Biaxial ratchetting with novel variations of kinematic hardening

Kinematic hardening and the associated concept of back-stress and its evolution are fundamental constitutive ingredients of classical plasticity theory used to simulate the inelastic material response under stress reversals. Cyclic plasticity addresses such response under a sequence of repeated stress reversals, which results in plastic strain accumulation, called ratchetting. Biaxial ratchetting occurs whenever the material is loaded in two directions although typically the cyclic loading is only in one direction. The realistic description of the material response during cyclic loading depends strongly on the kind of kinematic hardening used.This paper investigates the performance of some existing and novel kinematic hardening rules in the prediction of ratchetting. The multiplicative AF model by Dafalias et al., 2008a and Dafalias et al., 2008b, which was originally applied to the simulation of uniaxial ratchetting, will be used here to simulate also biaxial ratchetting and will be compared with a model using the concept of a hardening stress threshold. The suggestion of Delobelle et al. (1995) to combine the Armstrong/Frederick and Burlet and Cailletaud (1986) kinematic hardening rules is incorporated in the aforementioned model and used to obtain improved simulations of biaxial ratchetting. After showing a deficiency of the foregoing suggestion which results in the possibility for the back-stress to cross it’s bounding surface and induce a negative plastic modulus, a variation is proposed void of the foregoing deficiency, which is successfully tested in the simulation of multiple biaxial ratchetting experimental results on carbon steel 1026.