Anisotropic hardening of aluminum alloy sheets under biaxial proportional loading

Anisotropic hardening, where work-hardening behavior varies with loading direction and deformation mode, has been widely observed in sheet metals, even under proportional loading. However, existing models typically describe anisotropic hardening through yield surface distortion, which raises concerns about convexity of yield surface and physical validity. The anisotropic hardening behavior of aluminum alloy sheets under proportional loading was investigated. Crystal plasticity simulations showed that as plastic deformation progressed, the plastic work contour gradually flattened and eventually concave near the plane-strain tension state, while the subsequent yield surface remained convex. Based on these observations, a novel anisotropic hardening model was developed. In this model, the yield surface expands without changing its shape, and the hardening rate is governed by both the stress state and equivalent plastic strain. Convexity of the yield surface is preserved if the initial yield surface is convex. Coefficients in the stress-state-dependent hardening rate are analytically derived from stress–strain curves. The proposed model accurately captures the anisotropic stress–strain response under proportional loading and reproduces the distortion and concavity of the plastic work contour. Implemented in a finite element framework, the model was used to simulate the hydraulic bulge test of an AA6016-T4 sheet. The simulation provided improved predictions of internal pressure and strain distribution compared to conventional isotropic hardening model. Finally, the feasibility of extending the model to account for asymmetric hardening, Bauschinger effect, and cross-loading effect are also examined. The proposed model demonstrates strong potential for improving the accuracy of sheet metal forming simulations by capturing anisotropic hardening effects.