A Continuum Model for Single Crystal Cyclic Plasticity

Abstract

A constitutive model was developed to bridge the cyclic plasticity behavior of single crystals and the corresponding characteristic dislocation structures. Yield and flow were built on the individual slip systems. The Armstrong-Frederick kinematic hardening rule was invoked to capture the Bauschinger effect. A material memory parameter was introduced to consider the amplitude dependence of cyclic hardening. Latent hardening considering the interactions among the slip systems was used to describe the anisotropic cyclic behavior. The experimental results of copper single crystals were used to validate the model developed. It was found that the model was able to adequately describe the well-known three distinctive regions in the cyclic stress-strain curve of the FCC single crystal oriented for single slip and the associated dislocation substructures. The model was capable of capturing the enhanced hardening observed in copper single crystals in multi-slip orientations. For a given loading history, the model can predict not only the saturated stress-strain response but also the detailed evolution of the transient cyclic behavior. The characteristic dislocation structures can be featured with the slip evolution.