X / A combined experimental and computational investigation of the deformation behavior of pure magnesium single crystal at the micron length scale has been carried out. Employing the recently exploited method of microcompression testing, uniaxial microcompression experiments have been performed on magnesium single crystals with [0001], [2-1-12], [10-11], [11-20] and [10-10] compression axes. The advantage of the microcompression method over conventional mechanical testing techniques is the ability to localize a single crystalline volume which is characterizable after deformation. The stress-strain relations resulting from microcompression experiments are presented and discussed in terms of orientation dependent slip activity, twinning mechanisms and an anisotropic size effect. Such a mechanistic picture of the deformation behavior is revealed through SEM, EBSD and TEM characterization of the deformation structures, and further supported by 3D discrete dislocation dynamics simulations. The [0001], [2-1-12], and [10-11] compression axes results show dislocation plasticity. Specifically, the deformation due to [0001] compression is governed by pyramidal slip and displays significant hardening and massive unstable shear at stresses above 500MPa. In the case of the two orientations with compression along an axis 45 degrees to the basal plane, unsurpringly it is found that basal slip dominates the deformation. In contrast, compression along the [11-20] and [10-10] directions show deformation twinning in addition to dislocation plasticity. In the case of compression along [11-20], the twinning leads to easy basal slip, while the twin resultant during compression along [10-10] does not lead to easy basal slip. In all cases, a size effect in the stress-strain behavior is observed; the flow stress increases with decreasing column diameter. Furthermore, the extent of the size effect is shown to depend strongly on the number of active slip systems; compression along the [0001] axis is associated with 12 slips systems and displays a saturation of the size effect at a diameter of 10μm, while the other orientations still show a significant size effect at this diameter. The experimental evidence of an orientation-dependent deformation behavior in flow stress has been investigated by 3D discrete dislocation dynamics simulations. Here, the code TRIDIS was modified for hcp structure and c/a ratio of Mg. By matching the simulation results to experimental results, some proper constitutive material parameters such as initial dislocation density, dislocation source length, the critical resolved shear stress were suggested. For the case of [0001] and [2-1-12] orientation, dislocation feature in the pillar during the deformation was exhibited and strain burst was discussed.

Cette étude s’insère dans le cadre d’une modélisation multi-échelles du durcissement et de la fragilisation par irradiation de l’acier de cuve des Réacteurs nucléaires à Eau Pressurisée (REP). Des simulations en Dynamique des Dislocations (DD) ont été menées pour décrire la plasticité du fer pur irradié à l’échelle du grain et fournir aux échelles supérieures des informations quantitatives telles que la force d’épinglage des dislocations par les boucles induites par l’irradiation. Nous avons débuté notre étude par l’analyse des interactions élémentaires entre une dislocation coin et différents types de boucles. Un nouveau modèle de DD a été identifié puis validé, que ce soit d’un point de vue qualitatif (mécanismes d’interaction) ou quantitatif (contrainte critique), en comparant ces résultats à ceux obtenus en Dynamique Moléculaire dans la littérature. L’influence de la taille des boucles et de la vitesse de déformation a été particulièrement étudiée.Des simulations élémentaires impliquant cette fois-ci une dislocation vis et les mêmes défauts d’irradiation ont permis d’étendre le domaine de validité du modèle de DD, en se comparant toujours aux résultats de DM de la littérature. Enfin, un premier jeu de simulations massives entre une dislocation coin et différents types de boucles a permis d’obtenir une première estimation de la valeur de la force d’obstacle pour ce type de défauts, α≈0,26. Cette valeur est en accord avec différents travaux précédents, expérimentaux ou numériques, et permet d’envisager avec confiance de futurs travaux s’appuyant sur ce nouveau modèle de DD. / This study is a contribution to the multi-scale modeling of hardening and embrittlement of the vessel steel in Pressurized Water Reactors (PWR) under irradiation conditions. Dislocation Dynamics simulations (DD) were conducted to describe the plasticity of irradiated iron at grain scale. Quantitative information about the pinning strength of radiation-induced loops was extracted and can be transferred at crystal plasticity scale. Elementary interactions between an edge dislocation and different types of loops were first analyzed. A new model of DD was identified and validated, both qualitatively in terms of interaction mechanisms and quantitatively in terms of critical stress, using Molecular Dynamics results available in the literature. The influence of the size of the loops and of the strain rate was particularly studied. Elementary simulations involving a screw dislocation and the same radiation-induced defects were conducted and carefully compared to available MD results, extending the range of validity of our model. Finally, a set of massive simulations involving an edge dislocation and a large number of loops was performed and allowed a first estimation of the obstacle strength for this type of defects (α≈0.26). This value is in a good agreement with previous experimental and numerical studies, and gives us confidence in future work based on this new DD model.

