Orientador: Paulo Sollero / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-10T03:16:07Z (GMT). No. of bitstreams: 1 Paiva_SeilaVastiFariade_M.pdf: 1387945 bytes, checksum: 04ad3c76f01698f24ef5fd7ebfb49264 (MD5) Previous issue date: 2006 / Resumo: Nesta dissertação é apresentada uma análise de problemas da mecânica da fratura elástica linear em estruturas bimateriais anisotrópicas. Utilizando o método dos elementos de contorno é possível calcular os fatores de intensidade de tensão em problemas planos (2D) devido à presença de trincas interfaciais entre as lâminas que compõem o material. A estrutura pode estar submetida à carregamento em modo I ou modo misto. O problema é modelado usando-se a técnica de sub-regiões para descrever cada um dos diferentes subdomínios, representado por cada material. Na interface das sub-regiões, em que o domínio é dividido, são impostas condições de equilíbrio de forças e continuidade de deslocamentos, exceto na região que corresponde à trinca. O comportamento singular apresentado pelo campo de tensões próximo à ponta da trinca é modelado com elementos de ponto a um quarto com singularidade de forças de superfície. São apresentados exemplos numéricos de problemas com carregamentos no plano. Foi também apresentada a análise de convergência de malhas, mostrando uma pequena dependência da discretização mesmo quando malhas pouco refinadas foram usadas. Alguns dos exemplos têm correspondentes na literatura, os quais foram utilizados para comparação com os resultados obtidos. Observou-se uma boa concordância na comparação dos resultados / Abstract: This thesis presents an analysis of problems of linear elastic fracture mechanics in anisotropic bimaterial structures. Using the boundary element method, it is possible to evaluate stress intensity factors in plane problems (2D) due to the presence of interfacial cracks between the laminae that constitute the material, when the structure is submitted to a mode I or in mixed mode loading. The problem is modeled using the subregion technique to describe each one of the different subdomains, represented by each material. On the interface of subregions, which the domain is divided, conditions of tractions equilibrium and displacements continuity are imposed, except in the corresponding crack region. The singular behavior presented by the stress field near the crack tip is modeled by traction singular quarter point element. Numerical examples of problems with in-plane loading are presented. Mesh convergence analyses are also presented, showing little dependence on the discretization even when coarse meshes were used. Some of these examples have correspondents in literature, that were used for comparisons with the obtained results. A good agreement in the comparisons of results was observed. / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Anisotropic tertiary creep damage formulations have become an increasingly important prediction technique for high temperature components due to drives in the gas turbine industry for increased combustion chamber exit pressures, temperature, and the use of anisotropic materials such as metal matrix composites and directionally-solidified (DS) Ni-base superalloys. Typically, isotropic creep damage formulations are implemented for simple cases involving a uniaxial state of stress; however, these formulations can be further developed for multiaxial states of stress where materials are found to exhibit induced anisotropy. In addition, anisotropic materials necessitate a fully-developed creep strain tensor. This thesis describes the development of a new anisotropic tertiary creep damage formulation implemented in a general-purpose finite element analysis (FEA) software. Creep deformation and rupture tests are conducted on L, T, and 45°-oriented specimen of subject alloy DS GTD-111. Using the Kachanov-Rabotnov isotropic creep damage formulation and the optimization software uSHARP, the damage constants associated with the creep tests are determined. The damage constants, secondary creep, and derived Hill Constants are applied directly into the improved formulation. Comparison between the isotropic and improved anisotropic creep damage formulations demonstrates modeling accuracy. An examination of the off-axis creep strain terms using the improved formulation is conducted. Integration of the isotropic creep damage formulation provides time to failure predictions which are compared with rupture tests. Integration of the improved anisotropic creep damage produces time to failure predictions at intermediate orientations and any state of stress. A parametric study examining various states of stress, and materials orientations is performed to verify the flexibility of the improved formulation. A parametric exercise of the time to failure predictions for various levels of uniaxial stress is conducted.

