Institute of Fundamental Technological Research

In honour of Professor Henryk Petryk on the occasion of his 70th Birthday

A model of crystal plasticity is developed in which the effects of plastic flow non-uniformity are described through the full dislocation density tensor. The micromorphic approach is used in which the dislocation density tensor is represented by the curl of an independent constitutive variable called microdeformation. The microdeformation tensor is enforced by an energetic penalty term to be close to the actual plastic distortion tensor. The curl of microdeformation tensor enters the constitutive model in two independent but complementary ways. First, it is an argument of the free energy density function, which describes the kinematic-type hardening in cyclic non-uniform deformation. Second, its rate influences the rates of critical resolved shear stresses, which corresponds to additional isotropic hardening caused by incompatibility of the plastic flow rate. The latter effect, missing in the standard slip-system hardening rule, is described in a simple manner that does not require any extra parameter in comparison to the non-gradient theory. In the proposed model there are two independent internal length scales whose interplay is examined by means of 1D and 2D numerical examples of plastic shearing of a single crystal.

gradient theory, crystal plasticity, dissipation, length scale, cyclic deformation, numerical regularization