emprega-se o modelo constitutivo que tem como critério de degradação o segundo invariante do tensor de tensão desviador (critério de Von Mises ou J2). Para simular o aparecimento de fissuras de tração, usa-se o modelo de dano com critério de degradação baseado na energia de deformação da parte positiva do tensor efetivas. A integração dos modelos é feita com base em tensões efetivas associadas a duas escalas distintas (escala grosseira e refinada). O modelo é apto para representar a formação de descontinuidades no campo de deslocamento (descontinuidades fortes) em materiais quase-frágeis. Nesse caso, a região de localização de deformação (zona de processo da fatura) pode ser descrita pelo modelo de dano combinado, com lei de abrandamento de tensões (softening) exponencial, que estabelece dissipação compatível com a energia de fratura. A região contínua pode ser descrita pelo modelo de dano J2, com parâmetros ajustados com base no comportamento não linear à compreensão. Valida-se o modelo proposto mediante testes básicos, focando a capacidade do modelo em representar os principais aspectos do comportamento de materiais quase-frágeis. A aplicabilidade do modelo é demonstrada através do estudo da capacidade de rotação plástica de vigas de concreto armado, confrontando-se os resultados numéricos com os experimentais / A combined constitutive model based on the Continuum Damage Mechanics (CDM) is presented to represent the nonlinear behavior of quasi-brittle materials, which present different response when subjected to tension or compreession. The constitutive model is a composition of two simple and specific models designed to treat each type of behavior. The combined model is able to deal with alternating load (tension-compression), involving formation, closure and reopening cracks. To model the compressive behavior, a degradation criterion based on the second invariant of the deviatoric part of the effective stress tensor (Von Miser or J2 criterion) is used. To simulate cracking, a damage model with degradation criterion based on the strain energy associated to the positive part the effective stress tensor is adopted. The combination of the models is made on the basis of the effective stresses associated to two distinct scales (coarse and fine scales) The model is able to represented the formation of discontinuities in the displacement field (strong discontinuities) for quasi-brittle materials. The region of strain localization (fracture process zone) is described by a softening law which establishes dissipation energy compatible with the fracture energy. The continuous region is described by the J2 damage model, with parameters ajusted to describle the compressive nonlinear behavior in compression. Some basic tests are performed to asses the ability of the model to represent the main aspects of the behavior of quasi-brittle materials. The applicability of the model is demonstrated by the study of the plastic rotation capacity of reinforced concrete beams, comparing the numerical responses with the experimental ones

A crescente necessidade por parte da indústria óptica e eletrônica por componentes que possuam características como elevada precisão de forma e acabamento em materiais frágeis, vem despertando um grande interesse nas pesquisas dos processos de usinagem de ultraprecisão. Neste sentido, a retificação e o torneamento de materiais frágeis com ferramentas de diamante têm se destacado como substitutos dos processos tradicionais de fabricação de precisão como a lapidação e polimento. Propõe-se o estudo da retificação de ultraprecisão de materiais frágeis através da realização de ensaios de corte em uma retificadora de ultraprecisão com rebolo de diamante de forma a estabelecer os parâmetros de corte compatível com a remoção dúctil de material. Foram usinadas amostras de silício monocristalino através de retificação tangencial de mergulho plana sob diferentes condições de usinagem para posteriormente avaliar a integridade superficial da peça. A amostra foi montada sob um aparato especial com uma inclinação conhecida a fim de se realizar um corte em cunha. Com isso, três situações distintas de remoção de material foram investigadas: totalmente dúctil, dúctil-frágil e totalmente frágil. O parâmetro de corte variado foi a profundidade de corte; o avanço e velocidade de corte foram mantidos constantes. / The requirements of components that demand high precision finishes and form in brittle materials has roused a huge interest in the ultraprecision machining process in the optical and electronic industries. The diamond grinding and turning of brittle materials have been used more and more as replacements to the tradicional lapping and polishing. The study of ultraprecision grinding of brittle materials is proposed. Cutting experiments on an ultraprecision grinding machine using a diamond wheel were carried out stablish cutting parameters compatible with ductile material removal. Silicon samples were machined through flat plunging tangencial grinding under different machining conditions and the sample surface integrity was assessed. The sample was mounted on a special apparatus with a known inclination so as to carry out a edge cutting. Thereby, three different material removal situations were investigated: whole ductile, ductile/brittle, whole brittle. The depth of cut was the parameter varied. Feedrate and cutting speed of the wheel were held constant.

