Polycrystal models, beginning with the work of Sachs (1928) and Taylor (1938), have been used to predict very complex material behavior. The basis of these models is single crystal plasticity theory, which is then extended to model an actual (polycrystalline) material composed of a large number of single crystals or grains. Crystal plasticity models are formulated at the scale of the individual grain, which is viewed as a fundamental material element. To first order this is a reasonable approximation, and results in qualitatively good predictions. However, it is also well known that the grain is not a uniform entity, and that a great deal of non-uniform activity, including the development of well-defined dislocation structures, occurs within individual grains. The goals of this research are to complete an experimental data set for validation of material modeling, and to then improve the physical basis of predictive polycrystal plasticity models. Preferred orientations (textures) of oxygen free high conductivity (OFHC) copper were measured using reflection x-ray diffraction techniques. Monotonic strain paths included a variety of strain levels for both compression and torsion. One of the significant contributions of this research was the measurement of textures resulting from non-monotonic deformation histories, specifically compressive prestrain (to two different levels) followed by torsion to an effective plastic strain of 1.00. We also concluded synchrotron radiation experiments to map Laue images to examine subgrain microtexture formation at various stages of finite deformation. The second major contribution is to polycrystal plasticity modeling. Improvements to the plasticity model were achieved by including the effects of gradually developing, sub-grain scale microstructures, without explicitly modeling the structures, in terms of both crystallographic texture formation and work hardening. The effects of these microstructures were incorporated through the use of new internal state variables. They result in a broadening of the peaks of the macroscopic texture and a reduction of the rate of texture formation. Predictions of crystallographic orientation distributions were verified by plotting stereographs, which were shown to match measured crystallographic textures. The microstructural hardening law was introduced through a new form of latent hardening, which was shown to match experimental stress-strain behavior more closely than the basic model of Pierce, Asaro, and Needleman (1982). This latent hardening form augmented a Taylor-type term, which reflected statistically stored dislocations in the slip system hardness. Significantly, this improvement was also noted in the case of non-monotonic loading, which the standard model could not predict even to first order. Also, in the course of this research a planar double slip model was used as a precursor to the full three-dimensional modeling. The objective was to use the planar model to test various formulations, at least qualitatively, since it is a simpler model. As a result of comparisons between the three-dimensional simulations and the planar ones, the planar model was shown to be an insufficient tool for developing new texture and hardening evolution schemes as compared to the three-dimensional models. The planar model was unsuitable for modeling any but the most basic crystal plasticity relations and most simple deformation paths in a qualitative manner.

Titanium is a widely used metal in industrial and commercial applications. It retains anisotropic mechanical properties at room temperature due to its HCP crystal structure. The effects of crystal orientation have been studied theoretically and through modeling though there is a lack of empirical data available on the topic. The work presented here uses laser-machined voids along with EBSD analysis to study the ductility of grains in different orientations to better understand the microscale fracture process in α-titanium. Experimental results show that hard grains with their c-axis parallel to the tensile direction behave in a less ductile manner than grains with their c-axis oriented away from the tensile direction. This is due to the basal slip systems activating in the former case and prismatic slip systems in the latter. Models utilized include the McClintock model for void growth, Brown-Embury model for void coalescence and FEM crystal plasticity simulations

