Mechanism-based strain gradient plasticity—II. Analysis

A mechanism-based theory of strain gradient (MSG) plasticity has been proposed in Part I of this paper. The theory is based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic strain and strain gradient. This theory is motivated by our recent analysis of indentation experiments which strongly suggest a linear dependence of the square of plastic flow stress on strain gradient. Such a linear dependence is consistent with the Taylor plastic work hardening model relating the flow stress to dislocation density. This part of this paper provides a detailed analysis of the new theory, including equilibrium equations and boundary conditions, constitutive equations for the mechanism-based strain gradient plasticity, and kinematic relations among strains, strain gradients and displacements. The theory is used to investigate several phenomena that are influenced by plastic strain gradients. In bending of thin beams and torsion of thin wires, mechanism-based strain gradient plasticity gives a significant increase in scaled bending moment and scaled torque due to strain gradient effects. For the growth of microvoids and cavitation instabilities, however, it is found that strain gradients have little effect on micron-sized voids, but submicron-sized voids can have a larger resistance against void growth. Finally, it is shown from the study of bimaterials in shear that the mesoscale cell size has little effect on global physical quantities (e.g. applied stresses), but may affect the local deformation field significantly.