L’identification de certaines lois de comportement demeure délicate surtout pour des comportements non linéaires. Plusieurs stratégies d’identification ont été développées en s’appuyant principalement sur le dialogue essai-calcul. La partie expérimentale consiste à mesurer une ou plusieurs quantités physiques qui caractérisent le comportement du matériau testé et la partie théorique permet de calculer ces mêmes quantités. Pour remonter aux propriétés matérielles recherchées, un accord entre les quantités mesurées et calculées doit être visé. Dans cette thèse, on s’intéresse au zinc qui un matériau polycristallin. Celui-ci est modélisé à travers des lois de plasticité cristalline qui permettent de prédire son comportement mécanique sous chargements complexes ainsi que l’évolution de sa microstructure. Les lois de plasticité cristalline implémentées dans le logiciel commercial Abaqus par Huang et Marin que nous avons adapté au cas du zinc ont été utilisées. L’étape d’identification de ces lois non linéaires est basée sur une approche inverse qui tient compte des hétérogénéités des déformations à l’échelle des grains. Pour cela, nous avons utilisé l’essai de nanoindentation qui est un essai hétérogène permettant d’extraire plus d’informations que les essais homogènes. A cet effet, et pour caractériser la plasticité cristalline du zinc, nous avons utilisé les courbes charge - profondeur de pénétration et les profils de déplacements mesurés sur l’empreinte résiduelle sur des grains de différentes orientations cristallographiques mesurées par EBSD. La confrontation des résultats expérimentaux et montrent la bonne adéquation entre les données expérimentales et les modèles identifiés. Les résultats obtenus ont ainsi permis de caractériser les mécanismes de déformation des monocristaux de zinc. / The identification of certain behavior laws of remains delicate especially for nonlinear behaviors. Several identification strategies have been developed based mainly on the experiment-calculation dialogue. The experimental part consists in measuring one or more physical quantities which characterize the behavior of the tested material and the theoretical part makes it possible to calculate these same quantities. To go back to the material properties sought, an agreement between the quantities measured and calculated must be aimed at. In this thesis, we are interested in zinc, which is a polycrystalline material. It is modeled through crystal plasticity laws that predict its mechanical behavior under complex loadings and the evolution of its microstructure. The crystal plasticity laws implemented in the commercial software Abaqus by Huang and Marin that we adapted to the case of zinc were used. The step of identifying these non-linear laws is based on an inverse approach that takes into account the heterogeneities of the deformations at the grain scale. For this, we used the nanoindentation test which is a heterogeneous test to extract more information than the homogeneous tests. For this purpose, and to characterize the crystal plasticity of zinc, we used the load - penetration depth curves and the displacement profiles measured on the residual imprint on grains of different crystallographic orientations measured by EBSD. The confrontation of the experimental and numerical results show the good agreement between the experimental data and the identified models. The results obtained made it possible to characterize the deformation mechanisms of zinc single crystals.

No description available.

<p>Over the past two decade, there have been renewed interests in the use of continuum models of dislocation to predict the plastic strength of metals from basic properties of dislocations. Such interests have been motivated by the unique self-organized dislocation microstructures that develop during plastic deformation of metals and the need to understand their origin and connection with strength of metals. This thesis effort focuses on the theoretical development of a vector-density based representation of dislocation dynamics on the mesoscale accounting for the kinematics of finite deformation. This model consists of two parts, the first is the development of the transport-reaction equations governing dislocation dynamics within the finite deformation setting, and the second focuses on the computational solution of the resulting model. The transport-reaction equations come in the form of a set of hyperbolic curl type transport equations, with reaction terms that nonlinearly couple these equations. The equations are also geometrically non-linear due to finite deformation kinematics and by their constitutive closure. The solution of the resulting model consists of two parts that are coupled in a staggered fashion, the crystal mechanics equations are lumped in the stress equilibrium equations, and the dislocation transport-reactions equations. The two sets of equations are solved by the Galerkin and First-Order System Least-Squares (FOSLS) finite element methods. A special attention is given to the accurate modeling of glissile dislocation junctions using de Rahm currents and graph theory ideas. The introduction of these measures requires the derivation of further transport relations. Using homogenization theory, we specialize the proposed model to a mean deformation gradient driven bulk plasticity model. Lastly, we simulate bulk plasticity behavior and compare our results against experiments.</p>

