A Criterion for the Effective Work of Adhesion in Loading and Unloading of Adhesive Soft Solids from Rough Surfaces

Recently, Dalvi and co-authors have shown detailed experimental data of adhesion of soft spheres with rough substrates with roughness measured down to almost the atomic scale, finding that the Persson and Tosatti theory gave satisfactory predictions of the apparent work of adhesion during loading, once the increase of the surface area due to roughness is correctly computed at extremely small scales. We show that unloading data would show similar correlation with the Persson-Tosatti's simple criterion, but for a much larger effective work of adhesion, which therefore becomes not an "intrinsic" property. This suggests either strong hysteresis even at apparently very low peeling velocities or the need to use a criterion that has different behavior during loading and unloading. We attempt this inspired by the results of Guduru for a simple case of axisymmetric waviness, and a much better fit of the experimental data by Dalvi and co-authors is obtained using the entire set of data at loading and unloading, even assuming a single work of adhesion value. However, we cannot rule out that both (viscoelastic) and (roughness-induced) enhancement effects coexist in these data.