A conventional theory of strain gradient crystal plasticity based on the Taylor dislocation model

Single crystal metallic materials display strong size effects when the characteristic length of plastic deformation is 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 [Han, C.S., Gao, H.J., Huang, Y., Nix, W.D., 2005a. Mechanism-based strain gradient crystal plasticity – I. Theory. Journal of the Mechanics and Physics of Solids 53, 1188–1203; Han, C.S., Gao, H.J., Huang, Y., Nix, W.D., 2005b. Mechanism-based strain gradient crystal plasticity – II. Analysis. Journal of the Mechanics and Physics of Solids 53, 1204–1222] has been modified to incorporate a new quasi rate-independent formulation for the slip rate. Its major advantage is that it is 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 is identified from the Taylor dislocation model as l=α2(μτ0)2b, where μ is the shear modulus, τ0 is the initial yield stress (critical resolved shear stress) in slip systems, b is the magnitude of Burgers vector, and α is an empirical coefficient between 0.3 and 0.5. For non-uniform plastic deformation with the characteristic length of deformation comparable to the intrinsic material length l, the present theory gives higher plastic work hardening than the classical crystal plasticity theory due to geometrically necessary dislocations.