Determination of instability of a DP 980 steel sheet under different stress states based on experiment and theoretical models

It is generally accepted that the formability of sheet metal is limited by the onset of instability which can be described by forming limit diagram (FLD) in e1-e2 space. Common tests for FLD data usually cover strain ratio range from uniaxial to equal biaxial stretching, −1/2 < e2/e1 < 1. In this paper a new design of cruciform type specimen for uniaxial stretching is proposed to test formability with strain ratios in the range from shear to tension, −1 < e2/e1 < −1/2 which can be controlled by the geometry parameters. The forming limit of a DP 980 steel sheet was determined using both conventional method and proposed specimen with strain ratios from −1 < e2/e1 < 1. Then the experimental results were drawn in both e1− e2 and eeq−sm/seq spaces, and the predicted results based on Hill, Swift, M-K, and Hora instability models were compared with the experimental ones. The formability features of the studied steel in whole strain ratio range and differences among the investigated theoretical models were finally discussed. The results indicate that the M-K instability model shows better prediction of the studied steel compared to the other models investigated in this research.