Stress analysis of rectangular cup drawing

Experimental test and numerical simulation of rectangular cup drawing have greatly enhanced the engineering knowledge on its deformation characteristics. To facilitate theoretical analysis, a “three-segment-approach” was adapted by the authors on the rectangular cup drawing. Due to a twofold symmetry, only a quarter of the drawings were analyzed. Sheet material on areas corresponding to the two straight flange areas and one corner flange area were treated as three independent deformation zones. For the blank material located in the corner flange area, a concept of “equivalent circle” was put forward to simplify the stress analysis. Theoretical stress distributions on the straight flange areas and corner flange area were obtained separately from the analysis. Comparison of predicted results from the theoretical model with experimental and FEM simulation results showed a good agreement. It was found that the maximum radial stress along the punch opening is always located at the cup corners. The location with the predicted leading radial stress during the drawing was found always at the upper tangential point of the punch shoulder, where the sheet material disengaged from the punch. It was therefore justified as the most split-critical location of deep drawing of a rectangular cup. For the straight cup side, both the experimental and the FEM simulation results showed that the higher radial stress was at the upper tangential point of the punch. Since there is no complete theory available for the rectangular cup drawing problem, current three-segment-approach can be considered as a practical engineering method. Combining with results obtained from experiment and FEA simulation, this theoretical analysis can help the optimization of control scheme for stamping panels by using an advanced variable blank holder force rather than using a constant binder force.