Le sujet de l'étude concerne la caractérisation thermique à hautes températures de matériaux anisotropes dont la diffusivité thermique varie selon la direction considérée. Cette mesure de la diffusivité est permise par l'observation des variations transitoires de température d'un matériau soumis à un flux de chaleur de type impulsionnel. L’excitation provient d’un Laser et la mesure de température est réalisée par thermographie infrarouge sur la face opposée à l'excitation thermique. Le champ de température ainsi obtenu permet de déterminer les trois diffusivités du matériau selon ses directions d'anisotropie. En effet, grâce à des transformations intégrales du champ de température, il est possible d'obtenir un modèle théorique décrivant les variations de température au sein du matériau. Les estimations des diffusivités s'obtiennent alors par la minimisation de la somme des écarts quadratiques entre les modèles théoriques et leurs équivalents expérimentaux. Il s'agit de problèmes d'optimisation non linéaire et les estimations sont réalisées dans le domaine des fréquences spatiales et dans le temps grâce à une inversion numérique de Laplace. Basée sur des dispositifs optiques, cette méthode est non intrusive et grâce aux modèles analytiques les mesures sont rapides et précises même à haute température. La méthode ainsi que le nouveau banc expérimental mis en place rendent possible la mesure des trois diffusivités en une unique expérience pour des excitations de forme quelconque en espace et non nécessairement Dirac en temps / The study concerns the thermal characterization at high temperatures of anisotropic materials whose thermal diffusivity varies according to the direction considered. This measurement of diffusivity is allowed by the observation of the transient variations of temperature of a material subjected to a heat pulse source. The excitation is performed by a Laser and the temperature measurement is carried out by infrared thermography on the opposite face of the thermal excitation. The temperature field thus obtained makes it possible to determine the three diffusivities of the material according to its directions of anisotropy. Indeed, thanks to integral transforms of the temperature field, it is possible to obtain a theoretical model describing the temperature variations within the material. The estimates of diffusivities are then obtained by the minimization of the sum of squared residuals between the theoretical models and their experimental equivalents. These are problems of nonlinear optimization and the estimations are carried out in the spatial frequency domain and in time thanks to a numerical inversion of Laplace. Based on optical devices this method is non-intrusive and thanks to the use of analytical models the estimations are fast and accurate even at high temperatures. The method and the new experimental facility make it possible to estimate the three thermal diffusivities in a single experiment and this for excitations of any shape in space and not necessarily Dirac’s delta function in time

Este trabalho tem por objetivo a extensão de métodos numéricos baseados em diferenças finitas no domínio do tempo (FDTD) e no domínio da freqüência (FD-BPM) para a simulação da propagação de ondas eletromagnéticas em materiais com propriedades ópticas diversas, por exemplo, isotrópicos, anisotrópicos, lineares, não-lineares, bem como a combinação destes em uma mesma estrutura. Inicialmente foram elaborados formalismos bidimensionais (FDTD e FD-BPM), dos quais foram investigados modos com polarização TM (Magnético Transversal) que se propagam em estruturas planares magnetoópticas/não-lineares/lineares. Esta polarização foi escolhida tendo em vista o campo magnetostático dc adotado, o qual possibilitou a observação do fenômeno não-recíproco associado ao não-linear simultaneamente. Por outro lado, é bem sabido que o método FDTD é computacionalmente muito intensivo. Portanto, um grande esforço foi dedicado aos formalismos no domínio da freqüência, os quais foram implementados em duas e três dimensões. Este último foi estendido para um formalismo totalmente vetorial, capaz de simular modos híbridos ou até mesmo a transferência de energia entre modos de polarizações ortogonais. Isto nos permitiu investigar geometrias ainda mais complexas, tais como um isolador óptico baseado em um guia de onda tip rib utilizando material magnetooptico. Adicionalmente, fenômenos de natureza complexa, tais como a dinâmica dos condensados de luz em materiais com não-lineares do tipo Kerr com saturação, também conhecidos como meios não-lineares cúbico-qüínticos, foram investigados pela primeira vez com um formalismo vetorial. Finalmente, métodos numéricos capazes de considerar qualquer combinação de materiais com propriedades ópticas distintas (linear e/ou não-linear e/ou magnetoóptico) são uma ferramenta extraordinária