Non-Linear Increase of the Real Contact Area of PMMA Blocks and the Related Contact Model

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Many experiments have supported the contact models, such as the GW and MB models, but the majority of previous validations have been performed under light loads, resulting in a linear relationship between normal force and contact area. However, the real contact area fraction should never equal one; there must be a limit smaller than the apparent area, implying that the real contact area cannot increase linearly indefinitely. In this paper, the real contact area between two polymethylmethacrylate (PMMA) blocks under heavy load is measured using the total reflection method, and the contact area is analyzed using the image processing method. The results show that the real contact area increases with normal load linearly in light loads but non-linearly in heavy loads; the number of contact spots increases with load linearly in light loads but also non-linearly in heavy loads, synchronous with the change in the real contact area. The GW, MB, and Zhao, Maietta, and Chang (ZMC) models were used to predict the experiment results, but none of them predicted the non-linear stage. A revised GW model based on the bulk deformation hypothesis performs better in predicting the non-linear stage. The study’s findings can be applied to PMMA or other similar materials, and they can serve as a useful reference for future research on the contact mechanisms of other materials.