Analysis of brittle coating fragmentation under uniaxial tension for Weibull strength distributions

We investigate the sequential cracking of thin brittle coatings attached ad hesively to substrates. The focus of our study are uniaxial tensile loading conditions, where we monitor the behavior in a continuous picture and the coating strength follows a two-parameter Weibull distribution. For fracture well under way we derive an approximate analytical expression for the dist ribution of fragment lengths. We recover that the distribution scales with the average fragment length (l) and that (l) is a power function of the app lied strain epsilon, i.e. (l) proportional to epsilon(-kappa), where kappa depends on the distribution of the strength of the coating and on the adhes ive's nonlinearity. Furthermore we compare our approximate analytical expre ssion with numerical solutions and with simulations' findings.