This thesis focuses on the effects of slip-slip, slip-twin, and slip-precipitates interactions on strain hardening, with the intent of developing comprehensive modelling capabilities enabling to investigate unit processes and their collective effects up to the macroscopic response. To this end, the modelling strategy adopted in this work relies on a two-way exchange of information between predictions obtained by discrete dislocation dynamics (DDD) simulations and crystal plasticity laws informed by DDD. At the scale of lattice defects, a DDD tool enabling simulations on any crystalline structure is developed to model dislocation-dislocation, dislocation-twin and dislocation-particles interactions. The tool is first used to quantify the collective effect and strength of dislocation-dislocation interactions on latent-hardening, especially in the case of pure Mg. With regards to slip-twin interactions, a transmission mechanism is implemented in the DDD framework so as to investigate the collective effects of dislocation transmission across a twin-boundary. With respect to slip-particles interactions, an efficient novel DDD approach based on a Fast Fourier Transform (FFT) technique is developed to include the field fluctuations related to elastic heterogeneities giving rise to image forces on dislocation lines. In addition, the DDD-FFT approach allows for the efficient treatment of anisotropic elasticity, thereby paving the way towards performing DDD simulations in low-symmetry polycrystals. The information extracted from the collective dislocation interactions are then passed to a series of constitutive models, and later used to quantify their effects at the scale of the polycrystal. For such purpose, a constitutive framework capable of receiving information from lower scales and establishing a direct connection with DDD simulations is notably developed.

No description available.

The goal of this research work is to further the understanding of crystal plasticity, particularly at reduced structural and material length scales. Fundamental understanding of plasticity is central to various challenges facing design and manufacturing of materials for structural and electronic device applications. The development of microstructurally tailored advanced metallic materials with enhanced mechanical properties that can withstand extremes in stress, strain, and temperature, will aid in increasing the efficiency of power generating systems by allowing them to work at higher temperatures and pressures. High specific strength materials can lead to low fuel consumption in transport vehicles. Experiments have shown that enhanced mechanical properties can be obtained in materials by constraining their size, microstructure (e.g. grain size), or both for various applications. For the successful design of these materials, it is necessary to have a thorough understanding of the influence of different length scales and evolving microstructure on the overall behavior. In this study, distinction is made between the effect of structural and material length scale on the mechanical behavior of materials. A length scale associated with an underlying physical mechanism influencing the mechanical behavior can overlap with either structural length scales or material length scales. If it overlaps with structural length scales, then the material is said to be dimensionally constrained. On the other hand, if it overlaps with material length scales, for example grain size, then the material is said to be microstructurally constrained. The objectives of this research work are: (1) to investigate scale and size effects due to dimensional constraints; (2) to investigate size effects due to microstructural constraints; and (3) to develop a size dependent hardening model through coarse graining of dislocation dynamics. A discrete dislocation dynamics (DDD) framework where the scale of analysis is intermediate between a fully discretized (e.g. atomistic) and fully continuum is used for this study. This mesoscale tool allows to address all the stated objectives of this study within a single framework. Within this framework, the effect of structural and the material length scales are naturally accounted for in the simulations and need not be specified in an ad hoc manner, as in some continuum models. It holds the promise of connecting the evolution of the defect microstructure to the effective response of the crystal. Further, it provides useful information to develop physically motivated continuum models to model size effects in materials. The contributions of this study are: (a) provides a new interpretation of mechanical size effect due to only dimensional constraint using DDD; (b) a development of an experimentally validated DDD simulation methodology to model Cu micropillars; (c) a coarse graining technique using DDD to develop a phenomenological model to capture size effect on strain hardening; and (d) a development of a DDD framework for polycrystals to investigate grain size effect on yield strength and strain hardening.

