Single crystal metallic materials displayed strong size effects when the characteristic length of plastic deformation was on the order of microns. The classical crystal plasticity theory cannot explain the size effects since its constitutive model possesses no intrinsic material length. The strain gradient crystal plasticity theory was modified so as to incorporate a new quasi rate-independent formulation for the slip rate. Its major advantage was that it was not necessary to distinguish plastic loading and unloading in a rate-independent formulation, and therefore avoids the complexity of determining the set of active slip systems in single crystals. The intrinsic material length was identified from the Taylor dislocation model as L = α2(μ/τ0)2b, where μ was the shear modulus, τ0 was the initial yield stress (critical resolved shear stress) in slip systems, b was the magnitude of the Burgers vector, and α was an empirical coefficient which was between 0.3 and 0.5. For non-uniform plastic deformation with an characteristic length of deformation comparable to the intrinsic material length, l, the present theory predicted higher plastic work hardening than did the classical crystal plasticity theory due to geometrically necessary dislocations.

A Conventional Theory of Strain Gradient Crystal Plasticity Based on the Taylor Dislocation Model. H.Wang, K.C.Hwang, Y.Huang, P.D.Wu, B.Liu, G.Ravichandran, C.S.Han, H.Gao: International Journal of Plasticity, 2007, 23[9], 1540-54