1,721,007 research outputs found
Phase field modeling of deformation twinning in β-metastable titanium alloys
No full textLes alliages de titane beta-métastables ont des propriétés mécaniques remarquables à température ambiante, liées à l'évolution sous contrainte de la microstructure. Un mode de déformation spécifique à ces alliages joue un rôle essentiel : le système de maclage {332}. On s'intéresse ainsi à une modélisation champ de phase de l'évolution sous contrainte des variants de macle {332}. Une première partie est consacrée à un modèle champ de phase de type Allen-Cahn avec prise en compte d'une élasticité dans un formalisme géométriquement linéaire (GL). On utilise une énergie d'interface isotrope ou anisotrope afin d'étudier l'influence de cette dernière sur la croissance et le degré d'anisotropie des variants de macle. Le rôle d'une élasticité formulée dans le formalisme géométriquement non-linéaire (GNL) est ensuite discuté et donne lieu à la deuxième partie de ces travaux. Un solveur mécanique dans le formalisme GNL par méthode spectrale est alors mis en place et validé. Il est ensuite utilisé dans le développement d'un modèle champ de phase de type Allen-Cahn avec prise en compte d'une élasticité GNL. Nous procédons alors à une étude comparative fine des microstructures obtenues en GL et GNL. Les résultats montrent une différence majeure entre les microstructures obtenues dans les deux cadres élastiques, concluant sur la nécessité d'une élasticité dans le GNL pour reproduire les microstructures de macle observées. Enfin, nous présentons une étude prospective d'un modèle basé sur une méthode de réduction de Lagrange, qui permettrait de prendre en compte le caractère reconstructif du maclage et la nature hiérarchique des microstructures observées expérimentalement.Beta-metastable titanium alloys exhibit remarkable mechanical properties at room temperature, linked to the microstructure evolution under stress. A specific deformation mode plays an essential role: the {332} twinning system. This thesis work thus concerns a modeling, by the phase field method, of {332} twin variants evolution under stress. The first part is devoted to an Allen-Cahn type phase field model with an elasticity taken into account in a geometrically linear formalism. This model is used with an isotropic or anisotropic interface energy in order to study the influence of the latter on the growth of twin variants. The role of an elasticity formulated in finite strain is then discussed and gives rise to the second part of this work. A mechanical equilibrium solver formulated in the geometrically non-linear formalism using a spectral method is then set up and validated. It is then used in the development of an Allen-Cahn type phase field model considering a geometrically non-linear elasticity. We then proceed to a fine comparative study of the microstructures obtained in linear and non-linear geometries. The results show a major difference between the microstructures obtained in the two elastic frameworks, concluding on the need for elasticity in finite strain formalism to reproduce the twin microstructures observed experimentally. Finally, we present a prospective study of a more general phase field formalism than the previous ones, based on a Lagrange reduction method, which would allow to fully take into account the reconstructive character of twinning and the hierarchical nature of the microstructures observed experimentally
Phase-field modeling of Widmanstätten growth
No full textL'arrangement complexe des phases d'un alliage métallique, appelé microstructure, conditionne fortement ses propriétés mécaniques. Pour les optimiser, il est essentiel de comprendre comment les microstructures apparaissent et évoluent. Nous nous intéressons ici à une microstructure en particulier, appelée Widmanstätten. Ces structures de morphologie aciculaire sont observées dans plusieurs alliages métalliques (FeC, CuZn ...). Leur croissance, pilotée par la diffusion des éléments d'alliage, a lieu à vitesse constante en conditions isothermes. Plusieurs aspects de cette croissance restent cependant mal compris, ce qui justifie cette étude. Grâce à la méthode des champs de phase, nous montrons tout d'abord que l'anisotropie de l'énergie élastique joue un rôle clé sur cette croissance, en 2D et en 3D. Nous observons que le rayon de courbure de la pointe ne dépend pas de la dynamique mais résulte plutôt de la compétition entre énergie élastique et énergie d'interface. Puis, pour des alliages de titane, nous avons montré que notre modèle rend bien compte de la taille de la pointe. Nous avons ensuite développé deux modèles pour étudier le rôle joué par deux mécanismes de relaxation par déformation plastique: dislocations d'accommodation et activité plastique dans la matrice. Nous avons observé que la plasticité ne modifiait pas le caractère stationnaire de la croissance mais modifiait la vitesse et la taille de la pointe. Enfin, nous avons développé un formalisme à une échelle plus fine capable de décrire la nucléation et la croissance de marches, souvent observées dans les structures de Widmanstätten. Les premiers résultats pour un champ non-conservé sont présentés ici.He complex rearrangement of the phase domains in a metallic alloy, called microstructure, strongly impacts its mechanical properties. To optimize them, it is therefore important to understand the formation and evolution of the microstructures. The present work is devoted to a specific type of microstructures, called