Adhesion Calculator for Rough Surfaces – Bearing Area Model

TriboNet

February, 11 2018

This calculator can be used to calculate the adhesion pressure and pull-off pressure between two elastic rough surfaces (macroscopically flats). The calculator is based on a simplified theory developed by Professor Ciavarella (see details here). Also, you can find a detailed description in [1]. For more details, please contact Professor Ciavarella [email protected].

For a given separation $u$ , adhesive pressure $P$ is calculated according to a folowing expression:

$P/P_{th} = 3/(8 \gamma) * q_0*h_{RMS}*E^*/P_{th}*exp(\frac{-u}{\gamma*h_{RMS}}) - 1/{2k}*(Erfc(\frac{u-dr}{\sqrt(2)h_{RMS}}) - Erfc(\frac{u}{sqrt(2)h_{RMS}}))$ .

Here, $\gamma=0.4$ , $k=2$ , $q_0$ is the roll-off wavelength, $P_{th}=w/dr$ with $w$ being the work of adhesion and $dr$ atomic spacing. $h_{RMS}$ is the comined RMS roughness and $1/{E^*} = (\frac{1-\nu_1^2}{E_1} + \frac{1-\nu_2^2}{E_2})$ is the reduced Young’s modulus, $\nu_1, E_1, \nu_2, E_2$ are the Poisson and Young’s moduli of the bodies. Pull-off pressure is calculated as the minimum adhesion pressure for all possible separations.

[1] A very simple estimate of adhesion of hard solids with rough surfaces based on a bearing area model, M. Ciavarella, Meccanica, DOI 10.1007/s11012-017-0701-6.