Effect of plastic anisotropy on the prediction of the ductility for HCP sheet metals

Due to their lightness, low stiffness and high strength, Hexagonal Closed Packed (HCP) materials are widely used in aeronautic and aerospace industries. In this paper, the ductility limit of HCP sheet materials at room temperature (25° C) is predicted by coupling the Cazacu yield function and the Marciniak and Kuczyński (MK) necking criterion. Based on transformed principal stresses, the phenomenological constitutive model of Cazacu is used to take into account the initial plastic anisotropy and strength differential (SD) effects. For plane stress and orthotropic symmetry, two linear transformations are required to use a number of anisotropy coefficients which are more suitable for practical applications. Under these circumstances, a prediction of formability for HCP sheet materials with more than one linear transformation is performed using the numerical tool Mathematica

Prediction of the ductility limit of magnesium AZ31B alloy

In many engineering applications (automotive, computer and mobile device industries, etc.), magnesium alloys have been widely used owing to their interesting physical and mechanical parameters. However, magnesium alloys are identified by the low ductility at room temperature, due to their strong plastic anisotropy and the yielding asymmetry between tension and compression. In this work, the ductility limit of a rolled magnesium AZ31 sheet metal at room temperature is numerically investigated. This investigation is based on the coupling between a reduced-order crystal plasticity model and the Marciniak– Kuczyński localized necking approach. This reduced-order model is used to describe the anisotropic behavior of this material taking into account the strong plastic anisotropy (e.g., yielding asymmetry between tension and compression) due to the limited number of slip systems (i.e., twinning mode). To accurately describe the plastic anisotropy due to slip and twinning modes, a combination of two separate yield functions (according to Barlat and Cazacu) is used. The coupling between the adopted constitutive framework and the Marciniak–Kuczyński instability approach is numerically implemented via an implicit algorithm. Comparisons between experimental results from the literature and numerical results obtained by using our calculation tool are carried out to validate the choice of the reducedorder crystal plasticity model

An anisotropic model with linear perturbation technique to predict HCP sheet metal ductility limit

In this paper, hexagonal closed packed (HCP) sheet metal ductility for a viscoplastic material is analyzed by using a linear perturbation technique. It can be used for the analysis of localized necking. This technique is used to perturbate the material behavior in a rate-dependent formulation by superimposing a perturbation to the basic flow, whose stability or instability is characterized by the increasing or decreasing of the perturbation. Hardening and initial anisotropic parameters are fitted by experimental results from the literature. In this investigation, Cazacu yield function is used to predict the forming limit diagrams (FLDs) of HCP sheet metals. The coupling between analytic perturbation method and the behavior modelling is provided by an efficient implicit algorithm to solve the constitutive equations. After verifications and validations of the numerical simulations from the literature, the ductility limit of a particular HCP magnesium alloy is numerically predicted. A parametric study is presented to analyze the effect of instability and mechanical parameters, viscosity and distortion on the FLDs. Moreover, a comparative study between Marciniak and Kuckzynski ductility approach and linear perturbation technique is done in this contribution

Prediction of necking in HCP sheet metals using a two-surface plasticity model

In the present contribution, a two-surface plasticity model is coupled with several diffuse and localized necking criteria to predict the ductility limits of hexagonal closed packed sheet metals. The plastic strain is considered, in this two-surface constitutive framework, as the result of both slip and twinning deformation modes. This leads to a description of the plastic anisotropy by two separate yield functions: the Barlat yield function to model plastic anisotropy due to slip deformation modes, and the Cazacu yield function to model plastic anisotropy due to twinning deformation modes. Actually, the proposed two-surface model offers an accurate prediction of the plastic anisotropy as well as the tension–compression yield asymmetry for the material response. Furthermore, the current model allows incorporating the effect of distortional hardening resulting from the evolution of plastic anisotropy and tension–compression yield asymmetry. Diffuse necking is predicted by the general bifurcation criterion. As to localized necking, it is determined by the Rice bifurcation criterion as well as by the Marciniak & Kuczynski imperfection approach. To apply both bifurcation criteria, the expression of the continuum tangent modulus associated with this constitutive framework is analytically derived. The set of equations resulting from the coupling between the Marciniak & Kuczynski approach and the constitutive relations is solved by developing an efficient implicit algorithm. The numerical implementation of the two-surface model is assessed and validated through a comparative study between our numerical predictions and several experimental results from the literature. A sensitivity study is presented to analyze the effect of some mechanical parameters on the prediction of diffuse and localized necking in thin sheet metals made of HCP materials. The effect of distortional hardening on the onset of plastic instability is also investigated

Vers une meilleure prédiction des limites de formabilité des matériaux polycristallins à structure hexagonale.

