Neste trabalho, uma abordagem micromecânica com aproximação da geometria dada por funções de Bézier triangulares com continuidade geométrica G1 é inserida ao Método dos Elementos de Contorno, o qual é aplicado em problemas da elastostática tridimensional. Para consideração do efeito microestrutural, foi utilizado a teoria gradiente elástica simplificada de Aifantis, a qual é uma particularização da teoria geral de Mindlin. Nesta teoria, um argumento variacional é estabelecido para determinar todas as possíveis condições de contorno, clássica e não-clássica, para o problema de valor de contorno geral. A partir deste argumento, a solução fundamental da elasticidade gradiente é explicitada e com o auxílio da identidade integral recíproca é construído a representação integral de contorno. Para tornar o problema de valor de contorno bem-posto, em adição à representação integral de contorno para deslocamento, uma segunda representação integral para derivada normal do deslocamento foi utilizada. Expressões integrais para deslocamento e tensão em pontos internos são apresentadas. Todos os núcleos das equações integrais são explicitamente desenvolvidos. Para a discretização do MEC foram utilizados elementos triangulares curvos, aproximados tanto para a geometria quanto para os parâmetros físicos por funções de Proriol (com características espectrais) e por funções aqui chamadas de Polinomiais, onde esta última é construída a partir de uma base nodal equidistante e pela imposição da partição da unidade. Entretanto estas funções aproximadoras garantem apenas continuidade C0 entre os elementos triangulares, ou seja, a garantia da continuidade do plano tangente não necessariamente é satisfeita. Com o objetivo de anular o termo de integral de linha presente na formulação microestrutural, a hipótese de superfície suave se faz necessária e assim funções de Bézier com continuidade geométrica G1, a qual depende apenas da posição e das normais dos nós nos vértices da malha triangular é utilizada. Para auxiliar na obtenção das coordenadas e das normais nodais para geometrias complexas foi utilizado o software de computação gráfica BlenderTM 2.7, o qual foi acoplado ao programa do MEC elastostático gradiente. Na sequência foi verificada, por meio de exemplos, a suavidade na intersecção entre os elementos triangulares G1 e estes foram comparados com as aproximações de Proriol e Polinomial. Em seguida, as singularidades presentes nas soluções fundamentais foram tratadas através da expansão em série de Laurent aplicada à técnica de subtração de singularidade. Condições necessárias e suficientes para a convergência das expansões em série das soluções fundamentais, estimador do erro para estas expansões, assim como, a correlação matemática entre o tamanho da malha e o parâmetro micromecânico g foram estabelecidos. Expressões explicitas da série de Laurent dos núcleos das integrais singulares e hipersingulares do MEC clássico e não clássico foram apresentadas. A verificação do tratamento da singularidade aplicado a elementos triangulares curvos foi realizada, tanto na direção radial quanto na direção angular. E pôde ser observado que ocorre uma perda de eficiência no tratamento da singularidade na direção angular, devida a presença do efeito de camada limite para elementos curvos distorcidos. Entretanto, este efeito de quase singularidade pode ser amenizado por meio da abordagem micromecânica, uma vez que foi observado menor presença do efeito da camada limite à medida que o parâmetro g é diminuído. Por último, foi desenvolvido um programa na linguagem FORTRAN 11.0, o qual contempla as abordagens clássica e micromecânica com continuidade geométrica G1. Sua validação foi feita por meio de exemplos considerados Benchmarks. / In this work, a micromechanical approach with approximation of geometry solved by Bézier triangular functions that guaranty continuity G1 is inserted to the Boundary element Method (BEM). This formulation is applied in three-dimensional elastostatic problems. The simplified elastic gradient theory proposed by Aifantis, which is a particularization of the general theory of Mindlin is used to consider the microstructural effect. In this theory a variational argument is established to determine all possible boundary conditions, classical and non-classical, for the general boundary value problem. From this argument, the fundamental solution of the gradient elasticity is explicited and by the reciprocal integral identity the boundary integral representation is achieved. In addition to the boundary integral representation for dispacement, a second integral representation regarding its normal derivative is used to make the well-posed boundary value problem. Integral expressions for displacement and stress on internal points are also presented. All kernels in the integral equations are explicitly developed. Curved triangular elements are used for the discretization of the BEM. The approximation of both the geometry and physical parameters is performed by Proriol functions (with spectral characteristics) and by Polynomial functions. The last is built from an equidistant nodal basis enforcing the partition of unity. However these approximating functions ensure only C0 continuity between the triangular elements, that