Nous étudions numériquement la solidification directionnelle d'un alliage binaire à base de succinonitrile. Pour cela, nous développons un code s'appuyant sur le formalisme du champ de phase adapté au cas de la croissance dans des lames minces. Les résultats numériques obtenus sont comparés qualitativement et quantitativement avec les observations expérimentales. Une bonne confirmation des lois expérimentales et de nouvelles informations sur la dynamique des microstructures sont obtenues.La direction de croissance est généralement limitée par deux axes : l'axe cristallin principal et la direction du gradient thermique. Une première partie de la thèse porte sur l'étude des effets de la désorientation de l'axe cristallin sur la direction de croissance des structures et sur leurs morphologies. Nos résultats sont directement comparés à la loi expérimentale qui donne la réponse en orientation des microstructures sur l'ensemble de leur domaine d'existence en fonction du nombre de Péclet. Nous obtenons un accord très satisfaisant entre simulation et expérience. Dans la seconde partie de la thèse, une instabilité oscillante (mode 2λ − O) est étudiée en se basant sur le diagramme de stabilité expérimental. Dans ce mode deux cellules voisines oscillent en opposition de phase en largeur et en hauteur. Nos simulations reproduisent ce mode oscillant dans des lames minces et permettent une comparaison quantitative avec les expériences. Le régime des oscillations forcées est notamment exploré pour obtenir des informations sur la réponse en fréquence du système. / We report on a numerical study of directional solidification in thin samples of succinonitrile-based dilute alloy. This thesis is based on 3D phase-field simulations. Numerical results are compared qualitatively and quantitatively with experimental observations. The comparison gives a good confirmation of the experimental laws, while providing new information on the dynamics of microstructures. Growth direction of the microstructure is constrained by two axes : the main crystal axis and the direction of the thermal gradient. Simulations allow us to test the variations of the growth direction and the microstructure stability at various misorientation angles. Our results are directly compared with the experimental law that gives the microstructure orientation response in a large domain of Péclet numbers. We obtain a good agreement, both on qualitative and quantitative grounds, between experiments and 3D simulations.In the second part of this manuscript, an oscillatory instability (2λ − O mode) is numerically studied. This mode involves oscillations of both cell width and cell tip position. This instability is reproduced in numerical simulations with the aim of allowing a fine and relevant comparison with experiments of the domain of existence and the periods of oscillation. In particular, the forced oscillation regime is explored to obtain information on the frequency response of the system.

Este trabalho trata da modelagem de sinais ultrassônicos gerados por transdutores circulares (plano e côncavo) no modo de pulso-eco, inspecionando uma região de interesse predeterminada. Para essa análise, dois modelos da resposta impulsiva de um transdutor piezelétrico foram implementados: um do transdutor circular plano e outro do transdutor circular côncavo focalizado. Este último sendo o modelo proposto pelo autor com uma geometria baseada em anéis concêntricos como elementos de área do emissor. A adição de diversos anéis concêntricos, deslocados ao longo de seu eixo e de raios sucessivamente menores, permitiu calcular o campo acústico, gerado por uma abertura côncava, bem como seu eco refletido. A resposta impulsiva de cada anel resulta da diferença entre as respostas impulsivas calculadas para um emissor circular grande e um pequeno. O modelo implementado para o cálculo dos sinais de eco foi utilizado na varredura de uma região contendo um conjunto de pontos com refletividade acústica igual a 1. A reconstrução da imagem foi feita com esses sinais aplicando-lhes a técnica de regularização de Tikhonov. A qualidade das reconstruções das imagens obtidas foi avaliada e comparada a das imagens convencionais. Dentre as métricas de avaliação das imagens reconstruídas estão a influência na variação da velocidade de propagação da onda acústica no meio, a extensão e a discretização do grid e o parâmetro de regularização alfa. Todas as reconstruções foram analisadas segundo o Erro Médio Quadrático (MSE). Finalmente, ensaios experimentais foram conduzidos para a obtenção de A-scans (imagens em modo de amplitude) os quais foram inseridas no modelo teórico para a reconstrução de imagens e analisadas pelo MSE. / This work deals with the modeling of ultrasonic signals generated by circular transducers (planar and concave pistons) in pulse-echo mode, inspecting a predetermined region of interest (ROI). For this analysis, two models of the impulse response of a transducer were implemented: one using a plane piston transducer and the other, a model proposed by the author of this work, using a concave transducer with concentric rings as elements of the emitting area. The addition of several concentric rings moved along its axis allowed us to calculate the acoustic field generated by a concave opening and the echo reflected from each point in space. The impulse response of each ring represents the difference between the impulse responses calculated for a large circular transmitter and a small one. The model implemented for calculating the echo signals is used to scan a region, within a ROI, containing a set of points with acoustic reflectivity of 1. Simulations of the regions are made with these signals by applying the Tikhonov regularization method. To evaluate the quality of image reconstruction, the images are compared with the conventional images. Among the metrics to evaluate the reconstructed images are the influence of the variation of the acoustic wave propagation in the media, the grid range and discretization and the parameter of regularization alpha. All of the image reconstructions were analyzed through the Mean Square Error (MSE) criterion. Finally, experiments were conducted in order to obtain A-scans which were then re-inserted in the theoretical model to reconstruct and analyze the images.