para a comunidade científica para o projeto de novos dispositivos ópticos, bem como a investigação de novos efeitos físicos com vistas à aplicações em computação óptica, que podem resultar em um menor e mais eficiente número de componentes para sistemas de comunicações ópticos. / This work introduces three improved formalisms for the analysis of electromagnetic wave propagation through materials with distinct optical properties, i.e., isotropic, anisotropic, linear, nonlinear, or any combination of them. Two finite difference approaches were extensively investigated in this work for this purpose, namely the finite difference in time domain (FDTD), and the finite difference beam propagation method (2D and 3D FD-BPM), these in frequency domain. Initially, a TM (transverse magnetic) mode propagating through a planar magnetooptic/nonlinear/linear waveguide was investigated by way of a two-dimensional formalism (FDTD and FD-BPM). This mode polarization was chosen based on the orientation of the external magnetostatic field adopted, which favored the observation of non-reciprocal and nonlinear effects simultaneously. On the other hand, it is well known that FDTD formalisms are computationally intensives. Therefore, a great effort was dedicated to its frequency domain counterpart (FD-BPM), which was implemented in two and three dimensions. The later was further extended to a fully vectorial formalism, which is capable of simulating hybrid modes or even the energy transfer between orthogonal modes. This enabled us to investigate more complex geometries, such as an optical isolator based on magnetooptic rib waveguide. Additionally, complex phenomena, such as the dynamic of light condensates in bulk nonlinear Kerr media with saturation, also known as cubic-quintic nonlinear media, were investigated for the first time with a 3D vectorial formalism. Finally, numerical methods capable of handling any combination of materials with distinct optical properties (linear and/or nonlinear and/or magnetooptic) are an extraordinary tool for the scientific community for the design of new optical devices, as well as the investigation of new physical effects aimed for optical computing, that may result in fewer and more efficient components for optical communication systems.

Este trabalho tem por objetivo a extensão de métodos numéricos baseados em diferenças finitas no domínio do tempo (FDTD) e no domínio da freqüência (FD-BPM) para a simulação da propagação de ondas eletromagnéticas em materiais com propriedades ópticas diversas, por exemplo, isotrópicos, anisotrópicos, lineares, não-lineares, bem como a combinação destes em uma mesma estrutura. Inicialmente foram elaborados formalismos bidimensionais (FDTD e FD-BPM), dos quais foram investigados modos com polarização TM (Magnético Transversal) que se propagam em estruturas planares magnetoópticas/não-lineares/lineares. Esta polarização foi escolhida tendo em vista o campo magnetostático dc adotado, o qual possibilitou a observação do fenômeno não-recíproco associado ao não-linear simultaneamente. Por outro lado, é bem sabido que o método FDTD é computacionalmente muito intensivo. Portanto, um grande esforço foi dedicado aos formalismos no domínio da freqüência, os quais foram implementados em duas e três dimensões. Este último foi estendido para um formalismo totalmente vetorial, capaz de simular modos híbridos ou até mesmo a transferência de energia entre modos de polarizações ortogonais. Isto nos permitiu investigar geometrias ainda mais complexas, tais como um isolador óptico baseado em um guia de onda tip rib utilizando material magnetooptico. Adicionalmente, fenômenos de natureza complexa, tais como a dinâmica dos condensados de luz em materiais com não-lineares do tipo Kerr com saturação, também conhecidos como meios não-lineares cúbico-qüínticos, foram investigados pela primeira vez com um formalismo vetorial. Finalmente, métodos numéricos capazes de considerar qualquer combinação de materiais com propriedades ópticas distintas (linear e/ou não-linear e/ou magnetoóptico) são uma ferramenta extraordinária para a comunidade científica para o projeto de novos dispositivos ópticos, bem como a investigação de novos efeitos físicos com vistas à aplicações em computação óptica, que podem resultar em um menor e mais eficiente número de componentes para sistemas de comunicações ópticos. / This work introduces three improved formalisms for the analysis of electromagnetic wave propagation through materials with distinct optical properties, i.e., isotropic, anisotropic, linear, nonlinear, or any combination of them. Two finite difference approaches were extensively investigated in this work for this purpose, namely the finite difference in time domain (FDTD), and the finite difference beam propagation method (2D and 3D FD-BPM), these in frequency domain. Initially, a TM (transverse