Second-order crystal plasticity: internal stress effects and cyclic loading

This paper studies dislocation induced internal stresses as introduced in a strain gradient crystal plasticity approach. The need for a second-order crystal plasticity approach is motivated in the context of the analysis of free-standing metal films used in radio-frequency micro-electro-mechanical systems (RF-MEMS). The presented second-order framework incorporates the influence of inter- and intragranular deformation inhomogeneities in the constitutive description, generally assumed to be the basic origin of scale dependent behaviour and associated size effects. Focusing on the dynamic loading of thin RF-MEMS films, attention is given to dislocation induced kinematical hardening effects. The corresponding internal stresses are discussed with respect to their contribution to the solution of the underlying elasto-plastic framework which implicitly accounts for elastic incompatibilities. Within the loading regime of interest, the response in loading-unloading-reloading and cyclic loading is assessed.