Mechanism-based strain gradient crystal plasticity-I. Theory

We have been developing the theory of mechanism-based strain gradient plasticity (MSG) to model size-dependent plastic deformation at micron and submicron length scales. The core idea has been to incorporate the concept of geometrically necessary dislocations into the continuum plastic constitutive laws via the Taylor hardening relation. Here we extend this effort to develop a mechanism-based strain gradient theory of crystal plasticity. In this theory, an effective density of geometrically necessary dislocations for a specific slip plane is introduced via a continuum analog of the Peach-Koehler force in dislocation theory and is incorporated into the plastic constitutive laws via the Taylor relation.