The effect of tension-compression asymmetry on the formation of dynamic necking instabilities under plane strain stretching

This paper brings to light the effect of tension-compression asymmetry in flow stresses on the formation of dynamic necking instabilities in isotropic metallic plates subjected to plane strain stretching. For that purpose, a two-pronged approach which includes finite element calculations and linear stability analysis has been used. In both approaches, for the description of the plastic behavior the isotropic form of Cazacu et al. (2006) criterion and isotropic hardening was assumed. It is shown that although this criterion involves dependence of the third-invariant of the stress deviator, it is possible to develop a linear stability analysis and obtain the value of the growth rate of the perturbation at different loading times, and track the history of the growth rate of all the growing modes during the post-critical deformation process. Furthermore, an original procedure for calibration of linear stability analysis from finite element calculations was developed. Both linear stability analysis and finite element results indicate an important effect of the tension-compression asymmetry on the necking behavior and the same overall trends. In particular, the results show that while the necking time, and thus the specimen elongation when necking occurs, is roughly the same irrespective of the tension-compression asymmetry ratio, the necking strain and the necking energy are significantly greater for a material that displays a larger flow stress in uniaxial compression than in uniaxial tension. A key outcome of this investigation is to demonstrate that such behavior is due to the larger plastic dissipation undergone, under plane strain stretching, by such a material as compared to a von Mises material and a material with larger flow stress in uniaxial tension than in uniaxial compression.