Cette thèse porte sur la description du processus de fissuration du béton soumis à des sollicitations mécaniques. L'objectif principal est d'améliorer la description macroscopique à l'aide d'un modèle continu. Un modèle décrivant de façon cohérente le comportement à la rupture du béton devrait au moins représenter : (i) la transition continu/discret et l'effet d'écran induit par une macrofissure, (ii) la discontinuité du déplacement, (iii) l'interaction entre le processus de fissuration et un bord libre (iv) il doit aussi être capable de reproduire la réponse mécanique obtenue expérimentalement. Dans un premier temps, nous avons fait une analyse comparative entre le modèle d'endommagement non-local classique et différents modèles continus améliorés proposés dans la littérature. Des outils de comparaison ont été proposés pour cette analyse : (i) du point de vue numérique, deux exemples considérant la rupture dynamique d'une barre (barre en traction et test d'écaillage) et (ii) du point de vue expérimental, une base de données issue d'une série d'essais sur des poutres homothétiques entaillées et non-entaillées en flexion trois points. Nous avons conclu que seule une combinaison entre différentes formulations peut rendre compte de tous les mécanismes mis en jeu lors du processus de fissuration. Elle inclue à la fois la façon dont l'information non-locale est transmise, la croissance de défauts et la description des effets de bord. Nous avons mis en évidence que son implémentation 2D ou 3D reste complexe et donc la comparaison avec des données expérimentales s'avère impossible. Dans un deuxième temps, nous avons choisi de changer l'échelle d'analyse pour connaitre en détail les mécanismes ayant lieu au sein de la mésostructure du béton (pâte, granulat, interface) à l'aide d'un modèle mésoscopique basé sur des éléments lattice. Cette analyse a permis de conclure que la prise en compte des interactions entre les composants de la mésostructure du béton fournit des résultats numériques plus proches de la réalité que ceux obtenus avec le modèle non-local macroscopique classique. Le mésomodèle est capable de représenter aussi bien la charge maximale (effet d'échelle) que la phase adoucissante pour toutes les tailles de poutre et pour toutes les géométries d'entaille. Nous avons transposé la prise en compte des interactions de l'échelle mésoscopique à l'échelle macroscopique au travers de la fonction poids d'un nouveau modèle non-local. Elle est estimée en décrivant le matériau comme étant un ensemble d'inclusions qui interagissent entre elles lors du chargement. Ces inclusions sont dilatées élastiquement et successivement afin de caractériser le transfert d'information au sein du matériau et de reconstruire la fonction poids du modèle proposé. Ce nouveau modèle est capable de décrire la transition continu/discret et l'effet d'écran, la discontinuité du déplacement et de retrouver un effet de bord cohérent avec les résultats de la micromécanique. Son implémentation en 2D est présentée et les premiers résultats de calculs illustrent la démarche. Finalement, nous revenons sur la modélisation mésoscopique du comportement du béton. Sa richesse en information peut conduire à une compréhension plus fine du processus de fissuration et de la création puis l'évolution de la zone d'élaboration. / This work focuses on the description of the process of cracking of concrete subjected to mechanical stresses. The main objective is to improve the understanding of the mechanisms involved using a continuous macroscopic model. A model describing consistently the fracture behavior of concrete should at least represent: (i) the continuous / discrete transition and the shielding effect induced by a macrocrack, (ii) the discontinuity of displacement, (iii) the interaction between the cracking process and a free boundary, (iv) it must also be able to reproduce the mechanical response obtained experimentally. At first, we made a comparative analysis of the classical non-local damage model and others improved continuous models proposed in the literature. Comparison tools have been proposed for this analysis: (i) from a numerical point of view, two examples considering the dynamic rupture of a bar (tensile test and spalling test) and (ii) from an experimental point of view, a database obtained from three-point bending test on notched and unnotched geometrically similar beams made