Use of stress based forming limit diagram to predict formability in two-stage forming of tailor welded blanks

In the present work, laboratory scale two-stage stretch forming processes were designed and fabricated where an interstitial free (IF) steel was first pre-strained in biaxial tensile mode, and subsequently it was deformed in a limiting dome height (LDH) test set up in tension-tension and tension-compression modes. Tailor welded blanks (TWB) of dissimilar materials were fabricated by laser welding of dual phase (DP) and IF steels, and these TWBs were subjected to the above two-stage stretch forming processes to characterize the influence of pre-strain, strain path and weld line orientation on formability. A mathematical framework was developed to estimate stress based forming limit diagram (σ-FLD) from strain based forming limit diagram (ε-FLD) using Hill-48 and Barlat-89 anisotropic plasticity theories incorporating three different strain hardening laws. The forming behaviour of pre-strained IF steel material and TWBs was predicted by finite element analysis (FEA) implementing both the ε-FLD and σ-FLD. It was found that the LDH was over-predicted by ε-FLD compared to σ-FLD in case of bi-axial tensile pre-strained IF steel specimens. However, the ε-FLD under-predicted the LDH of circular pre-strained TWBs and similar LDH was predicted by both the FLDs in case of pre-strained longitudinal TWBs. It was observed that the σ-FLD was more robust compared to the ε-FLD, and it was capable to predict formability of TWBs in multi-stage forming processes taking care of deformation histories. Lastly, the predicted thickness distribution, maximum thinning location and load progression curve during the second stage LDH test were validated with experimental results.