On the thermodynamics of higher-order gradient plasticity for size-effects at the micron and submicron length scales

A physically motivated and thermodynamically consistent formulation of higher-order gradient plasticity theory is presented. This proposed model is a two non-local parameter framework that takes into consideration: (1) the presence of plastic strain gradients, which is motivated by the evolution of dislocation density tensor that results from non-vanishing net Burgers vector and, hence, incorporating additional kinematic hardening and (2) the presence of gradients in the equivalent (effective) plastic strain (history variable), which is motivated by the accumulation of geometrically necessary dislocations and, hence, incorporating additional isotropic hardening. It is demonstrated that the non-local yield condition, flow rule and non-classical microscopic boundary conditions can be derived directly from the principle of virtual power. It is also shown that the local Clausius-Duhem inequality does not hold for gradient-dependent material and, therefore, a non-local form should be adopted. Applications of the proposed theory for size effects in metallic thin films are presented.