Physically based criterion for prediction of instability under stretchbending of sheet metal

This research focuses on the prediction of the forming limit of certain Advanced High Strength Steel grades under stretch-bending conditions. For these types of steels it is experimentally observed and shown that when there is a bending component added to the main membrane deformation the formability predicted by the regular FLCs underestimate the material behavior. Due to the added effects of thickness stress due to contact and small radius bending as well as bending stresses, a through-thickness stress gradient forms which gives additional stability to the material beyond the forming limits determined by tests that generate mostly uniform membrane deformation. It is observed experimentally and by the detailed simulations that the cross-sectional stability is not lost instantaneously but gradually. A surface dent forms first on the outer surface and progresses in a stable manner towards the contact side since on the contact side the material has still potential to harden. This process delays the localization of the strains and stabilizes the formation of the local neck. For the prediction of this phenomenon theoretically and using shell elements, a modified incremental form of the maximum tension stability criterion is proposed to be applied at integration points through thickness. It is shown that with this criterion the phenomenon of gradual loss of stability can be captured during stretch-bending with shell elements.