Construction and Application of Wrinkling Limit Diagram (WLD)

本研究的目的是提供一种计算工具来预测薄壁体在一般成形过程中起皱的发生。假设阀体足够薄，可以沿着完全润滑的工具表面变形，以满足膜应力条件直至起皱。建立了薄壁体具有一般各向异性二次屈服函数的角型本构方程。皱褶的发生被认为是由膜型变形向弯曲型变形的分叉。将Hill的一般分岔和唯一性理论与Donnell-Mushtari-Vlasov的薄壳理论和Naghdi的线性薄壳理论相结合来表述问题。本文给出了不同厚度弯曲薄板在不同应力条件下起皱条件的解析解。结果被总结为皱褶极限图（WLD），它给出了假设皱褶模式下的临界主应力组合。这可以用来预测在成形过程中起皱的发生，就像用成形极限图（FLD）通过计算模拟估计的局部应力来预测板料的成形极限一样。对于这些复杂的问题，采用了起皱临界应力条件的直接数值搜索策略。这也可以引入到胫骨板成形过程的计算模拟中。在此基础上，利用等参数壳单元和相同的本构方程进行了三维分析。对材料特性、边界条件和板料形状对起皱过程的影响进行了参数化研究。

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.