Implementation of a robust algorithm for prediction of forming limit diagrams

In this article, a robust algorithm for prediction of forming limit diagrams (FLD) has been presented. The presented model is based on the "Marciniak and Kuczynski" (M-K) theory. Solution to the system of equations has been obtained by applying the Newton's method. Since the Newton's method usually has nonconverging problem, a particular backtracking algorithm has been developed and applied. In this algorithm, a technique for step length selection in the frame of gradient descent method has been implemented. Also for the convergence criterion the so-called "Armijo" condition has been used. For verification of the results, BBC2000 yield function and Swift hardening law for AK steel metal have been used. To obtain the necking angle, the effect of groove orientation on the left- and right-hand sides of FLD has been considered. Finally, the predicted FLD has been compared with the published experimental results.