The size and morphology of the dendrite growth patterns are simulated for laser powder deposition of Ti-Nb alloys under steady-state and transient growth conditions. A phase field model using an adaptive grid technique was employed to simulate the steady-state growth of dendrites on rather small domains, in which fixed local solidification conditions are present. For simulation of dendrite growth patterns at transient conditions, a cellular automaton model was used along with a virtual front tracking technique on larger domains, containing various initial orientations of the solid-liquid (SL) interface. To obtain the required input thermal data, i.e., the temporal distribution of temperature, a finite element analysis was performed along with a novel numerical approach for the real-time addition of new deposition material in each time step, thus building the deposition geometry momentarily. Using the output of the thermal model, the motion and morphology of the SL interface was determined through tracking the isotherm of the solidification temperature. First, in this study, the appropriate set of processing parameters was found through an optimization process using a new concept, laser supplied energy Es, which combines the effects of the energy and powder density in the process. With the developed analytical/experimental procedure, crack and pore-free coatings of Ti-Nb with continuous beads were produced by examining the effects of a few sets of processing parameters, including laser power, laser scan velocity, laser beam diameter and powder feed rate. The results of the thermal model for the optimized set of parameters matched with the thermocouple temperature measurements with only ~5% deviation. The thermal model was able to predict realistic profiles for the temporal development of deposition geometry, thus predicting meaningful morphologies of the SL interface. The model output was easily treated for extraction of local processing parameters, such as the temperature gradient and solidification velocity. These data are very useful when simulating the dendrite growth patterns at steady-state conditions in directional solidification of selected regions in the microstructure. In order to define transient growth conditions, the simulated distribution of temperature can be also directly fed into the microstructure model at each solution time step. Phase field simulations of steady-state growth of dendrites during directional solidification showed a remarkable agreement with the experimental observations for the local dendrite arm spacing across the microstructure. Also qualitatively agreeing with the experiment, the simulated dendrite spacing exhibited a minimum around the mid-height region of the microstructure, which is explained by the counter effect of the temperature gradient and solidification velocity along the height of the sample. On a large domain containing different initial orientations of the SL interface, cellular automaton simulations for transient growth patterns of dendrites could reproduce most qualitative features observed in the microstructure. The dendrite arm spacing gradually decreased from the top of the microstructure. The competition was won by the dendrites growing in areas with higher cooling rates, i.e., in the regions closer to the top of the microstructure. The secondary arms of the primary dendrites, which are initially inclined on the vertical axis, grew extensively only along the overall growth direction and eventually became primary arms in some cases.

PhD / When modeling a system as complex as the brain, considerable simplifications are inevitable. The nature of these simplifications depends on the available experimental evidence, and the desired form of model predictions. A focus on the former often inspires models of networks of individual neurons, since properties of single cells are more easily measured than those of entire populations. However, if the goal is to describe the processes responsible for the electroencephalogram (EEG), such models can become unmanageable due to the large numbers of neurons involved. Mean-field models in which assemblies of neurons are represented by their average properties allow activity underlying the EEG to be captured in a tractable manner. The starting point of the results presented here is a recent physiologically-based mean-field model of the corticothalamic system, which includes populations of excitatory and inhibitory cortical neurons, and an excitatory population representing the thalamic relay nuclei, reciprocally connected with the cortex and the inhibitory thalamic reticular nucleus. The average firing rates of these populations depend nonlinearly on their membrane potentials, which are determined by afferent inputs after axonal propagation and dendritic and synaptic delays. It has been found that neuronal activity spreads in an approximately wavelike fashion across the cortex, which is modeled as a two-dimensional surface. On the basis of the literature, the EEG signal is assumed to be roughly proportional to the activity of cortical excitatory neurons, allowing physiological parameters to be extracted by inverse modeling of empirical EEG spectra. One objective of the present work is to characterize the statistical distributions of fitted model parameters in the healthy population. Variability of model parameters within and between individuals is assessed over time scales of minutes to more than a year, and compared