from the same concrete formulation. We found that only a combination of this formulations may account for the different mechanisms involved in the process of cracking. It includes the transmission of the non-local information, the growing of voids and the description of boundary effects. We shown that its implementation in 2D or 3D remains complex and thus comparison with experimental results are impossible. In a second step, we decided to change the scale of analysis to precise the mechanisms which are taking place within the mesostructure of concrete using a mesomodel based on lattice elements. This analysis shown that since the mesomodel intrinsically took into account the interactions evolution within the structure, it is able to provide relevant results when classical macroscopic non-local models failed. It is able to represent both the maximum load (size effect) and the softening regime whatever the beam size or the pre-notch geometry. In addition, we proposed a new non-local framework where the interactions were upscale from the mesoscale to the macroscale through a new weight function. This function is estimated by describing the material as a set of inclusions that interact upon loading. These inclusions are successively elastically dilated to characterize the transfer of information within the material and rebuild the non-local weight function. This new model is able to describe the continuous / discrete transition, the shielding effect and the discontinuity of displacement. The model has been implemented in 2D in a finite element code and first results shown its capabilities to reproduce experimental results in term of maximum loads. In a third step, the richness of the mesoscopic approach has been used to describe precisely the local process of failure in term of fracture process zone evolution.

Resumo: No presente trabalho desenvolve-se um modelo constitutivo baseado na mecânica do dano contínuo para representar o comportamento de materiais que apresentam diferentes respostas quando solicitados à tração ou à compreensão. obtem-se uma representação constitutiva através da composição de modelos simples e específicos para tratar cada tipo de solicitação. Este modelo combinado é capaz inclusive de lidar com carregamentos alternados (tração e compreensão), envolvendo fechamento e reabertura de fissuras existentes. Para modelar o comportamento em compreensão emprega-se o modelo constitutivo que tem como critério de degradação o segundo invariante do tensor de tensão desviador (critério de Von Mises ou J2). Para simular o aparecimento de fissuras de tração, usa-se o modelo de dano com critério de degradação baseado na energia de deformação da parte positiva do tensor efetivas. A integração dos modelos é feita com base em tensões efetivas associadas a duas escalas distintas (escala grosseira e refinada). O modelo é apto para representar a formação de descontinuidades no campo de deslocamento (descontinuidades fortes) em materiais quase-frágeis. Nesse caso, a região de localização de deformação (zona de processo da fatura) pode ser descrita pelo modelo de dano combinado, com lei de abrandamento de tensões (softening) exponencial, que estabelece dissipação compatível com a energia de fratura. A região contínua pode ser descrita pelo modelo de dano J2, com parâmetros ajustados com base no comportamento não linear à compreensão. Valida-se o modelo proposto mediante testes básicos, focando a capacidade do modelo em representar os principais aspectos do comportamento de materiais quase-frágeis. A aplicabilidade do modelo é demonstrada através do estudo da capacidade de rotação plástica de vigas de concreto armado, confrontando-se os resultados numéricos com os experimentais / Abstract: A combined constitutive model based on the Continuum Damage Mechanics (CDM) is presented to represent the nonlinear behavior of quasi-brittle materials, which present different response when subjected to tension or compreession. The constitutive model is a composition of two simple and specific models designed to treat each type of behavior. The combined model is able to deal with alternating load (tension-compression), involving formation, closure and reopening cracks. To model the compressive behavior, a degradation criterion based on the second invariant of the deviatoric part of the effective stress tensor (Von Miser or J2 criterion) is used. To simulate