The effect of voids shape on hypervelocity cylindrical cavity expansion and shock waves formation in transversely isotropic porous materials

Abstract

This paper investigates the steady-state dynamic radial expansion of a pressurized circular cylindrical cavity in an infinite porous medium modeled with the constitutive framework developed by Monchiet et al. (Int J Plast 24:1158–1189, 2008), which considers the material to display a periodic porous microstructure with spheroidal voids and matrix described by the orthotropic yield criterion of Hill (Proc R Soc Lond Ser A Math Phys Sci 193:281–297, 1948). For that purpose, we have extended the formulation of dos Santos et al. (Int J Impact Eng 132:103325, 2019b) to consider oblate and prolate voids, which allows to assess the role of the initial voids shape on the elastoplastic–anisotropic fields that develop near the cavity. The theoretical development follows the cavity expansion formalism of Cohen and Durban (J Appl Mech 80:011017, 2013) and employs the artificial viscosity approach of Lew et al. (J Comput Aided Mater Des 8:213–231, 2001) to avoid singularities in the field variables due to the formation of plastic shock waves. The main outcome of this work is a relationship between the critical cavity expansion velocity for which plastic shocks emerge and the initial aspect ratio of the spheroidal voids. The results show that the formation of shocks is delayed for oblate voids, in comparison with spherical and prolate voids. These findings have been substantiated for different anisotropic behaviors and initial void volume fractions.