Papangelo's criterion for stickiness of rough (hard) random surfaces

A generalized Johnson parameter for pull-off decay in the adhesion of rough surfaces

• December 2017
• Physical Mesomechanics

AbstractThere is no simple theory at present to predict accurately the decay of pull-off in the adhesion of randomly rough surfaces. The asperity model of Fuller and Tabor has shown significant error in recent numerical investigations by Pastewka and Robbins of self-affine random roughness from micrometer to atomic scale which corresponds to low values of Tabor parameter. For sinusoidal contact, the Johnson parameter, originally introduced for the JKR regime (from Johnson–Kendall–Roberts) is the dominant parameter ruling the pull-off at intermediate Tabor values. Hence, we define a generalized Johnson parameter as the ratio between the adhesive energy to the elastic strain energy to flatten the surface in the case of multiscale roughness and find that it correlates very well with the data of Pastewka and Robbins spanning almost five orders of magnitude of reduction from theoretical strength, improving significantly with respect to other possible single parameter criteria. For the most important case in practice, that of low fractal dimensions, this suggests the product of amplitude and slope of the largest wavelength components of roughness dominate pull-off decay, and not small scales features like slopes and curvatures, as suggested by Pastewka and Robbins.A preprint can be found here.

Full reference:   M Ciavarella and A Papangelo, A generalized Johnson parameter for pull-off decay in the adhesion of rough surfaces, Physical Mesomechanics, 20, 65-72, 2017.

PS.  I have just noticed that a criterion proposed by Papangelo has been noticed by Prof. Steven Abbott who is very active in teaching and consultancy of "practical adhesion" of Pressure Sensitive Adhesive".  His site seems quite interesting. 

https://www.stevenabbott.co.uk/practical-adhesion/dahlquist.php

Best regards