Les procédés de mise en forme de tôles minces sont très largement répandus dans l’industrie. Néanmoins, l’utilisation de ces procédés est limitée par le niveau de formabilité du matériau formé, notamment dans le cas des alliages d’aluminium. Afin d’améliorer ces limites de formabilité, des procédés de mise en forme à chaud peuvent être envisagés. L’objectif de cette thèse est d’étudier à l’aide d’approches expérimentale et numérique l’effet de la température et de la vitesse de déformation sur la formabilité des tôles en alliage d’aluminium AA5086 et de proposer une modélisation capable de prédire ces effets. Une campagne d’essais a été réalisée sur ce matériau à partir d’un essai d’emboutissage de type Marciniak. Des courbes limites de formage (CLF) ont été établies sur une plage de température allant de l’ambiant jusqu’à 200°C et pour des vitesses de déformation allant du quasi-statique à 2s-1. Des effets, positif de la température et négatif de la vitesse de déformation sur la formabilité ont été mis en évidence. La prise en compte des effets de la température et de la vitesse de déformation dans les modèles prédictifs des CLF, qu’ils soient analytiques ou numériques, est à ce jour très limitée. Dans ce travail, un modèle numérique prédictif basé sur la simulation par éléments finis du modèle géométrique de Marciniak et Kuczynski (M-K) est proposé. Les déformations limites obtenues avec de ce modèle sont très sensibles à la description du comportement thermo-viscoplastique du matériau et à la calibration du défaut géométrique pilotant l’apparition de la striction dans le modèle M-K. Des essais de traction uniaxiale réalisés dans les mêmes conditions opératoires que les essais de mise en forme de Marciniak ont permis d’identifier des lois d’écrouissage de nature très différentes (rigidifiante, saturante ou mixte). Ces lois conduisent à des prédictions très différentes de la formabilité du matériau pour une valeur donnée du défaut géométrique du modèle EF M-K. Différentes stratégies de calibration de la taille de ce défaut initial ont été envisagées. L’utilisation du point expérimental de la CLF correspondant à des conditions de déformation plane permet de calibrer de manière satisfaisante la valeur de ce défaut. Cette procédure de calibration a été appliquée pour l’ensemble des lois identifiées. Les lois de nature rigidifiante de type Ludwick se sont montrées les plus effficaces alors que les lois saturante de type Voce se sont avérées incapables de prédire la formabilité du matériau pour certaines conditions opératoires. Finalement, il est démontré qu’une valeur constante du défaut géométrique ne peut être retenue pour l’ensemble des conditions opératoires étudiées même si le modèle M-K s’est avéré assez efficace pour représenter l’effet de la température plutôt que celui de la vitesse de déformation. / Sheet metal forming processes are widely used in industry. Nevertheless, the use of these processes is limited by the formability of the considered material, in particular in the case of the aluminium alloys. To improve the formability, warm forming processes can be considered. The objective of this work is to study by means of both experimental and numerical approaches, the effects of temperature and strain rate on the formability of AA5086 aluminium alloy sheets and to propose a modeling suitable to predict these effects. Experimental tests have been carried out on this material by means of the Marciniak stamping experimental device. Forming limit curves (FLCs) have been established on a temperature range going from ambient temperature to 200°C and on a strain rate range going from quasi-static up to 2s-1. A positive effect of the temperature and a negative effect of the strain rate on the formability limits were highlighted. To date, very few predictive models of the FLCs taking into account temperature and strain rate effects are proposed in the literature. In this work, in order to predict the experimental temperature and strain rate sensitivities, a predictive model based on the finite element simulation of the Marciniak and Kuczynski (M-K) geometrical model is proposed. The limit strains obtained with this model are very sensitive to the description of the thermo-viscoplastic behaviour modeling and to the calibration of the initial geometrical imperfection controlling the onset of the necking. Thanks to tensile tests carried out for the same operating conditions that those of Marciniak forming tests, several types (power law, saturation and mixed) of hardening laws have been identified. These hardening laws have been implemented in theFE M-K model to obtain numerical limit strains. Very different formability limits have been observed for a given value of the geometrical defect. Several strategies for the calibration of this initial imperfection size have been tested. The use of the experimental point of the FLC0 corresponding to plane strain condition allows a good calibration of the initial imperfection value. This calibration procedure was carried out for all hardening laws. It is shown that the power law type models such as Ludwick law are more efficient while saturation laws such as Voce law are unable to predict the material formability for some conditions. Finally, it is shown that a constant value of the geometrical defect cannot be used to the whole operating conditions studied even if FE M-K model is shown to be efficient to represent the temperature effect rather than strain rate one.

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.

Les procédés de mise en forme de tôles minces sont très largement répandus dans l'industrie. Néanmoins, l'utilisation de ces procédés est limitée par le niveau de formabilité du matériau formé, notamment dans le cas des alliages d'aluminium. Afin d'améliorer ces limites de formabilité, des procédés de mise en forme à chaud peuvent être envisagés. L'objectif de cette thèse est d'étudier à l'aide d'approches expérimentale et numérique l'effet de la température et de la vitesse de déformation sur la formabilité des tôles en alliage d'aluminium AA5086 et de proposer une modélisation capable de prédire ces effets. Une campagne d'essais a été réalisée sur ce matériau à partir d'un essai d'emboutissage de type Marciniak. Des courbes limites de formage (CLF) ont été établies sur une plage de température allant de l'ambiant jusqu'à 200°C et pour des vitesses de déformation allant du quasi-statique à 2s-1. Des effets, positif de la température et négatif de la vitesse de déformation sur la formabilité ont été mis en évidence. La prise en compte des effets de la température et de la vitesse de déformation dans les modèles prédictifs des CLF, qu'ils soient analytiques ou numériques, est à ce jour très limitée. Dans ce travail, un modèle numérique prédictif basé sur la simulation par éléments finis du modèle géométrique de Marciniak et Kuczynski (M-K) est proposé. Les déformations limites obtenues avec de ce modèle sont très sensibles à la description du comportement thermo-viscoplastique du matériau et à la calibration du défaut géométrique pilotant l'apparition de la striction dans le modèle M-K. Des essais de traction uniaxiale réalisés dans les mêmes conditions opératoires que les essais de mise en forme de Marciniak ont permis d'identifier des lois d'écrouissage de nature très différentes (rigidifiante, saturante ou mixte). Ces lois conduisent à des prédictions très différentes de la formabilité du matériau pour une valeur donnée du défaut géométrique du modèle EF M-K. Différentes stratégies de calibration de la taille de ce défaut initial ont été envisagées. L'utilisation du point expérimental de la CLF correspondant à des conditions de déformation plane permet de calibrer de manière satisfaisante la valeur de ce défaut. Cette procédure de calibration a été appliquée pour l'ensemble des lois identifiées. Les lois de nature rigidifiante de type Ludwick se sont montrées les plus effficaces alors que les lois saturante de type Voce se sont avérées incapables de prédire la formabilité du matériau pour certaines conditions opératoires. Finalement, il est démontré qu'une valeur constante du défaut géométrique ne peut être retenue pour l'ensemble des conditions opératoires étudiées même si le modèle M-K s'est avéré assez efficace pour représenter l'effet de la température plutôt que celui de la vitesse de déformation.