Prediction of flange wrinkling in deep drawing process using bifurcation criterion

Surface distortions in the form of wrinkles are often observed in sheet metals during stamping and other forming operations. Because of the trend in recent years towards thinner, higher-strength sheet metals, wrinkling is increasingly becoming a more common and troublesome mode of failure in sheet metal forming. The prediction and prevention of wrinkling during a sheet forming process are important issues for the design of part geometry and processing parameters. This paper treats the phenomenon of flange wrinkling as a bifurcated solution of the equations governing the deep drawing problem when the flat position of the flange becomes unstable. Hill’s bifurcation criterion is used to predict the onset of flange wrinkling in circular and square cup drawing. In particular, the maximum cup height that can be drawn without the onset of flange wrinkling is predicted for the given set of process parameters. A parametric study of the maximum cup height is also carried out with respect to various geometric, material and process parameters. Finite element formulation, based on the updated Lagrangian approach, is employed for the analysis. The incremental logarithmic strain measure, which allows the use of a large incremental deformation, is used. The stresses are updated in a material frame. The material is assumed to be elastic–plastic, strain hardening, yielding according to an anisotropic yield criterion of Barlat et al. (2005) 23] (named as Yld2004-18p). Isotropic power law hardening is assumed. Inertia forces are neglected due to small accelerations. Modified Newton–Raphson iterative technique is used to solve the nonlinear incremental equations.