Modified kinematic hardening rules for simulations of ratchetting

In order to simulate multiaxial ratchetting, and as a preliminary step, common different variables introduced into the dynamic recovery term of recently developed hardening rules are presented and scrutinized in details. Subsequently, two modified kinematic hardening rules are formulated and presented. The proposed modified rules are based on the Ohno–Wang kinematic hardening rule in which accumulated plastic strain increment is contributed to the dynamic recovery term. The first modified rule is defined by introducing the radial evanescence term of Burlet–Cailletaud [Burlet, H., Cailletaud, G., 1986. Numerical techniques for cyclic plasticity at variable temperature. Eng. Comput. 3, 143–153] into the Ohno–Wang rule powered by specific material parameters. In the second modified rule a multiplying factor, depends on both the unit vector normal to the yield surface (n∼) and the deviatoric part of back stress (a∼), is utilized into the Ohno–Wang rule. The modified rules are examined in details to study their characteristics under uniaxial tensile, uniaxial cyclic and multiaxial loading conditions. Then, the validity and accuracy of these rules are scrutinized critically based on simulations of the well-known multiaxial ratchetting experiments of Corona et al. [Corona, E., Hassan, T., Kyriakids, S., 1996. On the performance of kinematic hardening rules in predicting a class of biaxial ratchetting experiments. Int. J. Plast. 12 (1), 117–145] as well as the recently carried out experiments of Chen et al. [Chen, X., Jiao, R., Kim, K.S., 2005. On the Ohno–Wang kinematic hardening rules for multiaxial ratchetting modeling of medium carbon steel. Int. J. Plast. 21, 161–184]. The two modified kinematic hardening rules simulate most of the considered multiaxial ratchetting experiments fairly well; nevertheless, the second one is relatively superior.