A Bifurcation Study of Wrinkling in Deep Drawing - Karima, Mohamed Nassouh Medhat (My University, 1980)
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.
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.
A number of ad-hoc modifications are made to the classical elastic-plastic model to make the predictions conform with the experimental results.
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.
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.
A theoretical study of wrinkling when drawing through a conical die is also presented.
Keywords: Mechanical Engineering; Mechanical Engineering