with the variability of classical quantitative EEG (qEEG) parameters. These parameters are generally not normally distributed, and transformations toward the normal distribution are often used to facilitate statistical analysis. However, no single optimal transformation exists to render data distributions approximately normal. A uniformly applicable solution that not only yields data following the normal distribution as closely as possible, but also increases test-retest reliability, is described in Chapter 2. Specialized versions of this transformation have been known for some time in the statistical literature, but it has not previously found its way to the empirical sciences. Chapter 3 contains the study of intra-individual and inter-individual variability in model parameters, also providing a comparison of test-retest reliability with that of commonly used EEG spectral measures such as band powers and the frequency of the alpha peak. It is found that the combined model parameters provide a reliable characterization of an individual's EEG spectrum, where some parameters are more informative than others. Classical quantitative EEG measures are found to be somewhat more reproducible than model parameters. However, the latter have the advantage of providing direct connections with the underlying physiology. In addition, model parameters are complementary to classical measures in that they capture more information about spectral structure. Another conclusion from this work was that a few minutes of alert eyes-closed EEG already contain most of the individual variability likely to occur in this state on the scale of years. In Chapter 4, age trends in model parameters are investigated for a large sample of healthy subjects aged 6-86 years. Sex differences in parameter distributions and trends are considered in three age ranges, and related to the relevant literature. We also look at changes in inter-individual variance across age, and find that subjects are in many respects maximally different around adolescence. This study forms the basis for prospective comparisons with age trends in evoked response potentials (ERPs) and alpha peak morphology, besides providing a standard for the assessment of clinical data. It is the first study to report physiologically-based parameters for such a large sample of EEG data. The second main thrust of this work is toward incorporating the thalamocortical system and the basal ganglia in a unified framework. The basal ganglia are a group of gray matter structures reciprocally connected with the thalamus and cortex, both significantly influencing, and influenced by, their activity. Abnormalities in the basal ganglia are associated with various disorders, including schizophrenia, Huntington's disease, and Parkinson's disease. A model of the basal ganglia-thalamocortical system is presented in Chapter 5, and used to investigate changes in average firing rates often measured in parkinsonian patients and animal models of Parkinson's disease. Modeling results support the hypothesis that two pathways through the basal ganglia (the so-called direct and indirect pathways) are differentially affected by the dopamine depletion that is the hallmark of Parkinson's disease. However, alterations in other components of the system are also suggested by matching model predictions to experimental data. The dynamics of the model are explored in detail in Chapter 6. Electrophysiological aspects of Parkinson's disease include frequency reduction of the alpha peak, increased relative power at lower frequencies, and abnormal synchronized fluctuations in firing rates. It is shown that the same parameter variations that reproduce realistic changes in mean firing rates can also account for EEG frequency reduction by increasing the strength of the indirect pathway, which exerts an inhibitory effect on the cortex. Furthermore, even more strongly connected subcircuits in the indirect pathway can sustain limit cycle oscillations around 5 Hz, in accord with oscillations at this frequency often observed in tremulous patients. Additionally, oscillations around 20 Hz that are normally present in corticothalamic circuits can spread to the basal ganglia when both corticothalamic and indirect circuits have large gains. The model also accounts for changes in the responsiveness of the components of the basal ganglia-thalamocortical system, and increased synchronization upon dopamine depletion, which plausibly reflect the loss of specificity of neuronal signaling pathways in the parkinsonian basal ganglia. Thus, a parsimonious explanation is provided for many electrophysiological correlates of Parkinson's disease using a single set of parameter changes with respect to the healthy state. Overall, we conclude that mean-field models of brain electrophysiology possess a versatility that allows them to be usefully applied in a variety of scenarios. Such models allow information about underlying physiology to be extracted from the experimental EEG, complementing traditional measures that may be more statistically robust but do not provide a direct link with physiology. Furthermore, there is ample opportunity for future developments, extending the basic model to encompass different neuronal systems, connections, and mechanisms. The basal ganglia are an important addition, not only leading to unified explanations for many hitherto disparate phenomena, but also contributing to the validation of this form of modeling.