Ce travail porte sur la résolution de problèmes faisant intervenir des mouvements d'interfaces. Dans les différentes parties de cette thèse, on cherche à déterminer ces mouvements d'interfaces en résolvant des modèles approchés consistant en des équations ou des systèmes d'équations sur des champs. Les problèmes obtenus sont des équations paraboliques et des systèmes hyperboliques. Dans la première partie (chapitre 2), on étudie un modèle simplifié pour la propagation d'une onde de souffle en dynamique des fluides compressibles. Ce modèle peut s'écrire sous la forme d'un système hyperbolique, et on construit un algorithme résolvant numériquement ce système par une méthode de type Fast-Marching. On mène également une étude théorique de ce système pour déterminer des solutions de référence et tester la validité de l'algorithme. Dans la deuxième partie (chapitres 3 à 5), les équations approchées sont de type parabolique, et on cherche à montrer l'existence de solutions de type régime permanent à ces équations. Dans les chapitres 3 et 4, on étudie une équation générique en une dimension associée à des phénomènes de réaction-diffusion. Dans le chapitre 3, on montre l'existence de solutions quasi-planes pour un terme de réaction (terme non-linéaire) assez général, et dans le chapitre 4 on utilise ces résultats pour montrer l'existence d'ondes pulsatoires progressives dans le cas spécifique d'une non-linéarité bistable. Le modèle étudié dans le chapitre 5 est un modèle de champ de phase approchant un modèle de dynamique des dislocations dans un cristal, dans un domaine correspondant physiquement à une source de Frank-Read / This work is about the resolution of problems associated with the motion of interfaces. In each part of this thesis, the goal is to determine the motion of interfaces by the use of approached models consisting of equations or systems of equation on fields. The problems we get are parabolic equations and hyperbolic systems. In the first part (Chapter 2), we study a simplified model for the propagation of a shock wave in compressible fluid dynamics. This model can be written as a hyperbolic system, and we construct an algorithm to solve it numerically by a Fast-Marching like method. We also conduct a theoretical study of this system to determine reference solutions and test the algorithm. In the second part (Chapters 3 to 5), the approached models yield parabolic equations, and our goal is to show the existence of permanent regime solutions for these equations. Chapter 3 and 4 are dedicated to the study of a generic one-dimensional equation modelling reaction-diffusion phenomena. In Chapter 3, we show the existence of plane-like solutions for a general reaction term, and in Chapter 4 we use this result to show the existence of pulsating travelling waves in the specific case of a bistable nonlinearity. In Chapter 5, we study a phase-field model approaching a model for the dynamics of dislocations in a crystal, in a domain corresponding to a Frank-Read source

A combined experimental and computational investigation of the deformation behavior of pure magnesium single crystal at the micron length scale has been carried out. Employing the recently exploited method of microcompression testing, uniaxial microcompression experiments have been performed on magnesium single crystals with [0001], [2-1-12], [10-11], [11-20] and [10-10] compression axes. The advantage of the microcompression method over conventional mechanical testing techniques is the ability to localize a single crystalline volume which is characterizable after deformation. The stress-strain relations resulting from microcompression experiments are presented and discussed in terms of orientation dependent slip activity, twinning mechanisms and an anisotropic size effect. Such a mechanistic picture of the deformation behavior is revealed through SEM, EBSD and TEM characterization of the deformation structures, and further supported by 3D discrete dislocation dynamics simulations. The [0001], [2-1-12], and [10-11] compression axes results show dislocation plasticity. Specifically, the deformation due to [0001] compression is governed by pyramidal slip and displays significant hardening and massive unstable shear at stresses above 500MPa. In the case of the two orientations with compression along an axis 45 degrees to the basal plane, unsurpringly it is found that basal slip dominates the deformation. In contrast, compression along the [11-20] and [10-10] directions show deformation twinning in addition to dislocation plasticity. In the case of compression along [11-20], the twinning leads to easy basal slip, while the twin resultant during compression along [10-10] does not lead to easy basal slip. In all cases, a size effect in the stress-strain behavior is observed; the flow stress increases with decreasing column diameter. Furthermore, the extent of the size effect is shown to depend strongly on the number of active slip systems; compression along the [0001] axis is associated with 12 slips systems and displays a saturation of the size effect at a diameter of 10μm, while the other orientations still show a significant size effect at this diameter. The experimental evidence of an orientation-dependent deformation behavior in flow stress has been investigated by 3D discrete dislocation dynamics simulations. Here, the code TRIDIS was modified for hcp structure and c/a ratio of Mg. By matching the simulation results to experimental results, some proper constitutive material parameters such as initial dislocation density, dislocation source length, the critical resolved shear stress were suggested. For the case of [0001] and [2-1-12] orientation, dislocation feature in the pillar during the deformation was exhibited and strain burst was discussed.

