This study focuses ontransient heat flow behavior in which centralizing energy on themetal makes metal surface come to aheat molten state with centralized heat source . This flow field is two-dimensional transient model, using Phase-field method and Two-phase flow to simulatemetal surface. In this study is under considerations of the mass conservation equation, momentum equation, energy equation and the level-set equation, regardless of the impact due to the concentration diffusion. At last it will show the flow of the molten zone caused by temperature, and the flows in molten zone forced by thermocapillary which is caused byvariation of temperature.

Steadily increasing heat dissipation in electronic devices has generated renewed interest in direct immersion cooling. The ideal heat transfer fluid for direct immersion cooling applications should be chemically and thermally stable, and compatible with the electronic components. These constraints have led to the use of Novec fluids and fluroinerts as coolants. Although these fluids are chemically stable and have low dielectric constants, they are plagued by poor thermal properties. These factors necessitate the development of new heat transfer fluids with improved heat transfer properties and applicability. Computer Aided Molecular Design (CAMD) approach was used in this work to systematically design novel heat transfer fluids that exhibit significantly better properties than those of current high performance electronic coolants. The candidate fluids generated by CAMD were constrained by limiting their boiling points, latent heat of vaporization and thermal conductivity. The selected candidates were further screened using a figure of merit (FOM) analysis. Some of the fluids/additives that have been identified after the FOM analysis include C₄H₅F₃O, C₄H₄F₆O, C₆H₁₁F₃, C₄ H₁₂O₂Si, methanol, and ethoxybutane. The heat transfer performance of these new fluids/fluid mixtures was analyzed through pool boiling and flow boiling experiments. All the fluid mixtures tested showed an improvement in the critical heat flux (CHF) when compared to the base fluid (HFE 7200). A pool boiling model was developed using the phase field method available in COMSOL. Although these simulations are computationally expensive, they provide an alternate solution to evaluate several candidate fluids generated using the CAMD approach.

Dans ce travail de thèse, nous nous sommes intéressés à la simulation de l’évolution de la microstructure d’un polymère. Plus précisément, nous avons étudié le changement de la morphologie du polyéthylène téréphthalate (PET) sous l’effet de différents mécanismes. Ces simulations sont réalisées par la méthode des champs de phase. Il s’agit d’une méthode basée sur l’équation de Cahn-Hilliard ou l’équation de Ginzburg-Landau. Elle utilise un paramètre d’ordre pour décrire l’état du matériau, des variables thermodynamiques et cinématiques. Ainsi on peut décrire l’évolution d’une microstructure sans suivre l’interface et ainsi reproduire l’évolution de la structure cristalline sphérolitique qui apparait lors d’une cristallisation induite par la température. Dans le cadre d’un changement de morphologie induit par la température, le calcul par champ de phase a été simulé par la méthode de différences finies et la méthode d’éléments finis. Le coefficient cinétique a été identifié à partir de données expérimentales de la littérature. En introduisant un modèle du champ de phases multiples (the MPF model) on a aussi simulé l’évolution de plusieurs sphérolites et gérer la jonction lorsque deux sphérolites se rencontrent. La croissance et la jonction des sphérolite a été modélisée par la méthode d’éléments finis : elle reproduit parfaitement l’évolution expérimentale de cristallisation isotherme d’un polymère. En comparant ces résultats avec le modèle macroscopique d’Avrami, une évaluation de la constante d'Avrami, K(T), a été discutée en fonction des fluctuations des conditions initiales (positions et taille des germes).Dans le cadre de la cristallisation induite par la déformation mécanique, nous avons couplé le champ de phase aux équations de la mécanique pour un comportement viscoélastique différent pour chaque phase. L’influence, sur la cristallisation et l’orientation, de la déformation, de la vitesse de sollicitation, du contraste entre les phases sont étudiées et comparées qualitativement aux observations expérimentales. Il s’agit d’une étude préliminaire qui devra être poursuivie et affinée afin de prédire une morphologie plus réaliste / In this thesis work, we are interested in simulating the evolution of the microstructure of a polymer. In particular, we have studied in the morphology change of polyethylene terephthalate (PET) under different mechanisms. These simulations carried out by the phase field simulation. This method based on the Cahn-Hilliard equation or the Ginzburg-Landau equation. It uses an order parameter to describe the state of material, thermodynamic and kinetic variables. Thus we can describe the microstructure evolution without tracking the interface (which would require complex remeshing) and reproduce the evolution of the crystalline structure within the polymers, for example the growth of spherulites which appear during crystallization induced by temperature. Within the scope the morphology changing by the temperature, the evolution of phase field simulation is performed by the finite difference method and the finite element method. The kinetic coefficient is adjusted in order to fit the experiment data in of the literature. We introduce the multiphase field model (the MPF model) in order to simulate the evolution of several spherulites and to describe the junction of spherulites. The growth and junction of spherulites have been modeled by the finite element method and nicely reproduced in comparing the experimental evolution of isothermal crystallization of a polymer. Comparing these results with the Avrami macroscopic model, an evaluation of the Avrami constant, K (T), was discussed according to the fluctuations of the initial conditions (positions and size of the germs).In the following part, we study the crystallization induced by mechanical deformation. We are interested in the viscoelastic model to simulate the induced crystallization of PET in plane stress. The phase field model coupled to mechanics will be presented. Different viscoelastic behaviors have been considered for each phase. The influence on crystallization and orientation of the deformation, the stress velocity and the contrast between the phases are studied and compared qualitatively with the experimental observations. This is a preliminary study that will have to be continued in order to predict a more realistic morphology

