Numerical determination of the forming limit curves of anisotropic sheet metals using GTN damage model

• A comprehensive description of an anisotropic GTN damage model.
• Calibration of the GTN model with experimental data.
• ABAQUS/Explicit implementation of the GTN model as a VUMAT routine.
• Providing an objective method for constructing a theoretical forming limit curve.
• Comparing the forming limit curves at the necking/fracture onset with experiments.

In this paper, the Gurson–Tvergaard–Needleman (GTN) damage model is used to determine the forming limit curve of anisotropic sheet metals. The mechanical behavior of the matrix material is described using Hill’48 quadratic yield criterion and an isotropic hardening rule. For this purpose, a VUMAT subroutine has been developed and used inside the ABAQUS/Explicit finite element code. The implementation of the constitutive model in the finite element code is presented in detail. Finally, the forming limit curve of an AA6016-T4 sheet metal is constructed using the developed VUMAT subroutine and running numerical simulation of Nakjima tests. The quality of the numerical results is evaluated by comparison with an experimental forming limit curve. Furthermore, theoretical forming limit curves of the AA6016-T4 sheet are obtained using Marciniak–Kuczynski (M–K) and modified maximum force criterion (MMFC) models. The results show that the forming limit curve predicted by the anisotropic GTN model is in better agreement with the experimental results especially in the biaxial tension region. This fact indicates that the GTN model is a useful tool in analyzing the formability of anisotropic sheet metals.