is, the tangent plane continuity assurance is not necessarily satisfied. In order to cancel line integral terms in the microstructural approach, the hypothesis of smooth surface is required and thus Bézier function with geometric continuity G1, which depends only on the position and the normal of the nodes at the vertices of the triangular mesh is used. In this study the computer graphics software called BlenderTM 2.7 is used to assist in obtaining coordinates and normal vectors at nodes when complex geometries are analyzed. BlenderTM 2.7 is coupled to the gradient elastic BEM program. The smoothness of the resulting mesh using G1 elements is compared to Proriol and Polynomial approximations by means of simple examples. The singularities present in the fundamental solutions are treated by employing the expansion in Laurent series and the singularity subtraction technique. Necessary and sufficient conditions for the convergence of expansions in series of fundamental solutions, error estimator for these expansions, as well as the mathematical correlation between the size of the mesh and the micromechanical parameter, g, are established. Explicit expressions of Laurent series of the classical and micromechanical kernels forthe singular and hipersingular BEM integrals are presented. Treatment of singularity, both in the radial direction and in the angular direction, applied to curved triangular elements is verified. It can be observed that there is a loss of efficiency in the treatment of singularity in the angular direction, due to the presence of the boundary layer effect for distorted curved boundary elements. However, this nearly singularity effect could be alleviated by micromechanics approach, since minor boundary layer effect was observed as the parameter g is decreased. Finally, using FORTRAN 11.0 language, a computational code is developed, which includes the classic and micromechanics approach with geometric continuity G1, and its results are validated by means of Benchmark examples.

This Thesis relates to the continually advancing field of microelectromechanical systems (MEMS). With MEMS technology, there are many different areas of concentration available for research. This Thesis addresses analysis and preliminary characterization of a cantilever-type MEMS chemical sensor for detection of chemicals and organic components operating at room temperature (20˚C and sea level pressure of 1 atm). Such sensors can be useful in a wide variety of applications. There currently exist several different types of MEMS chemical sensors. Each is based on a different detection method, e.g., capacitive, thermal, resistive, etc., and is used for specific tasks. Out of all currently available detection methods, the most common is the gravimetric method. The gravimetric sensor works by absorbing the chemical in a special material, usually a polymer, which alters the overall mass of the sensing element that can then be measured, or detected, to identify the chemical absorbed. One of the more exciting developments in the field of gravimetric chemical MEMS has been with the advancement of cantilever-type sensors. These cantilevers are small and usually on the order of only about 300 m in length. In order to utilize the gravimetric method, a cantilever is coated with a polymer that allows an analyte to bond to it and change its mass, which in turn changes the resonant frequency of the cantilever. The change in frequency can then be measured and analyzed and from it, the amount of absorbed mass can be calculated. Current research in the cantilever-type resonating sensors for the detection of hydrogen is developing measurement capabilities of 1 ppm (part-per-million). In this Thesis number of sample cantilevers were qualitatively assessed and their dimensional geometry measured. Based on these measurements, frequency data were obtained. In addition, the overall uncertainty in the resonant frequency results was calculated and the contributing factors to this uncertainty were investigated. Experimental methods that include laser vibrometry, optoelectronic laser interferometric microscopy (OELIM), and atomic force microscopy (AFM), were utilized to measure the frequency responses of the samples. The analytically predicted natural frequencies were compared to the experimental data to determine correlation subject to the uncertainty analysis. Parametric analyses involving chemical absorption processes were also conducted. Such analyses considered different parameters, e.g., damping and stiffness as well as changes in their values, to determine contributions they make to the quality of the frequency data and the effect they have on sensitivity of the MEMS cantilever-type chemical sensors. Once these parametric analyses were completed, it was possible to estimate the sensitivity of the cantilever, or the ability for the cantilever to detect frequency shifts due to absorption of the target chemical. Results of the parametric analyses of the fundamental resonant frequency were then correlated with the sensitivity results based on the chemical absorption. This Thesis correlates many results and ideas and probes problems revolving around the analysis and characterization of a MEMS cantilever-type chemical sensor.

