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Adiabatic shear banding induced degradation in a thermo-elastic/viscoplastic material under dynamic loading

Abstract : In the approach presented, adiabatic shear banding (ASB) is considered as a form of anisotropic deterioration. The anisotropic mechanical degradation induced in the structural material by the bands is dealt with by using a second-order tensor internal variable. The kinematical consequences of the presence of the bands are described by means of the corresponding part (deterioration-induced part in addition to the genuinely plastic part) of the velocity gradient embodying the notion of a “super-dislocation”. The kinematical framework involves finite strain anisotropic elastic-irreversible formulation based on the multiplicative decomposition of the deformation gradient. Constitutive equations integrating ASB-deterioration-like process are derived from thermodynamic potentials namely the free energy and dissipative potentials in the general framework of the internal state variables formulation. The hypothesis of a single yield function has been put to describe the chronology of the viscoplastic dissipative mechanisms and to account for the strong coupling between plasticity and band induced deterioration. An auxiliary indicator needed for determining the conditions for shear bands initiation and orientation has been obtained from a simplified analysis based on the linear theory of perturbations. This three-dimensional constitutive model, including anisotropic effects due to the ASB-induced deterioration in the context of finite elastic–plastic strains, rate sensitivity, strain hardening and thermal softening, has been implemented as ‘user material’ in the finite element code LS-DYNA. Three-dimensional numerical simulations of adiabatic shear banding-induced degradation have been performed considering the hat shape structure under dynamic shearing employing a direct Hopkinson pressure bar device. Depending on the impact velocity and on the loading duration, deterioration bands propagate or arrest inside the hat shape structure. Numerical results show the evolution of the band tip velocity during the deterioration process. Numerical deterioration maps inside the hat shape structure and the load transmitted to the output bar are in good agreement with experimental evidence including band orientation. Because of the modelling scale we use herein, mesh refining in the areas crossed by the bands—which usually supposes the a priori knowledge of the band trajectory—is not necessary. Thanks to the regularising effects of viscosity (in the model viscosity is double, concerning plasticity but also deterioration) and a further adaptive time procedure, a weak mesh dependency of the numerical results has been observed.
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Patrice Longère, André Dragon, Hervé Trumel, Xavier Deprince. Adiabatic shear banding induced degradation in a thermo-elastic/viscoplastic material under dynamic loading. International Journal of Impact Engineering, 2005, 32, pp.285-320. ⟨10.1016/j.ijimpeng.2005.03.002⟩. ⟨hal-00443816⟩



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