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The influence of sheet thickness on sheet metal forming limits is a controversial issue; while some investigations indicate the considerable influence of thickness on forming limit diagrams (FLDs), others suggest that it is of negligible importance. In the present work, it has been demonstrated that if the thickness-reduction process is chosen so as not to alter the micro structure of the material, the forming limits do not change with variations of thickness. A material which has extensive usage in sheet metal forming processes of automotive industry (St14) has been provided. The initial thickness of the sheet is 1.5mm and using grinding process (which does not alter the microstructure) the initial thickness is reduced to different thicknesses, namely 1 and 0.5mm. Afterwards, the FLDs for all three thicknesses were determined using standard test methods. The FLDs for specimens which were ground to various thicknesses differ slightly.

To determine the curvature of the exit profile in the extrusion process of non-symmetrical flat dies, the dead metal zone profile was predicted using the energy minimization method. The dead zone is a natural non-linear die for the process and it is pragmatic to use this non-linear die to estimate the value of the exit profile curvature and the required bearing length for reducing this deviation. The velocity field is calculated based on Hermite cubic spline and some additional assumptions. In non-symmetrical dies the entrance section of the deformation region is not flat. Considering this fact, axial velocity decreases with increasing the distance to die center line which is in agreement with experiment. After determination of the velocity field, the strain rates in different directions are calculated. Subsequently, the required power for the process is estimated using the upper bound method.

Major forming limit prediction models and calibration methods are reviewed briefly and their advantages and disadvantages are discussed. Two modified Marciniak-Kuczynski (M-K) models and one modified NADDRG (Keeler-Brazier) model are also presented which have some advantages over conventional models. In the first modified M-K model, material non-homogeneity has been substituted for geometrical non-homogeneity to reduce the sensitivity of the traditional model to variations of the initial non-homogeneity. Using this important advantage, a semi-empirical relation is proposed to predict the value of the initial material non-homogeneity. In the second modified M-K model, the conventional calibration method (which requires an experimental point, corresponding to plain strain condition, to find the initial non-homogeneity and calibrate the model) is revised and the uniaxial tensile point, which is easily obtained, is proposed to be used in the calibration process.