The objective of this dissertation is to further the understanding of inelastic behavior in metallic materials. Despite the increasing use of polymeric composites in aircraft structures, high specific strength metals continue to be used in key components such as airframe, fuselage, wings, landing gear and hot engine parts. Design of metallic structures subjected to thermomechanical extremes in aerospace, automotive and nuclear applications requires consideration of the plasticity, creep and fracture behavior of these materials. Consideration of inelasticity and damage processes is also important in the design of metallic components used in functional applications such as thin films, flexible electronics and micro electro mechanical systems. Fracture mechanics has been largely successful in modeling damage and failure phenomena in a host of engineering materials. In the context of ductile metals, the Gurson void growth model remains one of the most successful and widely used models. However, some well documented limitations of the model in quantitative prediction of the fracture strains and failure modes at low triaxialities may be traceable to the limited representation of the damage microstructure in the model. In the first part of this dissertation, we develop an extended continuum model of void growth that takes into account details of the material microstructure such as the texture of the plastically deforming matrix and the evolution of the void shape. The need for such an extension is motivated by a detailed investigation of the effects of the two types of anisotropy on the materials' effective response using finite element analysis. The model is derived using the Hill-Mandel homogenization theory and an approximate limit analysis of a porous representative volume element. Comparisons with several numerical studies are presented towards a partial validation of the analytical model. Inelastic phenomena such as plasticity and creep result from the collective behavior of a large number of nano and micro scale defects such as dislocations, vacancies and grain boundaries. Continuum models relate macroscopically observable quantities such as stress and strain by coarse graining the discrete defect microstructure. While continuum models provide a good approximation for the effective behavior of bulk materials, several deviations have been observed in experiments at small scales such as an intrinsic size dependence of the material strength. Discrete dislocation dynamics (DD) is a mesoscale method for obtaining the mechanical response of a material by direct simulation of the motion and interactions of dislocations. The model incorporates an intrinsic length scale in the dislocation Burgers vector and potentially allows for size dependent mechanical behavior to emerge naturally from the dynamics of the dislocation ensemble. In the second part of this dissertation, a simplified two dimensional DD model is employed to study several phenomena of practical interest such as strain hardening under homogeneous deformation, growth of microvoids in a crystalline matrix and creep of single crystals at elevated temperatures. These studies have been enabled by several recent enhancements to the existing two-dimensional DD framework described in Chapter V. The main contributions from this research are: (i) development of a fully anisotropic continuum model of void growth for use in ductile fracture simulations and (ii) enhancing the capabilities of an existing two-dimensional DD framework for large scale simulations in complex domains and at elevated temperatures.

No description available.

Explaining the work-hardening behavior of crystalline materials and the size dependent plasticity has been a long lasting problem. Plastic deformation mainly arises from the collective motion of dislocations. Although individual dislocation processes are well studied, the study of the overall effects of these processes was challenging before the emergence of computer modeling. Of the computer simulation techniques, discrete dislocation dynamics (DDD) is the most suitable method to model thin films at the micron scale and below. This method allows us to study the quantitative effects of certain mechanisms. / Engineering and Applied Sciences

Experimental micromechanics of materials is a branch of science that seeks to build tight connections between composition, structure, processing and performance of materials under specific operating conditions required for particular technology applications. The present project is focused on the development of techniques that use the combination of electron, ion and X-ray microscopies to study the deformation behaviour of a particularly important class of metallic alloys used in the manufacture of aeroengines, namely, the so-called Ni-base superalloys. The complex hierarchical structure of these materials means that their macroscopic response is controlled to a great extent by the phenomena that play out on very fine scales, from angstroms (lattice spacing dimension) to nanometres (precipitates, phase boundaries, dislocations, chemical inhomogeneities) to microns (grains and their boundaries, defects and their clusters, dislocation pileups) to millimetres (component scale). Understanding the fine structure and deformation behaviour requires the development of specially configured experimental setup that allow the observation and quantification of deformation to external loading. In this study, FIB-SEM methods for sample characterization and fabrication were combined with synchrotron-based X-ray diffraction and imaging techniques, and backed up by theoretical analysis and numerical simulation, to elucidate the origins of the strength of these alloys. Micropillar compression tests using in-SEM nanoindentation were used to reveal the size dependence of the apparent strength, and connection was made with the dislocation-mediated crystal slip to provide an explanation of the observed Hall-Petch type dependence with a modified Hall-Petch equation considering both intrinsic and extrinsic characteristic lengths introduced. X-ray scattering was used in the polychromatic micro-Laue mode and using Bragg coherent diffractive imaging to reveal the crystal distortion arising due to plastic deformation. A Discrete dislocation dynamics in the 2.5D formulation was used to obtain a model description of the observed phenomena. The key outcome of the work presented in this thesis lies in the successful development of advanced observational tools and relevant theoretical or computational models for mesoscale plasticity problems for crystal with complex microstructure.

