This study focuses on developing explicit analytical and numerical process models for mechanical micro-machining of heterogeneous materials. These models are used to select suitable process parameters for preparing and micro-machining of these advanced materials. The material system studied in this research is Magnesium Metal Matrix Composites (Mg-MMCs) reinforced with nano-sized and micro-sized silicon carbide (SiC) particles. This research is motivated by increasing demands of miniaturized components with high mechanical performance in various industries. Mg-MMCs become one of the best candidates due to its light weight, high strength, and high creep/wear resistance. However, the improved strength and abrasive nature of the reinforcements bring great challenges for the subsequent micro-machining process. Systematic experimental investigations on the machinability of Mg-MMCs reinforced with SiC nano-particles have been conducted. The nanocomposites containing 5 Vol.%, 10 Vol.% and 15 Vol.% reinforcements, as well as pure magnesium, are studied by using the Design of Experiment (DOE) method. Cutting forces, surface morphology and surface roughness are characterized to understand the machinability of the four materials. Based on response surface methodology (RSM) design, experimental models and related contour plots have been developed to build a connection between different materials properties and cutting parameters. Those models can be used to predict the cutting force, the surface roughness, and then optimize the machining process. An analytical cutting force model has been developed to predict cutting forces of MgMMCs reinforced with nano-sized SiC particles in the micro-milling process. This model is iv different from previous ones by encompassing the behaviors of reinforcement nanoparticles in three cutting scenarios, i.e., shearing, ploughing and elastic recovery. By using the enhanced yield strength in the cutting force model, three major strengthening factors are incorporated, including load-bearing effect, enhanced dislocation density strengthening effect and Orowan strengthening effect. In this way, the particle size and volume fraction, as significant factors affecting the cutting forces, are explicitly considered. In order to validate the model, various cutting conditions using different size end mills (100 µm and 1 mm dia.) have been conducted on Mg-MMCs with volume fraction from 0 (pure magnesium) to 15 Vol.%. The simulated cutting forces show a good agreement with the experimental data. The proposed model can predict the major force amplitude variations and force profile changes as functions of the nanoparticles’ volume fraction. Next, a systematic evaluation of six ductile fracture models has been conducted to identify the most suitable fracture criterion for micro-scale cutting simulations. The evaluated fracture models include constant fracture strain, Johnson-Cook, Johnson-Cook coupling criterion, Wilkins, modified Cockcroft-Latham, and Bao-Wierzbicki fracture criterion. By means of a user material subroutine (VUMAT), these fracture models are implemented into a Finite Element (FE) orthogonal cutting model in ABAQUS/Explicit platform. The local parameters (stress, strain, fracture factor, velocity fields) and global variables (chip morphology, cutting forces, temperature, shear angle, and machined surface integrity) are evaluated. Results indicate that by coupling with the damage evolution, the capability of Johnson-Cook and Bao-Wierzbicki can be further extended to predict accurate chip morphology. Bao-Wierzbiki-based coupling model provides the best simulation results in this study. v The micro-cutting performance of MMCs materials has also been studied by using FE modeling method. A 2-D FE micro-cutting model has been constructed. Firstly, homogenized material properties are employed to evaluate the effect of particles’ volume fraction. Secondly, micro-structures of the two-phase material are modeled in FE cutting models. The effects of the existing micro-sized and nano-sized ceramic particles on micro-cutting performance are carefully evaluated in two case studies. Results show that by using the homogenized material properties based on Johnson-Cook plasticity and fracture model with damage evolution, the micro-cutting performance of nano-reinforced Mg-MMCs can be predicted. Crack generation for SiC particle reinforced MMCs is different from their homogeneous counterparts; the effect of micro-sized particles is different from the one of nano-sized particles. In summary, through this research, a better understanding of the unique cutting mechanism for particle reinforced heterogeneous materials has been obtained. The effect of reinforcements on micro-cutting performance is obtained, which will help material engineers tailor suitable material properties for special mechanical design, associated manufacturing method and application needs. Moreover, the proposed analytical and numerical models provide a guideline to optimize process parameters for preparing and micro-machining of heterogeneous MMCs materials. This will eventually facilitate the automation of MMCs’ machining process and realize high-efficiency, high-quality, and low-cost manufacturing of composite materials.

