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Effect Of Atomic Mobility In The Precipitate Phase On Coarsening : A Phase Field StudySarkar, Suman 03 1900 (has links)
In this thesis, we have used a phase field model for studying the effect of atomic mobility inside the precipitate phase on coarsening behaviour in two dimensional (2D) systems. In all the available coarsening theories, the diffusivity inside the precipitate phase is not explicitly taken into account; this would imply that there is no chemical potential gradient inside the precipitate. This assumption is valid if (a) the atomic mobility inside the precipitate is much higher than that in the matrix, or (b) the precipitate volume fraction is small (i.e. the interparticle spacing is far higher than the average particle size).
We undertook this study to evaluate the potential effect of diffusivity in the precipitate on coarsening in situations where conditions (a) and (b), above, do not hold, by studying systems with moderate volume fractions (20% and 30%) and with low atomic mobilities in the precipitate. In our study, we have fixed the atomic mobility in the matrix at a constant value.
We have used the well known Cahn-Hilliard model in which the microstructure is described in terms of a composition field variable. The evolution of microstructure is studied by numerically solving a non-classical diffusion equation known as the Cahn-Hilliard equation. We have used a semi-implicit Fourier spectral technique for solving the CH equation using periodic boundary conditions.
The coarsening behaviour is tracked and analyzed using number density of particles, their average size and their size distribution. The main conclusion from this study is that, contrary to expectations, the atomic mobility in the precipitate phase has only a small effect on coarsening behavior. Specifically, with decreasing atomic mobility in the precipitate phase, we report a small increase in the number density, a slightly wider size distribution and a slightly smaller coarsening rate. We also add that these effects are too small to allow experimental verification. These results indicate that the need for chemical potential equilibration within each precipitate is not an important factor during coarsening.
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Precipitate Growth Kinetics : A Phase Field StudyMukherjee, Rajdip 08 1900 (has links) (PDF)
No description available.
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Propriétés mécaniques des verres métalliques massifs : Influence de la microstructure / Mechanical properties of bulk metallic glasses : Influence of microstructureQiao, Jichao 31 January 2013 (has links)
Ce travail a porté sur l’étude des propriétés thermiques et mécaniques des verres métalliques massifs. Dans le premier chapitre nous avons rappelé l’historique des verres métalliques massifs, leurs propriétés intéressantes et quelques applications de ces matériaux et nous les avons situés par rapport aux autres matériaux amorphes, tels que les polymères ou les verres d’oxydes. Nous avons analysé par différentes méthodes expérimentales (calorimétrie, analyse mécanique dynamique, diffraction des rayons X, microscopies électroniques) les caractéristiques de cette évolution et leur incidence sur les propriétés mécaniques. Différents alliages base zirconium, cuivre, titane ou lanthane ont été étudiés. Nous avons notamment montré que : ● Un chauffage à une température inférieure à la température de transition vitreuse (Tg) conduit à une relaxation structurale, dont la cinétique, étudiée par calorimétrie, peut être modélisée par une fonction de type exponentielle étendue. Les paramètres caractéristiques ont été déterminés pour les différents alliages étudiés. Cette relaxation conduit à une augmentation du module élastique de stockage, mais à une diminution de la composante viscoélastique de ce module, autrement dit à une diminution de la mobilité atomique. Une déformation plastique conduit à un effet inverse. Ces évolutions ont été interprétées à l’aide d’un modèle reposant sur l’existence de défauts, dont la concentration diminue lors de la relaxation structurale, mais augmente lors de la déformation plastique. ● Lorsqu’une contrainte mécanique périodique de faible amplitude est appliquée, on observe des relaxations mécaniques. Quelle que soit la composition de l’alliage, une relaxation importante est toujours observée au voisinage de la transition vitreuse, comme dans tous les autres matériaux amorphes. En plus, dans certains verres métalliques massifs, (exemple les verres base Lanthane), une relaxation secondaire est détectée à basse température. Cette relaxation, de faible énergie d’activation, est attribuée à des mouvements locaux qui se produisent dans les zones faibles du matériau, zones résultant de l’existence d’hétérogénéités à une échelle nanoscopique. ● Lorsque qu’une contrainte de forte amplitude est appliquée (cas des essais de compression), on observe un comportement caractéristique de tous les matériaux amorphes : comportement essentiellement fragile à basse température et écoulement viscoplastique à haute température. Une courbe maitresse a pu être tracée pour la viscosité. La transition d’un régime newtonien à un régime non-newtonien apparait lorsque la vitesse de déformation augmente. Tous les résultats expérimentaux ont été discutés dans le cadre d’un modèle physique, basé sur l’existence de défauts activés par une augmentation de température ou par une contrainte. / In the current work, we investigated the thermal and mechanical properties of bulk metallic glasses. The history of the bulk metallic glasses was described in the Chapter I. The clear interesting properties and applications of the bulk metallic glasses, compared with other amorphous materials, i.e. polymers and glassy oxides, were discussed. Different experimental methods [DSC, DMA, X-ray diffraction, electron microscopy] were used to investigate the features of evolution of the microstructure on mechanical properties for bulk metallic glasses. The different bulk metallic glasses, i.e. Zr-, Cu-, Ti- and La-based, have been studied in the current research. In particular, the main results as follows: ● A heat treatment performed below the glass transition temperature Tg induces the structural relaxation. The kinetics of the enthalpy relaxation was studied by differential scanning calorimetry and can be well fitted by a stretched exponential relaxation function. The characteristic parameters can be determined in different bulk metallic glasses. The structural relaxation leads to an increase of the storage modulus, on the contrary to a decrease of the visco-elastic component of the modulus. Namely, the structural relaxation induces a diminution of the atomic mobility. The plastic deformation leads to an inverse influence. Results are interpreted using a physical model, based on the existence of defects in the material, called quasi-point defects. Atomic mobility is reduced by structural relaxation due to decrease of the concentration of defects. In contrast, plastic deformation increases the concentration of defects and therefore enhances the atomic mobility. ● When a periodic mechanical stress with a low amplitude is applied, one can observe mechanical relaxation. The main (α) relaxation has been clearly observed near to the glass transition temperature in all the investigated bulk metallic glasses as well as other amorphous materials. In addition, in some cases of bulk metallic glasses (for example, Lanthanum-based metallic glass), a distant secondary relaxation has been detected at lower temperature. This relaxation presents lower activation energy, which is associated to dynamic heterogeneities and is related to local movements of “defect” on the nature of nanoscale order in glasses. ● When a large-amplitude stress is employed (case of the compression tests), one can acquire the characteristic behaviour of the amorphous materials: A typical brittle fracture phenomenon is observed at lower temperature and the flow stress can be detected at higher temperature. A master curve of the viscosity can be acquired based on the experimental results. The transition from a Newtonian to non-Newtonian regime appears when the strain rate increases. All the experimental results are discussed in the framework of physical models, based on existence of the defects, which can be activated by increasing temperature or stress.
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