The objective of the work presented in this thesis is to implement high-Q silicon capacitive micromechanical resonators operating in the HF, VHF and UHF frequency bands. Several variations of a fully silicon-based bulk micromachining fabrication process referred to as HARPSS have been developed, characterized and optimized to overcome most of the challenges facing application of such devices as manufacturable electronic components. Several micromechanical structures for implementation of high performance capacitive silicon resonators covering various frequency ranges have been developed under this work. Design criteria and electromechanical modeling of such devices is presented. Under this work, HF and VHF resonators with quality factors in the tens of thousands and RF-compatible equivalent electrical impedances have been implemented successfully. Resonance frequencies in the GHz range with quality factors of a few thousands and lowest motional impedances reported for capacitive resonators to date have been achieved. Several resonator coupling techniques for implementation of higher order resonant systems with possibility of extension to highly selective bandpass filters have been investigated and practically demonstrated. Finally, a wafer-level vacuum sealing technique applicable to such resonators has been developed and its reliability and hermeticity is characterized.

Primary water stress corrosion cracking (SCC) of metals in pressurized water reactors (PWRs) is known to be one of the most challenging and cost intensive modes of failure in the nuclear industry. Even though it is known that cracking in Ni-base alloys proceeds mainly intergranular (IG), the initiation and propagation of cracks in ductile metals are not yet understood and a much-desired accurate prediction of SCC related failure seems unobtainable. In this thesis, a combination of microcantilever fracture experiments, scanning electron- (SEM) and transmission electron microscopy (TEM) techniques was employed to study and compare the failure of oxidized grain boundaries of Ni-base Alloy 600 with high and low intergranular carbide coverage and different sample history. A new technique for lifting-out whole cantilevers after testing and for performing 3D focussed ion beam sequencing (3D FIB-SEM) while preserving a thin central region of the cantilever for further TEM sample preparation was developed and is presented. In lieu with recent efforts of the main project sponsor Électricité de France (EDF) to build a predictive model for IGSCC based on localized/microscopic information, one of the main objectives was the extraction of the stress at failure of individual oxidized GBs. Supported by finite element simulations, microcantilever fracture tests revealed that surface oxides on top of individual GBs have the capability to alter the mechanical response by delaying/suppressing the onset of failure. An overestimation of the failure stress (> 230 MPa) was observed, proving that the presence of the surface oxide on top of the test structures cannot be neglected. The failure stress on both samples, tested without influence of the surface oxide, was found to cover a range of 300 - 600 MPa, which agreed well with finite element simulations of the tests and further demonstrates the reliability of the obtained data. The second objective was to gain a better understanding of the observed fracture behaviour and the role of local microstructure. Using the gathered microscopy data, it was found that the crack clearly favours a progression along the IG oxide-metal interface in the presence of carbide precipitates. Electron energy loss spectroscopy (EELS) revealed that the observed crack path can be linked to compositional and density variations of the IG oxide. In the presence of carbides the oxide was layered. An oxide close to the stoichiometry of chromia was located at the original GB and next to the carbides. Next to this Cr-rich oxide, Fe-rich mixed spinel oxides of varying composition and density were found. An explanation for density variations based on the possible formation of defective spinel oxides of the type A²⁺B³⁺₂O₄, due to an unavailability of certain cation species is presented. No clear interface preference was observed in the absence of precipitation, where the IG oxide was found to be thin and often incomplete with Cr-richer oxides preferentially located at the original GB. While these observations were consistent on both samples (high and low carbide coverage), bigger void-like defects were located at the Fe-richer oxide-metal interface of the cold worked sample with high IG carbide precipitation only. These weak spots seemed to be the preferred path for crack propagation on this sample. The sample with low intergranular carbide coverage showed no obvious porosities at this interface but a Cr- depleted region was seen. Introducing a multi-faceted investigation strategy, supported by finite element simulations, the presented thesis provides the most accurate determination of the failure stress of oxidized GBs on Alloy 600 to date and and adds new valuable insights to our understanding of IGSCC and the future prediction of SCC related failures.