Les méthodes conçues pour être incorporées dans des polycristaux de modélisation multi-échelles sont présentées dans ce travail en deux tâches. Ce travail contient des méthodes à moyenne échelle pour capturer les effets des interactions de dislocations de glissement rencontrant des joints de grains maclage et la croissance simultanée de plusieurs fractions de volume de grains maclage sur le durcissement mécanique et l’évolution de la texture. Celles-ci sont mises en œuvre dans un cadre de plasticité cristalline utilisant le code visco-plastic-self consistent de Los Alamos, VPSC-7. Présentés ici, les effets de la croissance simultanée de multiples variantes maclage sur l’évolution de la texture sont suivis à l’aide d’un schéma de transfert de volume double de type Kalidindi. Dans la tâche 1, la mise en œuvre de ce schéma afin de simuler la texture des aciers à plasticité induite par maclage (TWIP) soumis au pressage angulaire à canal égal (ECAP) est résumée. Dans la tâche 2, les effets de durcissement de deux types d’interaction entre les dislocations de glissement et les joints de grain maclage rencontrés, à savoir la transmutation et la dissociation de dislocation, sont capturés au moyen de la modification du modèle de durcissement basé sur la densité de dislocation de [11]. Les interactions du premier type sont présentées dans une relation constitutive calculant la quantité de densité de dislocations attribuée à un système de glissement donné contenu dans la fraction de volume maclage rencontrée à partir de chaque système de glissement en interaction dans la fraction de volume mère. La quantité transmutée à partir de chaque système de glissement en interaction décrit à l’aide de la méthode de correspondance, sur la cartographie des systèmes de glisse- ment d’un grain parent à des systèmes de glissement dans des grains maclage considérés. Des interactions du second type sont ensuite introduites dans cette relation constitutive en tant que paramètre de dissociation, dont la valeur est établie par les observations tirées des résultats des simulations de dynamique moléculaire de [8] et [53]. Ces méthodes sont implantées pour simuler le comportement de durcissement anisotrope du magnésium HCP sous plusieurs chemins de charge / Methods designed for incorporation into multiscale modeling polycrystals are presented in this work in two tasks. This work contains mesoscale methods for capturing the effects of both the interactions of slip dislocations encountering twin grain boundaries and the simultaneous growth of multiple twin grain volume fractions on mechanical hardening and texture evolution. These are implemented in a crystal plasticity framework using the Los Alamos viscoplastic self-consistent code, VPSC-7. Presented here, the effects of simultaneous growth in multiple twin variants on textural evolution is tracked using a Kalidindi-type twin volume transfer scheme. In Task 1, the implementation of this scheme in order to simulate the texture of Twinning Induced Plasticity steels (TWIP) subjected to Equal Channel Angular Pressing (ECAP) are summarized. In Task 2, the hardening effects of two types of interactions between slip dislocations and encountered twin grain boundaries, namely dislocation transmutation and dissociation, are captured by way of modifying the dislocation density based hardening model of [11]. Interactions of the first type are presented in a constitutive relation calculating the amount of dislocation density apportioned to a given slip system contained within the encountered twin volume fraction from each interacting slip system in the parent volume fraction. The amount transmuted from each interacting slip system described using the Correspondence Method, an on to mapping of slip systems in a parent grain to slip systems in considered twin grains. Interactions of the second type are then introduced into this constitutive relation as a disassociation parameter, the value of which is established by observations gleaned from the results of the molecular dynamics simulations of [8] and [53]. These methods are implanted to simulate the anisotropic hardening behavior of HCP magnesium under multiple load paths

abstract: Interstitial impurity atoms can significantly alter the chemical and physical properties of the host material. Oxygen impurity in HCP titanium is known to have a considerable strengthening effect mainly through interactions with dislocations. To better understand such an effect, first the role of oxygen on various slip planes in titanium is examined using generalized stacking fault energies (GSFE) computed by the first principles calculations. It is shown that oxygen can significantly increase the energy barrier to dislocation motion on most of the studied slip planes. Then the Peierls-Nabbaro model is utilized in conjunction with the GSFE to estimate the Peierls stress ratios for different slip systems. Using such information along with a set of tension and compression experiments, the parameters of a continuum scale crystal plasticity model, namely CRSS values, are calibrated. Effect of oxygen content on the macroscopic stress-strain response is further investigated through experiments on oxygen-boosted samples at room temperature. It is demonstrated that the crystal plasticity model can very well capture the effect of oxygen content on the global response of the samples. It is also revealed that oxygen promotes the slip activity on the pyramidal planes. The effect of oxygen impurity on titanium is further investigated under high cycle fatigue loading. For that purpose, a two-step hierarchical crystal plasticity for fatigue predictions is presented. Fatigue indicator parameter is used as the main driving force in an energy-based crack nucleation model. To calculate the FIPs, high-resolution full-field crystal plasticity simulations are carried out using a spectral solver. A nucleation model is proposed and calibrated by the fatigue experimental data for notched titanium samples with different oxygen contents and under two load ratios. Overall, it is shown that the presented approach is capable of predicting the high cycle fatigue nucleation time. Moreover, qualitative predictions of microstructurally small crack growth rates are provided. The multi-scale methodology presented here can be extended to other material systems to facilitate a better understanding of the fundamental deformation mechanisms, and to effectively implement such knowledge in mesoscale-macroscale investigations. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2018