Widmanstätten. These acicular structures are observed in many metallic alloys (FeC, CuZn ...). Their growth, driven by the diffusion of alloying elements, occurs at constant velocity, in isothermal conditions. Yet, several aspects of this growth remain poorly understood, which justifies this study. Using phase-field models, we first show that the anisotropy of the elastic energy plays a key role on the growth, in both 2D and 3D. We observe that the tip radius of curvature does not depend on a dynamical process but relies on the competition between interfacial and elastic energy. Then, we illustrate the ability of our model to correctly describe the size of the tip. We have then developed two models to take into account two different mechanisms of relaxation by plastic deformation: misfit dislocations and plastic activity in the matrix. We have observed that plasticity does not change the singular growth at constant velocity but yet modifies the value of the growth velocity and the tip radius of curvature. Finally, we have developed a formalism at a thinner scale which is able to describe step nucleation and growth, which are often observed in Widmanstätten structures. Preliminary results, for a non-conserved field, are presented here
Thermodynamic and kinetic scale transfer for diffusion in alloys
No full textLa prédiction des microstructures représente un enjeu majeur pour l'étude des processus de vieillissement des alliages métalliques, en particulier sous irradiation. Les résultats des calculs ab initio de structure électronique peuvent être utilisés pour paramétrer les méthodes cinétiques de Monte Carlo Atomique et permettent ainsi de simuler quantitativement la diffusion des atomes et l'évolution de la microstructure qui en résulte. Cette méthode est cependant limitée par le temps de calcul qu'elle exige. Les simulations mésoscopiques évitent cet écueil, mais souffrent généralement de ne pouvoir être paramétrées sur les résultats obtenus aux échelles inférieures, limitant ainsi leur pouvoir de prédiction. Dans ce travail, une méthode de simulation appelée Monte Carlo cellulaire cinétique a été développée pour relier les échelles atomiques et mésoscopiques tout en conservant la nature discrète des atomes. Une procédure de paramétrisation basée sur les simulations Monte Carlo à l'échelle atomique a été établie. Elle permet de reproduire quantitativement les propriétés macroscopiques d'équilibre des alliages indépendamment de la taille des cellules utilisées. Une application à l'alliage fer-cuivre est présentée. Afin de décrire les propriétés cinétiques à ces échelles, un outil générique de calcul de la matrice d'Onsager dans les alliages a été mis en place. Il est fondé sur la theorie du Champ Moyen Auto-Cohérent. Les résultats obtenus sur des cinétiques de diffusion et de précipitation dans un alliage modèle sont présentés et validés par une comparaison systématique avec des simulations Monte Carlo à l'échelle atomique.Predicting microstructural evolution is a decisive step in the study of aging processes in alloys, especially under irradiation. The results of ab initio calculations of electronic structures can be used to parameterize kinetic methods such as Atomic Kinetic Monte Carlo simulations that allow reproducing quantitatively atomic diffusion and the resulting microstructure. Their use is however limited by their computational cost. Mesoscopic simulations are less concerned by such limitation, but suffer from the lack of reliable parameterization method to use data from simulations at lower scales that leads to a limited prediction capacity. A simulation method called Cellular Kinetic Monte Carlo is developed in this work to bridge the gap scales between atomic and mesoscopic scale simulation of diffusion. A crystal is there modeled as a. This method is based on a description of the crystal as a lattice of cells described by the discrete number of solute atoms they represents. The properties are then obtained by a controlled coarse-graining procedure based on Atomic Kinetic Monte Carlo simulations. It allows reproducing quantitatively macroscopic equilibrium for all cell sizes and has been applied to the Iron-Copper alloy. In order to describe kinetic properties at these scales, a generic computational tool has been developed to compute the Onsager matrix of alloys, based on the Self Consistent Mean field method. Diffusion and precipitation simulations have been done and the results are presented and assessed by a systematic comparison with Atomic Kinetic Monte Carlo simulations
A tetrahedron-based discretization for FFT-based computational homogenization with smooth solution fields
No full textInternational audienceWe propose a new discrete FFT-based method for computational homogenization of micromechanics on a regular grid that is simple, fast and robust. The discretization scheme is based on a tetrahedral stencil that generates two independent mechanical problems on distinct face centered cubic subgrids. The resulting equilibrium problems may be merged into a single one that is solved by a gradient-based method equivalent to the original Moulinec-Suquet basic scheme.The tetrahedral stencil displays three crucial properties. First, and most importantly, the Fourier representation of the associated Green operator is defined for any finite q-vector generated by the periodic boundary conditions and that does not belong to the reciprocal lattice of the discrete grids. As shown in the paper, this property guarantees that, for any elastic