On anisotropic plasticity models using linear transformations on the deviatoric stress: Physical constraints on plastic flow in generalized plane strain

Abstract

The generation of anisotropic yield functions from isotropic yield criteria by applying linear transformations on the deviatoric stress tensor has many advantages for simulations of sheet metal forming. Linear transformations maintain convexity and can enforce incompressibility while multiple transformations can be employed depending upon the severity of the anisotropy to be described. The present study reveals that the use of linear transformations on associated yield functions or plastic potential functions requires a series of constraints to be imposed for generalized plane strain loading conditions to be physically-consistent with the assumptions of pressure-independent plasticity. A recently proposed plastic constraint for shear loading based upon experimental observations is shown to be part of a more general constraint upon the plastic potential that applies whenever the third deviatoric stress invariant is zero. Due to these constraints, models such as an associated Yld2000 may become over-constrained and either a non-associated or higher-order associated yield criterion may be required. A review of the experimental data for plane strain tension and shear in the literature provides strong support for the enforcement of the plastic constraints for FCC and BCC materials but not for HCP materials since plastic flow will be slip or twinning dominant depending upon the stress state. Several case studies are considered to demonstrate that the plastic flow constraints can be satisfied or significantly violated during the calibration procedure. In particular, improvements in the prediction of the thinning distribution in hole expansion tests reported in the literature can be attributed in part to the enforcement of the plane strain constraints on an associated Yld2000 model for a mild steel. Non-associated plasticity allows for a simpler yield function to be readily calibrated using experimental data while a more complex plastic potential can be selected to satisfy plastic anisotropy and the plane strain constraints. Enforcement of the plane strain constraints is not required for a non-associated yield function, but if enforced, will ensure that the highest yield stress will occur in plane strain and should maximize plastic dissipation during plane strain localization.