Perturbation analysis of crack front in simple cantilever plate peeling experiment

We have analyzed the effects of a single perturbation of the shape of a crack front on the energy release rate for a bonded joint. In the previous work, perturbation of the crack was introduced experimentally by variable adhesive properties. Accordingly a simple cantilever plate peeling experiment was performed on a specimen constituted from polycarbonate elastic plate bonded with a elastic fragile adhesive to aluminium rigid block. It have been found that fracture energy of such system differs from the expected rule of mixture values. In the following, using von Kármán plate theory, a relatively simple, first order approximation of the crack front perturbation effect is derived. The solution depends on two phenomenological quantities: the amplitude of perturbation and the perturbation wave length. The analytical solution matches reasonably well with existing experimental data.