Porous plasticity revisited: Macroscopic and multiscale modeling

Abstract

Porous plasticity aims to model the growth and coalescence of voids leading to ductile failure. The GTN model (1984), resulting from heuristic modifications to Gurson's homogenized hollow sphere model (1977), is used in numerous publications. The Rousselier model (1981), developed in the framework of continuum thermodynamics, is apparently similar. Both models are effective in numerical calculations, but the reasons why they perform well were not investigated in details in the existing literature, as regards transition to uniaxial deformation, relations between various modes of strain localization, finite element discretization, regularization. In the present paper, we propose first to revisit both models and to compare their fundamentally different mechanical behaviors. For stress triaxiality larger than some critical value, it is shown that theoretically the GTN model cannot achieve strain localization in a plane but only pointwise localization for the ultimate mechanical state (stress tensor equal to zero). The larger the void volume fraction (void growth), the smaller the stress triaxiality critical value. Fortunately, discretization transforms the pointwise localization into volume localization and with an appropriate Cartesian finite element mesh a more or less planar sheet of integration points can be obtained. The Rousselier model can achieve strain localization in a plane at all stress triaxialities and discretization also transforms this localization into volume localization with a characteristic element size. Second, multiscale modeling of both plasticity and ductile damage (not limited to void damage) is an essential way of progress for laboratory specimen calculations. The Rousselier model can be incorporated into polycrystalline models based on crystal plasticity, with reasonable computation times provided a reduced texture with a small number of crystallographic orientations is used. It can be coupled with a new Coulomb ductile fracture model at the slip system scale and with secondary void nucleation and growth models at the grain and slip system scales, respectively. The multiscale model is applied to aluminum CT and KAHN specimens and to steel round notched specimens.