Which asperity scales matter for true contact area? A multi-scale and statistical investigation

The true contact area between two surfaces is only a small fraction of the apparent macroscopic contact area; it governs many interfacial properties such as friction and contact resistance and depends sensitively on roughness. However, for real-world multi-scale surface topography, it is not clear which size scales of roughness govern the true contact area. This study investigates true contact area for a real-world surface that has been characterized across all scales from Angstroms to centimeters. Elastic and elastic-plastic contact is investigated using both a multiscale framework and a statistical roughness model. The multiscale method is a rough-surface contact-modeling technique based on Archard's stacked scales from a spectrum of the surfaces, which has shown promise when compared to previous experimental and numerical results. In contrast, statistical models assume that the asperities follow a defined height distribution and are in contact when taller than the mean surface separation. The results show that even the smallest scales can have a significant influence on the contact area, especially when the contact is elastic. However, when the contact is elastic-plastic, the influence of smaller scales can be limited depending on the character of the roughness. For self-similar, fractal-like roughness across some scales, the pressure tends to saturate at those scales. This work also explores the inclusion of scale-dependent yield strength. Both the multiscale and statistical models predict that the inclusion of scale-dependent strength causes the predicted contact area of the elastic-plastic models to come into closer agreement with that of the elastic model, especially when a wider range of size scales are included. In addition, both types of models predict that below a certain scale, smaller asperities flatten under contact pressure and will no longer influence the predicted contact area. Taken together, this work helps to guide the accurate modeling of rough-surface contact, and provides insights into which scales can be modified to improve performance in manufactured components.