Sheet metal forming limits under stretch-bending with anisotropic hardening

One of the important failure criteria of press operations in industry for forming simulations is the Forming Limit Diagram (FLD). The complex loading effects on FLD, in particular the localized necking phenomenon under stretch-bending condition, have not been fully investigated and well understood. In practical sheet metal applications, the deformation is invariably three dimensional with a combination of stretching and bending. For most sheet materials under these complex loading processes used in industry, strong Bauschinger effect is observed, and the material hardening behavior tends to be anisotropic. This study aims to understand and evaluate such anisotropic hardening effect on the forming limit prediction under stretch-bending condition. The extended through-thickness Marciniak–Kuczynski (M–K) analysis is incorporated with Yoshida–Uemori (YU) two-surface kinematic hardening constitutive model, which has a more accurate description of the reverse loading behavior than that of the conventional isotropic hardening model. The material parameters used in this paper for YU model are calibrated with the experimental data from uniaxial large-strain tension-compression cyclic test. Both the isotropic hardening and YU kinematic hardening models with Hillʹ48 yield surface are employed in the analysis for the purpose of comparison. The Forming Limit Average Stress Diagram (FLASD) under stretch-bending condition is proposed to extend the understanding of Forming Limit Stress Diagram (FLSD) from in-plane to out-of-plane deformations. The “bending-ratio-dependent” phenomenon in forming limit diagram is predicted and observed in both stress/strain space with the proposed method. It suggests that the individual stress/strain state cannot represent system behavior. Forming limits under stretch-bending is suggested as an occurrence of system instability, not individual material instability. The system behavior of sheet metal deformation is reinforced as critical to the understanding of necking instability in stretch bending processes. The analysis shows that the Bauschinger effect provides positive effect in delaying the necking instability, predicting higher formability for sheet metals under stretch-bending. The insight obtained in this paper provides further understanding of the localized necking phenomenon under stretch-bending condition.