Magnesium, with a Hexagonal Close-Packed (HCP) structure, is the eighth most abundant element in the earth’s crust and the third most plentiful element dissolved in the seawater. Magnesium alloys exhibit the attractive characteristics of low densities and high strength-to-weight ratios along with good castability, recyclability, and machinability. Replacing the steel and/or aluminum sheet parts with magnesium sheet parts in vehicles is a great way of reducing the vehicles weight, which results in great savings on fuel consumption. The lack of magnesium sheet components in vehicle assemblies is due to magnesium’s poor room-temperature formability. In order to successfully form the sheets of magnesium at room temperature, it is necessary to understand the formability of magnesium at room temperature controlled by various plastic deformation mechanisms. The plastic deformation mechanisms in pure magnesium and some of its alloys at room temperature are crystallographic slip and deformation twinning. The slip systems in magnesium at room temperature are classified into primary (first generation), secondary (second generation), and tertiary (third generation) slip systems. The twinning systems in magnesium at room temperature are classified into primary (first generation) and secondary (second generation, or double) twinning systems. A new comprehensive rate-dependent elastic-viscoplastic Crystal Plasticity Constitutive Model (CPCM) that accounts for all these plastic deformation mechanisms in magnesium was proposed. The proposed model individually simulates slip-induced shear in the parent as well as in the primary and secondary twinned regions, and twinning-induced shear in the primary and secondary twinned regions. The model also tracks the texture evolution in the parent, primary and secondary twinned regions. Separate resistance evolution functions for the primary, secondary, and tertiary slip systems, as well as primary and secondary twinning systems were considered in the formulation. In the resistance evolution functions, the interactions between various slip and twinning systems were accounted for. The CPCM was calibrated using the experimental data reported in the literature for pure magnesium single crystals at room temperature, but needs further experimental data for full calibration. The partially calibrated model was used to assess the contributions of various plastic deformation mechanisms in the material stress-strain response. The results showed that neglecting secondary slip and secondary twinning while simulating plastic deformation of magnesium alloys by crystal plasticity approach can lead to erroneous results. This indicates that all the plastic deformation mechanisms have to be accounted for when modelling the plastic deformation in magnesium alloys. Also, the CPCM in conjunction with the Marciniak–Kuczynski (M–K) framework were used to assess the formability of a magnesium single crystal sheet at room temperature by predicting the Forming Limit Diagrams (FLDs). Sheet necking was initiated from an initial imperfection in terms of a narrow band. A homogeneous deformation field was assumed inside and outside the band, and conditions of compatibility and equilibrium were enforced across the band interfaces. Thus, the CPCM only needs to be applied to two regions, one inside and one outside the band. The FLDs were simulated under two conditions: a) the plastic deformation mechanisms are primary slip systems alone, and b) the plastic deformation mechanisms are primary slip and primary twinning systems. The FLDs were computed for two grain orientations. In the first orientation, primary extension twinning systems had favourable orientation for activation. In the second orientation, primary contraction twinning systems had favourable orientation for activation. The effects of shear strain outside the necking band, rate sensitivity, and c/a ratio on the simulated FLDs in the two grain orientations were individually explored.

Magnesium, with a Hexagonal Close-Packed (HCP) structure, is the eighth most abundant element in the earth’s crust and the third most plentiful element dissolved in the seawater. Magnesium alloys exhibit the attractive characteristics of low densities and high strength-to-weight ratios along with good castability, recyclability, and machinability. Replacing the steel and/or aluminum sheet parts with magnesium sheet parts in vehicles is a great way of reducing the vehicles weight, which results in great savings on fuel consumption. The lack of magnesium sheet components in vehicle assemblies is due to magnesium’s poor room-temperature formability. In order to successfully form the sheets of magnesium at room temperature, it is necessary to understand the formability of magnesium at room temperature controlled by various plastic deformation mechanisms. The plastic deformation mechanisms in pure magnesium and some of its alloys at room temperature are crystallographic slip and deformation twinning. The slip systems in magnesium at room temperature are classified into primary (first generation), secondary (second generation), and tertiary (third generation) slip systems. The twinning systems in magnesium at room temperature are classified into primary (first generation) and secondary (second generation, or double) twinning systems. A new comprehensive rate-dependent elastic-viscoplastic Crystal Plasticity Constitutive Model (CPCM) that accounts for all these plastic deformation mechanisms in magnesium was proposed. The proposed model individually simulates slip-induced shear in the parent as well as in the primary and secondary twinned regions, and twinning-induced shear in the primary and secondary twinned regions. The model also tracks the texture evolution in the parent, primary and secondary twinned regions. Separate resistance evolution functions for the primary, secondary, and tertiary slip systems, as well as primary and secondary twinning systems were considered in the formulation. In the resistance evolution functions, the interactions between various slip and twinning systems were accounted for. The CPCM was calibrated using the experimental data reported in the literature for pure magnesium single crystals at room temperature, but needs further experimental data for full calibration. The partially calibrated model was used to assess the contributions of various plastic deformation mechanisms in the material stress-strain response. The results showed that neglecting secondary slip and secondary twinning while simulating plastic deformation of magnesium alloys by crystal plasticity approach can lead to erroneous results. This indicates that all the plastic deformation mechanisms have to be accounted for when modelling the plastic deformation in magnesium alloys. Also, the CPCM in conjunction with the Marciniak–Kuczynski (M–K) framework were used to assess the formability of a magnesium single crystal sheet at room temperature by predicting the Forming Limit Diagrams (FLDs). Sheet necking was initiated from an initial imperfection in terms of a narrow band. A homogeneous deformation field was assumed inside and outside the band, and conditions of compatibility and equilibrium were enforced across the band interfaces. Thus, the CPCM only needs to be applied to two regions, one inside and one outside the band. The FLDs were simulated under two conditions: a) the plastic deformation mechanisms are primary slip systems alone, and b) the plastic deformation mechanisms are primary slip and primary twinning systems. The FLDs were computed for two grain orientations. In the first orientation, primary extension twinning systems had favourable orientation for activation. In the second orientation, primary contraction twinning systems had favourable orientation for activation. The effects of shear strain outside the necking band, rate sensitivity, and c/a ratio on the simulated FLDs in the two grain orientations were individually explored.

