Micropolar regularization of crystal plasticity with the gradient-enhanced incremental hardening law

Abstract

A new model of gradient crystal plasticity is developed in which the incompatibility of plastic deformation field is simultaneously included in two different ways. The first one is well known and incorporates the gradient effect of accumulated rotation of the crystallographic lattice on the kinematic hardening in the Cosserat crystal plasticity model. The second way incorporates the effect of the current incompatibility of lattice spin on the total dislocation density rate, resulting in an additional isotropic hardening term in the gradient-enhanced hardening law. The latter effect involves a natural length scale that is fully determined in terms of standard quantities of a non-gradient hardening law and evolves during plastic deformation. The relative significance of the two effects depends on the values of material parameters, which is demonstrated by the results of calculations of 1D and 3D examples for a Cu single crystal. If the second effect is predominant, then the Cosserat formulation provides only a regularization, and then the model can be used to predict size effects. This is shown by 3D simulations of the size effect in spherical indentation of a copper single crystal. Since the gradient-enhanced hardening law does not involve any adjustable parameter, the obtained agreement of the model prediction with the experimental indentation size effect on hardness can be regarded as surprisingly good.