Este trabalho trata da análise da propagação de fissuras, independente do tempo, em domínios bidimensionais utilizando uma formulação alternativa do método dos elementos de contorno (MEC). O MEC vem sendo utilizado com sucesso na análise de diversos problemas de engenharia. Considerando problemas de mecânica da fratura, o MEC é especialmente eficiente devido à redução da dimensionalidade de sua malha, o que permite a simulação do crescimento das fissuras sem as dificuldades do processo de remalhamento. Nesta pesquisa, desenvolvem-se formulações não lineares do MEC para a análise da propagação de fissuras em materiais quase frágeis. Nesses materiais, a zona de processo à frente da ponta da fissura introduz efeitos fisicamente não lineares no comportamento estrutural. Assim, para a simulação da presença da zona de processo, modelos não lineares são necessários. Classicamente a formulação dual do MEC é utilizada para modelar propagação de fissuras na quais equações singulares e hipersingulares são escritas para elementos definidos ao longo das faces das fissuras. O presente trabalho propõe uma segunda formulação utilizando um campo de tensões iniciais para a representação da zona coesiva. Nesta formulação, o termo de domínio da equação integral clássica do MEC é degenerado, de forma a atuar somente ao longo do caminho de crescimento das fissuras, sendo que esse procedimento dá origem a uma nova variável denominada dipolo, responsável por garantir o atendimento das condições de contorno. Em conjunto com essa nova formulação, se propõe o uso do operador tangente (OT), que é deduzido no trabalho, a fim de acelerar o processo de convergência da solução. Os resultados obtidos, por meio da formulação alternativa, são comparados tanto com dados experimentais quanto com o MEC dual, ambos disponíveis na literatura. As respostas encontradas foram satisfatórias no sentido de conseguir reproduzir o comportamento real da estrutura explorando as vantagens computacionais proporcionadas pelo OT. / This work presents a time-independent crack propagation analysis, in two-dimensional domains, using an alternative boundary element method (BEM) formulation. BEM has been used successfully to analyze several engineering problems. Considering fracture mechanics problems, BEM is especially efficient due to its mesh reduction aspects, which allows the simulation of crack growth without remeshing difficulties. In this research, nonlinear BEM formulations are develop in order to analyze crack propagation in quasi-brittle materials. Considering these materials, the process zone ahead of the crack tip leads to nonlinear effects related to structural behavior. Thus, nonlinear models are required for simulating the presence of the process zone. Classically, the dual BEM is used for modeling the crack propagation, in which singular and hyper-singular equations are written for elements defined along the crack faces. This work proposes an alternative formulation using the initial stress field to represent the cohesive zone. In this formulation, the classic domain integral term is degenerated in order to be non-null only at the crack growth path. This procedure leads the creation of new variable called dipole, which is responsible for ensuring the compliance of the boundary conditions. In addition to this new formulation, it is proposed the use of the tangent operator (TO), which is derived in this work, in order to accelerate the convergence. The results obtained using the new formulation, are compared with experimental data and dual BEM results available in the literature. The responses were found satisfactory in reproducing the behavior of real structures exploiting the computational advantages provided by the TO.

