Bending of single crystal thin films modeled with micropolar crystal plasticity

The scale-dependent mechanical response of single crystal thin films subjected to pure bending is investigated using a dislocation-based model of micropolar single crystal plasticity via finite element simulations. Due to the presence of couple stresses, the driving force for plastic slip in a micropolar crystal contains an intrinsic back stress component that is related to gradients in lattice torsion-curvature. Strain gradient-dependent back stresses are a common feature of various types of generalized crystal plasticity theories; however, it is often introduced either in a phenomenological manner without additional kinematics or by designating the plastic slips as generalized degrees-of-freedom. The treatment of lattice rotations as fundamental degrees-of-freedom instead of plastic slips greatly reduces the complexity (computational expense) of the single crystal model, and leads to the incorporation of additional elastoplastic kinematics since the lattice torsion-curvature is taken as a work-conjugate continuum deformation measure. A recently proposed single criterion micropolar framework is employed in which the evolution of both the plastic strains and torsion-curvatures are coupled through the use of a unified flow rule. The deformation behavior is characterized by the moment-rotation response and the dislocation substructure evolution for various slip configurations and specimen thicknesses. The results are compared to analogous simulations carried out using a model of discrete dislocation dynamics as well as a statistical-mechanics inspired, flux-based model of nonlocal crystal plasticity. The micropolar model demonstrates good qualitative and quantitative agreement with the previous results up to certain inherent limitations of the current formulation.