Calibration of forming limit diagrams using a modified Marciniak–Kuczynski model and an empirical law

The major problem in determining the forming limit diagram (FLD) with the Marciniak–Kuczynski (M–K) model is the necessity of an experimental point in order to find the initial inhomogeneity coefficient and calibrate the diagram. The purpose of the present work is to eliminate this requirement. To do this, the usual assumption of geometrical inhomogeneity has been replaced with material inhomogeneity and it has been shown that the sensitivity of the diagram to variations of the inhomogeneity factor is reduced greatly with the new assumption. Using this advantage and collecting enough experimental data for different materials, an empirical law in terms of sheet thickness has been proposed which estimates the initial material inhomogeneity. Thus it is possible to determine the FLD in the absence of experimental data. The results show good agreement with experiments and this method has some advantages over other calibration methods.