Contact Measurements of Randomly Rough Surfaces

Abstract

This manuscript presents an experimental effort to directly measure contact areas and the details behind these scaled experiments on a randomly rough model surface used in the “Contact Mechanics Challenge” (2017). For these experiments, the randomly rough surface model was scaled up by a factor of 1000× to give a 100 mm square sample that was 3D printed from opaque polymethylmethacrylate (PMMA). This sample was loaded against various optically smooth and transparent samples of PDMS that were approximately 15 mm thick and had a range in elastic modulus from 14 kPa to 2.1 MPa. During loading, a digital camera recorded contact locations by imaging the scattering of light that occurs off of the PMMA rough surface when it was in contact with the PDMS substrate. This method of illuminating contact areas is called frustrated total internal reflection and is performed by creating a condition of total internal reflection within the unperturbed PDMS samples. Contact or deformation of the surface results in light being diffusely transmitted from the PDMS and detected by the camera. For these experiments, a range of reduced pressure (nominal pressure/elastic modulus) from below 0.001 to over 1.0 was examined, and the resulting relative contact area (real area of contact/apparent area of contact) was found to increase from below 0.1% to over 60% at the highest pressures. The experimental uncertainties associated with experiments are discussed, and the results are compared to the numerical results from the simulation solution to the “Contact Mechanics Challenge.” The simulation results and experimental results of the relative contact areas as a function of reduced pressure are in agreement (within experimental uncertainties).