Theoretical failure investigation for sheet metals under hybrid stretch-bending loadings

• Analytical models for sheet failure under typical hybrid stretch-bending loadings.
• The localized necking and ductile fracture are employed simultaneously.
• The isotropic and Y–U kinematic hardening models are adopted and compared.
• The new understanding of bending effect on forming limits is extended.
• Hybrid stretch-bending loadings give significant impact on the final failure mode.

The deformation limit of sheet metals predicted from forming simulations relies on the failure criteria employed. Localized necking and ductile fracture are two different failure mechanisms. They are applied to construct the Forming Limit Diagram (FLD) and Fracture Forming Limit Diagram (FFLD) in sheet metal forming processes. Recently, high strength steels and aluminum are extensively used as lightweight materials in road vehicle engineering to reduce fuel consumption. The deformation limit of those materials under stretch-bending condition shows significant bending radius dependent phenomenon. The bending process related to the stretch-bending loading of sheet metals is an out-of-plane effect, which has not been fully considered in traditional failure criteria. Most research efforts have been focused on the relationship between the localized necking phenomenon (ductile fracture) and the bending ratio (defined as the radius over the thickness). In this study, the different combinations of the tension and bending during the stretch-bending deformation referred as hybrid stretch-bending loading under the same bending ratio are investigated with proposed analytical models. The system instability and local material behavior are presented as two different failure mechanisms for forming limits and ductile fracture. Results from this study show that the localized necking failure is strongly affected by such loadings even under the same bending ratio. The final failure mode is a result of the competition between the localized necking and ductile fracture. It also suggested that the bending effect on forming limits is not just a function of the bending ratio but also a function of the specific hybrid stretch-bending loading applied on the sheet.