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.

L'estudi de la formació de microstructures en processos de solidificació té importants aplicacions científiques i tecnològiques. L'aparició d'aquestes estructures determina les propietats elèctriques i mecàniques del material solidificat, i té per tant un important interès tecnològic. La majoria d'aquestes estructures tenen el seu origen en una desestabilització morfològica de la interfase sòlid-líquid que es produeix a mesura que el front avança. Per aquest motiu, l'estudi del comportament dinàmic de la interfase resulta essencial per entendre els mecanismes que intervenen en la creació d'aquests patrons. Els processos de solidificació solen descriure's mitjançant problemes de contorn mòbil. Aquestes formulacions consten d'equacions per a la difusió del calor i de massa en les fases sòlida i líquida, que s'han de resoldre imposant l'acompliment de diverses condicions de contorn mòbils a la interfase. Els problemes de contorn mòbil, malgrat contenir tots els elements que intervenen en la dinàmica i ser de molta utilitat en l'àmbit de l'enginyeria, requereixen un cost computacional que no permet simular sistemes reals en règims interfacials complexos. Els mètodes de camp de fase (phase-field methods), van aparèixer a principis dels anys vuitanta com una eina computacional que permetia l'estudi de fenòmens interfacials de caire general. Aquests mètodes descriuen la forma de la interfase mitjançant un camp continu que pren valors diferents i constants en les dues fases. La dinàmica d'aquest camp és llavors acoblada al camp de difusió de calor o massa que determina l'avanç del front de solidificació. Un dels avantatges d'aquests mètodes és que la seva simulació no requereix d'algorismes de seguiment de la interfase (front tracking algorithsms). És ben conegut que les característiques principals de les microestructures en solidificació, es determinen durant els transitoris inicials en els que els corrents de massa i calor s'adapten a la evolució dinàmica del front. Un dels objectius en aquesta tesi és el de fer servir mètodes de camp de fase per descriure de forma quantitativa aquests transitoris. Per comprovar la validesa del nostre procediment, es realitza una comparació quantitativa entre els resultats numèrics obtinguts i diferents prediccions analítiques derivades del problema de contorn mòbil. Per un altra banda, la desestabilització del front es veu afectada per la presència de fluctuacions al sistema. Aquestes pertorbacions microscòpiques poden tenir el seu origen a les fluctuacions termodinàmiques internes, o bé ser conseqüència de imperfeccions experimentals que actuen com a font externa de soroll. El segon objectiu d'aquesta tesi és la introducció de fluctuacions en mètodes de camp de fase, de forma que es pugui estudiar l'amplificació dinàmica de les pertorbacions microscòpiques que acaben donant lloc a estructures macroscòpiques. Per finalitzar, analitzem el problema de la selecció en solidificació direccional. Estudiem els règims lineal i no-lineal, tot determinant les condicions, el moment i la forma en que apareixen les estructures dendrítiques i cel·lulars. / Crystal growth is a non-equilibrium process which involves physical mechanisms at very different scales. When a solidification front advances, mass and heat diffusion processes are combined with interfacial phenomena like capillarity or kinetic attachment. A complex interplay between these mechanisms gives rise to complex interfacial structures like snowflakes or cellular patterns. The formation of microstructures in solidification has both a scientific and a technological interest. On one hand, the study of the different interfacial structures constitutes a fundamental problem in the field of non-equilibrium pattern-forming systems. On the other side, from a technological point of view, the presence of microstructures determines the final mechanical and electrical properties of the processed material. Directional solidification is a controlled solidification technique which reproduces the conditions occurring in some important metallurgical processes like material casting or zone melting refining procedures. In a directional solidification experiment, the alloy sample is pulled at a constant velocity towards the cold region of an externally-imposed temperature gradient. Depending on the growth conditions, a morphological destabilization of the solid-liquid interface occurs during early transient stages. These initial transients are associated to a solute redistribution process due to the adaptation of the concentration field to the forced motion of the sample. The main objective of this thesis is to study the dynamical evolution of the morphological deformations of the front from these initial transients to the final stages where the properties of the interfacial pattern are determined. An important point in this process is that the internal fluctuations of the system play the role of an initiation mechanism for the morphological deformations of the front. During the initial transients, some of these microscopic perturbations are amplified by several orders of magnitude, and a range of wavelengths becomes morphologically unstable. The interfacial deformations of the front can be then characterized by means of power spectrum techniques. In order to study the dynamical evolution of the solidification front in directional solidification, we have used both theoretical and computational approaches: The main computational technique used in this thesis is the phase-field approach, which is a powerful method to simulate complex interfacial phenomena. The model equations describe the evolution of a continuous field , which takes different constant values at the solid and liquid bulks of the system. This field is then coupled with equations for the mass diffusion, and allows performing numerical studies without simulating the standard Stefan-like moving boundary problem. The phase-field method provides a diffuse interface description in which the transition from solid to liquid happens in a region of a certain thickness. The interface thickness introduces a new length in the simulations which must be taken into account to recover quantitative results. One major point in this thesis concerns with the introduction of fluctuations in phase-field methods. In the particular case of variational phase-field formulations -in which the model equations can be derived from a single free energy functional for the whole system-, the introduction of fluctuations can be done by applying the Fluctuation-Dissipation theorem. Variational formulations, however, although their appealing structure, present a poor computational efficiency and cannot be used to obtain quantitative results. To this extent, we have derived a general approach which does not relay in the Fluctuation-Dissipation assumption and permits to introduce fluctuations in both variational and non-variational phase-field formulations. Well-established analytical techniques like boundary integral methods for the transient front position and linear stability analysis of the interface during the transient have been used as theoretical predictions for the computational results. The dynamical evolution of the solidification front can be divided in two stages: A linear regime where the initial noise is amplified, and a non-linear coarsening process where the final properties of the interfacial pattern are selected. We have studied these different stages of the solidification process by using the phase-field approach, and good agreement is obtained when comparing with well-established theoretical and experimental predictions.