Este trabalho apresenta um estudo da solidificação de metais puros utilizando o modelo de campo de fases. O modelo é utilizado para simular a solidificação com o intuito de obter a morfologia da interface sólido-líquido sob diversas condições de transferência de calor. Foram realizados testes de validação comparando as morfologias da interface sólido-líquido obtida com as morfologias apresentadas em trabalhos anteriores para os casos bi e tridimensionais. O modelo do campo de fases adotado consiste principalmente de duas equações diferenciais: uma para calcular a variável de campo de fases e outra para calcular o campo de temperaturas. As equações foram solucionadas numericamente para um oitavo do domínio devido a simetria do problema. Os cálculos do modelo indicam que um sólido esférico com um raio inicial menor que o raio crítico de nucleação refunde. Entretanto uma esfera de raio maior cresce. Quando o sólido inicial cresce em uma malha numérica relativamente grosseira, a forma do sólido desvia da forma esférica devido perturbações na interface sólido-líquido. Quando a malha é refinada, as perturbações não são detectadas; contudo, quando introduzidas artificialmente as perturbações crescem e distorcem o formato esférico. / This work presents a study of the solidification of pure metals using the phase field model. The model is used to simulate solidification in order to obtain the morphology of the solid-liquid interface under different heat transfer conditions. Validation tests were performed comparing the morphology of the solid-liquid interface with the morphologies obtained from previous works for two and three dimensional cases. The adopted phase-field model consisted mainly of two differential equations: one to calculate the field of phase variable and another for the temperature field. The equations were solved numerically in only one eighth of the domain owing to the symmetry of the problem. Model calculations show that a solid sphere with an initial radius smaller than the critical radius for nucleation shrinks, whereas a sphere with a larger radius grows. When it grows in a relatively coarse numerical mesh, the initial solid shape deviates from a sphere owing to perturbations at the solid-liquid interface. When the numerical mesh is refined, the growth of perturbations is not detected, but artificially introduced perturbations grow and distort the spherical shape.

