An improved analytical approach for determination of forming limit diagrams considering the effects of yield functions

The purpose of this study is to develop a methodology for prediction of the forming limit diagrams (FLD). The methodology is based on the Marciniak and Kuczynski theory. Two yield functions proposed by “Hosford” and “BBC2000” and two hardening laws one with and the other without strain rate sensitivity have been applied. To solve the nonlinear systems of equations, the modified Newton–Raphson with globally convergence method has been used. In this process, a technique for step length selection in the frame of gradient descent method for unconstrained optimization has been applied. This technique has guaranteed the convergence of the solution with the Newton–Raphson method. Also for the purpose of rapid convergence the so-called “Armijo” condition has been used. The predicted results have been compared with the published experimental data for AK steel and AA5XXX alloys.