Description of elastic–plastic stress–strain transition in cyclic plasticity and its effect on springback prediction

In the cyclic plasticity deformation of metallic materials, nonlinear elastic unloading and subsequent smooth elastic–plastic stress–strain behavior is observed in reverse loading owing to the Bauschinger effect. To determine how accurately material models can describe the elastic–plastic transition behavior, cyclic stress–strain simulations were conducted and their results were compared with the corresponding results for DP980 and 590R high-strength steel (HSS) sheets. The two plasticity models, the Yoshida–Uemori (Y-U) pure kinematic hardening (KH) model and the Armstrong–Frederick KH combined with isotropic hardening (A-F–KH + IH) model, were used with four different types of elasticity models, Young’s modulus, plastic-strain-dependent chord modulus, yield-surface-average (YSA) elastic modulus, and nonlinear elastic model. The best model to describe the realistic elastic-plastic transition behavior was the Y-U model combined with the nonlinear elastic model. The effects of these material models on springback prediction were examined based on a plane-strain bending–unbending springback simulation. When using the Y-U model, the amounts of springback and residual stresses calculated by the two plastic-strain–dependent linear elastic models and the nonlinear elastic model were almost the same. By contrast, when using the A-F–KH + IH model, the calculated results using the linear elastic models were quite different from those of the nonlinear model calculation. The effect of the yield plateau on the springback calculation was minor.