contrast, even infinite, mechanical equilibrium is always mathematically stable, i.e. free of any unphysical patterns, such as oscillations, ringing or checker-boarding, a property which is not shared by the original Moulinec-Suquet discretization [1, 2] nor by the rotated scheme proposed by Willot [3]. Second, the components of tensorial quantities are all defined on the same location, which permits the use of any elastic anisotropy and any spatial variation of the material fields. Third, convergence to equilibrium using the simplest iterative scheme, i.e. the basic scheme, is fast and the number of iterates stabilizes at high contrast, so that infinite contrast is obtained without additional computational cost. The efficiency and accuracy of the proposed tetrahedral stencil are assessed through several case studies, including microstructures that consist of a single inclusion with various elastic properties (finite eigenstrain, void, hard precipitate), a microstructure that contains simultaneously soft and stiff inclusions and complex 3D microstructures with random spherical voids. Convergence of effective elastic properties with grid refinement is investigated. An implementation of the tetrahedral stencil within the polarization-based fixed point algorithm of Monchiet-Bonnet is also proposed
A fast and robust discrete FFT-based solver for computational homogenization
Full text linkWe propose a new discrete FFT-based method for computational homogenization
of micromechanics on a regular grid that is simple, fast and robust. The
discretization scheme is based on a tetrahedral stencil that displays three
crucial properties. First, and most importantly, the Fourier representation of
the associated Green operator is defined for any finite q-vector generated by
the periodic boundary conditions and that does not belong to the Reciprocal
Lattice of the discrete grids. As shown in the paper, this property guaranties
that, for any elastic contrats, even infinite, mechanical equilibrium is always
mathematically stable, i.e. free of any unphysical patterns, such as
oscillations, ringing or checkerboarding, a property which is not shared by the
original Moulinec-Suquet method \cite{moulinec1994fast,moulinec1998numerical}
nor by the rotated scheme proposed by Willot \cite{willot2015fourier}. Second,
the components of tensorial quantities are all defined on the same location,
which permits the use of any elastic anisotropy and any spatial variation of
the material fields. Third, convergence to equilibrium using the simplest
iterative scheme, the "basic scheme", is fast and the number of iterates
stabilizes at high contrasts, so that infinite contrast is obtained without
additional computational cost.Comment: 34 pages, 10 figure
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Modeling microstructural evolution of metallic materials under extreme conditions
No full textLa compréhension des mécanismes fondamentaux à l’origine de l’évolution des défauts cristallins tels que les lacunes, les dislocations ou encore les cavités, ainsi que de leurs interactions mutuelles, est essentielle pour prédire le comportement des matériaux métalliques en conditions extrêmes. Les couplages multi-physiques en jeu sont cependant difficiles à identifier, tant par des simulations qu'à l'aide de dispositifs expérimentaux. Nous proposons ainsi un modèle champ de phase pour décrire les interactions entres lacunes, cavités et dislocations. Nous présentons dans un premier temps sa construction ainsi que son implémentation numérique, pensée de manière à minimiser les coûts de calculs. Nous détaillons en particulier notre approche originale de la résolution de l’équilibre chimique qui nous permet de simuler des phénomènes mésoscopiques sur les temps longs de la diffusion. Nous validons dans un second temps notre modèle dans le cadre de l'évolution de microstructures qui peuvent être approchées de manière analytique. Enfin, dans une troisième partie, nous étudions le comportement d’une microstructure 2D comportant plusieurs cavités et des dislocations. Nous montrons notamment que la prise en compte des interactions élastiques entre les cavités et les dislocations, généralement négligées dans ce type d’étude, modifie significativement la cinétique d’évolution de la microstructure.The comprehension of the fundamental mechanisms controlling the evolution and mutual interactions of extended defects such as dislocation and cavities is crucial to understand the behaviour of materials under extreme conditions. Underlying phenomena are hard to capture, either by numerical simulations or by experimental approaches. Therefore, building a complete mathematical formalism which can be efficiently implemented is at stake. In this work we develop a phase-field variational model that couples vacancy diffusion, dislocation climb and pore evolution, with the consideration of elastic interactions. We first present the construction of the model as well as its numerical implementation, including an improved solver for the equation controlling the vacancy field evolution. This drastically decreases the computational time and allows us to tackle diffusion at mesoscopic scales. We then validate our model on microstructures whose evolution can be predicted analytically. We finally present 2D simulation results on the interactions between climbing dislocations and pore assemblies, revealing the role of elastic interactions on the microstructural evolution
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