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International audience; This article reviews the principles and applications of the phase field technique for modeling phase transformations and microstructural evolutions, with an emphasis on solid-solid transformations. Conventional phase field models, which rely on phenomenological thermodynamic and kinetic descriptions, are first presented and examples of application are discussed. Then, applications of the phase field method to phenomena induced by irradiation are reviewed, including radiation-enhanced and radiation-induced segregation and precipitation on sinks such as grain boundaries, dislocation and dislocation loops, the dynamical stabilization of compositional patterns and void lattices and the disordering of ordered precipitates.

A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible constitutive relationships and on the coupling of the numerous physical processes that are active. Phase changes are driven by temperature-dependent free-energy functions that become non-convex below a transition temperature. Higher-order spatial gradients are present in the model to account for phase boundary energy, and these terms necessitate the introduction of non-standard terms in the energy balance equation in order to satisfy the classical entropy inequality point-wise. To solve the resulting balance equations, a Galerkin finite element scheme is elaborated. To deal rigorously with the presence of high-order spatial derivatives associated with surface energies at phase boundaries in both the momentum and mass balance equations, some novel numerical approaches are used. Numerical examples are presented that consider boundary cooling of a domain at different rates, and these results demonstrate that the model can qualitatively reproduce the evolution of microstructural features that are observed in some alloys, especially steels. The proposed model opens a number of interesting possibilities for simulating and controlling microstructure pattern development under combinations of thermal and mechanical loading., Comment: To appear in Journal of the Mechanics and Physics of Solids

In this thesis, we formalize and study operatorial transformations of general dy- namic problems (nonlinear and/or nonlocal), to simplify or improve signi¯cantly problems like analysis, simulation, identication, control, estimation, etc. First, a generic formalism of dynamic problems, based on the notion of trajectorial formulations, is stated, and some operatorial transformations (a priori nonlocal and/or nonlinear) are studied, like time-scale transforamtions and operatorial parametrization of dynamic models. Then, the advantages of such transformations are highlighted on many concrete examples : desingularization of a nonlocal implicit ame front model, analysis and numerical scheme for a class of integrodierential wave equations, and control of a nonlinear model of fed-batch bioreactor.; L'objet de cette thèse est de formaliser et étudier la problématique de transformations opératorielles pour des problèmes dynamiques généraux (nonlinéaires et/ou nonlocaux), dans l'objectif d'apporter des simplifications ou améliorations significatives aux problèmes d'analyse, de simulation, d'identification, de commande, d'estimation, etc. Dans une première partie, un formalisme générique des problèmes dynamiques, centré autour de la notion de formulation trajectorielle, est posé, et plusieurs transformations opératorielles (\emph{a priori} elles aussi nonlinéaires et/ou nonlocales) sont étudiées, telles par exemple les transformations de type changement de temps ou la paramétrisation opératorielle de modèles dynamiques. L'intérêt de ces transformations est ensuite mis en lumière sur plusieurs exemples concrets, traités par voie analytique et mis en Suvre numériquement: désingularisation d'un modèle nonlocal implicite de front de flamme, analyse et schémas numériques pour une classe d'équations de propagation integro-differentielles, et contrôle d'un modèle nonlinéaire de bioréacteur fed-batch.

The heat treatment of steels is a process of fundamental importance for manipulating the properties of the steel. We present a consistent thermodynamic framework for modelling the heat treatment process which is able to capture both displacive and diffusive mechanisms. The present formulation is applicable to the a grain size level of observation. Some salient features of the thermodynamic framework are highlighted, especially those associated with surface energies, and a number of numerical experiments are presented.

International audience; We have developed a model which is able to describe the formation of high temperature microstructures in beta metastable titanium alloys. It is based on the classical theory of nucleation, and on growth laws obtained by assuming that the processes are controlled by the diffusion of the alloying chemical species only. Two morphologies are described: grain boundary allotriomorphs, and Widmanstatten plates gathered in colonies growing from the allotriomorphs. Moreover, a statistical description of the nucleation conditions on beta grain boundaries has been introduced in order to obtain the global kinetics of the transformation. The model predictions proved to be in good agreement with experimental results.