THE NAIL SOLUTION - ADHESION AT INTERFACES

As a useful model to examine adhesion at interfaces, we analyze the fo llowing 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 pro blem 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 pr ocess, and the exponent a = 0. The friction coefficients evaluated by simple tension pullout were found to be the same for cantilever beam d ebonding and were very sensitive to the pullout angle. The results of this simple friction-controlled fracture mechanics experiment, combine d with additional surface energy terms, are used to understand the adh esion 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 wetti ng, (3) incompatible polymer interfaces, (4) interfaces reinforced wit h diblock compatibilizers, and (5) fiber-reinforced composites.