Multi-scale numerical investigation of deep drawing of 6K21 aluminum alloy by crystal plasticity and a stress-invariant based anisotropic yield function under non-associated flow rule

In this research, the earing characteristics of 6K21 aluminum alloy in circular cup deep drawing are investigated by virtue of experiments and multi-scale simulations including anisotropic Drucker, Hill48, Yld91 yield functions and crystal plastic finite element model (CPFEM). First, the deep drawing experiments of AA 6K21 are carried out to explore the influences of blank holding force (BHF) and blank diameter (BD) on earing profile and mechanical response. The user-defined material model subroutine is written for LS-DYNA explicit code, including constitutive model and ductile fracture criterion under associated or non-associated flow rule (NAFR). The parameters of the crystal plasticity model are calibrated by means of an optimization algorithm. Three yield functions under NAFR and CPFEM are used to predict earing in deep drawing simulation. The effects of five textures on the earing profiles and thickness variables are studied by CPFEM. The results demonstrate that the earing rate decreases slightly as the BHF increases. However, the mechanical response changes insignificantly. Moreover, as the BD increases, both the earing rate and mechanical response increase significantly. Considering computation accuracy and efficiency, the anisotropic Drucker function can accurately character the plastic deformation behavior of deep drawing. For five textures in CPFEM, Cube and Goss textures produce four ears at 0o and 90o from the rolling direction. Brass and S textures form six ears at 0o and 55o. Copper texture fabricates eight ears at 40o and 70o. The influences of five textures on earing rate are Goss > Cube > Copper > Brass > S. Furthermore, there are obvious thickness gradient fluctuations at the corner of the cup in Cube, Goss and Copper textures. It is expected to reduce the earing rate and improve the formability through reasonable allocations of experimental parameters and texture proportions.