A crystal plasticity constitutive model for body-centered cubic materials was introduced which was based upon dislocation movement and used dislocation density variables as internal state variables. Besides the statistically stored dislocations geometrically necessary dislocations were used to consider non-local effects as recently proposed by Ma, Roters and Raabe for the face-centered cubic crystal structure. The model was adopted here to the body-centered cubic crystal structure. Due to the special core structure of screw dislocations formed at low temperatures, the mechanical behavior of body-centered cubic crystals was controlled by the movement of screw dislocations rather than edge dislocations. The Peierls mechanism therefore had to be considered, and several modifications were introduced which included a new scaling relationship between the mobile and immobile dislocations and new flow rules for bulk and grain boundary elements. A pure Nb bicrystal was studied experimentally and numerically, under channel die compression boundary conditions, in order to demonstrate the applicability of the new model.

A Dislocation Density Based Constitutive Law for BCC Materials in Crystal Plasticity FEM. A.Ma, F.Roters, D.Raabe: Computational Materials Science, 2007, 39[1], 91-5