New formulation of nonlinear kinematic hardening model, part II: cyclic hardening/softening and ratcheting

The second part of the study presents development of the Dirac delta functions framework to modelling of cyclic hardening and softening of material during cyclic loading conditions for the investigated in Part I low carbon S355J2 steel. A new criterion of plastic strain range change is formulated. This provides more certainty in the cyclic plasticity modelling framework compared to classical plastic strain memorization modelling. Two hardening parameters from the developed kinematic hardening rule are written as functions of both plastic strain range and previously accumulated plastic strain. This representation of hardening parameters is able to accurately match experimental results with different types of loading programs including random loading conditions and considering initial monotonic behavior with yield plateau deformation. Ratcheting behaviour is simulated by the developed cyclic plasticity framework by considering an approximated form of the Dirac delta function for modelling the deviation effect and introducing an additional supersurface for better prediction of ratcheting rate. The proposed cyclic plasticity model requires up to 21 material constants, depending on application. A clear and straightforward calibration procedure, where sets of material constants are determined for each plasticity phenomenon considered, is presented. Application of the model to different materials under various tension-compression and non-proportional axial-torsion cycles shows very close agreement with test results.