O presente trabalho trata do desenvolvimento de formulações numéricas para avaliar o comportamento mecânico de estruturas compostas planas, no contexto de elasticidade linear e mecânica da fratura não linear. As formulações propostas são baseadas no Método dos Elementos de Contorno (MEC), por meio das representações integrais singular e hiper singular dos problemas elastostáticos. A técnica de multi-regiões é considerada para acoplar a interface de sólidos multifásicos. O MEC é uma técnica numérica robusta e precisa para analisar o fenômeno da fratura em sólidos. Esse método numérico apresenta uma natural redução na dimensionalidade do problema, tornando mais simples a modelagem das superfícies de fratura. Além disso, essa redução de dimensionalidade faz também com que o tratamento de interfaces materiais em estruturas compostas seja uma tarefa menos árdua. Com o uso da solução fundamental de Kelvin nas representações integrais, materiais isotrópicos podem ser considerados para constituir as estruturas compostas. Por outro lado, utilizando a solução fundamental de Cruse & Swedlow, também é possível lidar, de maneira geral, com materiais anisotrópicos em estruturas compostas. Nessas estruturas, as fraturas são assumidas como ocorrendo ao longo das interfaces e o comportamento não linear é introduzido pelo modelo coesivo de fratura, o qual é aplicável a materiais quase frágeis. Nessas análises, o sistema não linear de equações pode ser solucionado utilizando dois distintos algoritmos de resolução iterativa. O primeiro sempre leva em consideração a rigidez elástica da estrutura e é, portanto denominado Operador Constante (OC). Já o segundo é denominado Operador Tangente (OT), pois considera uma rigidez tangente à resposta estrutural não linear, o que resulta em melhores taxas de convergência em comparação ao OC. Como aplicações das formulações, estruturas compostas teóricas foram analisadas em regime elástico. Além disso, testes experimentais de fratura em espécimes de concreto e madeira também foram simulados. A comparação dos resultados com as referências demonstrou que, as formulações foram efetivas e precisas para avaliar respostas mecânicas de estruturas, seja em regime elástico linear ou nos testes de fratura quase frágil. / The present work deals the development of numerical formulations to evaluate the mechanical behaviour of plane composed structures, in the context of linear elasticity and nonlinear fracture mechanics. The proposed formulations are based on the Boundary Element Method (BEM), through its classical singular and hyper singular integral equations. The multi-region technique is adopted to couple the interfaces of non-homogeneous multiphase bodies. The BEM is a robust and accurate numerical technique to analyse fracture phenomena in solids. This numerical method presents a mesh dimensionality reduction, which makes easier the modelling of cracks surfaces. Besides, this dimensionality reduction also makes the treatment of interfaces in composed structures a less complex task. Considering the use of Kelvin fundamental solutions at the integrals equations, isotropic materials can be represent as parts of the composed structures. On the other hand, using Cruse & Swedlow fundamental solution it is also possible to deal with general anisotropic materials. At the composed structures, cracks can propagate along the materials interfaces and the cohesive crack model is responsible for the nonlinear structural behaviour of the quasi-brittle failures. The nonlinear system of equations at the fracture analyses is solved using two different algorithms for iterative resolution. The first always takes into account the structure elastic strength and, hence it is called Constant Operator (CO). On the other hand, the second is denominated Tangent Operator (TO) due to the fact that it considers strengths at the tangent directions of the nonlinear structural response. Therefore, convergence rates are faster when compared with the CO. As applications, composed structures were analysed with the developed formulations in linear elastic range. In addition, experimental fracture testes performed in concrete and wood specimens were also analysed. The confront of obtained results with the reference ones show that, the formulation was effective and accurate to evaluate the mechanical responses of composed structures in linear elastic range, and also to perform nonlinear quasi-brittle fracture tests.

Este trabalho trata da análise da propagação de fissuras, independente do tempo, em domínios bidimensionais utilizando uma formulação alternativa do método dos elementos de contorno (MEC). O MEC vem sendo utilizado com sucesso na análise de diversos problemas de engenharia. Considerando problemas de mecânica da fratura, o MEC é especialmente eficiente devido à redução da dimensionalidade de sua malha, o que permite a simulação do crescimento das fissuras sem as dificuldades do processo de remalhamento. Nesta pesquisa, desenvolvem-se formulações não lineares do MEC para a análise da propagação de fissuras em materiais quase frágeis. Nesses materiais, a zona de processo à frente da ponta da fissura introduz efeitos fisicamente não lineares no comportamento estrutural. Assim, para a simulação da presença da zona de processo, modelos não lineares são necessários. Classicamente a formulação dual do MEC é utilizada para modelar propagação de fissuras na quais equações singulares e hipersingulares são escritas para elementos definidos ao longo das faces das fissuras. O presente trabalho propõe uma segunda formulação utilizando um campo de tensões iniciais para a representação da zona coesiva. Nesta formulação, o termo de domínio da equação integral clássica do MEC é degenerado, de forma a atuar somente ao longo do caminho de crescimento das fissuras, sendo que esse procedimento dá origem a uma nova variável denominada dipolo, responsável por garantir o atendimento das condições de contorno. Em conjunto com essa nova formulação, se propõe o uso do operador tangente (OT), que é deduzido no trabalho, a fim de acelerar o processo de convergência da solução. Os resultados obtidos, por meio da formulação alternativa, são comparados tanto com dados experimentais quanto com o MEC dual, ambos disponíveis na literatura. As respostas encontradas foram satisfatórias