The aim of this thesis is to study the ductility of hexagonal close packed (HCP) materials, which are being increasingly used in a wide range of engineering applications (aircraft and aerospace industries). After the step of the understanding of the physical phenomena and the different mechanisms that contribute to the plastic deformation (plastic slip, twinning…), a set of constitutive frameworks are selected from the literature and improved. These different frameworks are numerically integrated by implementing numerical schemes ensuring the accuracy and the robustness of the time integration. The adopted models are then coupled with several plastic instability criteria: general bifurcation, initial imperfection approach of Marciniak-Kuczynski, Rice bifurcation theory, and linear perturbation method. The effect of some phenomena and mechanical parameters on the predicted ductility limits are particularly studied. The results obtained by phenomenological models are compared to various experimental results. Once fully developed, assessed and validated, the numerical tools based on the above-described modeling can be advantageously used to help in the optimization of mechanical properties (crystallographic texture…) in order to improve the formability of HCP materials.Cette thèse a pour objectif d’étudier la ductilité des matériaux à structure cristallographique hexagonale qui sont couramment utilisés dans différents secteurs de l’industrie, telles que les industries aéronautique et aérospatiale. Après compréhension de la physique des différents mécanismes de plasticité, tels que le glissement et le maclage, plusieurs modèles de comportement sont identifiés et enrichis pour décrire d’une manière pertinente le comportement mécanique des matériaux à structure hexagonale, à savoir l’alliage de titane et l’alliage de magnésium. Ces modèles sont intégrés numériquement en développant des schémas numériques assurant à la fois la robustesse et la fiabilité de l’intégration temporelle. Ils sont ensuite couplés aux critères d’instabilités plastiques suivants : bifurcation générale, imperfection initiale de Marciniak-Kuczynski, bifurcation de Rice et critère par perturbation linéaire. L’effet de plusieurs phénomènes et paramètres mécaniques sur la prédiction de la ductilité est particulièrement analysé. Les résultats numériques, en termes de limites de formabilité, sont comparés avec des résultats expérimentaux. Après leurs validations, les différents outils numériques développés dans le cadre de cette thèse peuvent être utilisés comme outil d’aide à l'optimisation des procédés de mise en forme des matériaux à structure hexagonale

Towards a better prediction of the ductility limit of hexagonal polycristalline materials

Cette thèse a pour objectif d’étudier la ductilité des matériaux à structure cristallographique hexagonale qui sont couramment utilisés dans différents secteurs de l’industrie, telles que les industries aéronautique et aérospatiale. Après compréhension de la physique des différents mécanismes de plasticité, tels que le glissement et le maclage, plusieurs modèles de comportement sont identifiés et enrichis pour décrire d’une manière pertinente le comportement mécanique des matériaux à structure hexagonale, à savoir l’alliage de titane et l’alliage de magnésium. Ces modèles sont intégrés numériquement en développant des schémas numériques assurant à la fois la robustesse et la fiabilité de l’intégration temporelle. Ils sont ensuite couplés aux critères d’instabilités plastiques suivants : bifurcation générale, imperfection initiale de Marciniak-Kuczynski, bifurcation de Rice et critère par perturbation linéaire. L’effet de plusieurs phénomènes et paramètres mécaniques sur la prédiction de la ductilité est particulièrement analysé. Les résultats numériques, en termes de limites de formabilité, sont comparés avec des résultats expérimentaux. Après leurs validations, les différents outils numériques développés dans le cadre de cette thèse peuvent être utilisés comme outil d’aide à l'optimisation des procédés de mise en forme des matériaux à structure hexagonale.The aim of this thesis is to study the ductility of hexagonal close packed (HCP) materials, which are being increasingly used in a wide range of engineering applications (aircraft and aerospace industries). After the step of the understanding of the physical phenomena and the different mechanisms that contribute to the plastic deformation (plastic slip, twinning…), a set of constitutive frameworks are selected from the literature and improved. These different frameworks are numerically integrated by implementing numerical schemes ensuring the accuracy and the robustness of the time integration. The adopted models are then coupled with several plastic instability criteria: general bifurcation, initial imperfection approach of Marciniak-Kuczynski, Rice bifurcation theory, and linear perturbation method. The effect of some phenomena and mechanical parameters on the predicted ductility limits are particularly studied. The results obtained by phenomenological models are compared to various experimental results. Once fully developed, assessed and validated, the numerical tools based on the above-described modeling can be advantageously used to help in the optimization of mechanical properties (crystallographic texture…) in order to improve the formability of HCP materials