<P> There is a growing interest in magnesium and its alloys due to their high strength to weight ratio. Magnesium is of particular interest to the automotive industry as a consequence of the current pressure to reduce green house gas emissions from the transportation sector through vehicle weight reduction. However, there is a lack of knowledge concerning the formability of magnesium. As a result, the application of magnesium as a commercial material has not been fully exploited. Much has been learned from the constitutive modeling of materials such as aluminum and steel. Therefore, this thesis considers the constitutive modeling of magnesium and its alloys. </p> <p> Based on this motivation, polycrystal plasticity theories that have been established and used to characterize aluminum and steel are studied. The validity of these theories is examined with respect to magnesium and its alloys. The magnesium system is composed of the hexagonal closed-packed (HCP) crystal structure. Therefore, a strong plastic anisotropy is induced in magnesium crystals due to the limited number of slip systems that may be activated with ease. The models proposed by Taylor and Sachs neglect strain and stress heterogeneities respectively. As a result, the models are either too stiff or too soft to study magnesium due to the anisotropic nature of the crystal structure. The intermediate models; self-consistent models, which are able to consider the heterogeneities among the grains in polycrystals, are believed to be more suitable to study magnesium and its alloys. Therefore, a large strain elastic-viscoplastic self-consistent (EVPSC) model is developed for polycrystalline materials. Both rate sensitive slip and twinning are included as mechanisms of plastic deformation, while elastic anisotropy is accounted for in the elastic modulus. The transition from single crystal plasticity to polycrystal plasticity is based on a completely self-consistent approach. It is shown that the differences in the predicted stress-strain curves and texture evolutions based on the EVPSC and the viscoplastic self-consistent (VPSC) model proposed by Lebensohn and Tome (1993) are negligible at large strains for monotonic loadings. For the deformations involving unloading and strain path changes, the EVPSC predicts a smooth elasto-plastic transition, while the VPSC model gives a discontinuous response because the model is incapable of modeling elastic deformation. In addition, it is demonstrated that the EVPSC model can capture some important experimental features which cannot be simulated by using the VPSC model. </p> <p> Various self-consistent schemes exist for EVPSC and VPSC models. However, the evaluations of these models are not complete. Therefore, an examination of various polycrystal plasticity models is made, based on comparisons of the predicted and experimental stress responses as well as the R values, to assess their validity. It is established that, among the models examined, the self-consistent models with grain interaction stiffuess values halfway between those of the limiting Secant (stiff) and Tangent (compliant) approximations give the best results. Among the available options, the Affine self-consistent scheme results in the best overall performance. Furthermore, it is demonstrated that the R values under uniaxial tension and compression within the sheet plane show a strong dependence on the imposed strain. This suggests that the development of anisotropic yield functions using measured R values, must account for the strain. dependence. </p> <p> The recently developed large strain elastic visco-plastic self-consistent (EVPSC) model, which incorporates both slip and twinning deformation mechanisms, is used to study .the lattice strain evolution in extruded magnesium alloy AZ31 under uniaxial tension and compression. The results are compared against in-situ neutron diffraction measurements done on the same alloy. For the first time, the effects of stress relaxation and strain creep on lattice strain measurements in respectively displacement controlled and load controlled in-situ tests are numerically assessed. It is found that the stress relaxation, has a significant effect on the lattice strain measurements. It is also observed that although the creep does not significantly affect the trend of the lattice strain evolution, a better agreement with the experiments is found if creep is included in the simulations. </p> <p> In conjunction with the M-K approach developed by Marciniak and Kuczynski (1967), the EVPSC model is applied to study the sheet metal formability of magnesium alloys in terms of the forming limit diagram (FLO). The role of crystal plasticity models and the effects of basal texture on formability of magnesium alloy AZ31 B sheet are studied numerically. It is observed that formability in HCP polycrystalline materials is very sensitive to the intensity of the basal texture. The path-dependency of formability is examined based on different non-proportional loading histories, which are combinations of two linear strain paths. It is found that while the FLO in strain space is very sensitive to strain path changes, the forming limit stress diagram (FLSO) in stress space is much less path-dependent. It is suggested that the FLSO is much more favourable than the FLO in representing forming limits in the numerical simulation of sheet metal forming processes. The numerical results are found to be in good qualitative agreement with experimental observations. </p> / Thesis / Doctor of Philosophy (PhD)