Further understanding of mesoscale slip mechanics is crucial to future development of polycrystalline metals with improved performance. The research contained within this thesis aims to characterize localized mesoscale slip on slip bands further through two studies. First, a comprehensive comparison of slip system identification techniques was carried out to further validate each method as well as compare advantages and disadvantages of each. Second, slip bands in the presence of grain boundaries were studied to better characterize the dislocation content and behavior. In the first study, the use of SEM-DIC, AFM, ECCI, and HR-EBSD to characterize slip-system activity was assessed on the same material volume of Ti-7Al. This study presents a robust comparison of the various methods for the first time, including an assessment of their advantages and disadvantages, and how they can be used effectively in a complementary manner. The analysis of the different approaches was carried out in a blind manner independently at three different universities. A Ti-7Al specimen was deformed in uniaxial tension to approximately 3% axial strain, and the active slip systems were independently identified using (i) trace analysis; (ii) in-SEM digital image correlation, (iii) observations of residual dislocations from ECCI, and (iv) long-range rotation gradients through HR-EBSD, with consistent trace identification in all cases. Displacement data from AFM was used to augment the SEM-DIC displacement data by providing complementary out of plane displacement information. Furthermore, short-range dislocation gradients (measured by DIC) provided insight into the residual geometrically necessary dislocation (GND) content, and was consistent with the GND content extracted from EBSD data and ECCI images, confirming the presence of residual GNDs on the dominant slip systems resulting in visible slip bands. These approaches can be used in tandem to provide multi-modal information on slip band identification, strain and orientation gradients, out-of-plane displacements, and the presence of GNDs and SSDs, all of which can be used to inform and validate the development of dislocation-based crystal plasticity and strain gradient models. In the second study, shear strain profiles along slip bands in a modified Rolls-Royce nickel superalloy (RR1000) were analyzed for a tensile sample deformed by 2%. The strain increased with distance away from a grain boundary (GB), with maximum shear strain towards the center of the grain, indicating that dislocation nucleation generally occurred in the grain interior. The strain gradients in the neighborhood of the GBs were quantified and generally correlated with rotation about the active slip system line direction. This leads to an ability to determine the active slip system in these regions. The dislocation spacing and pileup stresses were inferred. The dislocation spacing closely follows an Eshelby analytical solution for a single ended pileup of dislocations under an applied stress. The distribution of pileup stress values for GBs of a given misorientation angle follows a log-normal distribution, with no correlation between the pileup stress and the GB misorientation angle. Furthermore, there is no observed correlation between various transmissivity factors and slip band pileup stress. Hence it appears that the obstacle strength of any of the observed GBs is adequate to facilitate the dislocation pileups present in the slip bands. However, slip band transmission does correlate with transmissivity factors, with the current study focusing on the Luster and Morris m'-factor. Observation of strain profiles of transmitted bands indicate dislocation nucleation locations.

Des simulations de dynamique de dislocation (DD) sont utilisées pour l’étude de l'effet Hall-Petch (HP) et des contraintes internes à long-portée induites par les hétérogénéités de déformation dans les matériaux polycristallins.L'effet HP est reproduit avec succès grâce à des simulations de DD réalisées sur de simples agrégats polycristallins périodiques composés de 1 ou de 4 grains. De plus, l'influence de la forme des grains a été explorée en simulant des grains avec différents rapports d'aspect. Une loi généralisée de HP est proposée pour quantifier l'influence de la morphologie du grain en définissant une taille de grain effective. La valeur moyenne de la constante HP $K$ calculée avec différentes orientations cristallines à faible déformation est proche des valeurs expérimentales.Les dislocations stockées pendant la déformation sont principalement localisées à proximité des joints de grain et peuvent être traitées comme une distribution surfacique de dislocations. Nous avons utilisé des simulations DD pour calculer les contraintes associées aux parois de dislocations de différentes hauteurs, longueurs densités et caractères. Dans tous les cas, la contrainte est proportionnelle à la densité surfacique de dislocations géométriquement nécessaires (GNDs) et sa variation est capturée par un ensemble d'équations empiriques simples. Une prévision de contraintes à long-portée dans les grains est réalisée en sommant les contributions des GNDs accumulées de part et d’autre des joints de grains.L'augmentation de la contrainte interne liée au stockage de GNDs est linéaire avec la déformation plastique et est indépendante de la taille des grains. L'effet de taille observé dans les simulations de DD est attribué au seuil de déformation plastique, contrôlé par deux mécanismes concurrents : la contrainte critique de multiplication des sources et la contrainte critique de franchissement de la forêt. En raison de la localisation de la déformation dans les matériaux à gros grains, le modèle d’empilement des dislocations doit être utilisé pour prédire la contrainte critique dans ce cas. En superposant cette propriété aux analyses que nous avons fait à partir de simulations de DD dans le cas d'une déformation homogène, l'effet HP est justifié pour une large gamme de tailles de grains. / Dislocation Dynamics (DD) simulations are used to investigate the Hall-Petch (HP) effect and back stresses induced by grain boundaries (GB) in polycrystalline materials.The HP effect is successfully reproduced with DD simulations in simple periodic polycrystalline aggregates composed of 1 or 4 grains. In addition, the influence of grain shape was explored by simulating grains with different aspect ratios. A generalized HP law is proposed to quantify the influence of the grain morphology by defining an effective grain size. The average value of the HP constant K calculated with different crystal orientations at low strain is close to the experimental values.The dislocations stored during deformation are mainly located at GB and can be dealt with as a surface distribution of Geometrically Necessary Dislocations (GNDs). We used DD simulations to compute the back stresses induced by finite dislocation walls of different height, width, density and character. In all cases, back stresses are found proportional to the surface density and their spatial variations can be captured using a set of simple empirical equations. The back stress calculation inside grains is achieved by adding the contributions of GNDs accumulated at each GB facet.These back stresses are found to increase linearly with plastic strain and are independent of the grain size. The observed size effect in DD simulations is attributed to the threshold of plastic deformation, controlled by two competing mechanisms: the activation of dislocation sources and forest strengthening. Due to strain localization in coarse-grained materials, the pile-up model is used to predict the critical stress. By superposing such property to the analysis we made from DD simulations in the case of homogeneous deformation, the HP effect is justified for a wide range of grain sizes.

