Theoretical Forming Limit Diagram Based on Induced Stress in the Thickness Direction

The conventional theoretical forming limit diagram (FLD) based on the plane stress state has defects due to the neglect of the stress in the thickness direction of the sheet. It is urgent to study the FLD which considers the stress in the thickness direction. Through the finite element simulation, it is further confirmed that the stress in the thickness direction will be induced in the deformation process. At the same time, the effect of the induced stress in the thickness direction on FLD is not the same as that always applied stress in the thickness direction during the deformation process. Based on the Modified Maximum Force Criterion (MMFC) instability theory, C-H instability theory, Mises and Hill48 yield criterion, the effects of the two stresses on FLD are compared. The induced stress in the thickness direction also affects the sensitivity of the coefficient of normal anisotropy r, but does not significantly change the effect of the stress-strain index n on Forming Limit Curves (FLC). The theoretical calculations of the three materials TRIP780, AA5182, and 5754O are compared with the experimental data, which proves that the FLD which considers induced stress in the thickness direction is more accurate than the FLD of the plane stress.