cracking, a damage model with degradation criterion based on the strain energy associated to the positive part the effective stress tensor is adopted. The combination of the models is made on the basis of the effective stresses associated to two distinct scales (coarse and fine scales) The model is able to represented the formation of discontinuities in the displacement field (strong discontinuities) for quasi-brittle materials. The region of strain localization (fracture process zone) is described by a softening law which establishes dissipation energy compatible with the fracture energy. The continuous region is described by the J2 damage model, with parameters ajusted to describle the compressive nonlinear behavior in compression. Some basic tests are performed to asses the ability of the model to represent the main aspects of the behavior of quasi-brittle materials. The applicability of the model is demonstrated by the study of the plastic rotation capacity of reinforced concrete beams, comparing the numerical responses with the experimental ones / Orientador: Osvaldo Luís Manzoli / Coorientador: André Luís Gamino / Banca: Leonardo José do Nascimento Guimarães / Banca: Edson Antonio Capello Sousa / Mestre

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2016-01-07T16:28:03Z No. of bitstreams: 2 Dissertação - Dannilo Carvalho Borges - 2015.pdf: 3073251 bytes, checksum: 5efdd805f96baaf801696402a7ed039b (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-01-08T11:35:34Z (GMT) No. of bitstreams: 2 Dissertação - Dannilo Carvalho Borges - 2015.pdf: 3073251 bytes, checksum: 5efdd805f96baaf801696402a7ed039b (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2016-01-08T11:35:34Z (GMT). No. of bitstreams: 2 Dissertação - Dannilo Carvalho Borges - 2015.pdf: 3073251 bytes, checksum: 5efdd805f96baaf801696402a7ed039b (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-08-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work deals with a proposed numerical modeling of mechanical behavior in brittle heterogeneous materials, such as concrete. For this propose, a two-dimensional meso-scale model is presented. The material is considered as a three-phase material consisting of interface zone, matrix and inclusions – each constituent modeled by an appropriate constitutive model. The Representative Volume Element (RVE) consists of inclusions idealized as circular shapes randomly placed into the RVE. The interface zone is modeled by means of cohesive contact finite elements the inclusions are considered as linear elastic media and matrix region is considered as elastoplastic material. The main goal here is to show that simple constitutive modeling of the microstructure can be employed with a computational homogenization-based approach as an alternative to complex macroscopic constitutive models for the mechanical behavior of the heterogeneous materials using a finite element procedure within a purely kinematical multi-scale framework. A set of numerical examples, involving the microcracking and plasticity processes, is provided in order to illustrate the qualitative performance of the proposed modeling. / Este trabalho apresenta uma proposta para a modelagem numérica do comportamento mecânico da microestrutura de materiais heterogêneos e frágeis, tal como o concreto. Para este fim, apresenta-se um modelo 2D de escala mesoscópica. O material é considerado como composto por três fases consistindo de zona de interface, matriz e inclusões, onde cada constituinte é modelado adequadamente. O Elemento de Volume Representativo (EVR) consiste de inclusões idealizadas de forma circular aleatoriamente dispostas no EVR. A zona de interface é modelada por meio de elementos finitos coesivos e de contato e as inclusões são modeladas como meio elástico linear. Já a matriz é considerada como material elastoplástico. O principal objetivo é mostrar que modelos constitutivos simples empregados na microestrutura em conjunto com uma formulação baseada numa homogeneização computacional são uma alternativa aos modelos constitutivos macroscópicos complexos para o comportamento mecânico de materiais heterogêneos usando um procedimento baseado no Método dos Elementos Finitos no âmbito de uma teoria Multiescala. Uma série de exemplos envolvendo processos de microfissuração e plasticidade é apresentada de modo a ilustrar qualitativamente a performance da modelagem proposta.