Il est communément admis aujourd'hui que le contact entre deux surfaces se compose en réalité d'une multitude de contact ponctuels entre des aspérités. Cette considération amène à une surface de contact réelle significativement différente de l'aire de contact parfaite supposée dans la théorie de Hertz.De même, elle implique également la présence d'un espace libre entre les deux surfaces en contact. Dans cette situation, l'objectif principal de ces travaux de thèse est de développer des approches numériques permettant l'analyse du contact mécanique entre surfaces rugueuses dans le but de qualifier/quantifier l'étanchéité de ce contact rugueux.Deux approches différentes sont étudiées. La première consiste à analyser le contact mécanique entre une surface rugueuse et un plan rigide au moyen de la méthode des éléments finis et d'un nouveau modèle numérique. La seconde concerne l'estimation de la transmissivité d'un contact rugueux en considérant des simulations de l'écoulement d'un fluide au sein du champ des ouvertures présent entre les deux surfaces en contact.La comparaison de ces estimations numériques avec les résultats expérimentaux révèlent des écarts importants. Dans le but de comprendre ces écarts, l'influence du modèle de comportement matériau dans de telles simulations est étudiée. La plasticité cristalline, mais également l'élévation de la température dégagée par déformation plastique seront considérés. La question de la représentativité de notre problème vis-à-vis de l'approche fluide sera également discutée. / It is now widely accepted that the contact between two surfaces is in fact a one-to-one contact between many asperities, depending on the roughness of the contact pair. This represents a strong deviation from the perfect contact assumed in engineering approaches, with the real contact area being significantly smaller than the apparent contact area.In addition, such an approach also implies the presence of a free space between surfaces in contact. Thus, the purpose of our study is the development of numerical tools to analyse the mechanical contact between rough surfaces and the tightness of such a contact.Two different approches are studied. The first one is devoted to the observation of the mechanical contact between a rough surface and a rigid plane by means of the finite element method and a new numerical model. The second approach is related to the estimation of the contact transmissivity by considering simulations of the fluid flow in the resulting free space between surfaces in contact.The comparison between experimental and numerical estimations of the resulting flow rate shows significant deviations.In order to understand these deviations, the influence of material models on contact simulations is studied. In particular, the effect of using crystal plasticity and the effect of including plasticity-driven temperature changes are considered. The question of problem representation in fluid flow approaches is also addressed.

Titanium is a widely used metal in industrial and commercial applications. It retains anisotropic mechanical properties at room temperature due to its HCP crystal structure. The effects of crystal orientation have been studied theoretically and through modeling though there is a lack of empirical data available on the topic. The work presented here uses laser-machined voids along with EBSD analysis to study the ductility of grains in different orientations to better understand the microscale fracture process in α-titanium. Experimental results show that hard grains with their c-axis parallel to the tensile direction behave in a less ductile manner than grains with their c-axis oriented away from the tensile direction. This is due to the basal slip systems activating in the former case and prismatic slip systems in the latter. Models utilized include the McClintock model for void growth, Brown-Embury model for void coalescence and FEM crystal plasticity simulations

Une méthode de corrélation d'images numériques adaptée aux mesures cinématiques dans les polycristaux a été développée dans ce travail, dans le but d'identifier les paramètres de lois de plasticité cristalline. Des mesures de champs 2D sont réalisées à la surface d'un polycristal d'acier austénitique 316LN, à partir d'une série d'images acquises au Microscope Electronique à Balayage (MEB) au cours d'un essai de traction monotone in-situ, et pour différentes tailles moyennes de grains. Pour permettre la corrélation d'images, un mouchetis adapté à l'échelle microscopique est au préalable déposé à la surface de l'éprouvette par une technique de microlithographie. Les distorsions spatiales liées à l'imagerie MEB et à la technique de marquage sont quantifiées. La connaissance de la microstructure en surface par diffraction des électrons rétrodiffusés permet de réaliser les mesures cinématiques en utilisant un maillage éléments finis non-structurés s'appuyant sur les joints de grains ou de macles. Ce même maillage est ensuite utilisé pour la simulation de chaque essai de traction sur la microstructure expérimentale, avec comme conditions aux limites les déplacements nodaux mesurés au cours du temps sur les bords du domaine. Deux lois de plasticité cristalline d'approche locale sont alors considérées pour simuler les hétérogénéités des déformations observées : la loi de Méric-Cailletaud et la loi DD-CFC développée à EDF R&D et davantage basée sur la physique. Des comparaisons entre la mesure et la simulation sont menées, en termes de déplacements, de déformations, mais aussi de systèmes de glissement activés. Finalement, une méthode inverse d'identification des paramètres de loi est proposée, se basant sur le recalage à la fois des champs de déplacements locaux et du comportement homogène du matériau. Les paramètres de l'écrouissage isotrope de la loi de Méric-Cailletaud sont ainsi identifiés pour différentes tailles moyennes de grains. Il est également montré que certain coefficients de la matrice d'interaction entre systèmes de glissement peuvent être estimés. / A digital image correlation procedure adapted to kinematic measurements in polycrystals has been developed in this work to identify parameters of crystal plasticity laws. 2D kinematic measurements are performed on the surface of 316LN austenitic steel polycrystals from a sequence of images acquired using a Scanning Electron Microscope (SEM) during in-situ tensile tests for various mean grain sizes. To enable digital image correlation, a speckle adapted to the microscopic scale is deposited onto the specimen surface by a microlithography process. Spatial distortions resulting from both patterning and SEM imaging techniques are quantified. The knowledge of the microstructure at the surface by electron backscattered diffraction allows for kinematic measurements to be performed using an unstructured finite element mesh taking as support the grain or twin boundaries. This same mesh is then used for the simulation of each tensile test on the experimental microstructure with the measured nodal displacements prescribed as boundary conditions with their time evolution. Two local crystal plasticity laws are considered to simulate the observed strain heterogeneities, namely, the Méric-Cailletaud model and the DD-CFC law developed at EDF R&D. Comparisons between measurements and simulations are performed in terms of displacements, strains but also activated slip systems. Last, an inverse identification method is proposed for the identification of the sought constitutive parameters based on both the local displacement fields and the material homogenized behavior. The parameters associated with isotropic hardening of Méric-Cailletaud law are thus identified for various mean grain sizes. It is also shown that some of the interaction parameters of slip systems can be estimated.

