Investigation of the influence of the initial groove angle in the M–K model on limit strains and forming limit curves

Abstract

Marciniak–Kuczynski (M–K) model is the widely used method to theoretically obtain the forming limit curves (FLCs) of the sheet metal. However, in the applications of the M–K model, FLCs are generally assumed not to be dependent on the initial groove angle of the model, and are achieved with a zero groove angle. Nowadays, under positive strain paths, there is little research about whether the initial groove angle has influence on the limit strains and what the influence is. In addition, during the deduction of the M–K algorithm, the material׳s constitutive models with simple expressions are generally used, which cannot describe accurately the interacting effects of temperature and strain rate on forming limits. Therefore, above limitations greatly affect the accuracy of the predicted forming limits. In this work, three modified complex constitutive models (Voce, Ludwik and Khan–Huang–Liang model), considering the interacting effects of temperature and strain rate, are implemented into M–K model to investigate the sheet formability of AA5086 under different temperatures (20, 150 and 200°C) and strain rates (0.02, 0.2 and 2s−1). With the algorithm developed in this work, the influences of the initial groove angle on limit strains and FLCs are investigated. Results show that the initial groove angle has distinguishing influences on limit strains under different strain paths. When the strain path is in the range from 0 to 0.4, forming limits are always achieved with a zero groove angle. While when the strain path is not in the range from 0 to 0.4, limit strains depend greatly on the initial groove angle. The limit strains obtained with a zero groove angle in the literatures overestimate clearly its true sheet formability. Finally, the calculated limit strains are compared with experimental data obtained by Marciniak test under different forming conditions. Therefore, this work could provide an effective method to obtain the sheet formability more accurately by the M–K model.