A Modified Storen-Rice Bifurcation Analysis of Sheet Metal Forming Limit Diagrams

Bifurcation analysis is a theoretical prediction approach to measure the FLD when the localized neck causes development of vertex on subsequent yield surface as was adopted by Storen-Rice. Some analyses lead to solutions for special cases such as zero and minimum extension. They offer an equation which needs to be optimized with respect to the minimum limit strain versus neck orientation for the whole domain of FLD. Moreover, the previous reported results for the left-hand side of FLD are not quite satisfactory. In this paper, a re-investigation into bifurcation analysis adopted by S-R lead to modified equations which significantly improved FLD and could be respected as a more general approach to find FLD theoretically. The derivation and optimization procedure of equations are indicated and discussed in detail. The predicted limit strains are studied for different work hardening coefficients and compared with Storen-Rice, Zhu and some experimental data and the obtained results show more agreement. Furthermore, the present restrictions and the required conditions for validation of the Zhu approach are fully discussed.