Ce travail vise à améliorer la compréhension de la déformation locale des matériaux polycristallins. Pour cela, les comportements des grains individuels d'un polycristal d'aluminium déformé plastiquement sont étudiés par une approche couplant expériences in situ en synchrotron et simulation par élément finis.Dans l'expérience, la microstructure initiale est cartographiée par tomographie en contraste de diffraction (DCT). L'éprouvette est déformée en traction uniaxiale et 466 grains sont suivis par microscopie 3D par diffraction des rayons X (3DXRD) jusqu'à une déformation de 4.5%. De nouvelles méthodes d'analyse originales donnent accès aux orientations, déformations élastiques et contraintes, en moyenne par grain, et permettent de déterminer les distributions d'orientations intragranulaires à partir des données 3DXRD.Dans la simulation, la microstructure réelle (DCT) est modélisée par une partition de Laguerre, maillée finement et soumise au chargement expérimental. Les champs mécaniques et les champs d'orientations résultants peuvent être comparés aux données expérimentales.La comparaison entre expérience et simulation révèle un accord au premier ordre. Les rotations expérimentales montrent une forte variabilité associée à l'interaction intergranulaire et bien reproduite dans la simulation. Les distributions d'orientations ont des directions d'étalement privilégiées perpendiculaires à la direction de traction, ce qui est relié aux mécanismes de déformation du matériau. Les contraintes montrent un bon accord, dans la limite de la précision de mesure. Ces données, très riches, fournissent des pistes d'amélioration pour les modèles de plasticité cristalline. / This work aims to improve our understanding of the local deformation of polycrystalline materials. To this end, in situ synchrotron experiments and finite element simulations are coupled to study the individual grain responses in an aluminium polycrystal during plastic deformation.In the experiment, the initial microstructure is mapped by Diffraction Contrast Tomography (DCT). The specimen is deformed in uniaxial tension and 466 grains are followed by 3D X-Ray Diffraction (3DXRD) up to 4.5% plastic strain. New original analysis methods provide the grain average orientations, elastic strains and stresses, and allow determining the intra-grain orientation distributions from the 3DXRD measurements.In the simulation, the real microstructure (DCT) is modeled by a Laguerre tessellation, finely meshed and submitted to the experimental loading. The resulting mechanical and orientation fields can be compared to the experimental data.The comparison reveals a first-order agreement between experiment and simulation. The experimental rotations exhibit a high variability, associated to grain interaction and well reproduced in the simulation. The orientation distributions exhibit preferential spread directions perpendicular to the tensile direction, which can be related to the deformation mechanisms. Lastly, the stresses are found to be in agreement within the measurement accuracies. Such a rich dataset provides routes to improve crystal plasticity models.

