Forming limit evaluation by considering through-thickness normal stress: Theory and modeling

For hydroforming process and incremental forming, the plane stress assumption would be invalid to predict material formability. To consider the influence of normal stress on the forming limit strains, the instability perturbation approach proposed by Hu et al. is extended with normal stress. The M-K model with normal stress is chosen to compare with perturbation approach by implementing Hill'48 and Yld2000-2d yield criteria and swift and modified voce hardening laws. To guarantee the convergence of solving process in M-K model with normal stress, the modified increment method is implemented into it. Through comparing the experimental forming limit strains of AA5754-O under plane stress state and the corresponding theoretical values predicted by perturbation approach and M-K model, the suitable yield criterion and hardening law for these two methods are determined. The influences of through-thickness normal stress on the predicted forming limit strains under different stress states are investigated. The results show that forming limit curves (FLCs) in both forms of traditional Forming Limit Diagram (FLD) and equivalent plastic strain (EPS) based FLD (epFLD) enhance with increasing through-thickness normal stress under linear and nonlinear strain paths. The sensitivity of FLD to normal stress is related to the hardening law and the range of strain path in FLD is determined by the yield criterion.