Multiphase flow is a familiar phenomenon from daily life and occupies an important role in physics, engineering, and medicine. The understanding of multiphase flows relies largely on the theory of interfaces, which is not well understood in many cases. To date, the Navier-Stokes-Korteweg equations and the Cahn-Hilliard equation have represented two major branches of phase-field modeling. The Navier-Stokes-Korteweg equations describe a single component fluid material with multiple states of matter, e.g., water and water vapor; the Cahn-Hilliard type models describe multi-component materials with immiscible interfaces, e.g., air and water. In this dissertation, a unified multiphase fluid modeling framework is developed based on rigorous mathematical and thermodynamic principles. This framework does not assume any ad hoc modeling procedures and is capable of formulating meaningful new models with an arbitrary number of different types of interfaces. In addition to the modeling, novel numerical technologies are developed in this dissertation focusing on the Navier-Stokes-Korteweg equations. First, the notion of entropy variables is properly generalized to the functional setting, which results in an entropy-dissipative semi-discrete formulation. Second, a family of quadrature rules is developed and applied to generate fully discrete schemes. The resulting schemes are featured with two main properties: they are provably dissipative in entropy and second-order accurate in time. In the presence of complex geometries and high-order differential terms, isogeometric analysis is invoked to provide accurate representations of computational geometries and robust numerical tools. A novel periodic transformation operator technology is also developed within the isogeometric context. It significantly simplifies the procedure of the strong imposition of periodic boundary conditions. These attributes make the proposed technologies an ideal candidate for credible numerical simulation of multiphase flows. A general-purpose parallel computing software, named PERIGEE, is developed in this work to provide an implementation framework for the above numerical methods. A comprehensive set of numerical examples has been studied to corroborate the aforementioned theories. Additionally, a variety of application examples have been investigated, culminating with the boiling simulation. Importantly, the boiling model overcomes several challenges for traditional boiling models, owing to its thermodynamically consistent nature. The numerical results indicate the promising potential of the proposed methodology for a wide range of multiphase flow problems. / text