Ce travail vise à améliorer la compréhension des mécanismes et de la dynamique de sous-structuration des grains pendant la deformation des matériaux polycristallins. Pour cela, des experience in situ en synchrotron et des acquisitions EBSD ont été menées afin d’étudier les comportements des grains individuels d’un polycrystal d’Aluminium déformé plastiquement. Une éprouvette d’un alliage Al-0.1%Mn a été déformée en traction in situ et analysée par microscopie 3D par diffraction des Rayons-X (3DXRD). Une nouvelle méthode de dépouillement a été développée pour determiner les axes de désorientation intragranulaires et les distributions d’orientation, grâce à l’analyse de l’élargissement azimutal des taches de diffraction. La technique EBSD a été appliquée pour obtenir des cartographies de désorientation des grains individuels d’une éprouvette déformée en traction. Trois acquisitions ont été réalisées sur la même région d’intérêt à l’état non déformé et après l’application des deformations 1% et 5%. Ces résultats permettent une meilleure comprehension de la formation et de l’évolution des gradients d’orientations intragranulaires, et son ten bon accord avec les modèles théoriques pré-existants. Aussi, la caractérisation de la sous-structuration des grains et de la deformation intragranulaire a été réalisée grâce à la technique K-map. La deformation était très hétérogène avec des valeurs élevées de compression et de traction à l’intérieur des grains et en proximité de deux joints de grains, respectivement. La distribution de la norme des vecteurs de diffraction a montré que les dislocations sont à l’origine de la deformation. / This work aims to improve the understanding of grain sub-structuration mechanisms and dynamics during deformation of polycrystals. For this purpose, in situ synchrotron experiments and EBSD acquisitions were coupled to study the response of single grains of an Al-0.1%wt.Mn polycrystal during tensile deformation. The specimen deformed in situ at the synchrotron was analyzed by 3DXRD. A new method provided a grain-by-grain analysis of the intragranular misorientation axes and their orientation distribution, through the investigation of the azimuthal broadening of diffraction spots. The 3DXRD results were cross-checked by classical EBSD analysis. Three acquisitions were carried out over the same region of interest at the undeformed state and after the application of 1% and 5% strain. Thanks to the available spatial resolution, the EBSD results allow for a better comprehension of the creation and dynamics of intragranular orientation gradients, and are in good agreement with pre-existing theoretical models. In addition, the characterization of grain sub-structuration and intragranular strain was performed through a novel X-Ray scanning technique, the K-map. The strain was found to be very heterogeneous with high compressive and tensile values in the grain interior and near two grain boundaries, respectively. Dislocations were found to be at the origin of deformation.

Thermally induced phase transformation in NiTi shape memory alloys (SMA) shows strong size and shape, collectively termed length scale effects, at the nano to micrometer scales, and that has important implications for the design and use of devices and structures at such scales. This paper, based on a recently developed multiscale model that utilizes molecular dynamics (MD) simulations at small scales and MD-verified phase field (PhF) simulations at larger scales, reports results on specific length scale effects, i.e. length scale effects in martensite phase fraction evolution, transformation temperatures (martensite and austenite start and finish) and in the thermally cyclic transformation between austenitic and martensitic phase. The multiscale study identifies saturation points for length scale effects and studies, for the first time, the length scale effect on the kinetics (i.e. developed internal strains) in the B19 phase during phase transformation. The major part of the work addresses small scale single crystals in specific orientations. However, the multiscale method is used in a unique and novel way to indirectly study length scale and grain size effects on evolution kinetics in polycrystalline NiTi, and to compare the simulation results to experiments. The interplay of the grain size and the length scale effect on the thermally induced martensite phase fraction (MPF) evolution is also shown in this present study. Finally, the multiscale coupling results are employed to improve phenomenological material models for NiTi SMA.