The Fire Dynamics Simulator (FDS) code recently developed by the National Institute of Standards and Technology (NIST) is particularly well-suited for use by fire protection engineers for studying fire behavior. It makes use of Large Eddy Simulation (LES) techniques to directly calculate the large-scale fluid motions characteristic of buoyant turbulent diffusion flames. However, the underlying model needs further development and validation against experiment in the areas of soot formation/oxidation and radiation before it can be used to calculate flame heat transfer and predict the burning of solid or liquid fuels. WPI, Factory Mutual Research, and NIST have undertaken a project to make FDS capable of calculating the flame heat transfer taking place in fires of hazardous scale. The temperatures predicted by the FDS code were generally too high on the fuel side and too low on the oxidant side when compared to experimental data from small-scale laminar diffusion flames. For this reason, FDS was reformulated to explicitly solve the conservation of energy equation in terms of total (chemical plus sensible) enthalpy. This allowed a temperature correction to be applied by removing enthalpy from the fuel side and adding it to the oxidant side. This reformulation also has advantages when using probability density function (PDF) techniques in larger turbulent flames because the radiatively-induced nonadiabaticity is tracked locally with each fluid parcel. The divergence of the velocity field, required to obtain the flow-induced perturbation pressure, is calculated from an expression derived from the continuity equation. A new approach to soot modeling in diffusion flames was developed and added to the FDS code. The soot model postulated as part of this work differs from others because it is intended for engineering calculations of soot formation and oxidation in an arbitrary hydrocarbon fuel. Previous models contain several fuel-specific constants that generally can only be determined by calibration experiments in laminar flames. The laminar smoke point height, an empirical measure of a fuel?s sooting propensity, is used in the present model to characterize fuel-specific soot chemistry. Two separate mechanisms of soot growth are considered. The first is attributed to surface growth reactions and is dependent on the available surface area of the soot aerosol. The second is attributed to homogeneous gas-phase reactions and is independent of the available soot surface area. Soot oxidation is treated empirically in a global (fuel-independent) manner. The local soot concentration calculated by the model drives the rate of radiant emission. Calibration against detailed soot volume fraction and temperature profiles in laminar axisymmetric flames was performed. This calibration showed that the general approach postulated here is viable, yet additional work is required to enhance and simplify the model. The essential mathematics for modeling larger turbulent flames have also been developed and incorporated into the FDS code. An assumed-beta PDF is used to approximate the effect of unresolved subgrid-scale fluctuations on the grid-scale soot formation/oxidation rate. The intensity of subgrid-scale fluctuations is quantified using the principle of scale similarity. The modified FDS code was used to calculate the evolution of soot in buoyant turbulent diffusion flames. This exercise indicated that the subgrid-scale fluctuations are quantitatively important in LES of turbulent buoyant diffusion flames, although no comparison of prediction and experiment was performed for the turbulent case.

Establishing process-structure-property relationships is an important objective in the paradigm of materials design in order to reduce the time and cost needed to develop new materials. A method to link phase field (process-structure relations) and microstructure-sensitive finite element (structure-property relations) modeling is demonstrated for subsolvus polycrystalline IN100. A three-dimensional (3D) experimental dataset obtained by orientation imaging microscopy performed on serial sections is utilized to calibrate a phase field model and to calculate inputs for a finite element analysis. Simulated annealing of the dataset realized through phase field modeling results in a range of coarsened microstructures with varying grain size distributions that are each input into the finite element model. A rate dependent crystal plasticity constitutive model that captures the first order effects of grain size, precipitate size, and precipitate volume fraction on the mechanical response of IN100 at 650°C is used to simulate stress-strain behavior of the coarsened polycrystals. Model limitations and ideas for future work are discussed.