Les aciers austénitiques et alliages à base de nickel sont des matériaux de choix pour leurs propriétés mécaniques à haute température. L'enrichissement en chrome améliore leur durabilité de part la formation d'une couche d'oxyde protectrice à l'exemple de la chromine (Cr2O3).Il est néanmoins établi, par des essais mécaniques sous vide, que l'oxydation réduit de manière notable leur durée de vie en fatigue.En effet, la croissance d'oxyde peut être accompagnée d'une introduction de défauts tels que l'injection de lacunes, d'éléments délétères comme l'hydrogène mais également de contraintes résiduelles, etc., dans le métal.Les micromécanismes de fissuration sont ainsi régis par des interactions complexes entre l'environnement et la surface du métal, faisant intervenir composition chimique et microstructure.Aujourd'hui, les enjeux de sécurité et de compétitivité font de la prévision de la durée de vie de ces alliages une nécessité pour l'industrie nucléaire.L'augmentation de la dimension des modèles permet de prendre en compte de manière explicite les interactions multiphysiques du couple oxyde/métal sous l'action d'un chargement mécanique.La thèse s'inscrit dans cette démarche et propose une formulation d'un modèle de champ de phases couplé avec la mécanique et fondé sur les principes de la thermodynamique des milieux continus.Le comportement effectif de l'interface est présentement obtenu via des méthodes d'homogénéisation permettant de combiner des comportements mécaniques dissemblables, à l'image d'un substrat ductile et de son oxyde fragile.Les contraintes induites par la formation d'oxyde et également par le chargement mécanique peuvent être relaxées viscoplastiquement, de manière isotrope et anisotrope, respectivement dans l'oxyde et dans le substrat.Des simulations par éléments finis de l'oxydation généralisée ainsi que de l'oxydation intergranulaire sous chargement mécanique sont effectuées.Ces dernières mettent en évidence la possibilité d'un phénomène d'oxydation catastrophique par la génération de contraintes de tensions dans l'oxyde fragile, lesquelles peuvent être localisées le long des intrusions d'oxyde dans les joints de grains. / Austenitic stainless steels and nickel based alloys are widely used for their mechanical properties at high temperatures.Their durability can be increased by the addition of chromium resulting in the formation of a protective oxide layer such as chromia (Cr2O3).Nevertheless, it is established from vacuum mechanical tests that oxidation significantly decreases their fatigue life.In fact, oxide growth can be followed with the injection of defects such as vacancies, deleterious chemical elements and residual stresses, etc., into the metal.The resulting cracking micromechanisms are therefore governed by complex interactions between the environment and the metal surface, implying the chemical composition and the microstructure of the metal.To date, materials life prediction is a necessity for the nuclear industry due to safety and economic issues.The enhancement of the model dimensionality allow to explicitly account for multi-physics interactions between oxide and metallic phases under mechanical loads.The thesis is in line with it and relies on the development of a phase field model coupled with mechanics that heavily relies on the principles of continuum thermodynamics.The effective behaviour of the interface is obtained by homogenisation methods allowing the mixture of separate behaviours, as it is the case on a ductile metallic substrate and its fragile oxide.Oxide growth residual stresses and mechanical load induced stresses can be relaxed by viscoplasticity, which is isotropic and anisotropic respectively for the oxide and the substrate.Full field finite element simulations are performed to study both generalised and intergranular oxidation under mechanical loads.The simulations highlight the possibility of triggering breakaway oxidation by the generation of tensile stresses in the fragile oxide, which can be localised along oxide intrusions at grain boundaries.

