Construction and Application of Wrinkling Limit Diagram (WLD)

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This research aims at to provide a computational tool for predicting the onset of wrinkles during the general forming processes used on thin-walled bodies. It is assumed that the bodies are thin enough to deform along a completely lubricated tool surface to satisfy the membrane stress condition until wrinkling. A corner type constitutive equation with a general anisotropic quadratic yield function for a thin-walled bodies is developed. The onset of wrinkles is assumed to be a bifurcation from the membrane type of deformation to the bending type of deformation. Hill's general theory of bifurcation and uniqueness is employed in conjunction with Donnell-Mushtari-Vlasov's thin shell theory and Naghdi's linear thin shell theory to formulate the problem.An analytical solutions have been presented to the condition of the onset of wrinkling for the curved sheets with different thickness under the variety of stress conditions. The results are summarized as the wrinkling limit diagram (WLD) which present the combinations of the critical principal stresses for the assumed mode of wrinkles. This can be used to predict the onset of wrinkling during the sheet metal forming processes as is done for the prediction of the forming limit of sheet metals with Forming Limit Diagram (FLD) by using the local stresses estimated by the computational simulations.For the complicated problems, direct numerical searching strategies of the critical stress conditions for the onset of wrinkling have been employed. This can be also introduced to the computational simulation of shin sheet metal forming processes. Furthermore, to clarify the growth rate of wrinkles three dimensional analysis with isoparametric shell element and the same constitutive equation has been done. Parametric studies have been performed to investigate the effect of material characteristics, boundary condition and shape of the sheet metal on the wrinkling processes.