Mechanics of strain gradient plasticity with particular reference to decomposition of the state variables into energetic and dissipative components

The results of recent studies on strengthening and hardening mechanisms for micro/nano structured materials indicate that the use of only one type of energetic or dissipative description may be insufficient to accurately describe the size effects exhibited in metallic components. Therefore, it is important to incorporate more than one description of the thermodynamic processes into the modeling in order to have a better understanding of the hardening and strengthening mechanisms for micro/nano structured materials.The research presented here is based on this deficiency and the goal is to develop a strain gradient theory based on the decomposition of the state variables into energetic and dissipative components. This, in turn, endowed the constitutive equations to have both energetic and dissipative gradient length scales ℓenℓen and ℓdisℓdis, respectively. The effect of the material microstructural interface between two materials is also incorporated into the proposed formulation. Hence four material length scales are introduced: two for the bulk and the other two for the interface. The resulting formulation exhibits the following important physical phenomena: (i) standard energetic hardening associated with plastic strain and nonlocal energetic hardening associated with plastic strain gradients; (ii) size dependent increase in yield strength which is characterized by the dissipative strengthening associated with plastic strain gradient rate; (iii) the effect of interfacial yield strength and hardening; (iv) description of the boundary layer; and (v) the effect of the different boundary conditions. The problem is solved analytically by using for example, a thin film on elastic substrate under uniaxial uniform tension or a single phase bicrystal under uniform tension where the interface represents the grain boundary. The interface model here describes the internal boundary of the plastic region and characterizes the physical understanding of the dislocation mechanics at the interface between two phases. The results of the analytical results indicate that the proposed theory qualitatively captures the overall physical behavior. However there is strong debate in the literature on the choice of accurate physical boundary conditions at the elastic plastic boundaries. Therefore, more elaborate studies are needed for better assessment of the boundary conditions of the higher-order strain gradient plasticity theories.