This study focuses on molecular dynamics (MD) simulations, coupled with a discrete mathematical framework, and crystal plasticity (CP) simulations to investigate micro void nucleation and the plastic spin. The origin and historical use of the plastic spin are discussed with particular attention to quantifying the plastic spin at the atomistic scale. Two types of MD simulations are employed: (a) aluminum single crystals undergoing simple shear and (b) aluminum triple junctions (TJ) with varying grain orientations and textures undergoing uniaxial tension. The high-angle grain boundary simulations nucleate micro voids at or around the TJ and the determinant of the deformation gradient shows the ability to predict such events. Crystal plasticity simulations are used to explore the stress-state of the aluminum TJ from uniaxial tension at a higher length scale with results indicating a direct correlation between CP stress-states and the location of micro void nucleation in the MD simulations.

No description available.

A new model using a double-continuity relation for predicting the evolution of pair-correlation functions (PCFs) is presented. The proposed model was developed using statistical continuum theory and is employed to predict the viscoplastic behavior of polycrystalline materials. This model was built based upon the continuity relations and a double divergence law that guarantees the conservation of both orientation and mass; and also satisfies the field equations (equilibrium, constitutive, and compatibility) at every point of the polycrystalline material throughout the deformation process. In the presented model, motion of particles in the real space and rotation of crystallographic orientations in the Euler angle space is monitored using an iterative process assuming that all the amount of deformation is applied uniformly without taking into account the localization effects. To study the accuracy of the proposed model, a commercially pure nickel material was rolled to different amounts of cold work. Texture and statistical analyses of the experimental and simulated microstructures were carried out. For the texture analysis, pole figures, ODF sections, and volume fractions of some ideal orientations of cold-rolling were studied. For the statistical analysis, pair correlation functions (PCFs) were employed and the correlations (auto- and anti-correlations) between ideal orientations and also the coherence length were studied. Simulated results captured from the implementation of the new model are in good agreement with the experimental ones at low and medium rolling deformations (0 to 50% rolling reductions); however, at large levels of deformations (above 70% reductions), because of the formation of cell blocks and relevant inhomogeneity, the occurrence of ideal orientations and their correlation properties in the experimental microstructure is affected by grain subdivision phenomena. This causes distortions in the shape of crystallographic grains at large rolling reductions, and accordingly we observe larger errors in comparison of simulated and experimental microstructures.

No description available.

Titanium is a widely applied material in industries and characterized by highly anisotropic mechanical behaviour. To study the special property of titanium, many kinds of mechanical loading tests have been conducted. Moreover, researchers attempted to reproduce these experiments with numerical methods. This paper will present an overview about the deformation mechanisms and related representative studies of titanium. Among the numerical methods, Taylor type and self-consistent crystal plasticity models are two of the most common ones seen in literature. Simulation of some mechanical loading tests using visco-plastic self-consistent model was carried out and compared with the results given by Taylor type model. It has been found that self-consistent model prevails in the reproduction of stress-strain response and texture evolution. During the calculation of self-consistent model, there are totally 4 kinds of self-consistent schemes available for linearization process. The author investigated 4 groups of simulation works using different self-consistent schemes. But no evident distinction has been observed. The application of visco-plastic self-consistent model in commercial purity titanium is studied at the end. The simulation results successfully captured the general features of 9 mechanical loading tests. / Thesis / Master of Applied Science (MASc)