Determination of Forming Limit Diagrams Based on Ductile Damage Models and Necking Criteria

Abstract

Abstract In this paper, forming limit diagrams (FLDs) for an aluminum alloy are predicted through numerical simulations using various localized necking criteria. A comparative study is conducted for the FLDs determined by using the Lemaitre damage approach and those obtained with the modified Gurson-Tvergaard-Needleman (GTN) damage model. To this end, both damage models coupled with elasto-plasticity and accounting for plastic anisotropy have been implemented into the ABAQUS/Explicit software, through the user-defined subroutine VUMAT, within the framework of large plastic strains and a fully three-dimensional formulation. The resulting constitutive frameworks are then combined with four localized necking criteria to predict the limit strains for an AA6016-T4 aluminum alloy. Three of these necking criteria are based on finite element (FE) simulations of the Nakazima deep drawing test with various specimen geometries, while the fourth criterion is based on bifurcation theory. The simulation results reveal that the limit strains predicted by local criteria, which are based on FE simulations of the Nakazima test, are in good agreement with the experiments for a number of strain paths, while those obtained with the bifurcation analysis provide an upper bound to the experimental FLD.

Keywords

• GTN model
• Lemaitre damage approach
• plastic anisotropy
• forming limit diagram
• localized necking criteria
• bifurcation theory
• Nakazima deep drawing test