On modeling of geometrically necessary dislocation densities in plastically deformed single crystals

A computational method for strain gradient single crystal plasticity is presented. The method accounts for both recoverable and dissipative gradient effects. The mathematical solution procedure is predicated on two minimum principles along the lines of those devised by Fleck and Willis (2009) for isotropic plasticity.

An effective 2Dsolution valid for certain orientations of face centered cubic crystals is presented, where effective in-plane material properties are derived based on the crystallographic properties. The problems of void growth, pure shear and 2D wedge indentation are analyzed numerically and geometrically necessary dislocation densities are derived from the slip fields and discussed relative to experimental results in the literature (Kysar et al., 2010).