Modeling of multiple cracking and decohesion of a thin film on a polymer substrate

Thin brittle films on polymer substrates are finding increasing use as gas barriers for example in the medical and food packaging industries and also for the next generation of ultra-light displays based on flexible polymer substrates. In order to determine the durability of the barrier under thermal and mechanical loads, test procedures and corresponding data reduction methods are needed to feed the analysis models. One of the tests frequently employed for this kind of multi-layer material systems is the fragmentation test, whose designation comes from the progressively denser pattern of parallel cracks developing when the specimen is loaded under uniaxial tension. From the crack-density versus strain data obtained, a critical strain for crack growth and an assessment of the adhesion of the coating to substrate can be obtained. However, no accepted data reduction methods exist to extract material properties from the test or inversely, successfully predict the crack density as a function of a set of material properties without fitting parameters. In an earlier paper, the authors presented a finite element based analysis methodology to determine the fracture toughness of both the coating and the interface from the fragmentation data. In the simulations, the plastic constitutive behavior of the substrate and the debonding of the coating from the substrate were explicitly included, the latter by use of a cohesive zone model. In this paper an extension of this methodology is presented that enables crack-density evolution with strain to be predicted. The results presented comprise comparisons with experiments to validate the methodology and the influence of (i) coating toughness, (ii) interface toughness and (iii) coating thickness on crack density versus strain.