Analytical normalized stress invariant-based yield function to model anisotropic-strength differential effect

Uncovering and characterizing the direction- and stress state-dependent material behavior is very critical and significant to the simulation and design of the metal forming process. The study establishes an analytical model based on a normalized stress invariant-based yield function, where these material parameters are computed by six hardening curves under different loading conditions. The analytical model is used to describe the material behavior of DP980 and AA5754-O, showing the characterization ability prior to the Hou2020 yield function under plane strain tension and shear. The initial yield behavior of WE43 alloy is with the isotropic characteristic, and the strength declines when the loading direction is from 0° to 45° while that increases from 45° to 90°. This indicates that the hardening behavior possesses the enhanced anisotropic property with deformation history. The mechanical strength varies with stress state, showing a clear strength differential effect dependent on loading stroke. The convexity of the yield surface is analyzed to determine the numerical strain domain through adopting a newly proposed geometry-inspired numerical approach. The anisotropic-strength differential hardening behavior of WE43 alloy is modeled with high accuracy by the proposed analytical model, and the yield locus presents a non-proportional evolving characteristic with strain. The research provides an analytical mathematical model, which is conducive to plasticity characterization and the analysis of the metal forming process considering the anisotropic-strength differential hardening behavior.