H. Heidari - School of Mechanical Engineering, Iran University of Science and Technology,Tehran, Iran
R. Hashemi - School of Mechanical Engineering, Iran University of Science and Technology,Tehran, Iran

In many manufacturing companies such as aerospace, automotive and electronic industries numerical simulation and optimization of sheet metal forming processes hasbecome a key factor due to material and time saving, cost efficiency and quality improvement. Lots of efforts have been devoted to the development of mathematicalmodels and analytical tools to decrease the necessities of experimental works. In this research, a new numerical simulation of sheet metal forming process has been developed to predict the limit strains for deformation localization and subsequently forming limit diagrams. Strain gradient theory of plasticity is combined with conventional Marciniak and Kuczynski imperfection method to analyse the deformation state. The effect of adding second-order terms of equivalent strain gradients, which inserts an internal length scale into constitutive equations, on the prediction of limit strains carefully studied. Finite difference method used to solve nonlinear second order differential equations varied through the sheet thickness direction

Forming limit diagram; M-K Approach; Finite difference; Strain gradient theory