Pre-tension generates strongly reversible adhesion of a spatula pad on substrate

Abstract

Motivated by recent studies on reversible adhesion mechanisms of geckos and insects, we investigate the effect of pre-tension on the orientation-dependent adhesion strength of an elastic tape adhering on a substrate. Our analysis shows that the pre-tension can significantly increase the peel-off force at small peeling angles while decreasing it at large peeling angles, leading to a strongly reversible adhesion. More interestingly, we find that there exists a critical value of pre-tension beyond which the peel-off force plunges to zero at a force-independent critical peeling angle. We further show that the level of pre-tension required for such force-independent detachment at a critical angle can be induced by simply dragging a spatula pad along a substrate at sufficiently low angles. These results provide a feasible explanation of relevant experimental observations on gecko adhesion and suggest possible strategies to design strongly reversible adhesives via pre-tension.

Figure 1

An elastic thin film adhering on a surface subjected to a peeling force. The film resembles a spatula pad with plane-strain Young's modulus E=2 GPa, Poisson's ratio v=0.3 and thickness 5 nm. The system is under plane strain with a unit width in the out-of-plane direction. The adhesion energy across the contact interface is taken to be 0.01 J m⁻² and the theoretical strength of adhesion is 20 MPa.

Figure 2

Peel-off force of an elastic thin film/pad adhering to a substrate as a function of the peeling angle according to Kendall's model.

Figure 3

An elastic thin film/pad with pre-tension is attached to a rigid surface and then subjected to peeling at an inclined angle.

Figure 4

Effect of pre-tension on orientation-dependent adhesion of an elastic thin film/pad adhering to a substrate. (a) Peel-off force of the film as a function of the peeling angle at different levels of pre-tension. The presence of a pre-tension generally increases the peel-off force at low peeling angles. Beyond a critical pre-tension, the peel-off force plunges at a critical peeling angle. Solid curves represent the upper branch of the critical peel-off force, and dashed curves represent the lower branch of the peel-off force when it is positive. (b) Variation of the force-independent critical detachment angle as a function of the pre-tension magnitude. The critical angle exists only when the pre-tension exceeds $\sqrt{2EH\gamma }$.

Figure 5

Effect of mode mixity on orientation-dependent adhesion of an elastic thin film/pad adhering to a substrate. (a) Variations of the mode-mixity-dependent adhesion energy in equation (2.10) for different values of the parameter λ. The peel-off force of the film for different values of the mode-mixity parameter λ when (b) P₀/EH=0, (c) P₀/EH=0.02 and (d) P₀/EH=0.1.

Figure 6

Finite-element simulation of sequential attachment of contacting sites as a thin film is dragged along a substrate at a very low angle. (a) Schematic of the simulation process. At stage I, the film adheres to the first contacting site on the left under near 0° dragging. Right before it begins to detach from the substrate, the detached part of the film becomes attached to the second contacting site. (b) The simulated force–displacement relationship for the sequentially attached film. The film now has a built-in pre-tension and the peel-off force of 0.8 nN nm⁻¹ is about twice that predicted from Kendall's model in the absence of pre-tension.

Figure 7

The critical angle for spontaneous detachment of an elastic thin film/pad adhering to a substrate as a function of the dimensionless parameter γ/EH.