Ce travail porte sur l'incorporation de nanorenforts biosourcés, c'est-à-dire des nanofibrilles de cellulose (NFC), dans les matériaux composites à matrice polymère et les mousses. Ces nouveaux matériaux biosourcés peuvent par exemple être utilisés pour la conception de structures sandwich. L'étude à caractère expérimental, théorique et numérique s'articule autour de trois axes visant à optimiser tant les procédés d'élaboration que les propriétés en service de ces matériaux.Dans un premier temps, la rhéologie des suspensions concentrées de NFC, fluides à seuil thixotropes, a été étudiée aux échelles macro- et mésoscopiques en utilisant un dispositif original de rhéométrie couplé à des mesures de champs cinématiques par vélocimétrie ultra-sonore. Nous montrons ainsi que l'écoulement des suspensions de NFC est fortement hétéro-gène et présente des glissements aux parois, de multiples bandes de cisaillement couplés avec des écoulements de type « bouchon ». Sur la base de cette étude, un modèle rhéolo-gique multi-échelles est proposé. Ce modèle tient compte d'une part de l'architecture aniso-trope des réseaux connectés de NFC dans ces suspensions, et d'autre part des interactions mécaniques et physico-chimiques aux échelles nanométriques. Il permet de montrer que les interactions colloïdales et hydrodynamiques, ainsi que la tortuosité et l'orientation des NFC jouent un rôle majeur sur la contrainte seuil et sur le comportement rhéofluidifiant de ces suspensions.Dans un deuxième temps, des nanocomposites à matrice polymère ont été élaborés sous forme de films en faisant varier sur une très grande plage la fraction volumique de NFC. En utilisant d'une part des techniques de microscopie (AFM, MEB) et de diffraction aux rayons X, et d'autre part des essais mécaniques (traction, DMA) nous montrons (i) que les NFC ont une orientation plane et s'organisent en réseaux connectés par des liaisons hydro-gènes, (ii) que ces réseaux jouent un rôle majeur sur le comportement mécanique des nano-composites et (iii) que le comportement élastique des nanocomposites est bien en deçà des prévisions données par les modèles micromécaniques de la littérature. De là, nous proposons un modèle multi-échelles alternatif où les principaux nano-mécanismes de déformation sont ceux se produisant dans les parties amorphes des NFC et au niveau des très nombreuses interfaces entre NFC.Enfin, nous avons étudié l'influence des conditions d'élaboration, de la nature et de la con-centration des NFC sur les microstructures (microtomographie synchrotron à rayons X), les propriétés mécaniques (essais de compression) et les micro-mécanismes de déformation (essai in situ en microtomographie) de mousses préparées par cryodessiccation de suspensions aqueuses de NFC. / This study focuses on the use of cellulose nanofibrils (NFCs) as bio-based nano-reinforcement in polymer composites and foams. These renewable materials can be used in place of traditional materials such as for instance to produce sandwich panels. This experi-mental, theoretical and numerical work aims at optimizing the processing of these NFC-based materials as well as their use properties.In the first part of this work, the rheology of concentrated NFC suspensions, that behave as thixotropic yield stress fluids, is investigated at macro- and mesoscales using an original rheo-ultrasonic velocimetry (rheo-USV) setup allowing the local flow kinematic to be obtai-ned. We show that the flow of NFC suspensions is highly heterogeneous and exhibits com-plex situations with the coexistence of wall slippage, multiple shear bands and plug-like flow bands. Using this experimental database, we develop an original multiscale rheological model for the prediction of the rheology of NFC suspensions. The model takes into account the anisotropic fibrous nature of NFC networks as well as colloidal and mechanical interaction forces occurring at the nanoscale. The model predictions prove that colloidal and hydrody-namic interaction forces together with the orientation and the wavy nature of NFCs play a major role on the yield stress and shear thinning behaviour of the suspensions.In the second part of this work, NFC-reinforced polymer nanocomposite films are processed for a wide range of NFC contents. Using advanced microscopy techniques (AFM, SEM), X-ray diffraction and mechanical tests (tensile and DMA tests), we show (i) that NFCs form highly connected nanofibrous structures with in-plane random orientation, (ii) that these connected NFC networks play a leading role on the mechanical behaviour of the nanocompo-sites and (iii) that the elastic properties of nanocomposite films are much lower than those predicted from the micromechanical models of the literature. In light of these observations, we propose an alternative multiscale model in which the main involved deformation nano-mechanisms are those occurring both in the amorphous segments of the nanofibers and in the numerous nanofiber-nanofiber contact zones.Finally, in a third part we focus on the influence of the processing conditions, the suspension type and the NFC concentration on the microstructure (using X-ray synchrotron microto-mography), the mechanical properties (using compression tests) and the deformation micro-mechanisms (using in situ compression test with X-ray microtomography) of various foams prepared from NFC suspensions by freeze-drying.

