A Numerical Study on Roughness-Induced Adhesion Enhancement in a Sphere with an Axisymmetric Sinusoidal Waviness Using Lennard–Jones Interaction Law

Abstract

Usually, roughness destroys adhesion and this is one of the reasons why the “adhesion paradox”, i.e. a “sticky Universe”, is not real. However, at least with some special type of roughness, there is even the case of adhesion enhancement, as it was shown clearly by Guduru, who considered the contact between a sphere and a wavy axisymmetric single scale roughness, in the limit of short-range adhesion (JKR limit). Here, the Guduru’s problem is numerically solved by using the Boundary Element Method (BEM) with Lennard–Jones interaction law, which allowed us to explore the contact solution from the rigid to the JKR limit. It is shown that adhesion enhancement stops either for low Tabor parameter, or by large waviness amplitudes, due to the appearance of internal cracks within the contact patch. We do not seem to find a clear threshold for “stickiness” (complete elimination of adhesion), contrary to other recent theories on random roughness. The enhancement effect is well captured by an equation in terms of the Johnson parameter derived by Ciavarella–Kesari–Lew, and is much larger than the Persson–Tosatti enhancement in terms of increase of real contact area due to roughness. The Persson–Tosatti energetic argument for adhesion reduction seems to give a lower bound to the effective work of adhesion.

On the Interaction of Viscoelasticity and Waviness in Enhancing the Pull-Off Force in Sphere/Flat Contacts

“…Also, Guduru effect only holds for a quite special waviness (single scale, axisymmetric), when the contact area "peels" quite uniformly around a circle and requires the initial contact area to be compact. This poses some limits to the amplitude of roughness, hence, the amplification factor that can be reached (see a more general numerical solution using Lennard-Jones force-separation law in Papangelo and Ciavarella [33]). Regarding the non-axisymmetric effect, Li et al [34] numerical experiments for the pull-off of a sphere in contact with an elastic substrate with 2-dimensional wavy roughness, showed that the adhesion enhancement is further much reduced.…”

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

“…Although Eq. (4) would predict unbounded enhancement for large roughness amplitude h, the enhancement can only appear up to a certain amplitude, above which internal cracks appear within the contact area (see Papangelo and Ciavarella [32] for a numerical solution).…”

“…Especially for the limit case of the Guduru geometry, see Papangelo and Ciavarella[32] 5. Notice that PT had already derived Eq (14).…”

Meso-scale dislocations and friction of shape-complementary soft interfaces

“…Kesari & Lew [29] also showed theoretically how a model wavy rough surface can enhance effective adhesion as a result of mechanical instabilities. Ciavarella and Papangelo [30,31] similarly studied how rough surfaces can actually enhance adhesion for soft solids. This finding is different from the general rule that rough surfaces attenuate adhesion [32][33][34][35].…”