Size-dependent bending of thin metallic films

Size-dependent large curvature pure bending of thin metallic films has been analytically studied taking into account the associated strengthening mechanisms at different thickness scales. The classical plasticity theory is applicable to films thicker than 100 μm. Consequently, their bending capacity is governed by the competition between the material hardening and the thickness reduction. For films with a thickness ranging from fractions of a micron to a few microns, in addition to the above mechanisms, the strain gradient effect plays an important role and introduces an internal length scale. When the film thickness reduces to the nano-scale, the strain gradient effect is gradually replaced by the dominant surface stress/energy effect.