Tresca criterion for plasticity and viscoplasticity: Application to localization in biaxial loading conditions

It has been proved that plastic instabilities in biaxial stretching conditions were better reproduced by using a Tresca yield surface rather than a Von Mises one. The simulation of the phenomenon in an expanding TA6V4 (Ti-6Al-4V alloy) shell experiment is performed using the Tresca criterion and both elasto-plastic and viscoplastic constitutive models: in this aim, Tresca flow surfaces had to be defined in viscoplasticity. The two models exhibit localization but, whereas the elastoplastic case develops shear banding in times in agreement with the onset of instabilities in the experiment, the viscoplastic case develops diffuse necking at later times. On the contrary, the viscoplastic simulation exhibits patterns the size of which seems in better agreement with the experimental ones.