Finite element modeling using homogeneous anisotropic hardening and application to spring-back prediction

Abstract

A finite element (FE) implementation of the recently proposed constitutive model (Homogeneous yield function-based anisotropic hardening model or HAH; doi:10.1016/j.ij-plas.2011.03.003 in International Journal of Plasticity) that describes the plastic behavior of materials subjected to multiple strain path changes was developed. A complete formulation based on the return-mapping algorithm for the yield function was proposed. In particular, a multi-step Newton–Raphson method was introduced to calculate the gradient of the HAH model for the stress integration procedure. In addition to the numerical aspects, the theoretical proofs of the stability and convexity of the HAH model were discussed. For verification purpose, simple finite element simulations were conducted and the results were compared to those obtained from various constitutive models. Finally, mechanical characterization and U-draw bend experiments were performed on DP590 and TRIP590 steel sheet samples. The springback was quantified using the parameters defined at the NUMISHEET (1993) benchmark. Simulations of the 2D draw-bend test were performed with the FE code and the HAH constitutive description for DP590 and TRIP590 steel sheet samples. All the predicted springback values for these materials were in good agreement with experimental data.