A fractal approach to indentation size effect

In this paper, we propose an original interpretation of indentation size effect (ISE) in both single crystal and polycrystalline metals, which is based on the experimental evidence of the formation of fractal cellular dislocation patterns during the later stages of plastic deformation, in strain hardening metals, both under tensile loading and in compression. The proposed approach is a generalization of the arguments already proposed by the senior author in order to derive multifractal scaling laws (MFSL), which apply to tensile strength, fracture energy and the critical strain of brittle and quasi-brittle materials.This approach is thus in the mainstream of the geometrical interpretation of size-scale effects on the strength of solids, which has been counterposed, in recent years, to the mechanical interpretation. The proposed fractal approach aims at strengthening this view, which provides ease of interpretation, and at stimulating discussion on the central key role of dislocation evolution in the plastic deformation of metals, the fractal characteristics of which have not been adequately considered in literature.The obtained equation for ISE, based on the fractal approach, very closely resembles MFSL for tensile strength in quasi-brittle materials and the scaling equation already proposed by other authors, but it is based on a very different underlying physical model. Some experimental hardness data, obtained from microindentation on copper, have been fitted with MFSL, and show a very good agreement.