Stress State Analysis of Radial Stress Superposed Bending

Radial stress superposed bending is a sheet metal bending process, which superposes predetermined radial stresses. Stress superposition is mandatory to enable the reduction of the triaxiality in bending, resulting in delayed damage evolution and an improved product performance. The knowledge of the stress state is essential for damage-controlled bending as the triaxiality is the driving force for the void evolution. To control the stress state in radial stress superposed bending, an additional counter force responsible for the pressure in the outer fiber is applied. To predict the effect of the counter force on the radial stress and the triaxiality an analytical model is proposed. The prediction of the reaction forces in the system is required for the process design and for the calculation of the stress superposition. The stress state for plane strain bending with stress superposition is derived, and pressure calculations are made using the theory of Hertz. The model and the assumptions are verified in numerical and experimental studies for various counter pressures and bending ratios. Finally, a discussion of the load path depending on the transient counter pressure is carried out and experimental evidence for a inhibited damage evolution due to stress superposition is given.