Ce travail porte sur l'endommagement des matériaux composites stratifiés utilisés notamment pour la réalisation de pièces structurales minces. La dégradation de ces matériaux induite par la création et le développement de surfaces de décohésion internes est abordée sous deux angles. Une campagne expérimentale a tout d'abord été menée sur des stratifiés en carbone-époxy réalisés par infusion de résine liquide et sollicités en traction uniaxiale. Cette étude propose une analyse originale à l'aide de trois techniques optiques permettant une caractérisation de l'endommagement par mesures de champs : cinématiques (par stéréo-corrélation d'images), thermiques (par thermographie infrarouge) et densimétriques (par tomographie à rayons X). Le second volet du travail concerne la modélisation de la microfissuration dans le contexte d'une anisotropie initiale. A cette fin, une homogénéisation bidimensionnelle de milieux orthotropes fissurés permet la prise en compte de défauts d'orientation arbitraire et des effets unilatéraux (ouverture-fermeture des microfissures) au sein d'une formulation énergétique en déformation. Sur cette base, un modèle de comportement est proposé dans le cadre de la thermodynamique des processus irréversibles avec variables internes. Des simulations numériques permettent de démontrer les capacités prédictives de la formulation, en particulier la représentation du comportement non linéaire de ces matériaux, l'interaction entre les anisotropies initiale et induite et la restitution des propriétés élastiques lors de la fermeture de défauts. / This work deals with the damage of laminated composite materials used in particular for the production of thin structural parts. The degradation of these materials induced by the creation and growth of internal microcracks is considered from two angles. An experimental campaign was first conducted on carbon-epoxy laminates made by liquid resin infusion and loaded in uniaxial tension. This study proposes an original analysis using three advanced optical techniques that allow the damage characterization through full-field measurements : kinematic (with stereo-image correlation), thermal (with infrared thermography) and density (with X-ray tomography). The second part of the work concerns the modeling of microcracking in the context of initial anisotropy. To this end, a two-dimensional homogenization of orthotropic cracked media allows consideration of arbitrary orientation of defects and unilateral effects (opening and closing of microcracks) within a strain energetic formulation. On this basis, a constitutive model is proposed in the framework of thermodynamics of irreversible processes with internal variables. Numerical simulations demonstrate the predictive capabilities of the formulation, in particular the representation of the nonlinear behavior of these materials, the interaction between initial and induced anisotropies and the recovery of elastic properties at the closure of microdefects.

Durant ces dernières décennies les matériaux composites organiques ont subi un très grand essor dans le domaine des structures aéronautiques. Leur principal avantage est d’alléger les structures tout en gardant de bonnes propriétés mécaniques. De plus, leur microstructure leur permet d’avoir un caractère multi-fonctionnel, ce qui facilite leur intégration pour remplacer les technologies existantes. Dans l’industrie aéronautique, il existe un besoin croissant de grande quantité de petite et moyenne pièces (clips, éléments de jonctions). Cependant, il est aujourd’hui difficile de fabriquer en série des pièces ayant des formes tridimensionnelles complexes par des procédés conventionnels (autoclave). Ainsi, l’orientation envisagée est d’utiliser les procédés de la « famille » automobile pour des applications aéronautiques « semi-structurales », comme le moulage par injection de composites thermoplastiques renforcés de fibres courtes. Cette application nécessite une maîtrise et une fiabilisation du procédé ainsi que des propriétés induites. Ceci a été réalisé par l’identification et la quantification des effets des paramètres qui influent significativement sur la microstructure et les propriétés macroscopiques, par un plan d’expériences. De plus, le dimensionnement de telles pièces requiert une modélisation robuste du comportement mécanique pour prédire au mieux leur capacité d’utilisation. Les données sur la microstructure ont permis d’alimenter un modèle micromécanique comportant un critère d’endommagement de l’interface fibre/matrice. Développé sur un code éléments finis industriel, il a permis de prédire les résultats expérimentaux d’une pièce industrielle. / During the last decades, organic composite materials have undergone great development in the field of aeronautical structures. Their main avantage is to reduce the structures weight while maintaining good mechanical properties. In addition, their microstructure allows them to have a multi-fuctional nature, which facilitates their integration to replace existing technologies. In the aviation industry, there is a growing need for large amount of small and medium parts (clips, connecting elements). However, nowadays it is difficult to produce parts with complex by conventional methods dimensional shapes (autoclave). Thus, the considered path is tu use methods of the automotive “family” for “semi-structual” aerospace applications such as injection-moulding of thermoplastic composites reinforced by short fibres. This application requires a mastery and reliability of the process and the induced properties. This was achieved by the identification and quantification of the parameters effects that significantly influence the microstructure and macroscopic properties, by a design of experiments. Moreover, the dimensioning of such parts requires a robust mechanical behabior modelling to predict the best use of their capacity. The data on the microstructure enable to feed a micromechanical model featuring damage criteria of the fiber/matrics interface. Developed on a industrial finite element code, it was used to predict the experimental results of an industrial part.