Bentonite is regarded as an ideal geomaterial for the engineering barrier system of a deep geological repository (DGR) where nuclear wastes are disposed, as it has several desirable properties for sealing the nuclear wastes, including low permeability, low diffusion coefficient, high adsorption capacity and proper swelling ability. Nevertheless, gas migration in saturated bentonite may undermine the sealing ability of the geomaterial. Previous experimental studies showed that the gas migration process is accompanied by complex hydromechanical (HM) behaviors, such as gas breakthrough phenomenon, development of preferential pathways, build-up of water pressure and total stress, nearly saturated state after gas injection test, localized consolidation, water exchange between clay matrix and developed fractures and self-sealing process. These experimentally observed behaviors should be properly modelled for conducting a reliable performance assessment for the geomaterial over the lifespan of DGR. In this thesis, two different coupled HM frameworks, i.e., one based on double porosity (DP) concept, referred to as coupled HM-DP framework, and the other on phase field (PF) method, referred to as coupled HM-PF framework, are proposed to simulate the gas migration process in saturated bentonite. For the coupled HM-DP framework, the saturated bentonite is assumed as a superposition of a MAcro-Continuum (MAC) and a MIcro-Continuum (MIC). Two-phase flow is only allowed in the MAC, whereas the MIC is impermeable to both water and gas. Nevertheless, the water can transfer between the MIC and the MAC under the water pressure gap. The first coupled HM model in this framework is based on a double effective stress concept. Mechanical behaviors of the MAC and the MIC are respectively governed by Bishop-type effective stress and Terzaghi’s effective stress. The model can well simulate the evolutions of both gas pressure and gas outflow rate, the water exchange between clay matrix and developed pathways, the high degree of saturation and the consolidation of clay matrix. To account for the development of preferential pathways, the damaging effect has been introduced in the framework. In this improved model, Bishop-type effective stress for the MAC is replaced by the independent stress state variables, i.e., net normal stress and suction, since using the net normal stress is beneficial to simulating tensile failure under high gas pressure. Numerical results showed that the damage-enhanced model can well describe the effect of the development of preferential pathways on the build-up of water pressure and total stress. In addition, the proposed hysteretic models for intrinsic and relative permeabilities make the coupled HM framework more flexible to reproduce the experimental results. To explicitly simulate the development of preferential pathways, a coupled HM-PF framework is developed by using Coussy’s thermodynamic theory and the microforce balance law. The coupled HM-PF framework is implemented in the standard Finite Element Method (FEM). To avoid the pore pressure oscillation and enhance the computational efficiency, a stabilized mixed finite element, in which linear shape functions are selected for interpolating all primary variables, is adopted to discretize the whole domain. In the developed framework, swelling pressure (initial stress) is accounted for by introducing a modified strain tensor that is the sum of the strain tensor due to deformation and the strain tensor calculated from the initial stress. The numerical results showed that the developed coupled HM-PF framework can capture some important behaviors, such as the discrete pathways, localized gas flow, built-up of water pressure and total stress under constant volume condition and nearly saturated state in clay matrix. A spatially autocorrelated random field is introduced into the framework to describe the heterogeneous distribution of HM properties in bentonite. The heterogeneity is beneficial to simulating the fracture branching and the complex fracture trajectory. Numerical results showed that some factors, such as Gaussian random field, coefficient of variation, boundary condition and injection rate, have significant influences on the fracture trajectory. At the end of the thesis, the obtained numerical results are synthesized and analyzed. Based on the analysis, the pros and cons of the developed numerical models are discussed. Corresponding to the limitations, some recommendations are proposed for future studies.

Duplex Stainless Steels (DSS) are used extensively in various industrial applications where the properties of both austenite and ferrite steels are required. Higher mechanical strength and superior corrosion resistance are the advantages of DSS. One of the main drawbacks for Duplex steels is precipitation of sigma phase and other intermetallic phases adversely affecting the mechanical strength and the corrosion behavior of the steels. The precipitation of these secondary phases and the associated brittleness can be due to improper heat treatment. The instability in the microstructure of Duplex stainless steels can be studied by understanding the phase transformations especially the ones involving sigma phase. To reduce the time and effort to be put in for experimental work, computational simulations are used to get an initial understanding on the phase transformations. The present thesis work is on the phase transformations involving sigma phase for Fe-Cr system and Fe-Cr-Ni system using theoretical approach in 1D and 2D geometries. A phase field model is implemented for the microstructural evolution in DSS in combination with thermodynamic data collected from the Thermo-Calc software. The Wheeler Boettinger McFadden (WBM) model is used for Gibbs energy interpolation of the system. FiPy- Finite volume PDE solver written in python is used to simulate the phase transformation conditions first in Fe-Cr system for ferrite-austenite and ferrite-sigma phase transformations. It is then repeated for Fe-Cr-Ni ternary system. In the present study a model was developed for deriving Gibbs energy expression for sigma phase based on the common tangent condition. This model can be used to describe composition constrained phases and stoichiometric phases using the WBM model in phase field modeling. Cogswell’s theory of using phase order variable instead of an interpolating polynomial in the expression for Gibbs energy of whole system is also tried.

