On the theory of Hertzian fracture

The mechanics of adhesive failure have been investigated by using model adhesive joints between a cross-linked amorphous rubber and rigid polymeric substrates. The adhesive failure energy,$\theta $, was determined over a wide range of temperatures and rates of crack propagation. For any given rubber-substrate joint the results yield a single master curve when reduced to a reference temperature by means of the Williams-Landel-Ferry equation. It is shown that $\theta $ is the sum of two components: the energy dissipated viscoelastically within the rubber at the crack tip and the 'intrinsic' adhesive failure energy $\theta _{0}$. The value of the former is proportional to $\theta _{0}$, so that $\theta $ can also be represented as the product of $\theta _{0}$ and a function of rate and temperature. The parameter $\theta _{0}$ is governed by the surface properties and compositions of the materials forming the joint. When pure interfacial failure occurs, $\theta _{0}$ has a value in close agreement with the thermodynamic 'work of adhesion' determined independently.