Modeling of anisotropic hardening of sheet metals including description of the Bauschinger effect

The present paper proposes a framework for constitutive modeling of plasticity to describe the evolution of anisotropy and the Bauschinger effect in sheet metals. An anisotropic yield function, which varies continuously with increasing plastic strain, is defined as an interpolation between two yield functions at two discrete levels of plastic strain. Several types of nonlinear functions of the effective plastic strain are proposed for the interpolation. A framework for a combined anisotropic-kinematic hardening model of large-strain cyclic plasticity with small elastic strain is presented, and the details of modeling which is based on the Yoshida–Uemori model (Yoshida et al., 2002, Yoshida and Uemori, 2002, 2003) are described. The shape of the yield surface and that of the bounding surface are assumed in the model to change simultaneously. The model was validated by comparing the calculated results of stress–strain responses with experimental data on r-value and stress-directionality changes in an aluminum sheet ( Hu, 2007) and a stainless steel sheet (Stoughton and Yoon, 2009), as well as the variation of the yield surface of an aluminum sheet (Yanaga et al., 2014). Furthermore, anisotropic cyclic behavior was examined by performing experiments of uniaxial tension and cyclic straining in three sheet directions on a 780-MPa advanced high-strength steel sheet.