A random process asperity model for adhesion

TL;DR

This paper introduces a new asperity model incorporating adhesion using random process theory, deriving a key adhesion parameter that improves upon previous models and influences adhesion effects at certain thresholds.

Contribution

A novel asperity model with adhesion based on random process theory and a new adhesion parameter, enhancing understanding of surface interactions.

Findings

The model introduces a new adhesion parameter, θ, that depends on surface energy, elastic modulus, and asperity statistics.

Adhesion effects become significant when θ exceeds 0.15.

Comparisons with recent results show the model's potential for better predicting adhesion phenomena.

Abstract

A simple asperity model using random process theory is developed in the presence of adhesion. Using the DMT model for each individual asperity, and asymptotic results at large separations, a new adhesion parameter is found, on which the model depends, namely $\theta=\frac{w}{E^{\ast}\sqrt{m_{2}/\pi} m_{0}^{1/2}}$, where $w,E^{\ast},m_{2},m_{0}$ are respectively surface energy, combined elastic modulus, variance of slopes and of heigths of the asperities. This parameter perhaps improves the previous parameter proposed by Fuller and Tabor which assumed identical asperities. the effects of adhesion are found in practice only for {\theta}>0.15. Some implications are discussed and comparisons with recent results are attempted.