Evaluating the significance of hardening behavior and unloading modulus under strain reversal in sheet springback prediction

• The effect of hardening behavior and unloading modulus on springback is quantitatively estimated.
• The hardening behavior involves Bauschinger effect, transient behavior and permanent softening.
• The importance of unloading behavior is emphasized.
• The ANK model incorporating with a changed unloading modulus is evaluated.

Springback is one of the most important problems that should be compensated in sheet metal forming process with the increasing application of advanced high strength steels and light-weight alloys. In the finite element analyses for the springback, accurate modeling of Bauschinger effect, transient behavior and permanent softening under cyclic loading has been recognized as the most critical hardening behavior in the constitutive modeling aspect. However, if parts of these hardening behavior are not well modelled, is the accuracy of springback prediction seriously deteriorated? To answer this question, in this paper the significance of Bauschinger effect and transient behavior, permanent softening and unloading modulus in springback prediction were estimated using the springback problem of U-draw/bending simulations proposed at Numisheet2011 Benchmark. A recent anisotropic non-linear kinematic (ANK) model [Zang S, Guo C, Thuillier S, Lee M. A model of one-surface cyclic plasticity and its application to springback prediction. Int J Mech Sci 2011;53:425–35.] was adopted to estimate the significance of hardening behavior and unloading modulus because of its special feature. The ANK model can predict exactly the same monotonous stress–strain curves for different hardening schemes, while different Bauschinger effect and transient behavior under one-dimensional cyclic loading can be also modelled. This feature is quite suitable to quantitatively evaluate the effects of the aforementioned hardening behaviors in springback prediction. Initial anisotropy is described by the anisotropic yield function Yld2000-2d. The unloading behavior is also considered by defining Young's modulus as a function of equivalent plastic strain. Several quantitative analyses were carried out to distinguish the effect of each hardening component and unloading elastic modulus scheme. Finally, the predicted springback by different models were compared with experiments for both as-received and pre-strained DP780 steel sheets.