Sintering is a primary particulate manufacturing technology to provide densification and strength for ceramics and many metals. A persistent problem in this manufacturing technology has been to maintain the quality of the manufactured parts. This can be attributed to the various sources of uncertainty present during the manufacturing process. In this work, a two-particle phase-field model has been analyzed which simulates microstructure evolution during the solid-state sintering process. The sources of uncertainty have been considered as the two input parameters surface diffusivity and inter-particle distance. The response quantity of interest (QOI) has been selected as the size of the neck region that develops between the two particles. Two different cases with equal and unequal sized particles were studied. It was observed that the neck size increased with increasing surface diffusivity and decreased with increasing inter-particle distance irrespective of particle size. Sensitivity analysis found that the inter-particle distance has more influence on variation in neck size than that of surface diffusivity. The machine-learning algorithm Gaussian Process Regression was used to create the surrogate model of the QOI. Bayesian Optimization method was used to find optimal values of the input parameters. For equal-sized particles, optimization using Probability of Improvement provided optimal values of surface diffusivity and inter-particle distance as 23.8268 and 40.0001, respectively. The Expected Improvement as an acquisition function gave optimal values 23.9874 and 40.7428, respectively. For unequal sized particles, optimal design values from Probability of Improvement were 23.9700 and 33.3005 for surface diffusivity and inter-particle distance, respectively, while those from Expected Improvement were 23.9893 and 33.9627. The optimization results from the two different acquisition functions seemed to be in good agreement with each other. The results also validated the fact that surface diffusivity should be higher and inter-particle distance should be lower for achieving larger neck size and better mechanical properties of the material.

This thesis develops a new quantitative multi-phase field model for polycrystalline solidification of binary alloys. We extend the thin interface formalism of Karma and co-workers to multiple order parameters. This makes it possible to model segregation and interface kinetics during equiaxed dendritic growth quantitatively, a feature presently lacking from polycrystalline or multi-phase solidification models. We study dendrite tip speed convergence as a function of interface width during free dendritic growth. We then analyze the steady state and grain coalescence properties of the model. It is shown that the model captures the correct physics of back diffusion and repulsive grain boundary coalescence as outlined by Rappaz and co-workers. Finally, the model is applied to simulate solidification and coarsening in delta-ferrite solidification. / Thesis / Master of Applied Science (MASc)

The workshop is composed of two main parts: the first part devoted to atomistic Monte Carlo simulations and the second part devoted to the Phase Field modelling. In each part a lecture will be accompanied by exercise activities.

