Patterns of fragmentation for polymer coatings

We investigated the fragmentation of thin coatings on substrates under unia xial tension. Theoretical models based on linear elasticity predict a power -law dependence of the mean fragment length <L> on the strain epsilon to wh ich the substrate is subjected; namely, one has <L> proportional to epsilon (-alpha) with alpha less than or equal to 1/2. Experimentally, such a relat ion is obeyed in the fragmentation of thin SiOx coatings on polyethylene te rephthalate (PET) substrates. In our experiments, we used brittle paints to coat rubber substrates; the ensuing mean fragment lengths also obey power laws in epsilon; we found, however, alpha = 0.71 +/- 0.03. Such values of a lpha can be reproduced theoretically by taking into account the nonlinearit y of the coupling between coating and substrate.