Journal of Adhesion Science and Technology, Vol.10, No.4, 305-325, 1996
The nail solution: Adhesion at interfaces
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, n(row) nails may be placed in a single row at distance a from the beam ends. How does the fracture energy G(lc) and critical load P-cr depend on n, n(row), 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) G(lc) 1/2 mu(0) V(a)nL(2), (b) P-cr similar to L root n, (c) G(lc) similar to L(2)n(row)(2), and (d) P-cr similar to Ln(row), where mu(0) approximate to 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.