Modeling dynamic formability of porous ductile sheets subjected to biaxial stretching: Actual porosity versus homogenized porosity

Abstract

This paper investigates the eect of porous microstructure on the necking formability of ductile sheets subjected to dynamic in-plane stretching. We have developed an original approach in which finite element calculations which include actual void distributions obtained from additively manufactured materials are compared with simulations in which the specimen is modeled with the Gurson-Tvergaard continuum plasticity theory (Gurson, 1977; Tvergaard, 1982) which considers porosity as an internal state variable. A key point of this work is that in the calculations performed with the continuum model, the initial void volume fraction is spatially varied in the specimen according to the void distributions included in the simulations with the actual porous microstructure. The nite element computations have been carried out for dierent loading conditions, with biaxial strain ratios ranging from 0 (plane strain) to 0.75 (biaxial tension) and loading rates varying between 10000 s^-1 and 60000 s^-1. We have shown that for the specific porous microstructures considered, the necking forming limits obtained with the Gurson-Tvergaard continuum model are in qualitative agreement with the results obtained with the calculations which include the actual void distributions, the quantitative dierences for the necking strains being generally less than 25% (the calculations with actual voids systematically predict greater necking strains). In addition, the spatial distribution of necks formed in the sheets at large strains is very similar for the actual porosity and the homogenized porosity models. The obtained results demonstrate that the voids promote plastic localization, acting as preferential sites for the nucleation of fast growing necks. Moreover, the simulations have provided individualized correlations between void volume fraction, maximum void size and necking formability, and highlighted the in uence of the heterogeneity of the spatial distribution of porosity on plastic localization.