Optimization of initial blank shape predicted based on inverse finite element method

Abstract

For stamping of sheet metals and converting them to specific product shapes without failure, the initial blanks should be correctly designed. Therefore, initial blank design is a critical step in stamping design procedure. In the present paper for calculating the total deformation gradient and its relation to each step's deformation gradient tensor ( F ) , a modified kinematics formulation will be introduced. This formulation has been used in connection with the ideal forming theory for predicting the initial blank shape of the specified products with defined thickness. In the ideal forming theory, each material element is prescribed to deform in a minimum plastic work path and ideal process is obtained when the deformations are most evenly distributed in the final products. The latter has been assumed for developing an inverse finite element method (FEM) code to predict the blank shape and size in one step, which has been applied for rectangular cup. Even the results show the capability of the new algorithm in designing the initial blank shape for stamping products but the predicted blank shapes are oversized. For overcoming such problem, some kind of optimization must be applied. By considering all the conditions, forward FEM has been selected for optimization of blank shape and size. The accuracy of optimized blank shape and size has been evaluated using experimental work. For strain measurements, over the surface of blanks square grid have been printed. The results of experimental work confirmed the applied procedure for defining the shape and size of rectangular blank. The examination of thickness strain using printed grids show the superiority of optimized blanks.