A random process asperity model for adhesion

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.