Two scaling domains in multiple cracking phenomena
The fragmentation of two-phase composite systems such as coatings on substrates and fibers in matrices under uniaxial tension shows two regimes: the evolution of the mean fragment length with applied strain displays different power laws for small and for large strains. From theoretical arguments, we find that in both cases the scaling exponent depends on the shape parameter of the strength distribution. The exponent for large applied strains depends also, as we show, on the way (linear or nonlinear) in which the stress transfer between the two constituents takes place. We present experimental data on the sequential cracking of SiOx coatings on thermoplastic substrates that indeed show the two regimes; the detailed analysis of the data supports our theory.