Modeling of Cyclic Bending of Thin Foils Using Higher-Order Strain Gradient Plasticity

The plastic behaviors of thin metallic foils,including size effect,Bauschinger effect,and passivation effect,are studied under cyclic bending condition using the strain gradient visco-plasticity theory.The finite element simulations are performed on the cyclic bending of the elasto-viscoplastic thin foils with passivated and unpassivated surfaces.The study is also conducted on the transition from a passivated surface to an unpassivated one.The roles of the dissipative and energetic gradient terms are emphasized.From the results,it is found that the dissipative gradient terms increase the yield strength,while the energetic gradient terms increase the strain hardening,resulting in an anomalous Bauschinger effect.Further,it is observed that the surface passivation effect increases both the normalized bending moment at initial yielding and strain hardening.The comparison between the numerical results of cases with and without passivation demonstrates that the switching of boundary conditions significantly affects the plastic behavior of the foils under cyclic bending.