In this thesis, a robust, reliable and efficient isogeometric analysis framework is presented that allows for an adaptive spatial discretization of non-linear and time-dependent multi-field problems. In detail, B\'ezier extraction of truncated hierarchical B-splines is proposed that allows for a strict element viewpoint, and in this way, for the application of standard finite element procedures. Furthermore, local mesh refinement and coarsening strategies are introduced to generate graded meshes that meet given minimum quality requirements. The different strategies are classified in two groups and compared in the adaptive isogeometric analysis of two- and three-dimensional, singular and non-singular problems of elasticity and the Poisson equation. Since a large class of boundary value problems is non-linear or time-dependent in nature and requires incremental solution schemes, projection and transfer operators are needed to transfer all state variables to the new locally refined or coarsened mesh. For field variables, two novel projection methods are proposed and compared to existing global and semi-local versions. For internal variables, two different transfer operators are discussed and compared in numerical examples. The developed analysis framework is than combined with the phase-field method. Numerous phase-field models are discussed including the simulation of structural evolution processes to verify the stability and efficiency of the whole adaptive framework and to compare the projection and transfer operators for the state variables. Furthermore, the phase-field method is used to develop an unified modelling approach for weak and strong discontinuities in solid mechanics as they arise in the numerical analysis of heterogeneous materials due to rapidly changing mechanical properties at material interfaces or due to propagation of cracks if a specific failure load is exceeded. To avoid the time consuming mesh generation, a diffuse representation of the material interface is proposed by introducing a static phase-field. The material in the resulting transition region is recomputed by a homogenization of the adjacent material parameters. The extension of this approach by a phase-field model for crack propagation that also accounts for interface failure allows for the computation of brittle fracture in heterogeneous materials using non-conforming meshes.

The prediction of fracture is of utmost importance regarding the design of modern, specifically tailored engineering materials. These materials are often heterogeneous, \ie their properties vary in space. This can either be achieved purposefully by combining two or more constituents to profit from a more resilient composite material, or happen due to unavoidable imperfections. In any case, purely experimental assessment of failure is tedious and circuitous as soon as the structure of interest gets more complex, and the involvement of numerical models is inevitable. In this work, the phase-field approach to fracture is applied which is able to capture manifold crack phenomena inherently and sidesteps the need for remeshing by describing the crack as a continuous field. The phase-field model is extended to a fully diffuse incorporation of heterogeneities: A static order parameter smoothly transitions from one to the other bulk material constituent, while the weak, brittle interface is incorporated via a continuous fracture toughness distribution. The sharp interface jump conditions still hold for the diffuse representation since a partial rank-1 relaxation is employed in accordance with the unilateral contact condition of the phase-field model. Moreover, a compensation procedure ensures the independence of the interface fracture toughness from interface and phase-field length scales. The model is validated by a comparison to analytical results and the predictive power is demonstrated by the deduction of direction-dependent, effective fracture properties of heterogeneous microstructures. / Die Vorhersage des Bruchverhaltens ist für die Entwicklung moderner, speziell zugeschnittener technischer Werkstoffe von größter Bedeutung. Diese Materialien sind oft heterogen, d.h. ihre Eigenschaften variieren im Raum. Dies kann entweder absichtlich durch die Kombination zweier oder mehrerer Bestandteile erreicht werden, um von einem widerstandsfähigeren Verbundwerkstoff zu profitieren, oder durch unvermeidbare Imperfektionen geschehen. In jedem Fall ist eine rein experimentelle Versagensbewertung komplexer Strukturen mühsam und umständlich, und die Nutzung numerischer Modelle unvermeidlich. In dieser Arbeit werden Brüche mittels Phasenfeldmethode modelliert, wodurch vielfältige Rissphänomene erfasst werden können und die Notwendigkeit einer Neuvernetzung durch die Beschreibung des Risses als kontinuierliches Feld entfällt. Das Phasenfeldmodell wird um eine vollständig diffuse Einbindung von Heterogenitäten erweitert: Ein statischer Orderparameter beschreibt den glatten Übergang zwischen zwei Bestandteilen des Materials, während die geschwächte, spröde Grenzfläche durch eine kontinuierliche Bruchzähigkeitsverteilung eingebunden wird. Die scharfen Grenzflächensprungbedingungen gelten auch für die diffuse Darstellung, da eine partielle Rang-1 Relaxation in Übereinstimmung mit der unilateralen Rissflächenkontaktbedingung genutzt wird. Darüber hinaus gewährleistet ein Kompensationsverfahren die Unabhängigkeit der Grenzflächenbruchzähigkeit von inhärenten Längenskalen der Grenzfläche und des Rissphasenfelds. Das Modell wird durch einen Vergleich mit analytischen Ergebnissen validiert und die Vorhersagekraft wird durch die Ableitung richtungsabhängiger, effektiver Brucheigenschaften heterogener Mikrostrukturen demonstriert.

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