Modéliser la déformation plastique des polycristaux est un objectif majeur de la science des matériaux. Tous les modèles actuels comportent une partie phénoménologique n´ecessitant un ajustement de paramètres sur des résultats expérimentaux. Cette thèse vise à mettre en place un nouveau modèle, justifié physiquement, sans paramètre ajustable et adapté à la modélisation du polycristal CFC en sollicitation monotone. Afin de mesurer les champs mécaniques à l’échelle du micromètre, des mesures de microdiffraction Laue ont été réalisées sur un tricristal de cuivre à une faible déformation plastique. Ces mesures nous renseignent sur les mécanismes plastiques intervenant très près des joints de grains et définissent des états de référence pour les simulations. On montre principalement que la déformation plastique s’accompagne d’un stockage de dislocations géométriquement nécessaires (GND) aux joints de grains, en relation avec l’apparition de contraintes internes à longue distance. Des simulations de Dynamique des Dislocations dans des bicristaux ont ´et´e réalisées afin de caractériser les phénomènes physiques mis en œuvre. Ces simulations confirment que l’interaction dislocations - joints de grains s’accompagne d’un stockage de GND sous la forme de microstructures tridimensionnelles très inhomogènes. Les propriétés mécaniques induites par ce phénomène complexe peuvent être quantifiées par des lois continues élaborées à partir de l’approximation théorique d’un empilement unidimensionnel. Les lois de comportement ainsi définies ont ensuite été incorporées dans une modélisation micromécanique de plasticité cristalline, jusqu’ici dédiée au monocristal CFC. Le modèle ainsi construit a maintenant la capacité de prédire les mesures réalisées sur le tricristal de cuivre. Nous avons ainsi mis en place un modèle physiquement justifié et adapté `a la modélisation du polycristal CFC en sollicitation monotone. / The modeling of strain hardening in polycrystals is a difficult and still standing task. Current existing models are partly phenomenological, as they always consider constitutive parameters adjusted on the experiment. The aim of the present study is to design a physically based model for the basic problem of monotonic deformation in the FCC polycrystal. Laue microdiffraction is used to measure the mechanical fields in the vicinity of grain boundaries in a copper tricrystal compress at 0.2%. These measurements aim to characterize the plastic phenomena involved and to provide experimental data as bench results for the simulations. Evidences of geometrically necessary dislocations (GND) storage close to the grain boundaries are given in relation with the apparition of longrange internal stresses. Dislocations Dynamics simulations are used to study the plastic strain close to a grain boundary in Cu bicrystals. We show that close to the boundaries plastic strain is associated to the storage of heterogeneous GNDs in complex 3D microstructures. The mechanical properties associate to such microstructure can be described with continuous laws based on a theoretical approximation assuming a 1D pile-up. The corresponding constitutive laws are then introduced in a crystal plasticity model initially devoted to FCC single crystal plasticity and solved with Finite Elements simulations. The new model we propose as now the capacity to reproduce or predict the experimental results we first obtained in the Cu tricrystal. In conclusion, a physically justified model is proposed to predict plastic deformation for the FCC polycrystal in monotonic deformation.

Understanding the relationships between microstructures and properties of materials is a key to developing new materials with more suitable qualities or employing the appropriate materials in special uses. In the present world of material research, the main focus is on microstructural control to cost-effectively enhance properties and meet performance specifications. This present work is directed towards improving the fundamental understanding of the microscale deformation mechanisms and mechanical behavior of metallic alloys, particularly focusing on face centered cubic (FCC) structured metals through a unique computational methodology called three-dimensional dislocation dynamics (3D-DD). In these simulations, the equations of motion for dislocations are mathematically solved to determine the evolution and interaction of dislocations. Microstructure details and stress-strain curves are a direct observation in the simulation and can be used to validate experimental results. The effect of initial dislocation microstructure on the yield strength has been studied. It has been shown that dislocation density based crystal plasticity formulations only work when dislocation densities/numbers are sufficiently large so that a statistically accurate description of the microstructure can be obtainable. The evolution of the flow stress for grain sizes ranging from 0.5 to 10 µm under uniaxial tension was simulated using an improvised model by integrating dislocation pile-up mechanism at grain boundaries has been performed. This study showed that for a same initial dislocation density, the Hall–Petch relationship holds well at small grain sizes (0.5–2 µm), beyond which the yield strength remains constant as the grain size increases.

<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>