A two-surface hardening plasticity model based on non-associated flow rule for anisotropic metals subjected to cyclic loading

• Modified Yoshida–Uemori two surface hardening model is combined with a quadratic non-associated flow rule.
• The model accurately captures the cyclic response of metals at large strains for multiple cycles.
• The model describes the anisotropy of yield stresses and plastic strains simultaneously by using simple quadratic yield and potential functions.
• A return mapping algorithm was developed to implement the model into finite element programs.
• The computational cost of the model is lower than Yld-2000 non-quadratic yield function.

In this paper a phenomenological material model for simulation of sheet metal forming processes was introduced. This model is able to describe the anisotropic behavior of sheet metals in both yield stresses and plastic strain ratios (r-values) by using the non-associated flow rule and quadratic yield and potential functions. Additionally, to reproduce an accurate prediction of cyclic plastic deformation phenomena, a two-surface mixed isotropic-nonlinear kinematic hardening model was combined with the quadratic non-associated anisotropic formulation. This mixed kinematic hardening model is amongst the most sophisticated models with acceptable degree of complexity and minimum requirement of experimental tests for material coefficients. The main advantage of the model over the more complex nonquadratic yield and potential functions along with associated or non-associated flow rules is its simplicity and computational efficiency. The plasticity foundation of the model was introduced and then a general return mapping algorithm for numerical stress integration of the constitutive model was developed in order to implement it into a finite element code. Finally, the model was used to simulate both forming stage and subsequent springback of a deep drawing problem. The results showed that the model can accurately predict springback as well as earing phenomenon of the stamped part.