no sentido de conseguir reproduzir o comportamento real da estrutura explorando as vantagens computacionais proporcionadas pelo OT. / This work presents a time-independent crack propagation analysis, in two-dimensional domains, using an alternative boundary element method (BEM) formulation. BEM has been used successfully to analyze several engineering problems. Considering fracture mechanics problems, BEM is especially efficient due to its mesh reduction aspects, which allows the simulation of crack growth without remeshing difficulties. In this research, nonlinear BEM formulations are develop in order to analyze crack propagation in quasi-brittle materials. Considering these materials, the process zone ahead of the crack tip leads to nonlinear effects related to structural behavior. Thus, nonlinear models are required for simulating the presence of the process zone. Classically, the dual BEM is used for modeling the crack propagation, in which singular and hyper-singular equations are written for elements defined along the crack faces. This work proposes an alternative formulation using the initial stress field to represent the cohesive zone. In this formulation, the classic domain integral term is degenerated in order to be non-null only at the crack growth path. This procedure leads the creation of new variable called dipole, which is responsible for ensuring the compliance of the boundary conditions. In addition to this new formulation, it is proposed the use of the tangent operator (TO), which is derived in this work, in order to accelerate the convergence. The results obtained using the new formulation, are compared with experimental data and dual BEM results available in the literature. The responses were found satisfactory in reproducing the behavior of real structures exploiting the computational advantages provided by the TO.

O presente trabalho trata do desenvolvimento de formulações numéricas para avaliar o comportamento mecânico de estruturas compostas planas, no contexto de elasticidade linear e mecânica da fratura não linear. As formulações propostas são baseadas no Método dos Elementos de Contorno (MEC), por meio das representações integrais singular e hiper singular dos problemas elastostáticos. A técnica de multi-regiões é considerada para acoplar a interface de sólidos multifásicos. O MEC é uma técnica numérica robusta e precisa para analisar o fenômeno da fratura em sólidos. Esse método numérico apresenta uma natural redução na dimensionalidade do problema, tornando mais simples a modelagem das superfícies de fratura. Além disso, essa redução de dimensionalidade faz também com que o tratamento de interfaces materiais em estruturas compostas seja uma tarefa menos árdua. Com o uso da solução fundamental de Kelvin nas representações integrais, materiais isotrópicos podem ser considerados para constituir as estruturas compostas. Por outro lado, utilizando a solução fundamental de Cruse & Swedlow, também é possível lidar, de maneira geral, com materiais anisotrópicos em estruturas compostas. Nessas estruturas, as fraturas são assumidas como ocorrendo ao longo das interfaces e o comportamento não linear é introduzido pelo modelo coesivo de fratura, o qual é aplicável a materiais quase frágeis. Nessas análises, o sistema não linear de equações pode ser solucionado utilizando dois distintos algoritmos de resolução iterativa. O primeiro sempre leva em consideração a rigidez elástica da estrutura e é, portanto denominado Operador Constante (OC). Já o segundo é denominado Operador Tangente (OT), pois considera uma rigidez tangente à resposta estrutural não linear, o que resulta em melhores taxas de convergência em comparação ao OC. Como aplicações das formulações, estruturas compostas teóricas foram analisadas em regime elástico. Além disso, testes experimentais de fratura em espécimes de concreto e madeira também foram simulados. A comparação dos resultados com as referências demonstrou que, as formulações foram efetivas e precisas para avaliar respostas mecânicas de estruturas, seja em regime elástico linear ou nos testes de fratura quase frágil. / The present work deals the development of numerical formulations to evaluate the mechanical behaviour of plane composed structures, in the context of linear elasticity and nonlinear fracture mechanics. The proposed formulations are based on the Boundary Element Method (BEM), through its classical singular and hyper singular integral equations. The multi-region technique is adopted to couple the interfaces of non-homogeneous multiphase bodies. The BEM is a robust and accurate numerical technique to analyse fracture phenomena in solids. This numerical method presents a mesh dimensionality reduction, which makes easier the modelling of cracks surfaces. Besides, this dimensionality reduction also makes the treatment of interfaces in composed structures a less complex task. Considering the use of Kelvin fundamental solutions at the integrals equations, isotropic materials can be represent as parts of the composed structures. On the other hand, using Cruse & Swedlow fundamental solution it is also possible to deal with general anisotropic materials. At the composed structures, cracks can propagate along the materials interfaces and the cohesive crack model is responsible for the nonlinear structural behaviour of the quasi-brittle failures. The nonlinear system of equations at the fracture analyses is solved using two different algorithms for iterative resolution. The first always takes into account the structure elastic strength and, hence it is called Constant Operator (CO). On the other hand, the second is denominated Tangent Operator (TO) due to the fact that it considers strengths at the tangent directions of the nonlinear structural response. Therefore, convergence rates are faster when compared with the CO. As applications, composed structures were analysed with the developed formulations in linear elastic range. In addition, experimental fracture testes performed in concrete and wood specimens were also analysed. The confront of obtained results with the reference ones show that, the formulation was effective and accurate to evaluate the mechanical responses of composed structures in linear elastic range, and also to perform nonlinear quasi-brittle fracture tests.

