Non-Associated Flow Rule Constitutive Modeling Considering Anisotropic Hardening for the Forming Analysis of Orthotropic Sheet Metal

The evolution of anisotropy has an important influence on the forming of parts under large deformation. However, most of the current yield criteria do not consider the evolution.

An anisotropic constitutive model based on non-associated flow rule (non-AFR) was established for orthotropic sheet metal. The classical quadratic Hill48 model was used to describe the yield anisotropy and plastic deformation anisotropy, respectively.

According to the principle of equivalent plastic work, the existence and significance of anisotropy evolution with plastic deformation were revealed. In order to improve the prediction accuracy of the model, a continuous capture scheme considering anisotropic hardening was proposed.

The evolution of directional yield stress, directional r-value and yield locus was well captured by the developed model. To further verify the model, square box deep drawing tests of different strokes of the punch were carried out. Compared with the experimental results, the developed model could predict the material flow behavior in flange area and thickness thinning behavior, which actually reflected the evolution behavior of directional flow stress and directional r-value of sheet metal respectively.

The developed model improves the prediction accuracy of anisotropic sheet metal forming, and can provide an effective reference scheme for large deformation problems in industrial production.