This thesis is devoted to several aspects of geometry and morphology in wetting problems and hard sphere packings. First, we propose a new method to simulate wetting and slip on nanostructured substrates: a phase field model associated with a dynamical density theory approach. We showed omniphobicity, meaning repellency, no matter the chemical properties of the liquid on monovalued surfaces, i.e. surfaces without overhangs, which is in contradiction with the macroscopic Cassie-Baxter-Wenzel theory, can produce so-called We checked systematically the impact of the surface parameters on omniphobic repellency, and we show that the key ingredient are line tensions, which emerge from needle shaped surface structures. Geometrical effects have also an important influence on glassy or jammed systems, for example amorphous hard sphere systems in infinite pressure limit. Such hard sphere packings got stuck in a so-called jammed phase, and we shall demonstrate that the local structure in such systems is universal, i.e. independent of the protocol of the generation. For this, robust order parameters - so-called Minkowski tensors - are developed, which overcome robustness deficiencies of widely used order parameters. This leads to a unifying picture of local order parameters, based on geometrical principles. Furthermore, we find with the Minkowski tensor analysis crystallization in jammed sphere packs at the random closed packing point

Anticiper l’évolution de la microstructure d’un matériau en condition d’usage est d’une importance cruciale pour l’industrie. Cette maîtrise du vieillissement nécessite une compréhension claire des mécanismes sous-jacents, qui agissent sur une large gamme d’échelles spatiales et temporelles. Dans cette optique, ce travail de thèse a choisi d’appliquer la méthode de champ de phase qui, en raison du saut d’échelle qu’elle réalise naturellement, est un outil intensivement employé dans le domaine des matériaux, pour prédire l’évolution en temps long de la microstructure. L’enjeu de l’étude a été d’étendre cette méthode à un système porté loin de l’équilibre thermodynamique, en particulier en présence d’irradiation. Nous avons ainsi adopté le formalisme du mélange ionique, introduit par Gras-Marti pour décrire le mélange balistique au sein d’une cascade de déplacements. Par l’utilisation conjointe d’un schéma numérique et d’une approche analytique, il nous a été possible d’établir le diagramme de phase générique d’un matériau irradié. Nous avons ensuite étudié le vieillissement de l’alliage binaire test AgCu sous irradiation, par l’utilisation conjointe de la méthode du champ de phase et d’approches atomistiques, dans une démarche multi-échelles. En fixant les paramètres de contrôle que sont le flux d’irradiation et la température, il nous a ainsi été possible de prédire la taille,la concentration ainsi que la distribution spatiale des nodules de cuivre produits sous irradiation dans cet alliage. La connaissance de ces informations a permis de simuler un diagramme de diffraction en incidence rasante, directement comparable aux diagrammes expérimentaux. / It is of dramatic matter for industry to be able to predict the evolution of material microstructure under working conditions. This requires a clear understanding of the underlying mechanisms, which act on numerous space and time scales. Because it intrinsically performs a scale jump, we chose to use a phase field approach, which is widely used amidst the condensed matter community to study the aging of materials. The first challenge of this work was to extend this formalism beyond its thermodynamic scope and embrace the case of far from equilibrium systems when subjected to irradiation. For that purpose, we adopted the model of ion mixing, developed by Gras Marti to account for ballistic exchanges within a displacements cascade. Based on a numerical scheme and ananalytical method, we were able to describe the generic microstructure signature for materials under irradiation.We then applied this formalism to the particular case of the immiscible binary alloy AgCu.With the joined use of the phase field approach and atomistic methods, we managed to predict how the temperature and the irradiation flux tailor the main microstructure features such as the size, the concentration and the distribution of copper precipitates. This eventually allowed us to simulate a diffraction pattern in grazing incidence, which is directly comparable to experimental ones.

