Modeling of tension–compression asymmetry and orthotropy on metallic materials: Numerical implementation and validation

Abstract

The details concerning the implementation of the yield criterion developed by Cazacu et al. 2006 (CPB06) [1], which accounts for both tension–compression asymmetry and orthotropy of the plastic flow, in the fully implicit FE solver DD3IMP (contraction of ‘Deep Drawing 3-D IMPlicit') are presented in this work. The implemented constitutive model is extensively described, including the analytical first and second order derivatives required to the stress update algorithm. A set of anisotropy parameters describing the mechanical behavior of two metallic materials at room temperature, namely Zirconium and AZ31-Mg alloy, are identified with the DD3MAT (contraction for ‘Deep Drawing 3-D MATerial’) in-house code (Alves, 2004) [2]. The anisotropy parameters are identified for both the CPB06 and the Cazacu and Barlat (2001) (CB2001) [3] yield criteria, in order to emphasize the importance and role of the strength differential effect. The results clearly show that the CPB06 yield criterion is able to accurately describe both the in-plane anisotropy and tension–compression asymmetry, as well a different anisotropic behavior in uniaxial tension and uniaxial compression. The numerical simulation of a four-point bending test is performed, considering different orientations of the beam, i.e. of the hard/soft to deform direction relatively to the load direction, allowing to validate the implementation. The results obtained with the CPB06 show its ability to describe with accuracy the strain fields in the beam's central cross-section, the distribution of the tensile and compressive layers and, consequently, the shift of the neutral layer. The comparison with the results obtained with CB2001 indicates that the strength differential effect affects the final deformed shape of the beam, particularly for materials exhibiting strong tension–compression asymmetry.