La prédiction de la géométrie d'une pièce mise en forme par déformation plastique grâce à un logiciel de calcul par éléments finis (EF) s'effectue en suivant séquentiellement différentes étapes : la caractérisation thermo-mécanique du matériau, la modélisation de son comportement et son intégration dans un logiciel EF, puis la mise en données et la simulation de l'opération de formage. La phase de modélisation consiste entre autre à identifier quel type de modèle de comportement est le plus approprié pour prédire les réactions du matériau lors de l'opération de formage. Ces modèles sont essentiellement développés dans le cadre de la mécanique des milieux continus (MMC). L'hypothèse forte, si ce n'est centrale, de la MMC consiste à considérer que les variables qui servent à déterminer le comportement du matériau sont continues et dérivables. Cependant, les connaissances les plus élémentaires de métallurgie indiquent que les grandeurs locales dans les matériaux métalliques sont discontinues. La majorité des modèles de comportement mécanique des matériaux métalliques repose sur la définition d'un volume élémentaire représentatif dont la taille est assez grande pour permettre une homogénéisation de la description du comportement en gommant l'influence des hétérogénéités localesL'objet de ces travaux est de montrer que la prise en compte des hétérogénéités locales dans la modélisation du comportement des matériaux métalliques est pertinente et contribue à l'amélioration de la prédiction des simulations d'opérations de mise en forme en élargissant le potentiel prédictif des modèles ainsi construits. Un modèle élasto-plastique prenant en compte les hétérogénéités locales est alors proposé. / To obtain a relevant shape of a formed part during its finite element simulation, several steps are needed: thermo-mechanical caracterization of the material, definition of the most relevant model and integration of this model in the FE software and finally after data converting and computing processes. The modelling step include, among other things, the identification of the most appropriate model to fit the experimental material behaviour. Those models are essentially developped within the framework of continuum mechanics (CM). A strong, if not the main assumption of the CM consists in considering that mechanical description variables are continuous and differentiable. However, the basic knowledge of metallurgy indicates that local data in metallic materials are discontinuous. For metallic materials, the majority of constitutive models are based on the definition of a representative elementary volume (REV). This REV is supposed to be large enough to erase the incidence of local heterogeneities. Then those constitutive models are assumed to be homogeneous.The aim of this work is to show that introducing local heterogeneities in the description of constitutive models is relevant and contribute to improve the simulation accuracy. Those models also provide an enlargement of the simulation predictive potential. Then an elasto-plastic model, based on local heterogeneities description, is proposed.

