Quantitative Analysis of Load–Displacement Curves in Erichsen Cupping Test for Low Carbon Steel Sheet

Effect of punch diameter and sheet thickness on the load–displacement curves was systematically investigated in Erichsen cupping test for a low carbon steel sheet, and the obtained load–displacement curves were quantitatively analyzed. For the analysis, total displacement in the Erichsen cupping test was separated into uniform and post-uniform displacements: the former is a displacement from the beginning to the maximum load and the latter is a displacement from the maximum load to the point at which a through crack appears. It was found that maximum load in the Erichsen cupping test increases proportional both to the punch diameter and to the sheet thickness. It was also found that the uniform displacement increases proportional to the punch diameter but is independent of the sheet thickness, while the post-uniform displacement increases proportional to the sheet thickness but is less affected by the punch diameter. Based on the mechanics of sheet metal forming, an equation to predict the punch load during the Erichsen cupping test was developed and applied for the data obtained in the present study. It was demonstrated that the developed equation can reasonably explain the experimentally-obtained load–displacement curves. A method to normalize the Erichsen cupping index was also proposed, where the Erichsen cupping index divided by the punch diameter shows a linear relationship with a ratio of the sheet thickness and punch diameter.