Este trabalho trata da modelagem de sinais ultrassônicos gerados por transdutores circulares (plano e côncavo) no modo de pulso-eco, inspecionando uma região de interesse predeterminada. Para essa análise, dois modelos da resposta impulsiva de um transdutor piezelétrico foram implementados: um do transdutor circular plano e outro do transdutor circular côncavo focalizado. Este último sendo o modelo proposto pelo autor com uma geometria baseada em anéis concêntricos como elementos de área do emissor. A adição de diversos anéis concêntricos, deslocados ao longo de seu eixo e de raios sucessivamente menores, permitiu calcular o campo acústico, gerado por uma abertura côncava, bem como seu eco refletido. A resposta impulsiva de cada anel resulta da diferença entre as respostas impulsivas calculadas para um emissor circular grande e um pequeno. O modelo implementado para o cálculo dos sinais de eco foi utilizado na varredura de uma região contendo um conjunto de pontos com refletividade acústica igual a 1. A reconstrução da imagem foi feita com esses sinais aplicando-lhes a técnica de regularização de Tikhonov. A qualidade das reconstruções das imagens obtidas foi avaliada e comparada a das imagens convencionais. Dentre as métricas de avaliação das imagens reconstruídas estão a influência na variação da velocidade de propagação da onda acústica no meio, a extensão e a discretização do grid e o parâmetro de regularização alfa. Todas as reconstruções foram analisadas segundo o Erro Médio Quadrático (MSE). Finalmente, ensaios experimentais foram conduzidos para a obtenção de A-scans (imagens em modo de amplitude) os quais foram inseridas no modelo teórico para a reconstrução de imagens e analisadas pelo MSE. / This work deals with the modeling of ultrasonic signals generated by circular transducers (planar and concave pistons) in pulse-echo mode, inspecting a predetermined region of interest (ROI). For this analysis, two models of the impulse response of a transducer were implemented: one using a plane piston transducer and the other, a model proposed by the author of this work, using a concave transducer with concentric rings as elements of the emitting area. The addition of several concentric rings moved along its axis allowed us to calculate the acoustic field generated by a concave opening and the echo reflected from each point in space. The impulse response of each ring represents the difference between the impulse responses calculated for a large circular transmitter and a small one. The model implemented for calculating the echo signals is used to scan a region, within a ROI, containing a set of points with acoustic reflectivity of 1. Simulations of the regions are made with these signals by applying the Tikhonov regularization method. To evaluate the quality of image reconstruction, the images are compared with the conventional images. Among the metrics to evaluate the reconstructed images are the influence of the variation of the acoustic wave propagation in the media, the grid range and discretization and the parameter of regularization alpha. All of the image reconstructions were analyzed through the Mean Square Error (MSE) criterion. Finally, experiments were conducted in order to obtain A-scans which were then re-inserted in the theoretical model to reconstruct and analyze the images.

A zone of high magnetization along the SE margin of Paleoproterozoic Laurentia in the United States is indicated by magnetic anomaly data. The SE edge corresponds to the geochemical Neodymium mantle derivation model age (TDM) boundary and the entire anomaly overlies the Paleoproterozoic Mazatzal Province. Two-dimensional gravity and magnetic models across the Nd boundary are created with Moho constrained from receiver functions with gravity, sedimentary thickness and the base of the crustal magnetization. Upper crustal magnetization does not show strong variation across this boundary and much of the strong magnetization appears to lie in the middle crust. Using magnetic modeling of several potential geologic scenarios, we estimate magnetization, depth extent, and width of this zone of high magnetization. The anomaly has variable width (~ 300 km) with amplitude of approximately 200 nT. Pre-1.55Ga Paleoproterozoic mid crustal blocks have significantly higher average effective susceptibility (0.06 SI) than those of the post-1.55Ga Mesoproterozoic (0.01 SI). In two of the three profiles, the Paleoproterozoic zone of high magnetization has the highest average susceptibility indicating the Mazatzal province is innately highly magnetic. The zone may have formed either by magmatism associated with westward subduction or from highly magnetic terranes wedging between accreting island arcs.

