Mathematical Modeling in Plane Strain Bending

Springback is one of the main problems in sheet metal bending operations. Theoretically, an accurate description of strain distribution and stress distribution is required in order to predict the springback behavior of a bending component. Prediction of strain distribution needs a good geometrical model while prediction of stress distribution needs both an accurate strain description and an accurate stress-strain relationship. In this paper, a new model is developed for strain calculation in plane strain bending. The displacement of the neutral surface, the thickness change, the stress and strain distributions over the sheet thickness, the bending moment and the springback curvature are examined using this new model and useful conclusions are obtained. The new model is also compared with Hill's pure bending model, the membrane theory (plus post-processing) and the shell theory. The application ranges and the limitations of the membrane theory and the shell theory are discussed.