Approche multi-échelles pour une prédiction fiable de la ductilité des matériaux métalliques

Abstract : The main objective of this PhD thesis is to develop a numerical tool capable of predicting the ductility of polycrystalline materials. This tool is based on the coupling of the self-consistent multiscale approach with two plastic instability criteria: the bifurcation theory and the initial imperfection approach. The self-consistent scheme is used to derive the mechanical behavior of a polycrystalline aggregate (assumed to be representative of the studied material) from that of its microscopic constituents (the single crystals). The constitutive framework at the single crystal scale follows a finite strain rate-independent formulation. Two different versions of the Schmid law are successively used to model the plastic flow: the classical version and a regularized one. To solve the constitutive equations at the single crystal scale, two numerical algorithms have been developed: one is based on the usual return-mapping scheme and the other on the so-called ultimate scheme. The equations governing the self-consistent approach have been revisited. To solve these equations, a new numerical scheme has been developed, which is shown to be more efficient than the existing schemes commonly based on the fixed point method. Also, a robust numerical approach has been developed to couple the self-consistent model to the initial imperfection approach. The performance and the robustness of the different numerical schemes and algorithms developed have been highlighted through several simulation results. The impact of various parameters and modeling choices on the formability prediction of sheet metals has been extensively analyzed.
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Holanyo Koffi Akpama. Approche multi-échelles pour une prédiction fiable de la ductilité des matériaux métalliques. Mécanique des matériaux [physics.class-ph]. Ecole nationale supérieure d'arts et métiers - ENSAM, 2017. Français. ⟨NNT : 2017ENAM0025⟩. ⟨tel-01702677⟩

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