<p>A wide variety of phase evolution phenomena observed in solids such as intermetallic growth at the junction between two metals subjected to high temperature, growth of oxide on metal surfaces due to atmospheric exposure and void evolution induced by electromigration in microelectronic devices for example, can be classified as being driven by reaction-diffusion processes. These phase evolution phenomena have a significant impact on material reliability for critical applications, and therefore, there is a requirement for modeling such reaction-diffusion driven phase evolution phenomena. It is difficult to analyze these due to the complexity of modeling the evolving interface between solid phases. Additional complexity is  due to the multi-physics nature of the diffusive and reactive processes. Diffusion in solids is driven by a variety of stimuli such as current, temperature and stress, in addition to the chemical potential. Therefore, there is a need for a model that accounts for the influence of such factors on phase evolution. In this thesis,  a generalized continuum based reaction-diffusion theory for phase and void evolution in solid state is developed. The derivation starts off with generalized interface balance laws for mass, momentum and energy. The thermodynamic entropy inequality for irreversible phase growth is derived for arbitrary anisotropic and inhomogeneous surface stress. These interface relations are combined with governing relations in the material bulk for the temperature, stress, electrical and concentration fields, to develop a general model capable of analyzing and describing phase evolution in solids. This theory is then applied to a variety of intermetallic phase and void evolution phenomena observed in microelectronics.</p> <p><br></p> <p>Electromigration induced voiding in thin metal films is an example of phase evolution that is an important reliability concern in microelectronics. Studies have reported that the electromigration induced void growth rate is inversely related to the adhesion of metal thin films with the base and capping layers. Electromigration experiments are performed on fabricated test devices with Cu thin films with SiNx and TiN capping layers. The observations from electromigration experiments on thin Cu metal films at a range of temperatures indicate that the contribution of interface adhesion strength to electromigration resistance decreases with an increase in temperature. The generalized reaction-diffusion theory developed here is modified to develop an expression to account for the effect of base and passivation layer adhesion and temperature on electromigration resistance of metal thin films. The void growth rates measured in the experiments are analyzed with the expression for void growth rate to estimate the interface adhesion strength for the Cu-TiN and Cu-SiNx interfaces. </p> <p><br></p> <p>Demand for increased bandwidth, power efficiency and performance requirements have resulted in a trend of reduction in size and pitch of Cu pillar-Solder micro-bump interconnects used in heterogeneously integrated packages. As the size of micro-bumps reduce, reliability challenges due to voiding in the solder joint and the growth of Cu-Sn intermetallics are observed. The underlying reaction-diffusion mechanisms responsible for Cu-Sn intermetallic growth and voiding in solder joints are unclear at this stage and require further investigation. The current practice of material characterization in micro-bumps involve destructive cross-sectioning and polishing of the micro-bumps after testing. These processes result in loss of continuity in the samples used for the experiments, and material removal due to abrasive polishing might result in a loss of critical information. Therefore, a novel test device capable of non-destructive characterization of Cu-Sn intermetallic growth and voiding in sub-30 micron size micro-bumps is designed and fabricated in this work. The fabricated test devices are subjected to thermal aging for over 1000 h and the underlying reaction-diffusion mechanisms behind the intermetallic phase and void evolution are investigated. </p> <p><br></p> <p>A reaction-diffusion mechanism is proposed explaining the evolution of  various Cu-Sn intermetallic phases and solder joint void observed from experiments. Using the reaction-diffusion mechanism inferred from the thermal aging experiments and the generalized reaction-diffusion theory for phase evolution developed in this thesis, a sharp interface model is developed for the evolution of Cu-Sn intermetallic phases and solder joint void. The diffuse interface phase field equivalent equations for the sharp interface model governing equations are developed using matched formal asymptotic analysis. The evolution of Cu-Sn intermetallic phase and voids in the solder joint are simulated for different temperatures and current density to demonstrate the validity of the phase field and sharp interface models.  </p> <p><br></p>

