Investigation into the wrinkling behaviour of thin sheets in the cylindrical cup deep drawing process using bifurcation theory

The initiation and growth of wrinkles are influenced by many factors such as stress ratios, the mechanical properties of the sheet material, the geometry of the workpiece, and contact condition. It is difficult to analyse wrinkling initiation and growth while considering all the factors because the effects of the factors are very complex and studies of wrinkling behaviour may show a wide scattering of data even for small deviations in factors. In the present study, the bifurcation theory is introduced for the finite element analysis of wrinkling initiation and growth. All the above mentioned factors are conveniently considered by the finite element method. Wrinkling initiation is found by checking the determinant of the stiffness matrix and wrinkling behaviour is analysed by successive iteration with the perturbed guess along the eigenvector. Wrinkling initiation and growth in the cylindrical cup deep drawing process are analysed by using the proposed bifurcation algorithm. The mechanism of wrinkling initiation and growth in the cylindrical cup deep drawing process is investigated in detail. The results of the finite element analysis are compared with the experimental results. Through the finite element analyses of wrinkling growth for various material constants, the effects of plastic anisostropy and the strain hardening coefficient on the wrinkling behaviour of sheet metal are investigated.