A Bifurcation Study of Wrinkling in Deep Drawing

Abstract

<p>This work is concerned with the wrinkling behaviour when deep drawing cylindrical cups from circular blanks. Wrinkling is a uniqueness problem, and the present work uses a bifurcation approach to predict its occurrence. The results are presented in terms of a critical ratio of blank diameter to thickness above which wrinkling commences, along with the number of waves into which the flange of the cup buckles.</p> <p>It is demonstrated that when the classical Prandtl-Reuss equations are incorporated into the bifurcation analysis, the theoretical predictions are at variance with the published experimental data.</p> <p>A number of ad-hoc modifications are made to the classical elastic-plastic model to make the predictions conform with the experimental results.</p> <p>A critical re-examination of both the flow and deformation theories of plasticity was carried out, leading to the proposal of a modified incremental theory. The modified constitutive equations is shown to reduce to an appropriate model for both elastic and rigid-plastic solids, as limiting cases. The consequence of the modified equations is non-coaxiality of the principal axes of stress and plastic strain increment, and this is supported by published experimental data. The proposed constitutive equations lead to a better prediction of the wrinkling behaviour vis a vis the other models discussed here-in.</p> <p>An experimental investigation of the wrinkling behaviour of a number of materials, drawn through a conical and a modified tractrix die, was undertaken. The study has resulted in proposals for certain material parameters as being beneficial for inhibiting wrinkling.</p> <p>A theoretical study of wrinkling when drawing through a conical die is also presented.</p>