Development of a new model for plane strain bending and springback analysis

A new mathematical model is presented for plane strain bending and springback analysis in sheet metal forming. This model combines effects associated with bending and stretching, considers stress and strain distributions and different thickness variations in the thickness direction, and takes force equilibrium into account. An elastic-plastic material model and Hill’s nonquadratic yield function are incorporated in the model. The model is used to obtain force, bending moment, and springback curvature. A typical two-dimensional draw bending part is divided into five regions along the strip, and the forces and moments acting on each region and the deformation history of each region are examined. Three different methods are applied to the two-dimensional draw bending problems: the first using the new model, the second using the new model but also including a kinematic directional hardening material model to consider the bending and unbending deformation in the wall, and the third using membrane theory plus bending strain. Results from these methods, including those from the recent benchmark program, are compared. University of Michigan, Dept. of Mechanical Engineering and Applied Mechanics, Ann Arbor, Mi 48109, USA.