Analytical elastic–plastic study on flange wrinkling in deep drawing process

Based on the two-dimensional plane stress wrinkling model of an elastic–plastic annular plate and a bifurcation functional from Hill’s general theory of uniqueness in polar coordinates, the critical conditions for the elastic and plastic wrinkling of the flange of a circular blank during the deep-drawing process are obtained to improve previous results of the literature. The influence of a blank-holder on wrinkling and on the number of waves generated can also be quantitatively predicted. A closed-form solution for the critical drawing stress is developed, based on the Tresca yield criterion, along with the assumption of perfectly plastic material. A nonlinear plastic stress field and the deformation theory of plasticity are used. It is demonstrated that using the large deflection theory for a strain tensor with neglecting nonlinear terms has the same result as the small deflection theory.