Mode-mixity-dependent adhesive contact of a sphere on a plane surface

Abstract

Tangential loading in the presence of adhesion is highly relevant to biological locomotion, but mixed-mode contact of biological materials or similar soft elastomers remains to be well understood. To better capture the effects of dissipation in such contact problems owing to viscoelasticity or irreversible interfacial adhesive processes, a model is developed for the combined adhesive and tangential loading of a rigid sphere on a flat halfspace which incorporates a phenomenological model of energy dissipation in the form of increased effective work of adhesion with increasing degree of mode mixity. To verify the model, contact experiments are performed on polydimethylsiloxane (PDMS) samples using a custom-built microtribometer. Measurements of contact area during mixed normal/tangential loading indicate that the strong dependence of the effective work of adhesion upon mode mixity can be captured effectively by the phenomenological model in the regime where the contact area stayed circular and the slip was negligible. Rate effects were seen to be described by a power-law dependence upon the crack front velocity, similar to observations of rate-dependent contact seen for pure normal loading.

Fracture Mechanics Simple Calculations to Explain Small Reduction of the Real Contact Area Under Shear

“…Johnson, Kendall and Roberts (JKR-theory) firstly applied fracture mechanics concepts [14,15] to adhesion between elastic bodies, and this was extended to the presence of tangential force by Savkoor and Briggs [3] who also conducted experiments between glass and rubber similar to [12] but less detailed, and clearly evidenced a reduction of the contact area when tangential load was applied, but the reduction is much less than what is expected by a "brittle model", as indeed is confirmed by [12], which in these respects is therefore not entirely surprising. Johnson [17,18] and Waters and Guduru [19] have proposed different models to take into account the interplay between two fracture modes, namely I and II (mode III is also present, but marginal) with empirical parameters and phenomenological models to generalize the "brittle" behaviour. We will refer to Johnson [18] in this short communication.…”

Evaluation of energy dissipation involving adhesion hysteresis in spherical contact between a glass lens and a PDMS block

“…Maugis and Barquins [10] first introduced a concept of linear elastic fracture mechanics into the Johnson-Kendall-Roberts (JKR) contact [6]. They experimentally showed that G has a dependency on the crack speed [10], which is the socalled empirical relationship [11][12][13][14]. However, the relationship does not represent how the total energy dissipation changes during the contact process, and the mechanism of adhesion hysteresis is still on discussion assuming capillary condensation or adsorbed layer, etc.…”

“…The energy dissipation in the adhesive contact is mainly investigated and discussed using the strain energy release rate G (i.e., the energy required to separate unit contact area J/m 2 ) [9][10][11][12][13][14][15][16][17][18]. Maugis and Barquins [10] first introduced a concept of linear elastic fracture mechanics into the Johnson-Kendall-Roberts (JKR) contact [6].…”

Tangential Displacement Influence on the Critical Normal Force of Adhesive Contact Breakage in Biological Systems

“…However, some investigations have shown that such dependence may occur [3,4,16]. For example, in [3] in order to take into account the influence of the tangential displacement, the surface energy dependence has been proposed in the form:…”

“…It is necessary to emphasize that the adhesive contact can be destroyed not only by an increase in the normal force value, but also by applying a tangential loading as, for example, shown in [3][4][5][6][7][8]. During the gecko's motion in a horizontal plane (on the "ceiling"), the normal component of the force plays a decisive role.…”