Elasto plastic formulation using a kinematic hardening model for springback analysis in sheet metal forming

Abstract The prediction of the sheet metal's springback after deep drawing is an important issue to solve for the control of manufacturing processes. Nowadays, the importance of this problem increases because of the use of steel sheeting with high yield stress and also aluminium alloys. A mechanical theory has been developed and implemented in a software called PLIAGE in order to predict the final shape of the drawing. The principle of calculations is the following one: first, the forming process is simulated geometrically in order to find the areas of the drawing which have experienced the same strain path. Stresses at the end of deep drawing and the residual stresses are computed for each identical strain history area by solving the Prandtl and Reuss plasticity equations associated with a non linear kinematic hardening model proposed by Lemaitre and Chaboche. The calculations take into account the change of the Young's modulus versus plastic strain because of the importance of this parameter for springback computation. After the final stress state is entirely computed, the residual radius of the identical history strain area is then calculated to determine springback. The complete shape, after springback, is rebuilt with the residual radius of each area. A new method to identify the coefficients of Lemaitre and Chaboche's law with a tensile test is also exposed.