Neste trabalho, uma abordagem micromecânica com aproximação da geometria dada por funções de Bézier triangulares com continuidade geométrica G1 é inserida ao Método dos Elementos de Contorno, o qual é aplicado em problemas da elastostática tridimensional. Para consideração do efeito microestrutural, foi utilizado a teoria gradiente elástica simplificada de Aifantis, a qual é uma particularização da teoria geral de Mindlin. Nesta teoria, um argumento variacional é estabelecido para determinar todas as possíveis condições de contorno, clássica e não-clássica, para o problema de valor de contorno geral. A partir deste argumento, a solução fundamental da elasticidade gradiente é explicitada e com o auxílio da identidade integral recíproca é construído a representação integral de contorno. Para tornar o problema de valor de contorno bem-posto, em adição à representação integral de contorno para deslocamento, uma segunda representação integral para derivada normal do deslocamento foi utilizada. Expressões integrais para deslocamento e tensão em pontos internos são apresentadas. Todos os núcleos das equações integrais são explicitamente desenvolvidos. Para a discretização do MEC foram utilizados elementos triangulares curvos, aproximados tanto para a geometria quanto para os parâmetros físicos por funções de Proriol (com características espectrais) e por funções aqui chamadas de Polinomiais, onde esta última é construída a partir de uma base nodal equidistante e pela imposição da partição da unidade. Entretanto estas funções aproximadoras garantem apenas continuidade C0 entre os elementos triangulares, ou seja, a garantia da continuidade do plano tangente não necessariamente é satisfeita. Com o objetivo de anular o termo de integral de linha presente na formulação microestrutural, a hipótese de superfície suave se faz necessária e assim funções de Bézier com continuidade geométrica G1, a qual depende apenas da posição e das normais dos nós nos vértices da malha triangular é utilizada. Para auxiliar na obtenção das coordenadas e das normais nodais para geometrias complexas foi utilizado o software de computação gráfica BlenderTM 2.7, o qual foi acoplado ao programa do MEC elastostático gradiente. Na sequência foi verificada, por meio de exemplos, a suavidade na intersecção entre os elementos triangulares G1 e estes foram comparados com as aproximações de Proriol e Polinomial. Em seguida, as singularidades presentes nas soluções fundamentais foram tratadas através da expansão em série de Laurent aplicada à técnica de subtração de singularidade. Condições necessárias e suficientes para a convergência das expansões em série das soluções fundamentais, estimador do erro para estas expansões, assim como, a correlação matemática entre o tamanho da malha e o parâmetro micromecânico g foram estabelecidos. Expressões explicitas da série de Laurent dos núcleos das integrais singulares e hipersingulares do MEC clássico e não clássico foram apresentadas. A verificação do tratamento da singularidade aplicado a elementos triangulares curvos foi realizada, tanto na direção radial quanto na direção angular. E pôde ser observado que ocorre uma perda de eficiência no tratamento da singularidade na direção angular, devida a presença do efeito de camada limite para elementos curvos distorcidos. Entretanto, este efeito de quase singularidade pode ser amenizado por meio da abordagem micromecânica, uma vez que foi observado menor presença do efeito da camada limite à medida que o parâmetro g é diminuído. Por último, foi desenvolvido um programa na linguagem FORTRAN 11.0, o qual contempla as abordagens clássica e micromecânica com continuidade geométrica G1. Sua validação foi feita por meio de exemplos considerados Benchmarks. / In this work, a micromechanical approach with approximation of geometry solved by Bézier triangular functions that guaranty continuity G1 is inserted to the Boundary element Method (BEM). This formulation is applied in three-dimensional elastostatic problems. The simplified elastic gradient theory proposed by Aifantis, which is a particularization of the general theory of Mindlin is used to consider the microstructural effect. In this theory a variational argument is established to determine all possible boundary conditions, classical and non-classical, for the general boundary value problem. From this argument, the fundamental solution of the gradient elasticity is explicited and by the reciprocal integral identity the boundary integral representation is achieved. In addition to the boundary integral representation for dispacement, a second integral representation regarding its normal derivative is used to