Correlation between the ratio between the tensile and shear yield strength on porosity evolution in isotropic ductile materials

Abstract

In this paper, we investigate the dilatational response of porous solids with matrix plastic behavior governed by Cazacu (2018) yield criterion that involves both invariants of the stress deviator, the relative weight of these invariants being described by a parameter $\alpha$. This parameter depends only on the ratio ${\tau }_Y/{\sigma }_T$ between the shear and tensile strengths; for $\alpha$ = 0, ${\tau }_Y/{\sigma }_T$ = $1/\sqrt{3}$ and the von Mises criterion is recovered. For both compressive and tensile loadings, FE unit-cell simulations were conducted at fixed stress triaxialities and various ordering of the principal stresses, namely loadings such that $J_3^{\Sigma }$ = 0 and axisymmetric loadings such that $J_3^{\Sigma }$ > 0 and $J_3^{\Sigma }$ < 0, respectively. Irrespective of the material's ${\tau }_Y/{\sigma }_T$ ratio, there is a combined effect of the sign of the mean stress and $J_3^{\Sigma }$ on the dilatational response. The value of the ratio ${\tau }_Y/{\sigma }_T$ dictates the rate at which the porosity evolves. Under axisymmetric tensile loadings, for a material with ${\tau }_Y/{\sigma }_T$ < $1/\sqrt{3}$ the rate of void growth is faster than for a porous von Mises material, the reverse holds true for a material with ${\tau }_Y/{\sigma }_T$ > $1/\sqrt{3}$. For axisymmetric compressive loadings, the larger is the ${\tau }_Y/{\sigma }_T$ ratio of the material, the slower is the rate at which porosity closes. For loadings at $J_3^{\Sigma }$ = 0 materials with ${\tau }_Y/{\sigma }_T$ < $1/\sqrt{3}$ exhibit slower rate of void growth or void collapse than for axisymmetric loadings, the opposite being true for materials with ${\tau }_Y/{\sigma }_T$ > $1/\sqrt{3}$.