Finite Element Implementation of Distortional Plasticity Hardening Model and Its Application to Commerical Sheet Metals

Abstract

In this thesis, the implementation of a distortional plasticity hardening model, namely, HAH20 (Barlat et al., (2020), IJSS), into the finite element method and its applications to strain path change and sheet metal forming simulations were mainly discussed. To this end, the performances of the FE-implemented HAH model were researched with respect to three topics. In the first topic, the main causes of divergence of FE-implemented anisotropic hardening models were discussed and a step size control method, namely, line-search, embedded in a fully-implicit stress update algorithm was utilize to implement HAH20 model into implicit finite element framework. In order to improve the accuracy and numerical stability (convergence), an additional step size control criterion was proposed. The numerical validation of the line-search method was carried out by comparing the simulation results from finite element method with that from the associated stand-alone code and experimental data. Also, the cross-loading effect predictivity of HAH20 and HAH14 (Barlat et al., (2014), IJP) was comparatively studied in various strain path change simulations. The numerical stability of the line-search method for the implemented HAH model was assessed by means of so-called convergence mapping technique at various trial stress levels. The second topic mainly investigated a distortional plasticity model targeted for anisotropic materials, namely, HAHε, with contains a strain-based fluctuation component. The FE-implemented HAH20ε was numerically validated by checking the agreement of simulation results from the stand-alone HAH20ε in various strain path change simulations. Through the comparative study between HAH20h and HAH20ε, the effect of yield surface distortion shape on strain path change effects was discussed in depth. In addition, an alternative formulation of a macroscopic latent hardening was proposed as part of this tehsis. The prediction of macroscopic latent hardening of HAH20ε was compared to that of HAH14h. The third topic discussed is the strength differential effect on sheet metal forming simulations of a giga-steel with an ultimate tensile strength is over 1 GPa. The strength differential effect was modelled with a pressure-dependent plasticity theory introduced by (Richmond and Spitzig, 1980) and adapted by Barlat et al., (2020). In the manuscript, the pressure theory was implemented by means of a fully-implicit stress update algorithm and numerically validated through a comparative study with the associated stand-alone code and experimental measurements. The SD effect in sheet metal forming simulations was investigated through the springback behavior after the completion of a forming step. For the purpose of considering both the strain path change and SD effects, HAH20 was embedded in the pressure theory and applied to U-draw bending simulations. Furthermore, a geometrical factor of a blank regarding the springback behaviors of a giga-steel was also discussed by running the forming simulation of a B-pillar automotive part.