Forming limits for three-dimensional stress states and nonlinear loading paths

Abstract

Another factor that has a very significant effect on sheet formability is the loading path. Indeed, non-linear strain paths cause the forming limit curve (FLC) to translate in principal strain space and therefore the actual FLC for a given location on a part may be quite different from the as-received FLC. Consequently, the virtual design of a forming process will only be reliable if the forming limits used to assess the forming severity of the part were determined with due consideration of the (non-linear) strain paths in each critical location of the part. The FLC of sheet metals have often been predicted using the MK method which was proposed by Marciniak and Kuczynski (1967) and which models the inhomogeneity of the sheet material by a very shallow groove. Predictions of theoretical FLC using the MK method generally assume plane stress conditions, but in this work the MK analysis was modified to consider both the nonlinearity of the loading path and the presence of a through-thickness stress, simultaneously. Different magnitudes of prestrain were applied to a virtual sheet so as to simulate bi-linear strain paths and different values of the normal stress were applied for the prediction of the FLC. Published experimental FLC data obtained for different bilinear loading conditions were used to validate the theoretical work in both plane stress and general three-dimensional stress conditions. It was found that this modified MK model predicts FLC that correlate well with the limited experimental data.