The vast majority of oil and gas reserves are trapped in fractured carbonate reservoirs. Most carbonate reservoirs are naturally fractured, with fractures ranging from millimeter- to kilometer-scale. These fractures create complex flow behaviors which impact reservoir characterization, production performance, and, eventually, total recovery. As we know, bridging the gas from plug to near-wellbore, eventually to field scales, is a persisting challenge in modeling Naturally Fractured Reservoirs (NFRs). This dissertation will focus on assessing the fundamental flow mechanisms in fractured rocks at the plug scale, understanding the governing upscaling parameters, and ultimately, developing fit-for-purpose upscaling tools for field-scale implementation. In this dissertation, we first focus on the upscaling of rock fractures under the laminar flow regime. A novel analytical model is presented by incorporating the effects of normal aperture, roughness, and tortuosity. We then investigate the stress-dependent hydraulic behaviors of rock fractures. A new and generalized theoretical model is derived and verified by a dataset collected from public experimental resources. In addition, an efficient coupled flow-geomechanics algorithm is developed to further validate the proposed analytical model. The physics of matrix-fracture interaction and fluid leakage is modeled by a high-resolution, micro-continuum approach, called extended Darcy-Brinkman-Stokes (DBS) equations. We observe the back-flow phenomena for the first time. Machine learning is then implemented into our traditional upscaling work under complex physics (e.g., initial and Klinkenberg effects). We finally consolidate the lab-scale upscaling tools and scale them up to the field scale. We develop a fully coupled hydro-mechanical model based on the Discrete-Fracture Model (DFM) in fractured reservoirs, in which we incorporate localized effects of fracture roughness at the field-scale.

The diploma thesis is focused on the evaluation of mechanical fracture parameters of concrete after exposure to high temperatures. In the introductory theoretical part general principles of fracture mechanics with the concentration on a linear elastic fracture mechanics and non-linear fracture models for the concrete are summarized. The meaning of the three-point bending fracture test used for determination of fracture parameters is also explained. Further the influence of high temperatures on the partial components of concrete and general modeling of temperature loading is described. The practical part is concerned with the evaluation of fire experiments on the concrete panels including numerical simulations using GiD and ATENA software. The evaluation of data obtained from the three-point bending test carried out on specimens with initial stress concentrator taken from concrete panels is a main part of the diploma thesis. The values of modulus of elasticity, effective fracture toughness, work of fracture and fracture energy are determined from the measured F–d and F–CMOD diagrams after their proper corrections in the GTDiPS application. The evaluation of the selected mechanical fracture parameters was performed by StiCrack software using effective crack model and work of fracture method and DKFM_BUT software using the double-K fracture model. Finally, the attention is paid to the analysis of the obtained data.

The purpose of dissertation is the analysis of the calculation of fracture parameters using Double-K fracture model for quasi-brittle specimens with the stress concentrator loaded by three-point bending or wedge splitting. To calculation of these parameters was used the developed DKFM_BUT software in Microsoft Excel application with using of Visual Basic programming language. Furthermore, the adequate shape functions and compliance functions were introduced for the selected wedge splitting test configurations. Main part of this dissertation is the series of comprehensively implemented and evaluated fracture experiments on specimens from advanced building materials, while the attention was paid to the analysis of experimental data. Finally, the selected results obtained using mentioned software support were presented and discussed.