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This study addresses the strength and toughness of generic fibrillar structures. We show that the stress σ c required to pull a fibril out of adhesive contact with a substrate has the form σ c = σ 0 Φ( χ ). In this equation, σ 0 is the interfacial strength, Φ( χ ) is a dimensionless function satisfying 0=Φ( χ )=1 and χ is a dimensionless parameter that depends on the interfacial properties, as well as the fibril stiffness and radius. Pull-off is flaw sensitive for χ ≫1, but is flaw insensitive for χ <1. The important parameter χ also controls the stability of a homogeneously deformed non-fibrillar (flat) interface. Using these results, we show that the work to fail a unit area of fibrillar surface can be much higher than the intrinsic work of adhesion for a flat interface of the same material. In addition, we show that cross-sectional fibril dimensions control the pull-off force, which increases with decreasing fibril radius. Finally, an increase in fibril length is shown to increase the work necessary to separate a fibrillar interface. Besides our calculations involving a single fibril, we study the concept of equal load sharing (ELS) for a perfect interface containing many fibrils. We obtain the practical work of adhesion for an idealized fibrillated interface under equal load sharing. We then analyse the peeling of a fibrillar surface from a rigid substrate and establish a criterion for ELS.
Hui et al. (Mon,) studied this question.