Fractal Model Developed for Elliptic Elastic-Plastic Asperity Microcontacts of Rough Surfaces

An elastic-plastic asperity fractal model for analyzing the contact of rough surfaces is presented. Instead of using the power-law relation, which is widely used to predict the number, N, of contact spots with the area larger than the area of $a′$ in per unit apparent area, the size-distribution functions valid in the elastic, elastoplastic, and fully plastic deformations have been individually developed in the present model for contact surfaces with elliptic asperities. These three size-distribution functions can be used in the calculations of the N value. The error in the number N, which exists between the results predicted by the present model and those obtained from experiments, is greatly reduced as compared with the error arising between the experimental results and those predicted by the power-law model. If the topothesy, G, and the fractal dimension, D, of contact surfaces are properly chosen to conform to those given plasticity indices, the results predicted by the present model are considerably closer to that predicted by one published study. Changes in the ellipticity parameter of contact spots may introduce a substantial difference in the relationship established for the real contact area and the total load.