Construction and Application of Wrinkling Limit Diagram (WLD)

本研究旨在提供一个计算工具，以预测在一般的成形过程中，用于薄壁机构的皱纹的开始。假设物体足够薄，可以沿着完全润滑的工具表面变形，以满足膜应力条件，直到磨损。本文提出了一种具有广义各向异性二次屈服函数的薄壁件角型本构方程。褶皱的发生被假定为从膜型变形到弯曲型变形的分叉。本文应用Hill的一般分歧和唯一性理论，结合Donnell-Mushtari-Vlasov的薄壳理论和Naghdi的线性薄壳理论，给出了不同厚度曲板在各种应力条件下发生屈曲的条件的解析解。结果被概括为褶皱极限图（WLD），该图给出了假设褶皱模式的临界主应力组合。该方法可用于预测板料成形过程中起皱的发生，类似于利用成形极限图（FLD）预测板料成形极限的方法;对于复杂问题，可采用直接数值搜索起皱临界应力条件的策略。这也可以引入到蒙皮成形过程的计算机模拟中。此外，为了明确皱纹的增长速率，用等参壳单元和相同的本构方程进行了三维分析。研究了材料特性、边界条件和板料形状对冲压成形过程的影响。

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.