Theoretical Analysis of the Effects of Hardening Laws, Normal and Through Thickness Shear Stresses on Forming Limit Curves of AA6016-T4

Forming limit Curves are one of the common tools to predict the necking in various forming processes. In this study, the Marciniak-Kuczynski instability theory by applying the Gotoh yield function is utilized to estimate the forming limit curves for the AA6016-T4 aluminum sheet in plane stress conditions. Also, the effect of three different hardening models including Swift, Voce, and a linear combination of the Swift and Voce models to determine the limit curves are investigated. The comparison between the theoretical forming limit curves and experimental results from the Nakajima test determines the accuracy of the hardening models in predicting the limit strains. Since in many new forming processes such as hydroforming and incremental sheet forming processes, investigation of the process in plane stress state is not an exact assumption, Therefore, in continuation of the paper, generalized forming limit curves are plotted based on the developed Marciniak-Kuczynski model by extending the Gotoh yield function, and the effect of compressive normal stress and through-thickness shear stress on forming limits of the sheet are investigated. The results indicated that by applying the compressive normal stress and through-thickness shear stresses, the limit strains increase, and the formability is improved, in contrast, limit stresses move down in the diagram.