magnetic) mode propagating through a planar magnetooptic/nonlinear/linear waveguide was investigated by way of a two-dimensional formalism (FDTD and FD-BPM). This mode polarization was chosen based on the orientation of the external magnetostatic field adopted, which favored the observation of non-reciprocal and nonlinear effects simultaneously. On the other hand, it is well known that FDTD formalisms are computationally intensives. Therefore, a great effort was dedicated to its frequency domain counterpart (FD-BPM), which was implemented in two and three dimensions. The later was further extended to a fully vectorial formalism, which is capable of simulating hybrid modes or even the energy transfer between orthogonal modes. This enabled us to investigate more complex geometries, such as an optical isolator based on magnetooptic rib waveguide. Additionally, complex phenomena, such as the dynamic of light condensates in bulk nonlinear Kerr media with saturation, also known as cubic-quintic nonlinear media, were investigated for the first time with a 3D vectorial formalism. Finally, numerical methods capable of handling any combination of materials with distinct optical properties (linear and/or nonlinear and/or magnetooptic) are an extraordinary tool for the scientific community for the design of new optical devices, as well as the investigation of new physical effects aimed for optical computing, that may result in fewer and more efficient components for optical communication systems.

This thesis explores using multi-scale topology optimization (TO) by utilizing inverse homogenization to automate the adjustment of each unit-cell's geometry and placement in a lattice structure within a pressure vessel (the design domain) to achieve desired structural properties. The aim is to find the optimal material distribution within the design domain as well as desired material properties at each discretized element and use machine learning (ML) to map microstructures with corresponding prescribed effective properties. Effective properties are obtained through homogenization, where microscopic properties are upscaled to macroscopic ones. The symmetry group of a unit-cell's elasticity tensor can be utilized for stiffness directional tunability, i.e., to tune the cell's performance in different load directions.  A few geometrical variations of a chosen unit-cell were homogenized to build an effective anisotropic elastic material model by obtaining their effective elasticity. The symmetry group and the stiffness directionality of the cells’ effective elasticity tensors were identified. This was done using both the pattern of the matrix representation of the effective elasticity tensor and the roots of the monoclinic distance function. A cell library of symmetry-preserving variations with a corresponding material property space was created, displaying the achievable properties within the library. Two ML models were implemented to map material properties to appropriate cells. A TO algorithm was also implemented to produce an optimal material distribution within a design domain of a pressure vessel in 2D to maximize stiffness. However, the TO algorithm to obtain desired material properties for each element in the domain was not realized within the time frame of this thesis.  The cells were successfully homogenized. The effective elasticity tensor of the chosen cell was found to belong to the cubic symmetry group in its natural coordinate system. The results suggest that the symmetry group of an elasticity tensor retrieved through numerical experiments can be identified using the monoclinic distance function. If near-zero minima are present, they can be utilized to find the natural coordinate system. The cubic symmetry allowed the cell library's material property space to be spanned by only three elastic constants, derived from the elasticity matrix. The orthotropic symmetry group can enable a greater directional tunability and design flexibility than the cubic one. However, materials exhibiting cubic symmetry can be described by fewer material properties, limiting the property space, which could make the multi-scale TO less complex. The ML models successfully predicted the cell parameters for given elastic constants with satisfactory results. The TO algorithm was successfully implemented. Two different boundary condition cases were used – fixing the domain’s corner nodes and fixing the middle element’s nodes. The latter was found to produce more sensible results. The formation of a cylindrical outer shape could be distinguished in the produced material design, which was deemed reasonable since cylindrical pressure vessels are consistent with engineering practice due to their inherent ability to evenly distribute load. The TO algorithm must be extended to include the elastic constants as design variables to enable the multi-scale TO.

