Strain gradient crystal plasticity attempts to predict material size effects by taking into account geometrically necessary dislocations that were required to accommodate gradients of crystallographic slip. Since these dislocations had a non-zero net Burgers vector within the material, dislocation induced long range stresses resulted in a back stress that influenced the effective driving force for crystallographic slip. A dislocation-induced back-stress formulation was proposed in which the full tensorial nature of the dislocation stress state was included in the continuum description. The significance of this proposed back stress formulation was that it intrinsically included latent kinematic hardening from dislocations lying on all slip systems. Using simple shearing of a semi-infinite cube oriented single crystal with either double-planar or octahedral slip system configurations, the proposed back stress formulation was examined in detail.

A Comparison of Dislocation Induced Back Stress Formulations in Strain Gradient Crystal Plasticity. C.J.Bayley, W.A.M.Brekelmans, M.G.D.Geers: International Journal of Solids and Structures, 2006, 43[24], 7268-86