Wrinkling initiation and growth in modified Yoshida buckling test: finite element analysis and experimental comparison

Wrinkling is one of the major defects in sheet metal products and may also play a significant role in the wear of the tool. The initiation and growth of wrinkles are influenced by many factors such as stress ratios, mechanical properties of the sheet material, geometry of the workpiece, contact condition, etc. It is difficult to analyze the wrinkling initiation and growth considering all the factors because the effects of the factors are very complex and the wrinkling behavior may show a wide scatter of data even for small deviations of factors. In this 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. The wrinkling initiation is found by checking the determinant of the stiffness matrix at each iteration and the wrinkling behavior is analyzed by successive iteration with the perturbed guess along the eigenvector. The effect of magnitude of perturbation on the wrinkling behavior can be avoided by the Newton-type iteration method. 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. For the verification of the analysis, the postbuckling of columns and circular plates are analyzed by finite element analysis using the bifurcation algorithm introduced in the study, and the results are compared with the exact solutions. In order to investigate the effects of geometry and stress ratio on the wrinkling initiation and growth, a modified Yoshida buckling test is proposed as an improved effective buckling test. In the modified Yoshida buckling test, the dimensions of the sheet specimen are varied to change the stress ratio and the degree of constraint. The finite element analysis is carried out for the modified Yoshida buckling test and compared with the experimental results.