Phase field modeling and simulation is employed to study the underlying mechanism of enhancing electromechanical properties in single crystals and polycrystals of perovskite-type ferroelectrics around the morphotropic phase boundary (MPB). The findings include: (I) Coherent phase decomposition near MPB in PZT is investigated. It reveals characteristic multidomain microstructures, where nanoscale lamellar domains of tetragonal and rhombohedral phases coexist with well-defined crystallographic orientation relationships and produce coherent diffraction effects. (II) A bridging domain mechanism for explaining the phase coexistence observed around MPBs is presented. It shows that minor domains of metastable phase spontaneously coexist with and bridge major domains of stable phase to reduce total system free energy, which explains the enhanced piezoelectric response around MPBs. (III) We demonstrate a grain size- and composition-dependent behavior of phase coexistence around the MPBs in polycrystals of ferroelectric solid solutions. It shows that grain boundaries impose internal mechanical and electric boundary conditions, which give rise to the grain size effect of phase coexistence, that is, the width of phase coexistence composition range increases with decreasing grain sizes. (IV) The domain size effect is explained by the domain wall broadening mechanism. It shows that, under electric field applied along the nonpolar axis, without domain wall motion, the domain wall broadens and serves as embryo of field-induced new phase, producing large reversible strain free from hysteresis. (V) The control mechanisms of domain configurations and sizes in crystallographically engineered ferroelectric single crystals are investigated. It reveals that highest domain wall densities are obtained with intermediate magnitude of electric field applied along non-polar axis of ferroelectric crystals. (VI) The domain-dependent internal electric field associated with the short-range ordering of charged point defects is demonstrated to stabilize engineered domain microstructure. The internal electric field strength is estimated, which is in agreement with the magnitude evaluated from available experimental data. (VII) The poling-induced piezoelectric anisotropy in untextured ferroelectric ceramics is investigated. It is found that the maximum piezoelectric response in the poled ceramics is obtained along a macroscopic nonpolar direction; and extrinsic contributions from preferred domain wall motions play a dominant role in piezoelectric anisotropy and enhancement in macroscopic nonpolar direction. (VIII) Stress effects on domain microstructure are investigated for the MPB-based ferroelectric polycrystals. It shows that stress alone cannot pole the sample, but can be utilized to reduce the strength of poling electric field. (IX) The effects of compressions on hysteresis loops and domain microstructures of MPB-based ferroelectric polycrystals are investigated. It shows that longitudinal piezoelectric coefficient can be enhanced by compressions, with the best value found when compression is about to initiate the depolarization process. / Ph. D.

L'objectif de ce travail est de prédire les évolutions microstructurales se produisant dans le tantale pur lors d'un traitement thermique en fonction de son état microstructural initial. La restauration, la recristallisation et la croissance de grains sont décrites à l'aide d'un modèle en champ moyen qui nécessite une description adéquate de la microstructure, en termes de distributions de tailles de grains et de densités de dislocations équivalentes. La densité de dislocation équivalente moyenne peut être évaluée par une simple mesure de dureté Vickers. L'établissement de la relation dureté-densité de dislocations nécessite l'utilisation d'une loi de comportement basée sur la densité de dislocations équivalente. Les évolutions microstructurales au cours d'un traitement thermique ont été observées et les paramètres pilotant ces phénomènes ont été identifiés à l'aide d'essais originaux comme l'observation in situ de la recristallisation ou l'utilisation d'essais à gradient de déformation pour déterminer le seuil de densité de dislocations équivalente pour déclencher la recristallisation. Des essais plus classiques ont permis d'obtenir des cinétiques de recristallisation dans la gamme 1000°C-1100°C pour différentes microstructures initiales. Les simulations des différents traitements thermiques à l'aide du modèle à champ moyen rendent bien compte des évolutions microstructurales en termes de fraction recristallisée et de taille des grains recristallisés pour des microstructures faiblement déformées ou fortement déformées et fragmentées, en utilisant une description adéquate du type de microstructure initiale. Le modèle devra en revanche être adapté pour traiter le cas de microstructures intermédiaires, en enrichissant non seulement la description de la microstructure initiale mais également celle de l'étape de germination des grains recristallisés. Il deviendra alors capable de prédire les évolutions de microstructures pour tout type de microstructure initiale de tantale. / This study aims at predicting the microstructural evolution of pure tantalum during annealing according the initial microstructural state. Static recovery and discontinuous recrystallization as well as grain growth are described using a mean-field model requiring an appropriate description of the microstructure, using both equivalent dislocation densities and grain sizes distributions. The average equivalent dislocation density can be assessed from Vickers microhardness measurements. The calibration of such a relation between microhardness and dislocation density involves the use of a dislocation density-based constitutive law. Microstructural evolutions during annealing have been observed and control parameters of these phenomena have been determined using original tests such as in situ observation of the recrystallization process or the use of strain gradient samples to assess the critical dislocation density for the onset of recrystallization. More classical tests have been carried out to get recrystallization kinetics in the range 1000-1100°C for different initial microstructures. Simulations of annealing using the mean-field model adapted for tantalum match the experimental evolution of both recrystallized fraction and recrystallized grain size, in either weakly deformed or severely deformed and fragmented microstructures. On the other hand, the model needs to be further adapted for intermediate microstructures, with both a more elaborate description of the initial microstructure and of the nucleation stage of the recrystallized grains. It will then be suitable to predict evolutions of any initial tantalum microstructure during annealing.

