The effect of normal stress on the formability of sheet metals under non-proportional loading

Abstract

Theoretical and experimental studies have shown that when a compressive stress is applied normal to the sheet surface its formability can be significantly improved. In forming processes such as hydroforming, the normal stress imposed at the surface of the sheet or tube can be very significant in specific locations and it is therefore necessary to account for this stress state when assessing the forming severity of industrial parts. It is also well known that the forming limit curve (FLC) can vary significantly in strain space as a result of non-linear strain paths. In this work, a numerical code based on the Marciniak and Kuczynski (MK) analysis (1967) was developed to predict the FLC of sheet metals by simultaneously accounting for the effects of strain path non-linearity and the normal stress. The FLC predicted with this code can be used to assess the forming severity of parts that are deformed under complex loading conditions in industrial metal forming processes. The predictive FLC model was validated using experimental data in which linear and bi-linear strain paths were applied to different steel and aluminum sheets or tubes under plane stress and three-dimensional stress conditions. This research work has two specific purposes: first, to investigate the influence of the magnitude of the prestrain in bi-linear loading on the sensitivity of the FLC to the normal stress, and second, to study the effect of the normal stress on the path dependence of the FLC. This work showed that, with increasing magnitudes of prestrain the influence of the normal stress on the formability of sheet metal will decrease, regardless of the loading path. Moreover, it was observed that even a significant normal stress will practically not affect the path dependence of the FLC. • Forming Limit Curves (FLC) were predicted in 3D stress states and non-linear loading paths. • The effect of prestrain magnitude on the sensitivity of the FLC to the through-thickness compressive stress was investigated. • The effect of normal stress on the path-dependence of FLC was studied. • It was shown that higher prestrain magnitudes will reduces the sensitivity of FLC to the normal stresses. • In most cases, the normal pressure on the sheet metal surface will not affect the path-dependence of FLC.