The contact mechanics of fractal surfaces

The role of surface roughness in contact mechanics is relevant to processes ranging from adhesion to friction, wear and lubrication1,2. It also promises to have a deep impact on applied science, including coatings technology and design of microelectromechanical systems3. Despite the considerable results achieved by indentation experiments4, particularly in the measurement of bulk hardness on nanometre scales5,6,7, the contact behaviour of realistic surfaces, showing random multiscale roughness, remains largely unknown. Here we report experimental results concerning the mechanical response of self-affine thin films indented by a micrometric flat probe. The specimens, made of cluster-assembled carbon8,9,10,11 or of sexithienyl12,13, an organic molecular material, were chosen as prototype systems for the broad class of self-affine fractal interfaces, today including surfaces grown under non-equilibrium conditions14, fractures15, manufactured metal surfaces16,17,18,19 and solidified liquid fronts20. We observe that a regime exists in which roughness drives the contact mechanics: in this range surface stiffness varies by a few orders of magnitude on small but significant changes of fractal parameters. As a consequence, we demonstrate that soft solid interfaces can be appreciably strengthened by reducing both fractal dimension and surface roughness. This indicates a general route for tailoring the mechanical properties of solid bodies.