M–K Analysis of Forming Limit Diagram Under Stretch-Bending

Since the Forming limit diagram (FLD) was introduced and developed by Keeler etc. about four decades ago, it has been intensively studied by researchers and engineers. Most work has been focused on the in-plane deformation which is considered as the dominant mode of the most forming processes. However the effect of out-of-plane deformation modes especially bending effect becomes important in accurate prediction of formability when thick sheet metal and smaller forming radii are encountered. Recent work on experiment research of stretch-bending induced FLD (BFLD) shows that it gives higher formability than conventional forming limit. In this paper, bending effect through the sheet metal thickness on right-hand side of FLD is studied. The Marciniak-Kuczynski (M-K) analysis is extended to include bending and models based on both flow theory and deformation theory are proposed. The radial return method is adopted as the frame to calculate the stress states from given strain and deformation history. The effect of bending and unbending process on the Right-Hand-Side FLD is investigated and compared. The obtained results show that the bending process slightly decreases the sheet metal formability on right-hand side in flow theory based model which is a discrepancy with the prediction of deformation theory based BFLD model. The insight gained from new proposed FLD prediction model in this paper provides an understanding of how the bending process effects on the FLD. This is important for the further research to reconsider the problems of how the bending effect evolves in forming process to enhance the conventional FLD and how to get a perfectly true theoretical explanation for this phenomenon.