A22 Wear of micro/nano structures

Topic

The insect's adhesive setae undergo progressive mechanical wear whenever the insect walks on abrasive surfaces, and this wear accumulates with every step of the insect's locomotion. Archard's law describes the nature of this wear: the volume of the seta lost is proportional to the normal load borne by the seta and the distance it slides across the surface, yet inversely proportional to the surface's hardness—meaning that a rock or concrete surface wears down the adhesive setae far more than a smooth glass surface does.

Each time this wear reduces the length of an adhesive seta, its point of optimal stiffness shifts: a shorter seta becomes stiffer, and this increased stiffness diminishes the seta's ability to conform to the irregularities of the surface the insect is traversing.

Furthermore, this loss of length directly affects the seta's adhesion: the shorter the seta becomes, the smaller the contact radius it can establish with the surface—as described by Hertzian contact theory—and adhesion drops more sharply than the length itself decreases. For instance, a seta shortened to eighty percent of its original length retains only seventy-two percent of its original adhesion; the loss of adhesion is proportionally greater than the loss of length that caused it.

Wear leaves another mark on the tips of the adhesive setae as well: sub-micrometric cracks appear and grow with each fatigue cycle—that is, with every cycle of adhesion and detachment the seta undergoes against the surface. These cracks do not grow at a constant rate; instead, they accelerate as the crack itself enlarges, following the behavior described by the Paris-Erdogan law: the more a crack has already grown, the faster it continues to grow in the subsequent cycle.

The accelerated growth of these cracks ultimately determines the lifespan of an adhesive mushroom structure: the Coffin-Manson fatigue life model predicts the total number of attachment and detachment cycles the structure can withstand before failure, based on the magnitude of the deformation it undergoes during each cycle. The greater the deformation per cycle, the fewer cycles the structure can endure before the crack growing at its tip renders it useless, thereby concluding the wear process that began with the simple rubbing of the structure against an abrasive surface.

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