Patterns of fragmentation for polymer coatings

We investigated the fragmentation of thin coatings on substrates under uniaxial tension. Theoretical models based on linear elasticity predict a power-law dependence of the mean fragment length < L> on the strain e to which the substrate is subjected: namely, one has <L> ∞?^?α with α ≤ 1/2. Experimentally, such a relation is obeyed in the fragmentation of thin SiO _x coatings on polyethylene terephthalate (PET) substrates. In our experiments, we used brittle paints to coat rubber substrates: the ensuing mean fragment lengths also obey power laws in ?: we found, however, α = 0.71 ± 0.03. Such values of α can be reproduced theoretically by taking into account the nonlinearity of the coupling between coating and substrate.