The Interplanetary Magnetic Field (IMF) has a controlling effect on the Magnetosphere and Ionosphere. The objective in this work is to investigate the probable effects of IMF on Ionospheric and Geomagnetic response. To fulfill the objective the concept of an event has been created based on the polarity reversals and rate of change of the interplanetary magnetic field components, Bz and By. Superposed Epoch Method (SPE) was employed with the three event definitions, which are based on IMF Bz southward turnings ranging from 6 to 11 nT in order to quantify the effects of IMF By and Bz. For the first event only IMF Bz turnings were taken into account while for the remaining, positive and negative polarity for IMF By were added. Results showed that the increase in the magnitude of IMF Bz turnings increased the drop of F layer critical frequency, f0F2. The drop was almost linear with the increase in magnitude of polarity reversals. Reversals with a positive IMF By has resulted in the continuation of geomagnetic activity more than 4 days, that is to say, the energy, that has penetrated as a consequence of reversal with a positive By polarity, was stored in outer Magnetosphere,whereas, with a negative IMF By the energy was consumed in a small time scale. At the second step of the work, although conclusions about geomagnetic activity could be done, as a consequence of data gaps for f0F2 in addition to having low numbers of events, characterization of f0F2 due to constant IMF By polarity could not be accomplished. Thus, a modeling attempt for the characterization of the response due to polarity reversals of IMF components with the Genetic Programming was carried out. Four models were constructed for different polarity reversal cases and they were used as the components of one general unique model. The model is designed in such a way that given 3 consecutive value of f0F2, IMF By and IMF Bz, the model can forecast one hour ahead value of f0F2. The overall model, GETY-IYON was successful at a normalized error of 7.3%.

Le maclage thermique est un défaut cristallographique largement discuté dans les métaux de type CFC à faible énergie de faute d'empilement. Malgré une importante littérature scientifique dédiée à ce sujet, les mécanismes expliquant précisément la formation de ces macles thermiques ne sont pas totalement élucidés à ce jour. Dans ce travail, nous avons cherché à améliorer notre compréhension de ce phénomène fondamental en métallurgie physique. Différents matériaux de type CFC (acier inoxydable 304L, nickel pur et Inconel 718) ont été considérés. Nous avons confirmé, grâce à des expériences de traitement thermique in situ couplées à des cartographies d'orientation, que la majorité des macles thermiques sont générées durant la recristallisation. De la même manière, par une expérience réalisée sur l'Inconel 718, nous avons mis en évidence que la croissance de grains pure n'était pas source de joints de macle. Par conséquent, il semble évident que les phénomènes de recristallisation et de croissance de grains ont des régimes totalement distincts associés à des mécanismes spécifiques du point de vue de la formation des macles thermiques, et doivent donc absolument être étudiés séparément. Nous avons ainsi proposé un nouveau modèle, dans lequel l'effet du signe de la courbure moyenne du front de recristallisation est pris en compte. Les influences de différents facteurs thermomécaniques, y compris le niveau de déformation, la taille de grains initiale, la température de recuit et la vitesse de montée en température, ont été étudiées à travers deux séries d'expériences. Suite à l'effet du signe de la courbure moyenne du joint de grain, nous avons proposé une méthode pour quantifier la tortuosité du front de recristallisation. Dans cette étude, nous montrons que cette quantité est corrélée à la densité de macles post-recristallisation. En sus des analyses expérimentales, des outils numériques de type champ moyen et champ complet ont également été développés dans cette étude afin de modéliser l'évolution des macles thermiques tout en tenant en compte des mécanismes physiques mis en évidence expérimentalement. Les bases d'un nouveau modèle de type champ moyen ont été proposées afin de modéliser l'évolution de la densité de macles moyenne durant le phénomène de croissance de grains. Ce modèle, dans lequel seulement un paramètre doit être identifié