Optimal blank shape prediction considering sheet thickness variation: An upper bound approach

Earing is a common defect that occurs in deep drawing process. Earing defect occurs due to non-uniform material properties within the plane of the sheet (i.e. anisotropy). There have been many attempts to predict initial blank shape for minimizing earing by using slip line, finite element and other techniques but the upper bound technique does not seem to have received much attention. In the present work, the deformation zone is divided into sub-zones and kinematically admissible velocity field is proposed for each zone satisfying appropriate boundary conditions. Proposed upper bound methodology is validated by comparing its load predictions with the available results in the literature. Blank shape prediction is done in two steps. In the first step, a circular blank is chosen and the cup height along its circumference is obtained. In the second step, the information obtained in the first step is used to obtain the optimal blank shape by minimizing the earing effect. The blank shape predictions of the proposed model are validated by comparing them with the experimental/numerical results available in the literature and they are found to be in good agreement.