Instabilités thermo-viscoplastiques aux grandes vitesses de déformation

Abstract : The instability of plastic deformation is widely observed in most materials. It often results in a localization of plastic flow which acts as a precursor of failure. In order to investigate these phenomena, constitutive laws suited to large strains and to high strain rates have to be proposed. Kinematic hardening models are presented which are based upon different objective derivatives and exhibit shading memory effects. Next, an approach of textural softening of metals at high strain rates is given where the crystallographic slips are assumed to obey a linear viscous law. The implications of such laws on plastic instability are discussed. The competition for localization between stabilizing mechanisms (strain and strain rate hardening, inertia and thermal conductivity) and destabilizing ones (thermal and geometrical softening) is shown in simple tension. Inertia and thermal effects are emphasized since they can play a major part at high strain rates. The linearization methods are discussed; linear results are compared to nonlinear closed form or numerical calculations. The comparison with available experimental data shows that the observed dynamic increase and adiabatic decrease of materials ductility may be well described by these models. It is shown that instability and localization of deformation are different concepts, and that shear band formation is generally predicted by a localization (not instability) analysis. This is done by means of a relative perturbation method; such a method accounts for the unsteadiness of plastic flow. Instability criteria and localization is discussed. Closed form and numerical nonlinear instability and localization results, related to shear band formation in non-strain hardening materials, are presented. Under isothermal boundary conditions, a critical shear stress is show to exist, beyond which plastic deformation is unstable. For adiabatic boundary conditions, a nonlinear relative perturbation method provides approximate critical shear strain for localization. This result is compared to nonlinear numerical calculations
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Claude Fressengeas. Instabilités thermo-viscoplastiques aux grandes vitesses de déformation. Autre. Université Paul Verlaine - Metz, 1986. Français. ⟨NNT : 1986METZ004S⟩. ⟨tel-01775696⟩

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