The nail solution: adhesion at interfaces

Abstract

As a useful model to examine adhesion at interfaces, we analyze the following problem: Consider two cantilever beams of wood nailed together by n nails per unit area with penetration length L. Optionally, nrow nails may be placed in a single row at distance a from the beam ends. How does the fracture energy G1c and critical load Pcr depend on n, nrow, L, and the deformation velocity V? The solution to this problem is called the 'nail solution'. Using pine wood beams and nails of varying length, we demonstrate that (a) Glc = 1/2μoVanL2, (b) Pcr ~ L√n, (c) G1c ~ L2n2 row, and (d) Pcr ~ Lnrow, where μo ~ 3000 N/m is the static friction coefficient per unit nail length during the pullout process, and the exponent a = 0. The friction coefficients evaluated by simple tension pullout were found to be the same for cantilever beam debonding and were very sensitive to the pullout angle. The results of this simple friction-controlled fracture mechanics experiment, combined with additional surface energy terms, are used to understand the adhesion strength development in more complex molecular systems such as (1) weak amorphous glassy polymers with molecular weights less than the critical entanglement molecular weight, (2) polymer welding and wetting, (3) incompatible polymer interfaces, (4) interfaces reinforced with diblock compatibilizers, and (5) fiber-reinforced composites.