L'objectif de la thèse est d'identifier et de quantifier les paramètres régissant l'épaississement des macles dans trois métaux hexagonaux (Zr, Ti, Mg). Le mécanisme que nous étudions est le glissement de dislocations d'interfaces, i.e. les disconnections, le long des joints de macles parfaits. Nous nous intéressons alors à la germination des disconnections avant de nous concentrer sur leur migration.Une première étude en potentiel empirique permet de valider un couplage original avec la théorieélastique afin d'extraire des simulations atomiques l'énergie de cœur des disconnections. Cette méthode permet de partitionner l'énergie entre une contribution de cœur, intrinsèque à la disconnection et une partie élastique qui dépend de l'environnement de la disconnection. Cette partition faite, nous modélisons alors l'énergie de formation de dipôles de disconnections isolés, pour chacun des différents joints de macles. Cette modélisation nous permet alors de sélectionner les dipôles de disconnections les plus pertinents que nous étudions par la méthode abinitio.Nous modélisons ensuite la migration des disconnections le long des joints de macles parfaits.Pour cela, nous montrons via l'utilisation de la méthode Nudged Elastic Band, que l'énergie demigration est d'un ordre de grandeur inférieur à l'énergie de formation. Ainsi, l'énergie de formation des dipôles de disconnections apparait comme prédominant dans la croissance des macles / The aim of this thesis is to identify and quantify the parameters of importance when dealing with twin thickening in three hcp metals (Zr, Ti, Mg). The mechanism we study is the glide of twinning dislocations, i. e. the disconnection, along the perfect twin boundaries. We first focus on the nucleation of disconnection before addressing their migration. A study using an EAM potential allows us to validate an original coupling between our atomistic simulations and linear elasticity in order to extract the core energy of disconnection.We then show how this coupling permits to divide the formation energy in two terms: the core contribution, intrinsec to the disconnections, and an elastic one, which depends on the disconnection's environment. Thanks to this partition, we model the formation of isolated disconnection that may appear along the different twin planes. We select the dipoles of lowest formation energies in order to perform ab initio calculations and compare the behavior observed the three different metals. We then model the migration of disconnections along the perfect twin planes. To do so, we use the Nudged Elastic Band method, and find out that the migration energy of disconnections is one order of magnitude lower than their formation energies. We therefor conclude that the disconnection nucleation is the rate limiting factor to explain twin thickening thanks to the creation and motion of disconnection

We envisage a fundamental study of the physical mechanisms (dislocation slip versus deformation twinning) involved in plastic deformation of hexagonal close-packed (HCP) metals like titanium and magnesium. A novel combination of X-ray imaging and diffraction techniques, termed X-ray diffraction contrast tomography (DCT), will be used to investigate details of the deformation process in the bulk of polycrystalline specimen. DCT provides access to the position, 3D shape, (average) orientation and elastic strain tensor of grains in polycrystalline sample volumes containing up to 1000 grains and more. Ultimately, an extension of the X-ray DCT technique is associated with a section topography methodology on the same instrument. This combination enables the measurement of local orientation and elastic strain tensors inside selected bulk grains. A very preliminary study of this approach is carried out on a magnesium alloy, underlying the current limitations and possible improvements of such approach. In this thesis, the data acquisition and analysis procedures required for this type of combined characterisation approach have been developed. The work is supported by the use of neutron diffraction, for an in-situ loading experiments, and two-dimensional electron backscatter diffraction (EBSD), for the initial microstructure of the materials and cross-validation of the results obtained with the X-ray DCT technique.