Micro-cantilever bending tests for understanding size effect in gradient elasticity

Higher-order deformation theories, such as the couple stress and strain gradient theory, have been widely used to predict the mechanical behavior of micro/nano-scale structures. In this paper, the additional length scale parameter introduced in the couple stress theory is measured by performing bulk-scale tensile and micro-scale cantilever bending experiments. Bulk-scale characterization provided microstructural information of the polycrystalline copper plate along with macroscopic mechanical properties. Micro-scale cantilevers with thicknesses ranging from 1.6 µm to 8.6 µm were fabricated within the copper plate using femtosecond laser machining followed by focused ion beam milling. Line load was applied on these samples utilizing a nanoindenter. Finite element analysis was performed to exclude the effect of substrate deformation. The measured effective elastic modulus increases from 94 GPa to 215 GPa with decreasing thickness. The increase of the bending rigidity is analyzed based on the couple stress theory, and the length scale parameter is measured as 0.78 µm. The physical origin of the length scale parameter is discussed by considering mobile dislocations escaping via the free surfaces during loading.