Analysis of blank thickening in deep drawing processes using the theory of a Cosserat generalized membrane

This paper analyzes a transient, nonlinear deep drawing process where a circular blank of a rigid-plastic material is forced by a rigid circular punch to deform into a cylindrical cup. Attention is focused on the plastic flow beneath the blank-holder. Using the Cosserat theory of a generalized membrane it is possible to obtain analytical solutions which examine the following two major effects: (a) the importance of added “rim pressure” acting on the outer edge of the blank; and (b) the importance of a controlled moveable blank-holder to allow blank thickening during the drawing process. Guided by these analytical results, a new deep drawing machine was built to exploit these effects and increase the limit drawing ratio (LDR) of the drawing process. Specifically, the LDR (in one stroke) reached the value of 3.16 compared with the value of about 2.0 in the conventional process. Moreover, the analytical prediction of the punch force versus the punch stroke is in good agreement with the experimental data and with simulations using the computer code DYTRAN.