Constitutive modeling and FE implementation for anisotropic hardening under proportional loading conditions

Abstract

Anisotropic hardening response (or evolution of yield surface) is an important issue for numerical modeling of sheet metal forming and springback. Lee et al. (2017) recently introduced an improved constitutive model based on the Stoughton and Yoon (2009)’s equation, called the S-Y2009 model in this paper, in order to capture the anisotropic hardening in proportional loading conditions. The Lee et al. (2017)’s model was built by coupling the S-Y2009 model and a non-quadratic model to control the curvature of the yield fitting for more accurate prediction of the yield surface. The Lee et al. (2017)’s model (called the coupled model in this paper) showed good agreements with the measured data. However, in the aforementioned paper, a simulation study for sheet metal forming process with the coupled model was not reported. This paper presents the coupled model in two points of view. The first is the ability of the coupled model to capture the evolution of the yield surface. The other is the performance of the coupled model to describe the anisotropic hardening in a bulge test simulation. Predicting the anisotropic hardening including the biaxial stress state is important to follow the measured data. For the simulation, the coupled model was implemented into Vectorized User MATerial interface (VUMAT) of ABAQUS. The Yld2000-2d model was also incorporated in the comparison because the Yld2000-2d model has been showing good agreements with the initial anisotropy. The results of this study show that capturing the anisotropic hardening is important and the presented approach can be a good model in the sheet metal forming simulation under the proportional loading conditions.