<p>    </p> <p>In this thesis, a thermodynamically consistent phase field formulation was developed to identify the physical origin of interfacial transitions that drive macroscopic phenomena, start- ing at the single-particle length scale and building up to the polycrystalline length scale. At the single-particle length scale, the framework identified two interfacial phases that are stable at the surface of Sn nanoparticles: 1) a disordered interfacial phase, i.e., the experimentally observed premelted surface layer; and 2) an ordered surficial phase displaying a remnant de- gree of order in fully melted particles. Regimes of melting behavior as a function of particle size and temperature are discussed. To bridge the gap between single-particle and densified polycrystals, an analytical model was developed to capture the physical driving forces for densification during electric field-assisted sintering. Here, the model acknowledges the struc- tural contributions of particle-particle interfaces to the strength of mechanical, electrical, and surficial driving forces for densification, and shows good agreement with experimental flash sintering data. Finally, the theory was applied to polycrystalline LiCoO₂ (LCO) and shows that the experimentally observed metal-insulator transition is driven by grain bound- ary lithium segregation, the interfacial misorientation, and the size of the abutting grains. A critical misorientation as a function of the macroscopic lithium content exists above which the grain boundaries undergo a metal-insulating transition, suggesting that the fabrication of textured LCO microstructures will delay the metal-insulator transition. </p>

Les pièces métalliques constituant le circuit primaire des installations nucléaires sont élaborées par forgeage à chaud. Pendant ce procédé, les transformations microstructurales induites par la déformation et les recuits déterminent une partie des propriétés mécaniques des produits finaux. L’orientation de la microstructure lors du processus de fabrication nécessite une connaissance précise des mécanismes physiques qui opèrent dans le matériau. Dans le cas de la déformation à chaud de l’acier austénitique 304L, ces modifications microstructurales dépendent de la recristallisation dynamique discontinue (DDRX) et de la recristallisation post-dynamique (PDRX). L’objet de ce projet est : (i) l’étude de la DDRX et de la PDRX dans les conditions de déformation du procédé de forgeage, (ii) l’étude de l’influence d’un ajout de niobium sur ces mécanismes, (iii) la modélisation de ces mécanismes afin de prédire les caractéristiques de la microstructure (moyenne et distribution de la taille des grains) à l’issue d’un procédé multipasses. Dans le cadre de l’étude, les conditions de déformation rencontrées lors du forgeage à chaud sont reproduites à l’aide d’essais de torsion sur des matériaux modèles contenant des teneurs en niobium différentes. La caractérisation et la modélisation des microstructures a permis de comprendre les effets respectifs de la température, de la vitesse de déformation ainsi que de l’ajout de niobium sur les mécanismes de la DDRX et de la PDRX. Dans cette étude, une nouvelle approche semi-topologique de l’hypothèse champs moyens est développée afin de permettre la prédiction de distributions de la taille de grain cohérentes avec les données expérimentales. / Cooling system of nuclear power plants is constituted of metallic parts obtained by hot forging. Thus during the manufacturing process, the microstructural trans- formations induced by the deformation and annealing process define partially the mechanical properties of the final products. A sharp knowledge of the physical mechanisms generated within the material is required to handle the microstructure. In the case of hot deformation of 304L austenitic stainless steel, the microstructural modifications depend on the discontinuous dynamic recrystallization (DDRX) and the post-dynamic recrystallization (PDRX). The aim of this project is: (i) the study of the DDRX and the PDRX under the conditions of deformation inherent in the forging process, (ii) the study of the influence of niobium addition on these mechanisms, (iii) the modeling of these me- chanisms in order to predict the microstructure characteristics (mean grain size and distribution) following a multipass process. As part of the research, the deformation conditions experienced during the hot forging process are replicated through torsion tests with model materials containing various niobium concentrations. Characterization and modeling of microstructures enable to understand the respective e ects of temperature, strain rate as well as niobium addittion on the DDRX and PDRX mechanisms. In this study, a new topological approach of mean-field hypothesis is developed in order to allow the prediction of realistic grain size distributions.

Presented dissertation discusses the influence of electromagnetic fields on the weight of the particles, which are considered in this work as substances with the hub. Theoretical knowledge was practically tested on plant organisms (early somatic embryos, fungal pathogens), theoretically the influence of electromagnetic field on cell structure was modeled. It was subsequently confirmed by a practical experiment assumption about the influence of electromagnetic fields on the weight of the particles. These experiments were preceded by a theoretical study of the problem and the formulation of a solution using Maxwell's equations, from which other descriptive equations and formulas were derived. The results of the experiments were presented at several professional conferences and published in professional journals and proceedings.