Apresenta-se um estudo, por meio do método dos elementos finitos, de problemas quase-estáticos de trincas em materiais anisotrópicos. Os fatores de intensidade de tensão em modo misto de carregamento foram determinados utilizando-se as metodologias da integral Jk, da correlação dos deslocamentos e da integral de fechamento de trinca modificada. Para a integral Jk, foi desenvolvida uma formulação baseada nas leis da conservação da elasto-estática e das integrais independentes do percurso. Na expressão, para a integral J2 levou-se em consideração o termo não singular da representação analítica do campo de tensões. Desta forma, foi obtida uma expressão analítica para a descontinuidade na densidade de energia de deformação, presente na integral J2. Com os valores da integral Jk, os fatores de intensidade de tensão puderam ser determinados diretamente. Com a mesma sistemática, desenvolvida para a integral J2, determinou-se a integral J1 para problemas envolvendo carregamento nas faces da trinca. Os resultados obtidos estão de acordo com os resultados presentes na literatura considerando ortotropia de material, ainda que para algumas configurações o mesmo é tratado como um caso de anisotropia geral. Assim como a integral J1 a integral J2 mostrou-se independente do contorno envolvendo a ponta da trinca. / A study is proposed based on crack quasi-static problems in anisotropic materials by the finite element method. The mixed-mode stress intensity factors were determined by the Jk integral, displacement correlation and modified crack closure integral methodologies. The Jk integral was derived from a conservation law of linear elasticity theory. In the formulation to obtain the J2 integral the non-singular term in the stress fields was considered. An analytical expression was obtained to discontinuity of the strain energy density in the crack faces, presented by J2 integral. A similar approach was applied to determine J1 integral in crack surface traction problems. The results confer with the results present in the literature considering orthotropic materials. In some configurations the problem is treated from general anisotropy theory. In the same way that J1 integral the path-independence property was established to J2 integral.

Apresenta-se um estudo, por meio do método dos elementos finitos, de problemas quase-estáticos de trincas em materiais anisotrópicos. Os fatores de intensidade de tensão em modo misto de carregamento foram determinados utilizando-se as metodologias da integral Jk, da correlação dos deslocamentos e da integral de fechamento de trinca modificada. Para a integral Jk, foi desenvolvida uma formulação baseada nas leis da conservação da elasto-estática e das integrais independentes do percurso. Na expressão, para a integral J2 levou-se em consideração o termo não singular da representação analítica do campo de tensões. Desta forma, foi obtida uma expressão analítica para a descontinuidade na densidade de energia de deformação, presente na integral J2. Com os valores da integral Jk, os fatores de intensidade de tensão puderam ser determinados diretamente. Com a mesma sistemática, desenvolvida para a integral J2, determinou-se a integral J1 para problemas envolvendo carregamento nas faces da trinca. Os resultados obtidos estão de acordo com os resultados presentes na literatura considerando ortotropia de material, ainda que para algumas configurações o mesmo é tratado como um caso de anisotropia geral. Assim como a integral J1 a integral J2 mostrou-se independente do contorno envolvendo a ponta da trinca. / A study is proposed based on crack quasi-static problems in anisotropic materials by the finite element method. The mixed-mode stress intensity factors were determined by the Jk integral, displacement correlation and modified crack closure integral methodologies. The Jk integral was derived from a conservation law of linear elasticity theory. In the formulation to obtain the J2 integral the non-singular term in the stress fields was considered. An analytical expression was obtained to discontinuity of the strain energy density in the crack faces, presented by J2 integral. A similar approach was applied to determine J1 integral in crack surface traction problems. The results confer with the results present in the literature considering orthotropic materials. In some configurations the problem is treated from general anisotropy theory. In the same way that J1 integral the path-independence property was established to J2 integral.