Application of a few necking criteria in predicting the forming limit of unwelded and tailor-welded blanks

Abstract

The limiting value of strain describing necking/failure during a sheet stamping operation is quantified, predicted by the forming limit curve (FLC). The main aim of the present work is to analyse the applicability of the few existing necking criteria, namely the effective strain rate based criterion (ESRC – RC1), major strain rate based criterion (MSRC – RC2), thickness strain rate based criterion (TSRC – RC3), and thickness gradient based criterion (TGNC – RC4), in predicting the forming limit of unwelded and tailor-welded blanks. In the case of unwelded blanks, dry ( μ = 0.12) and low-friction ( μ = 0.02) conditions are simulated and forming limit results are predicted. In the case of tailor-welded blanks, the forming limits of laser-welded steel blanks and friction-stir-welded blanks made of aluminium alloy are predicted using the chosen necking criteria and then compared with results in the literature. The influence of friction on the whole forming limit curve and the non-linearity of strain paths in the stretching side of the forming limit diagram (FLD) are also predicted and discussed. It is found that the FLCs predicted by ESRC, MSRC, TSRC, and TGNC are comparable with experimental FLCs. The predictions are accurate in the low-friction condition, indicating that the necking criteria are also valid under changing friction conditions. Moreover, the overall FLC does not change much with changing friction conditions. The strain paths are non-linear in the dry friction condition, but they become linear in the low-friction condition. In the case of laser-welded blanks, the original strain rate based criteria defined for unwelded blanks underestimate limit strains on the stretching side of the FLD, where failure near the weld region is witnessed. Hence they are modified as RC1 ≥ 25, RC2 ≥ 32, and RC3 ≥ 32, which show a better prediction level compared with the original criteria. The original and modified limit strain criteria show better correlation with results in the literature and the TGNC in the case of friction-stir-welded blanks modelled using the Hollomon and Swift strain-hardening laws.