make the well-posed boundary value problem. Integral expressions for displacement and stress on internal points are also presented. All kernels in the integral equations are explicitly developed. Curved triangular elements are used for the discretization of the BEM. The approximation of both the geometry and physical parameters is performed by Proriol functions (with spectral characteristics) and by Polynomial functions. The last is built from an equidistant nodal basis enforcing the partition of unity. However these approximating functions ensure only C0 continuity between the triangular elements, that is, the tangent plane continuity assurance is not necessarily satisfied. In order to cancel line integral terms in the microstructural approach, the hypothesis of smooth surface is required and thus Bézier function with geometric continuity G1, which depends only on the position and the normal of the nodes at the vertices of the triangular mesh is used. In this study the computer graphics software called BlenderTM 2.7 is used to assist in obtaining coordinates and normal vectors at nodes when complex geometries are analyzed. BlenderTM 2.7 is coupled to the gradient elastic BEM program. The smoothness of the resulting mesh using G1 elements is compared to Proriol and Polynomial approximations by means of simple examples. The singularities present in the fundamental solutions are treated by employing the expansion in Laurent series and the singularity subtraction technique. Necessary and sufficient conditions for the convergence of expansions in series of fundamental solutions, error estimator for these expansions, as well as the mathematical correlation between the size of the mesh and the micromechanical parameter, g, are established. Explicit expressions of Laurent series of the classical and micromechanical kernels forthe singular and hipersingular BEM integrals are presented. Treatment of singularity, both in the radial direction and in the angular direction, applied to curved triangular elements is verified. It can be observed that there is a loss of efficiency in the treatment of singularity in the angular direction, due to the presence of the boundary layer effect for distorted curved boundary elements. However, this nearly singularity effect could be alleviated by micromechanics approach, since minor boundary layer effect was observed as the parameter g is decreased. Finally, using FORTRAN 11.0 language, a computational code is developed, which includes the classic and micromechanics approach with geometric continuity G1, and its results are validated by means of Benchmark examples.

Au cours d'une irradiation neutronique à long-terme dans les Réacteurs à Eau Pressurisée (REPs), une modification importante du comportement mécanique des matériaux utilisés dans les internes de cuve (composés des aciers inoxydables austénitiques de la série 300) est observée, y compris un durcissement et un adoucissement induit par irradiation, une perte de la ductilité et de la ténacité. Jusqu'à présent, beaucoup efforts ont été contribués pour identifier les effets d'irradiation sur l'évolution microstructurale du matériau (dislocations, boucles de Frank, cavités, ségrégation, etc.). Le gonflement induit par irradiation, considéré comme un facteur limitant la durée de fonctionnement des réacteurs, pourrait modifier les propriétés mécaniques des matériaux (plasticité, ténacité, etc), même conduire à une distorsion des structures du fait des modifications dimensionnelles entre les différentes composantes.L'objectif principal de ce travail de thèse est d'étudier qualitativement l'influence de l'effet du gonflement sur le comportement mécanique des matériaux irradiés. Un modèle micromécanique constitutif en grandes déformations basé sur les évolutions de la densité de dislocations et de défauts d'irradiation (boucles de Frank) est développé et implémenté dans les codes de calcul éléments finis ZéBuLoN et Cast3M. Les simulations numériques sont réalisées pour calculer les propriétés mécaniques d'un agrégat polycristallin. Par ailleurs, la technique d'homogénéisation est appliquée pour développer un modèle de type Gurson. Les simulations d'une cellule poreuse sont utilisés pour étudier le comportement mécanique des monocristaux poreux, en tenant compte des différents effets de la triaxialité, de la porosité et de l'orientation cristallographique, afin d'étudier l'effet de la présence des cavités sur la plasticité et la rugosité du matériau irradié à l'échelle polycristallin. / During long-time neutron irradiation occurred in Pressurized Water Reactors (PWRs), significant changes of the mechanical behavior of materials used