A simulation-based approach to the determination of forming limit diagrams

This article presents the results of simulated hemispherical die stretching of low-carbon steel (ST12 and ST14) blanks of various thicknesses. The simulations were designed to obtain forming limit diagrams. Multiple criteria, including the second time derivatives of major strain, thickness strain and equivalent plastic strain extracted from the strain history of simulations, were used to accurately detect the start of necking in forming limit diagrams. This is to say that necking starts when the second derivative of the thickness strain, major strain or plastic strain reaches its maximum value. Knowing the onset of necking, one can measure the major and minor strains at the critical area and produce the corresponding forming limit diagram. Moreover, a modified Marciniak and Kuczynski method was used to predict the forming limit diagrams. The results from the proposed methods and those from experimental tests are compared to demonstrate the efficiency of the proposed methods.