Effects of reverse loading on forming limit predictions with distortional anisotropic hardening under associated and non-associated flow rules

Abstract

The recent development of metal sheet plastic theory shows that it is essential to consider the distortional behavior of yield surfaces when accounting for microstructure evolution and Bauschinger effects during plastic deformation under non-proportional loading. This methodology is especially applicable to plastic flows and reveals the distinct flow direction involved during loading reversal. Since localized necking is heavily affected by plastic flows, the evaluation of its impact in forming limits during reverse loading is necessary and important for the further application and understanding of this distortional behavior of metal sheets. For this work, the Marciniak–Kuczynski (MK) approach (Marciniak and Kuczynski [1]) is adopted and further extended with the homogeneous anisotropic hardening (HAH) model (Barlat et al. [2]) under associated and non-associated flow rule frameworks to accommodate complex reverse loading behavior. The evolution of the yield surface, stress transitions and necking angles is examined and compared in detail. Path independent forming limits are also investigated and probed to test their performance. When loading is reversed, the distortional curvature evolution of the yield surface has a critical impact on stress flow trajectories and yield surface normal and further determines final forming limits under associated flow rules, rendering its performance different from that of traditional isotropic and kinematic hardening. The non-associated flow rule framework can be used to measure the impact of twisted yield behavior and untwisted plastic potential, which is suggested to be a useful numerical approach to the theoretical study and engineering prediction of forming limits.