The effect of yield surface curvature change by cross hardening on forming limit diagrams of sheets

Abstract

The paper aims at clarification of the role of reduction in yield locus curvature on forming limit diagrams. To this end, a cross-hardening model showing a reduction of yield surface curvature is used which accounts for dynamic and latent hardening effects associated with dislocation motion during loading. The model's three-dimensional tensorial as well as reduced plane-stress vector formulations are given. The first quadrants of forming limit diagrams are numerically produced using finite element models of the Marciniak-Kuczyński test with spatially correlated random defect distribution as localization triggering mechanism. The effect of cross hardening is investigated in detail. It is demonstrated that for plane strain loading path there occurs no difference in localization predictions of the models with and without cross hardening whereas for biaxial strain paths a delayed localization is observed in the cross hardening model as compared to the one without cross hardening effects. This is in accordance with the relative bluntness of the yield surface at the points of load path change towards localization. These results are complemented by Nakazima test simulations where similar observations are made.