A dislocation density based constitutive model for face-centered cubic crystals was introduced and implemented into a crystal plasticity finite element framework. The approach assumed an homogeneous dislocation structure and tracked the dislocation evolution on each slip system. In addition to the statistically stored dislocations, a geometrically necessary dislocation density was introduced in order to consider strain gradients and thus make the model size-sensitive. A consistent algorithm was developed for up-dating the geometrically necessary dislocation density. A simple shear experiment, performed on an Al monocrystal, was used to calibrate the material parameters of the model and to establish its size-sensitivity.

A Dislocation Density Based Constitutive Model for Crystal Plasticity FEM Including Geometrically Necessary Dislocations. A.Ma, F.Roters, D.Raabe: Acta Materialia, 2006, 54[8], 2169-79