An extended stress-based forming limit diagram focusing on the wrinkling phenomenon and the effect of the normal pressure on clamped surfaces

Abstract

A novel wrinkling limit representation following the pattern of the conventional forming limit curves (FLCs) and the stress-based forming limit curves (SFLCs) as well as the application of the assumed criterion in finite element modelling are discussed in this manuscript. FLCs can partially refer to the wrinkling potential in the area left to the uniaxial tension line, but just like the SFLCs, cannot characterize the limits of the material behavior in a deeper sense, if negative in-plane stress and normal pressure act together on the sheet. This study predicts the wrinkling risk of clamped surfaces with a stress-based criterion through solving the analytical equations of the critical compressive stress causing wrinkling, and the corresponding blank holder pressure. The critical values were calculated based on the Wang and Cao’s theory using Hill48 anisotropic yield function coupled with the Swift hardening law. The results draw a novel wrinkling limit curve representation methodology, in which the minor stress responsible for wrinkling and its ratio to the major stress are distinguished in the function of the applied blank holder pressure. The applicability of the calculated curves was investigated using finite element simulations, which showed that this method provides the opportunity to quantitatively interpret how close a component is to the wrinkling limit. The calculated wrinkling tendencies were verified by standard cup drawing tests supplemented by round shape error measurements on three different automotive steel sheets. It can be stated that the obtained numerical conditions of wrinkling were fitted to the experiments fairly well.