(A) study on the growth and prediction of wrinkles in sheet metal forming processes using bifurcation theory

Abstract

Wrinkling is one of the major defects in sheet metal products together with tearing, springback and other geometric and surface defects. Wrinkling may be a serious obstacle to a successful forming process and in assembling the parts, and may also play a significant role in the wear of the tool. In order to improve productivity and quality of products, wrinkling must be essentially eliminated. Recently, sheet metal forming processes are widely used in various industrial sectors such as in automotive industry, electric home appliance industry, and aircraft industry, and also the needs for high precision and high value-added products are increased. In order to reduce the process development time, the prediction of defects and the modification of design in the design stage are needed. 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 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. 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 th...