La méthode d'élimination sur le terrain est devenu ces dernières années la méthode de choix pour modéliser la formation des motifs de la microstructure lors de la solidification. Pour monocristaux, accord quantitatif avec des expériences et des solutions analytiques ont été obtenues. La modélisation des polycristaux, qui sont composées de nombreux grains d'une même phase thermodynamique, mais différentes orientations du réseau cristallin, est beaucoup moins avancée. Deux types de modèles ont été proposés: les modèles multi-phase-champ d'utiliser un champ de phase pour chaque grain, et les modèles d'orientation-champ d'utiliser un petit nombre de domaines, mais ont des termes non analytiques dans leur énergie libre fonctionnel. Ce travail examine les divers aspects de la phase de modélisation du champ de polycristaux et est divisé en trois parties. Dans la première, une nouvelle possibilité de décrire l'orientation locale est explorée, en utilisant un paramètre d'ordre tensoriel qui représente automatiquement la symétrie locale du système. Cette approche est testée en phase de développement d'un modèle de champ pour la transition de phase nématique-isotrope dans les cristaux liquides. Le modèle est appliqué pour simuler la solidification directionnelle''''d'un cristal liquide. L'effet du couplage entre l'orientation et la forme nématique interface est étudiée. Les résultats de simulation pour la stabilité d'une interface plane en bon accord avec une analyse de stabilité généralisée, qui tient compte d'une condition nouvelle d'ancrage à l'interface: l'orientation à l'interface nématique est le résultat de l'interaction entre la déformation en vrac et l'anisotropie d'interface. La forme et la stabilité des cellules bien développé est également influencée par cet effet. Numériquement, l'utilisation d'un paramètre d'ordre tensoriel simplifie le traitement des symétries dans le système de manière significative, tandis que les équations de mouvements deviennent beaucoup plus compliquées. Dans la deuxième partie, les joints de grains sont étudiés sur une échelle plus petite longueur, en utilisant un modèle de cristal phase de terrain, où les propriétés élastiques et des dislocations apparaissent naturellement. Avec ce modèle, l'ordre local dans les interfaces est examiné et la stabilité des films liquides entre deux grains solides est étudiée ci-dessous le point de fusion. Cette situation peut être décrite par un potentiel d'interaction entre les deux interfaces solide-liquide, qui est extraite numériquement. Les résultats sont comparés avec un modèle phénoménologique qui se trouve à tenir pour les joints de grains à forte inclinaison, où les dislocations se chevauchent. Pour les joints de grains à faible angle, autour de préfusion dislocation ainsi qu'une brisure de symétrie (paires de dislocations forme) est observée. En conséquence, le potentiel d'interaction devient nonmonotonous, et se compose d'une attraction à longue portée et une répulsion à courte portée. Dans la troisième partie, un nouveau modèle de phase sur le terrain est développé en utilisant une variable d'angle pour décrire l'orientation cristalline. Contrairement aux modèles déjà existants, l'énergie libre est construit sans un terme proportionnel au module du gradient du champ de l'orientation. Au lieu de cela, le gradient de la norme au carré est utilisé, mais il est couplé à la phase du champ avec une fonction de couplage singulier. Diverses simulations référence sont réalisés afin de tester le modèle. Il se trouve qu'elle présente plusieurs artefacts tels que la rotation et le mouvement du grain parasite interface, mais ces effets sont extrêmement petites, telles que le modèle donne des résultats satisfaisants que si la surfusion est très faible. Enfin, les problèmes observés sont analysés et des moyens d'obtenir une meilleure description de la dynamique de l'angle de champ sont discutées.

In this thesis two kinds of phase change i.e., solid state phase transformation in steels and solid-to-liquid phase transformation in paraffin, have been modeled and numerically simulated. The solid state phase transformation is modeled using the phase field theory while the solid-to-liquid phase transformation is modeled using the Stokes equation and exploiting the viscous nature of the paraffin, by treating it as a liquid in both states.The theoretical base of the solid state, diffusionless phase transformation or the martensitic transformation comes from the Khachaturyan's phase field microelasticity theory. The time evolution of the variable describing the phase transformation is computed using the time dependent Ginzburg-Landau equation. Plasticity is also incorporated into the model by solving another time dependent equation. Simulations are performed both in 2D and 3D, for a single crystal and a polycrystal. Although the model is valid for most iron-carbon alloys, in this research an Fe-0.3\%C alloy is chosen.In order to simulate martensitic transformation in a polycrystal, it is necessary to include the effect of the grain boundary to correctly capture the morphology of the microstructure. One of the important achievements of this research is the incorporation of the grain boundary effect in the Khachaturyan's phase field model. The developed model is also employed to analyze the effect of external stresses on the martensitic transformation, both in 2D and 3D. Results obtained from the numerical simulations show good qualitative agreement with the empirical observations found in the literature.The microactuators are generally used as a micropump or microvalve in various miniaturized industrial and engineering applications. The phase transformation in a paraffin based thermohydraulic membrane microactuator is modeled by treating paraffin as a highly viscous liquid, instead of a solid, below its melting point.  The fluid-solid interaction between paraffin and the enclosing membrane is governed by the ALE technique. The thing which sets apart the presented model from the previous models, is the use of geometry independent and realistic thermal and mechanical properties. Numerical results obtained by treating paraffin as a liquid in both states show better conformity with the experiments, performed on a similar microactuator. The developed model is further employed to analyze the time response of the system, for different input powers and geometries of the microactuator. / <p>QC 20130219</p>

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.

