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.