Evaluation of anisotropic constitutive models: Mixed anisotropic hardening and non-associated flow rule approach

• A non-associated flow model with mixed isotropic-kinematic hardening is proposed.
• Prediction of permanent softening is included in our non-AFR with mixed hardening.
• The same order of accuracy of Yld2004-18p can be achieved by the non-AFR Yld2000-2d.
• Fully backward Euler scheme with arbitrary number of internal variables is proposed.

In this paper we present a non-associated plane stress anisotropic constitutive model with mixed isotropic-kinematic hardening. The quadratic Hill 1948 and non-quadratic Yld-2000-2d yield criteria [Barlat F, et al. Int J Plasticity 2003;19: 1297–1319.] are considered in the non-associated flow rule (non-AFR) model to account for anisotropic behavior. To predict accurate hardening in cyclic loading conditions, a modification of the hardening model proposed by Chun et al. [Chun BK, et al., Int J Plasticity 2002; 18: 571–595.] is adopted. This one-surface non-linear mixed isotropic-kinematic hardening model does not require loading criterion and can predict Bauschinger effect, transient behavior and permanent softening. The developed model was implemented as a user-defined material subroutine (UMAT) into the commercial finite element code ABAQUS/Standard based on fully implicit backward Euler's method. Cup drawing simulation results for an automotive sheet metal AA5754-O show that the implemented hardening model avoids under- and over-estimation of the cup height respectively generated by kinematic and isotropic hardening laws. Moreover, as will be seen in the results of highly textured AA2090-T3, both cup height and earing profile generated by non-associated flow models are in better agreement with experimental results. Finally, the Yld2004-18p and non-AFR Yld2000-2d models are compared in terms of prediction of directional Lankford coefficients and yield stresses. It is shown that a same order of accuracy that is obtained by Yld2004-18p can be achieved by the non-AFR Yld2000-2d.