Im Legierungssytem Ni-Mn-Ga tritt bei Zusammensetzungen nahe der stöchiometrischen Zusammensetzung Ni2MnGa der magnetische Formgedächtniseffekt auf. Darunter versteht man die Dehnung durch Bewegung von Zwillingsgrenzen im Magnetfeld. Einkristalle aus Ni-Mn-Ga mit einer tetragonalen 5M-Martensitstruktur zeigen magnetisch erzeugbare Dehnungen von bis zu 6 %. Diese großen Dehnungen verbunden mit der schnellen Schaltfrequenz von Magnetfeldern machen den Effekt interessant für technische Anwendungen z. B. als Aktoren. Derartige Einkristalle sind schwierig und teuer herzustellen, weshalb für technische Anwendung Polykristalle von Interesse sind. Diese lassen sich im Allgemeinen leichter und preiswerter herstellen. Um den magnetischen Formgedächtniseffekt in Polykristalle einzustellen, werden grobkörnige, texturierte Proben mittels des Verfahrens der gerichteten Erstarrung hergestellt. Die Gefügeuntersuchungen erfolgen mit metallographischen Schliffen und die Kornorientierungen werden mit der EBSD-Technik bestimmt. Um das Gefüge zu vergröbern, werden Glühungen nach einer aufgebrachten Warmverformung untersucht. Zur Verringerung der für die Bewegung der Zwillingsgrenzen notwendigen Spannung (Zwillingsspannung) werden die Proben im Druckversuch mechanisch trainiert. Dabei kann die Zwillingsspannung teilweise unter die magnetisch erzeugbare Spannung auf die Zwillingsgrenzen (Magnetospannung) abgesenkt werden. Eine weitere Absenkung der Zwillingsspannung wird durch eine plattenförmige Probengeometrie mit Dicken im Bereich der Korndurchmesser erreicht. An derartigen Proben wird magnetisch rückstellbare freie Dehnung durch Zwillingsgrenzenbewegung erzielt.

Ce travail s’inscrit dans la thématique classique en mécanique de l’endommagement de milieux polycristallin. Il a pour but d’étudier et de modéliser le comportement thermique et mécanique d’un matériau énergétique. Ce matériau, dont le comportement en compression est quasi-fragile, présente en particulier un coefficient de dilatation thermique qui diminue lors de cycles de refroidissement-réchauffement.L’étude repose sur un modèle morphologique de type Johnson-Mehl avec grains non convexes et une méthode numérique à champ complet par transformée de Fourier rapide. La précision de ces méthodes en termes de réponse effective et de champs en pointe de fissure est étudiée par comparaison avec des éléments finis. Plusieurs types de microstructures sont ensuite étudiés de façon heuristique par ordre croissant de complexité.Le comportement élastique du polycristal non endommagé, calculé par méthode FFT, surestime celui observé expérimentalement. L’ajout de liant et de porosité dans le matériau n’expliquant pas le comportement mécanique expérimental, on étudie l’influence de différentes populations de fissures.Seule l’ajout de fissures intergranulaires permet de rendre compte du comportement effectif du matériau à l’état initial. La chute du coefficient de dilatation thermique est prédite par méthode FFT dans le cas de fissures dans le plan graphitique des monocristaux, dont l’existence est confirmée par des images MEB. / This work aims to study the thermal and mechanical behavior of an energetic polycrystal. This material displays a quasi-brittle behavior and its thermal dilation coefficient decreases when it undergoes cooling-heating cycles.The study relies on the use of a Johnson-Mehl tessellation model which has non-convex grains, and a full-field numerical method based on the Fourier transform. The accuracy of such methods concerning cracked media are determined by comparison with Finite Elements computations. The numerical tool is then used to investigate different microstructural assumptions, from the simplest to the most sophisticated.The first computation is that of an undammaged polycrystal, which overestimates the overall mechanical properties. The attempt to account for porosity and the presence of binder gives interesting results, but the latter are not enough to reproduce the experimental behavior.Finally, different types of microcracks are investigated and two major conclusions are drawn. First, in its initial state, the material contains intergranular cracks, that are uncorrelated to the local microstructure. Such cracks can lower the elastic moduli and leave the thermal properties unaffected. To obtain a decrease in terms of thermal dilation coefficient, one must consider families of cracks which are correlated to the local crystal orientation, especially along the weak plane of the crystal.

No description available.