Effect of plastic anisotropy on compressive instability in sheet metal forming

The wrinkling behavior of a thin sheet with perfect geometry is associated with compressive instability. The compressive instability is influenced by many factors such as stress state, mechanical properties of the sheet material, geometry of the body, contact conditions and plastic anisotropy. The analysis of compressive instability in a plastically deforming body is difficult considering all the factors because the effects of the factors are very complex and the instability behavior may show a wide variation for a small deviation of the factors. In this study, the bifurcation theory is introduced for the finite element analysis of puckering initiation and growth of a thin sheet with perfect geometry. All the above mentioned factors are conveniently considered by the finite-element method. The instability limit is found by the incremental analysis and the post-bifurcation behavior is analyzed by introducing the branching scheme proposed by Riks. The finite-element formulation is based on the incremental deformation theory and elastic-plastic material modeling. The finite-element analysis is carried out using the continuum-based resultant shell elements considering the anisotropy of the sheet metal. In order to investigate the effect of plastic anisotropy on the compressive instability, a square plate that is subjected to compression in one direction and tension in the other direction is analyzed by the above-mentioned finite-element analysis. The critical stress ratios above which buckling does not take place are found for various plastic anisotropic modeling methods and discussed. Finally, the effect of plastic anisotropy on the puckering behavior in the spherical cup deep drawing process is investigated. From the results of the finite-element analysis, it is shown that puckering behavior of sheet metal is largely affected by plastic anisotropy.