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 in uenced by many factors such as stress ratios, the mechanical properties of the sheet material, the geometry of the workpiece, and contact condition. It is di cult to analyse wrinkling initiation and growth while considering all the factors because the e ects 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 nite element analysis of wrinkling initiation and growth. All the above mentioned factors are conveniently considered by the nite element method. Wrinkling initiation is found by checking the determinant of the sti ness 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 nite element analysis are compared with the experimental results. Through the nite element analyses of wrinkling growth for various material constants, the e ects of plastic anisotropy and the strain hardening coe cient on the wrinkling behaviour of sheet metal are investigated