Influence of punch shapes on the collar-drawing process of sheet steel

Abstract

Abstract An incremental elasto-plastic finite-element method based on the updated Lagrangian formulation was adopted to predict the limiting condition of collar-drawing until unloading for three punch shapes: conical, cylindrical and spherical. The high non-linearity of the process was taken into account in an incremental manner and an rmin technique was used to limit the size of each increment within a linear relation. Based on a series of collar-drawing tests for these three punch shapes, the fracture thickness under the simple tension test was measured and served as a necking criterion on the hole periphery for the limiting condition of collar-drawing. Predictions of the final shapes, the variation of thickness and the relationship of punch load to punch stroke under the limiting conditions were in good agreement with the results of the experiment. A simulation of the influence of process parameters on the collar-drawing for the three punch shapes indicates that the punch load increases sharply with punch angle in the case of the conical punch and increases gradually with friction coefficient for all of the punches, but decreases with strain-hardening exponent. The maximum punch load decreases with the initial diameter of the hole in the cases of spherical and cylindrical punches but not in the case of the conical punch. It is noted that the relation on the diameter of the hole before and after drawing is linear. Consequently, the initial diameter of the hole for an expanded hole with punch diameter can be determined and verified by the three punch shapes. This can be useful for the sheet metal industry.