A physically-based mixed hardening model for the prediction of the ductility limits of thin metal sheets using a CPFE approach

Abstract

An advanced Crystal Plasticity Finite Element (CPFE) approach is developed to accurately predict the ductility limit strains of thin metal sheets. This method uses polycrystalline unit cells to represent the metal sheets at the macroscopic level. The macroscopic behavior of these unit cells is determined based on that of the constituent single crystals using the periodic homogenization multiscale scheme. At the single crystal scale, the constitutive framework follows a finite strain rate-independent formulation, with the flow rule governed by the Schmid law. The evolution of the single crystal yield surface is described through a physically based mixed hardening model, where isotropic hardening is characterized by a dislocation density-based formulation, while kinematic hardening is described by the nonlinear Armstrong–Frederick model. The unit cell ductility limit strains are predicted by the Rice bifurcation criterion. The reliability of the mixed hardening model in accurately reproducing mechanical behavior is confirmed through simulations of uniaxial tension/compression loading. Then, the developed computational strategy is used to investigate the impact of key microstructural hardening parameters on the initiation of localized necking under linear strain paths. The numerical predictions reveal the significant influence of these parameters on the formability of thin metal sheets. Additionally, the analysis of ductility limits under non-linear strain paths demonstrates a strong dependency of the numerical predictions on strain path changes. The numerical predictions obtained by the developed CPFE multiscale strategy are compared with experimental results from the literature. In summary, the proposed approach provides a reliable tool for accurately predicting the ductility limits of thin metal sheets, offering valuable insights for engineering applications.