Les techniques avancées pour l’approximation de rang faible des matrices sont des outils de réduction de dimension fondamentaux pour un grand nombre de domaines du calcul scientifique. Les approches hiérarchiques comme les matrices H2, en particulier la méthode multipôle rapide (FMM), bénéficient de la structure de rang faible par bloc de certaines matrices pour réduire le coût de calcul de problèmes d’interactions à n-corps en O(n) opérations au lieu de O(n2). Afin de mieux traiter des noyaux d’interaction complexes de plusieurs natures, des formulations FMM dites ”kernel-independent” ont récemment vu le jour, telles que les FMM basées sur l’interpolation polynomiale. Cependant elles deviennent très coûteuses pour les noyaux tensoriels à fortes dimensions, c’est pourquoi nous avons développé une nouvelle formulation FMM efficace basée sur l’interpolation polynomiale, appelée Uniform FMM. Cette méthode a été implémentée dans la bibliothèque parallèle ScalFMM et repose sur une grille d’interpolation régulière et la transformée de Fourier rapide (FFT). Ses performances et sa précision ont été comparées à celles de la FMM par interpolation de Chebyshev. Des simulations numériques sur des cas tests artificiels ont montré que la perte de précision induite par le schéma d’interpolation était largement compensées par le gain de performance apporté par la FFT. Dans un premier temps, nous avons étendu les FMM basées sur grille de Chebyshev et sur grille régulière au calcul des champs élastiques isotropes mis en jeu dans des simulations de Dynamique des Dislocations (DD). Dans un second temps, nous avons utilisé notre nouvelle FMM pour accélérer une factorisation SVD de rang r par projection aléatoire et ainsi permettre de générer efficacement des champs Gaussiens aléatoires sur de grandes grilles hétérogènes. Pour finir, nous avons développé un algorithme de réduction de dimension basé sur la projection aléatoire dense afin d’étudier de nouvelles façons de caractériser la biodiversité, à savoir d’un point de vue géométrique. / Advanced techniques for the low-rank approximation of matrices are crucial dimension reduction tools in many domains of modern scientific computing. Hierarchical approaches like H2-matrices, in particular the Fast Multipole Method (FMM), benefit from the block low-rank structure of certain matrices to reduce the cost of computing n-body problems to O(n) operations instead of O(n2). In order to better deal with kernels of various kinds, kernel independent FMM formulations have recently arisen such as polynomial interpolation based FMM. However, they are hardly tractable to high dimensional tensorial kernels, therefore we designed a new highly efficient interpolation based FMM, called the Uniform FMM, and implemented it in the parallel library ScalFMM. The method relies on an equispaced interpolation grid and the Fast Fourier Transform (FFT). Performance and accuracy were compared with the Chebyshev interpolation based FMM. Numerical experiments on artificial benchmarks showed that the loss of accuracy induced by the interpolation scheme was largely compensated by the FFT optimization. First of all, we extended both interpolation based FMM to the computation of the isotropic elastic fields involved in Dislocation Dynamics (DD) simulations. Second of all, we used our new FMM algorithm to accelerate a rank-r Randomized SVD and thus efficiently generate multivariate Gaussian random variables on large heterogeneous grids in O(n) operations. Finally, we designed a new efficient dimensionality reduction algorithm based on dense random projection in order to investigate new ways of characterizing the biodiversity, namely from a geometric point of view.

Le mode de propagation complexe des fissures courtes observé dans les métaux ductiles sous chargement cyclique est généralement attribué à différents mécanismes de stabilisation intervenant à l’échelle de la microstructure, l’échelle mésoscopique. Parmi ces mécanismes, l’interaction de la fissure avec la microstructure de dislocation semble jouer un rôle majeur. La dynamique des dislocations contrôle la déformation plastique et le transfert de chaleur qui lui est associé et réduit ainsi la quantité d’énergie élastique stockée dans le matériau. De plus, la microstructure de dislocations peut « écranter » le champ élastique induit par la fissure par son propre champ de contraintes et modifier la géométrie de la fissure par l’émoussement des surfaces en pointe. Pour la première fois, ces mécanismes sont étudiés avec des simulations 3D de Dynamique des Dislocation avec le modèle Discrete-Continu. Trois orientations de fissure sont testées sous un chargement monotone en traction, promouvant une ouverture en fond de fissure en mode I. De manière surprenante, les simulations montrent que les effets d’écrantage et d’émoussement n’ont pas un rôle clé dans la stabilisation des fissures testées en mode I. Le mécanisme principal se trouve être la capacité du matériau à se déformer plastiquement sans mettre en oeuvre un durcissement important par le mécanisme de la forêt. Des recherches supplémentaires sur deux effets de taille confirment ces résultats et montrent également la contribution mineure d’une densité de dislocations polarisées et du durcissement cinématique associé à la stabilisation des fissures. / The erratic behaviour of short cracks propagation under low cyclic loading in ductile metals is commonly attributed to a complex interplay between stabilisation mechanisms that occur at the mescopic scale. Among these mechanisms, the interaction with the existing dislocation microstructure play a major role. The dislocation microstructure is source of plastic deformation and heat transfer that reduce the specimen stored elastic energy, screen the crack field due to its self generated stress field or change the crack geometry through blunting mechanisms. For the first time, these mechanisms are investigated with 3D-DD simulations using the Discrete- Continuous Model, modelling three different crack orientations under monotonic traction loading promoting mode I crack opening.Surprisingly, screening and blunting effects do not seem to have a key role on mode I crack stabilisation. Rather, the capability of the specimen to deform plastically without strong forest hardening is found to be the leading mechanism. Additional investigations of two different size effects confirm those results and show the minor contribution of a polarised dislocations density and the associated kinematic hardening on crack stabilisation.