In recent years, additive manufacturing (AM) of Alloy 718 has received increasing interest in the field of manufacturing engineering owing to its attractive features compared to those of conventional manufacturing methods. The ability to produce complicated geometries, low cost of retooling, and control of the microstructure are some of the advantages of the AM process over traditional manufacturing methods. Nevertheless, during the building process, the build material undergoes complex thermal conditions owing to the inherent nature of the process. This results in phase transformation from liquid to solid and solid state. Thus, it creates microstructural gradients in the built objects, and as a result,heterogeneous material properties. The manufacturing process, including the following heat treatment that is used to minimise the heterogeneity, will cause the additively manufactured material to behave differently when compared to components produced by conventional manufacturing methods. Therefore, understanding the microstructure formation during the building and subsequent post-heat treatment is important, which is the objective of this work. Alloy 718 is a nickel-iron based super alloy that is widely used in the aerospace industry and in the gas turbine power plants for making components subjected tohigh temperatures. Good weldability, good mechanical properties at high temperatures, and high corrosion resistance make this alloy particularly suitablefor these applications. Nevertheless, the manufacturing of Alloy 718 components through traditional manufacturing methods is time-consuming and expensive. For example, machining of Alloy 718 to obtain the desired shape is difficult and resource-consuming, owing to significant material waste. Therefore, the application of novel non-conventional processing methods, such as AM, seems to be a promising technique for manufacturing near-net-shape complex components.In this work, microstructure modelling was carried out by using multiphase-field modelling to model the microstructure evolution in electron beam melting (EBM) and laser metal powder directed energy deposition (LMPDED) of Alloy 718 and x subsequent heat treatments. The thermal conditions that are generated during the building process were used as input to the models to predict the as-built microstructure. This as-built microstructure was then used as an input for the heat treatment simulations to predict the microstructural evolution during heat treatments. The results showed smaller dendrite arm spacing (one order of magnitude smaller than the casting material) in these additive manufactured microstructures, which creates a shorter diffusion length for the elements compared to the cast material. In EBM Alloy 718, this caused the material to have a faster homogenisation during in-situ heat treatment that resulting from the elevated powder bed temperature (> 1000 °C). In addition, the compositional segregation that occurs during solidification was shown to alter the local thermodynamic and kinetic properties of the alloy. This was observed in the predicted TTT and CCT diagrams using the JMat Pro software based on the predicted local segregated compositions from the multiphase-field models. In the LMPDED Alloy 718 samples, this resulted in the formation of δ phase in the interdendritic region during the solution heat treatment. Moreover, this resulted in different-size precipitation of γ'/γ'' in the inter-dendritic region and in the dendrite core. Themicro structure modelling predictions agreed well with the experimental observations. The proposed methodology used in this thesis work can be an appropriate tool to understand how the thermal conditions in AM affect themicro structure formation during the building process and how these as-built microstructures behave under different heat treatments.

Made available in DSpace on 2015-03-26T13:45:37Z (GMT). No. of bitstreams: 1 texto completo.pdf: 600673 bytes, checksum: 5c37453f66b222da0e1fe0d0fc0c2e66 (MD5) Previous issue date: 2014-02-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this present Work We study a model Of phase ñeld rnodeling the evolution of solidiñcation process that Occurs in Certain binary alloys. We obtain existence Of solution and results under the hypotheses of regularity the nonlinearities are Lipschitz and limited. The non-linearity involved in the phase ñeld equation is a potential double-well type. We use throughout the Work the ñxed point theorern Of Leray-Schauder and the Galerkin method. / No presente trabalho estudamos urn modelo de Campo de fase que modela a evolução dos processos de solidiñcação que Ocorre ern Certas ligas binárias. Obte- rnos a existência de solução e resultados de regularidade sob as hipóteses das não linearidades serern Lipschitz e limitadas. A não linearidade envolvida na equação de Campo de fase é urn potencial do tipo poç0-duplo. Utilizamos ao longo do trabalho 0 teorerna do ponto ñXO de Leray-Schauder e 0 rnétodo de Galerkin.