Being able to predict the evolution of plastic deformation at the microstructural scale is of paramount importance in the engineering of materials for advanced applications. However, this is not straightforward because of the multiscale nature of deformation heterogeneity, both in space and time . The present thesis combines four related studies in a coherent work, which is aimed to develop experimental methods for studying crystal plasticity at the micro and mesoscale. A novel methodology for gold remodelling is initially proposed and used to apply high-density speckle patterns on the surface of stainless steel specimens. The unique proprieties of the speckle pattern enabled plastic deformation mapping with submicron resolution using digital image correlation (HDIC). It was therefore possible to study the concomitant evolution of microbands and transgranular deformation bands in such alloy. High-resolution deformation mapping also enabled comparison with high-resolution electron backscatter diffraction (EBSD) observations. The only partial correspondence of results proved the limits of EBSD in characterizing plastic deformation. The cause of such limitation is later identified in the reduced sensitivity to lattice slip of the EBSD technique. Hence, a novel method of HDIC data analysis is proposed to separate the contributions of lattice slip and lattice rotation from the deformation mapping. The method is adopted to characterize plasticity in austenitic stainless steel and at the plastic deformation zone (PDZ) around a silicon particle embedded in a softer aluminum matrix. Results show that the proposed experimental methodology has the unique capability of providing a complete description of the micro and mesoscale mechanics of crystal plasticity. HDIC therefore emerges as a key technique in the development of accurate physical-based multiscale crystal plasticity models.

Hlavním cílem této práce je analýza napěťových polí, indukovaných dvojčatěním ovlivněných přítomností precipitátu před čelem dvojčete. Zvolený případ popisuje tahové dvojče {1012} 101 1 s lamelarními precipitáty v hořčíkové slitině AZ31. Systém je modelován metodou konečnýh prvků jako 2D elastická eliptická inkluze, se dvěmi elastickými precipitáty tyčovitého tvaru, nacházející se před čelem elipsy obklopené plastickou matricí modelovanou pomocí krystalové plasticity. Analýza dvojčat a precipitátů s různou tlouštkou ukazje inhibující účinek precipitátů na růst tloušťky dvojčat. Velikost tohoto účinku se mění s tloušťkou dvojčete v důsledku komplexní interakce mezi dvojčetem precipitátem a indukovanou plastickou zónou.

Les observations de microscopie électronique in situ effectuées par Daniel Caillard (CEMES, Toulouse) au cours de la déformation de cristaux de symétrie cubique centrée ont montré que les dislocations vis effectuaient des sauts de plusieurs distances inter-atomiques alors que la théorie standard de Peierls prédit des sauts de une seul distance inter-atomique. Nous avons étudié par simulation atomique le glissement d'une dislocation vis dans un cristal de fer pure. Nous montrons que la propagation de décrochement le long de la dislocation induit un échauffement local qui favorise la nucléation de décrochements supplémentaires. L'accumulation de ces décrochements permet à la dislocation de parcourir plusieurs distances inter-atomiques. Ces simulations nous permettent de proposer une théorie pour l'explication des observations de D. Caillard. / In situ straining tests in high purity α-Fe thin-foils at low temperatures have demonstrated that crystalline defects, called dislocations, have a jerky type of motion made of intermittent long jumps of several nanometers. Such an observation is in conflict with the standard Peierls mechanism for plastic deformation in bcc crystals, where the screw dislocation jumps are limited by inter-reticular distances, i.e. of a few Angstroms. Employing atomic-scale simulations, we show that although the short jumps are initially more favorable, their realization requires the propagation of a kinked profile along the dislocation line which yields coherent atomic vibrations acting as traveling thermal spikes. Such local heat bursts favor the thermally assisted nucleation of new kinks in the wake of primary ones. The accumulation of new kinks leads to long dislocation jumps like those observed experimentally. Our study constitutes an important step toward predictive atomic-scale theory for materials deformation.