<p>A first-principles theory of plasticity in metals currently does not exist. While many plasticity models make reference to rules based on heuristic arguments regarding dislocations (the fundamental mediators of plastic deformation in crystals), the scientific community still does not have a theory of dislocation dynamics which can recover even basic features of plasticity theory. Discrete dislocation dynamics, though a valuable tool for understanding fundamentals topics in dislocation plasticity, becomes unusable beyond ~1.5\% strain due to the line length multiplication inherent in deformation. As a result, it is necessary to develop continuum theories of dislocation dynamics which treat dislocation densities rather than individual dislocations. This thesis examines the foundations of one such continuum theory: line bundle continuum dislocation dynamics, which assumes that dislocations are roughly parallel at every point. First, this assumption is given definite meaning and it is shown from discrete dislocation dynamics data that to be appropriate when modelling dislocation densities on fine length scales (resolving densities on lengths less than 100 nm). Second, it is found that an additional driving force, the correlation stress, emerges from coarse-graining the line bundle dynamics. This correction to the dislocation interactions is dependent on tensorial dislocation correlation functions describing the short-range errors in the products of dislocation densities lying on two slip systems. The full set of these dislocation correlation functions are evaluated from discrete density data with the aid of a novel left-and-right handed classification of slip system interactions in FCC crystals. Lastly, a study of the correlation stress in a representative dislocation system suggests that these stresses are roughly one tenth the magnitude of the mean-field dislocation interaction stress. Taken together, this thesis bridges discrete and continuum models of dislocation dynamics and provides a foundation for future work on a first-principles theory of metal plasticity. </p>

Materials intended for disposal of spent nuclear fuel require a particular combination of physical and chemical properties. The driving forces and mechanisms underlying the material’s behavior must be scientifically understood in order to enable modeling at the relevant time- and length-scales. The processes that determine the mechanical behavior of copper canisters and iron inserts, as well as the evolution of their mechanical properties, are strongly dependent on the properties of various defects in the bulk copper and iron alloys. The first part of the present thesis deals with precipitation in the cast iron insert. A nodular cast iron insert will be used as the inner container of the spent nuclear fuel. Precipitation is investigated by computing effective interaction energies for point defect pairs (solute–solute and vacancy–solute) in bcc iron using first-principles calculations. The main considered impurities in the iron matrix include 3sp (Si, P, S) and 3d (Cr, Mn, Ni, Cu) solute elements. By computing interaction energies possibility of formation of different second phase particles such as late blooming phases (LBPs) in the cast iron insert is evaluated. The second part is devoted to the fundamentals of dislocations and their role in plastic deformation of metals. Deformation of single-crystal copper under high strain rates is simulated by employing dislocation dynamics (DD) method to examine the effect of strain rate on mechanical properties as well as dislocation microstructure development. Creep deformation of copper canister at low temperatures is studied. The copper canister will be used in the long-term storage of spent nuclear fuel as the outer shell of the waste package to provide corrosion protection. A glide rate is derived based on the assumption that at low temperatures it is controlled by the climb rate of jogs on the dislocations. Using DD simulation creep deformation of copper at low temperatures is modeled by taking glide but not climb into account. Moreover, effective stresses acting on dislocations are computed using the data extracted from DD simulations. / <p>QC 20170428</p>

Microscopic beams of penetrating synchrotron radiation provide a unique tool for the analysis of material structure and deformation. This thesis describes my contributions to the development of new synchrotron X-ray micro-beam diffraction experimental techniques and data interpretation, and the use of experimental results for the validation of material deformation models. To study deeply buried material volumes in thick samples, the micro-beam Laue technique was extended to higher photon energies. Through-thickness resolution was achieved either by a wire scanning approach similar to Differential Aperture X-ray Microscopy (DAXM), or by applying tomographic reconstruction principles to grain-specific Laue pattern intensity. Both techniques gave promising first results. For reliable micro-beam Laue diffraction measurements of elastic strains in individual grains of a polycrystal, understanding of the error sources is vital. A novel simulation-based error analysis framework allowed the assessment of individual contributions to the total measurement error. This provides a rational basis for the further improvement of experimental setups. For direct comparison of experimental measurements and dislocation dynamics simulations, diffraction post-processing of dislocation models in two and three dimensions was developed. Simulated diffraction patterns of two-dimensional dislocation cell/wall type structures captured correctly some of the features observed experimentally in reciprocal space maps of a large-grained, lightly deformed aluminium alloy sample. Crystal lattice rotations computed from three-dimensional dislocation dynamics simulations of a Frank-Read source showed anisotropic orientation spread similar to that observed in micro-beam Laue experiments. For the experimental study of crystal lattice distortion, a novel technique was proposed that combines micro-beam Laue diffraction with scanning white-beam topography. Diffraction topography allows the study of lattice rotation at scales smaller than the scanning beam size. The new technique makes it possible to apply classical topography methods to deformed samples.