Hierarchical multi-scale approach in the prediction of forming limits diagram

Abstract

The aim of current research is to explore the anisotropic properties of an AA3003-H19 sheet and compute its forming limit strains through a hierarchical multi-scale method. The material behavior at the macroscale was described using the 8- and 16-parameter versions of the BBC2008 yield criterion. Based on the crystal plasticity theory, a 3D representative volume element (RVE) was generated and employed in micromechanical modeling. To collect the crystallographic texture of the material for RVE simulations, an X-ray diffraction measurement was accomplished. The macroscale mechanical responses of the material were determined by conducting virtual experiments on the RVE under various deformation modes. The material data including the plastic anisotropy coefficients and yield stresses along seven different orientations as well as the yield stresses under plane strain conditions in the rolling and transverse directions were also extracted experimentally. Five calibration strategies for the yield function using a combination of simulation results and experimental data were proposed. An error function was minimized to calculate the anisotropy parameters for each calibration strategy. The forming limit diagrams (FLDs) were determined by the calibrated yield functions and the Marciniak-Kuczynski (MK) model. The results were validated by performing the Nakajima test. The influence of the calibration strategies on the accuracy of FLD prediction and reproduction of anisotropic properties was investigated. The study demonstrates that virtual experimentation on the RVE accurately predicts the r-value and yield stress distribution trends of the AA3003-H19. The calibration strategy considerably impacts the material behavior description and the calculation of the FLD using the yield criterion.