Un fluide porté à une température et pression supérieures à celles du point critique est communément appelé fluide supercritique. Ce fluide possède des propriétés particulièrement intéressantes à cheval entre celles des gaz et celle des liquides. En effet, la masse volumique d’un fluide supercritique est proche de celle d’un liquide tandis que sa viscosité est proche de celle d’un gaz. Une des caractéristiques particulières de ces fluides quand ils s’approchent du point critique est que plusieurs des propriétés thermo-physiques montrent un comportement singulier (compressibilité divergente, diffusivité thermique évanescente etc). Dans ce travail, un modèle mathématique basé sur les équations de Navier-Stokes couplées à celle de l’énergie est proposé afin d’étudier les écoulements de ces fluides très proches de leur point critique. La validation du modèle a été effectuée sur un problème de propagation d’onde acoustique dans l'eau. Nous avons ainsi observé que des solutions précises avec des schémas implicites pour des systèmes non linéaires sont possibles avec des nombres de Courant élevés. L’étude des écoulements dans des fluides supercritiques, lorsqu'ils sont assujettis à une trempe thermique et à une vibration simultanées ont montré que de telles conditions pouvaient conduire à la formation d’instabilités thermo-vibrationnelles, en particulier les instabilités de Rayleigh-vibrationnelles et paramétriques. Les simulations numériques nous ont permis de relever deux phénomènes particulièrement surprenants : (i) la température du fluide à l’intérieur du domaine devient inférieure à la trempe de température imposée à la frontière et (ii) une oscillation des doigts d’instabilité apparaît dans la couche limite thermique dans la direction de la vibration. Dans le cas des fluides sous le point critique (cas diphasique), le modèle compressible développé est couplé à un de champ de phase (“phase field”) dans les conditions isothermes. Des cas tests élémentaires ont été considérés avec succès. Une discussion est proposée afin d’étendre le modèle dans le cas d’une transition continue du régime supercritique au régime sous-critique et vice-versa. / A fluid, in addition to its liquid and gas phase, is known to exist in another phase, wherein the fluid inherits some properties of both the phases. Such a fluid is called a supercritical fluid and the conditions (pressure and temperature) beyond which the fluid exists in this state is called the critical point. One of the peculiar feature of the fluids near the critical point is that the various thermo-physical properties show a singular behavior, such as diverging compressibility, vanishing thermal diffusivity etc. The flow behavior near the critical point leads to intriguing flow features ascribed to the strong thermo-mechanical coupling whose in-depth investigation can be limited by experimental constraints especially during a continuous transition from supercritical to subcritical regime. The current work focuses on analyzing the flow behavior in near-critical fluids with prime focus on supercritical fluids. This is achieved by developing a mathematical and numerical model which is followed by the validation study and error analysis of the numerical scheme wherein unusual behavior of the Courant number is observed. Subsequently, the flow behavior of supercritical fluid is studied when simultaneously subjected to thermal quench and vibration, mainly Rayleigh-vibrational and parametric instabilities, their physical mechanism and various parameters affecting them. In addition, two captivating phenomena, firstly where the temperature of the fluid region drops below the imposed boundary condition and secondly, the see-saw motion of the thermal boundary layer are observed and physical explanations are provided. In order to investigate the flow dynamics in subcritical regime, phase-field modelling approach is explored for isothermal conditions. The model is examined for elementary test cases illustrating the feasibility to extend the model for a continuous transition from supercritical to subcritical regime.

Cette thèse porte essentiellement sur l'étude des solutions stationnaires, en dimension 1 d'espace, d'unmodèle de champs de phase cristallin introduit par Elder en 2002. Ainsi, nous prouvons, par la méthode deréduction de Lyapunov-Schmidt et la technique des multiparamètres, l'existence de courbes de solutionsbifurquantes stationnaires lorsque le noyau de l'opérateur linéarisé, au voisinage de la solution triviale estde dimension 2. Une parenthèse est ouverte pour la comparaison de l'énergie de la solution bifurquantepar rapport à celle la solution triviale. Aussi, grâce au principe de la stabilité réduite, nous fournissonsdes ensembles précis de valeurs des paramètres de bifurcation pour lesquelles les solutions obtenues sontstables ou instables. Ces résultats théoriques sont corroborés par plusieurs tests numériques.Par ailleurs, dans le cas classique du noyau unidimensionel, nous établissons des diagrammes de phasespermettant de comprendre les différentes orientations de courbes de solutions non triviales au voisinage dechaque point de bifurcation. / This thesis is devoted to the study of stationary solutions of a Phase Field Crystal model, in one spacedimension, introduced by Elder in 2002. Thus, we prove by the Lyapunov-Schmidt method of reductionand the multiparameter technique, the existence of the curves of bifurcating stationary solutions whenthe kernel of the linearized operator near to trivial solution is of two dimension. A parenthesis is open forcomparing the energies of the bifurcating solution and the trivial solution. Also, thanks to the principle ofreduced stability, we provide specific sets of parameter values for wich the obtained solutions are stable orunstable. These theoretical results are confirmed by several numerical tests.Moreover, in the classical case of a one dimensional kernel, we establish the phase diagrams allowing tounderstand the different orientations of non-trivial solutions curves near to of each bifurcation point.

No description available.