par des donnés expérimentales, semble mieux décrire les résultats expérimentaux obtenus pour l'inconel 718 comparé au modèle de Pande, référence en la matière. Deux méthodes implicites i.e. la méthode level-set et la méthode champ de phase ont été comparées au niveau de leurs formulations et de leurs performances numériques pour des simulations de croissance de grains anisotrope. C'est la première fois que ces deux méthodes sont comparées dans le contexte de l'utilisation de maillages éléments finis non stucturés et hétérogènes en terme de taille de maille. Une nouvelle méthodologie a été ainsi proposée dans le cadre de l'approche level-set pour simuler l'évolution de macles thermiques durant le phénomène de croissance de grains. Dans cette nouvelle méthodologie, les joints de macles peuvent être insérés dans des microstructures synthétiques. De plus, les joints de macles peuvent être distingués selon leur nature cohérente ou incohérente. Nous avons montré à travers les différentes simulations réalisées que les propriétés spéciales des joints de macles peuvent être prises en compte avec ce nouveau formalisme. / Annealing twin is a crystallographic defect that is largely reported in F.C.C. metals especially those with low stacking fault energy. Despite the amount of work dedicated to the subject, the understanding of annealing twin formation mechansims is not complete in the literature. In the present work, by applying both experimental and numerical tools, we tried to have a more profound understanding of this phenomenon, which is essential to Physical Metallurgy. For this purpose, different F.C.C. Materials including 304L stainless steel, commercially pure nickel and nickel based superalloy Inconel 718 are investigated. We confirmed that annealing twins are mainly formed in the recrystallization regime, especially driven by the migration of recrystallization front into deformed regions by using in situ EBSD technique. In addition, we found in the in situ observations that there are almost no twins generated in the grain growth regime. This observation is confirmed by another grain growth experiment performed on Inconel 718. Therefore, curvature driven grain boundary migration by itself is not sufficient to generate annealing twins. A new atomistic model to explain annealing twin formation mechanism, in which the effect of migrating boundary curvature is considered, is proposed. The effects of different thermo-mechanical factors, including prior deformation level, initial grain size, annealing temperature and the heating velocity, on annealing twin formation are determined via two experiments performed on commercially pure nickel. Based on the idea of grain boundary curvature, we proposed a method to quantify recrsytallization front tortuosity. In the present study, we show evidence that this quantity is positively correlated with the twin density at the end of the recrystallization regime. In addition to experimental studies, numerical tools including both mean field and full field approaches are applied to model annealing twin evolution during grain growth by taking into account the revealed mechanisms. A basis of a new mean field model is proposed to model annealing twin density evolution during grain growth. This model, which has only one parameter to be identified, provides a better consistency with the experimental data of Inconel 718 compared to the Pande's model. Besides, full field approaches are also applied to simulate the overall microstructure evolution during grain growth. Two implicit methods i.e. the level set and the multi-phase-field methods are compared in terms of their formulations and their numerical performance in anisotropic grain growth simulations. It is the first time that these two methods are compared in the finite element context with non-structural mesh. In the present numerical context, the level set method is more suitable to describe strong anisotropy in grain boundary energy. A new methodology is thus developed in the level set framework to simulate annealing twin evolution during grain growth. This methodology, in which we can insert annealing twin boundaries into synthetic microstructures and distinguish coherent and incoherent twin boundaries, is proven to be able to counting for the strong anisotropy introduced by coherent annealing twin boundaries.

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.