Seminar of Dr. Marco Paggi, April 14th

The assumption of flat surfaces within the context of contact problems is very often an oversimplification of reality. In fact, when real surfaces are examined more in details using profilometers, roughness can be found over different length scales. This multiscale feature poses enormous difficulties on the mathematical modelling of contact problems. Nevertheless, the study of the effect of multiscale roughness on the tribological properties of materials in contact is essential from the engineering point of view.

Modelling rough surfaces as invasive fractals with a topological dimension intermediate between those of a flat surface and a volume, the two length scales that define the range of validity of self-affinity play an important role. On one side we have the lower cut-off length of the system, which often coincides with the breakdown of continuum mechanics at the nanoscale. On the other side we have the finite size of the sample, which may lead to important size-scale effects on the mechanical properties.

In this seminar, the effect of these two length scales on the tribological properties of rough surfaces is investigated using analytical and numerical methods. Regarding the normal contact problem, the resolution dependency of the statistical parameters input of micromechanical contact theories is discussed. Then it is shown that the coefficient of proportionality between real contact area and applied load is dependent on the bandwidth parameter, which is a function of the ratio between the lower and the upper cut-off lengths of the system. In this context, the effect of elastic interactions between asperities is found to be crucial for improving the predictions of classical micromechanical contact theories in order to capture the observed numerical trends. Regarding the tangential contact problem, fractal geometry and renormalization group theory are applied to interpret in a unified way the experimental results suggesting size-scale effects on the apparent shear strength, friction coefficient and fracture energy of rough surfaces in rock mechanics and geophysics. The breakdown of the proposed scaling laws at the nanoscale, due to the effect of adhesion, is also discussed.