in reactor core internals (made of 300 series austenitic stainless steels) are observed, including irradiation-induced hardening and softening, loss of ductility and toughness. So far, much effect has been made to identify radiation effects on material microstructure evolution (dislocations, Frank loops, cavities, segregation, etc.). The irradiation-induced cavity swelling, considered as a potential factor limiting the reactor lifetime, could change the mechanical properties of materials (plasticity, toughness, etc.), even lead to a structure distortion because of the dimensional modifications between different components.The principal aim of the present PhD work is to study qualitatively the influence of cavity swelling on the mechanical behaviors of irradiated materials. A micromechanical constitutive model based on dislocation and irradiation defect (Frank loops) density evolution has been developed and implemented into ZéBuLoN and Cast3M finite element codes to adapt the large deformation framework. 3D FE analysis is performed to compute the mechanical properties of a polycrystalline aggregate. Furthermore, homogenization technique is applied to develop a Gurson-type model. Unit cell simulations are used to study the mechanical behavior of porous single crystals, by accounting for various effects of stress triaxiality, of void volume fraction and of crystallographic orientation, in order to study void effect on the irradiated material plasticity and roughness at polycrystalline scale.

Les alliages de titane β-métastables biocompatibles suscitent un intérêt croissant pour les applications médicales grâce à leur comportement superélastique et/ou effet mémoire de forme, leur excellente résistance à la corrosion et leur bonne aptitude à la déformation à froid. Dans le cadre de cette thèse, un alliage superélastique Ti-26Nb et un alliage à mémoire de forme Ti-24Nb ont été élaborés en creuset froid en semi-lévitation magnétique et ont fait l'objet d'une caractérisation approfondie sur le plan microstructural et mécanique. Les mécanismes de déformation activés lors d'une sollicitation mécanique ont été identifiés pour les deux alliages au moyen d'essais de traction couplés à des mesures in-situ en diffraction des rayons X. Une procédure d'optimisation basée sur des traitements thermo-mécaniques nano-structurants a été développée pour augmenter simultanément la résistance mécanique et la superélasticité tout en conservant un bas module élastique. Un ensemble de propriétés qui conditionne la réussite de la pose d'implant en améliorant la qualité de transfert des contraintes à l'interface os/implant. Les évolutions microstructurales à l'origine de l'optimisation de ces propriétés ont été étudiées par diffraction des rayons X, microscopie électronique à transmission et essais mécaniques. Ce travail se conclut par une introduction à la modélisation micromécanique du comportement du Ti-26Nb. Les caractéristiques cristallographiques de la transformation martensitique ont été déterminées en se basant sur la théorie de Ball et James. L'influence de l'orientation cristallographique sur le comportement mécanique des monocristaux a été étudiée. / Biocompatible metastable β-titanium alloys have attracted much attention for biomedical applications in recent years thanks to their superelastic and/or shape memory behavior, their superior corrosion resistance and their excellent cold workability. In this present study, a superelastic Ti-26Nb alloy and a shape memory Ti-24Nb alloy were produced by the cold crucible levitation melting method. A detailed microstructural and mechanical characterization were performed. The deformation mechanisms occurring during uniaxial deformation were identified for these two alloys by coupling in situ tensile testing with X-ray diffraction measurement. An optimization route based on nanostructuring process was developed in order to enhance both strength and superelasticity while keeping a low elastic modulus. These properties are required to improve the load transfer along the bone/implant interface which is essential to the success of implants. The microstructural evolution during the thermomechanical process resulting in the optimization of properties was investigated through tensile tests, X-ray diffraction and transmission electron microcopy. The last part of this study deals with an introduction of micromechanical modeling of the Ti-26Nb behavior. The crystallographic features of the martensitic transformation were determined by applying the Ball and James theory. The influence of the crystallographic orientation on the mechanical response was investigated for tension and compression.