Sheet Metal Forming Limit Under Stretch-Bending

The Forming Limit Diagram (FLD) as developed by Keeler etc. has been widely used to assess sheet metal failure during a variety of forming operations. Its theoretical and empirical foundation is based on localized necking under biaxial loading for the sheet metal. While the in-plane deformation is generally the dominant mode for most forming operations, sheet metal bending is inevitably coupled to the deformation process, and the traditional Forming Limit Diagram has to be modified to take into account the bending effect, especially when the bending radius becomes smaller. This paper presents a theoretical formulation for the Bending-Enhanced Forming Limit model. The deformation theory of plasticity is employed for the instability analysis, and the bending is assumed only in the direction along one principal loading. The obtained results show that the forming limit is enhanced by the bending effect, consistent with experimental observations.