Bending of a single crystal thin foil of material with slip gradient effects

The simulation of the cyclic bending of a single crystal thin foil is presented. The simulations demonstrate a constitutive model that incorporates the effects of geometrically necessary dislocations that accompany slip gradients and includes a slip gradient proportional hardness and energetically conjugate long range stresses and strains proportional to the second gradient of slip. Results are presented for three cycles of bending and straightening for foil thicknesses of 25, 50 and 100 mu m. Various combinations of the gradient hardness coefficient and the long range strain length parameter are examined. The results show an isotropic type hardening behavior due to the gradient hardness and a kinematic type hardening behavior due to the long range strains. Comparing the results from the three different thickness specimens shows an obvious decrease in the effects of the gradient hardness and the long range strain with an increase in the foil thickness.