A comparison of dislocation induced back stress formulations in strain gradient crystal plasticity

Strain gradient crystal plasticity attempts to predict material size effects by taking into account geometrically necessary dislocations that are required to accommodate gradients of crystallographic slip. Since these dislocations have a non-zero net Burgers vector within the material, dislocation induced long range stresses result in a back stress that influences the effective driving force for crystallographic slip. A dislocation induced back stress formulation is proposed in which the full tensorial nature of the dislocation stress state is included in the continuum description. The significance of this proposed back stress formulation is that it intrinsically includes 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 is examined in detail.