Fitting probability distribution functions to saturation crack spacing distribution in substrate plastic straining test for thin films and coatings

Various approximations involving computer simulation, and the ab initio assumption of a suitable probability distribution prior to simulation, have been suggested in the literature for determining the critical crack spacing at saturation in the substrate plastic straining test for films or coatings on metallic substrates, i.e when the detachment of films from substrate occurs. An experimental investigation of silicon modified DLC films on steel substrates (304 stainless and mild steel) has employed a simple statistical procedure which reveals a very good match between the saturation crack spacing frequency distribution and the two parameter Weibull distribution function. This allows faster determination of the mean crack spacing distribution and eliminates the need for a further computer simulation stage in the analysis as is currently adopted in the literature. The approach reported is simpler and is applicable to the treatment of crack spacing frequency distributions matching other probability functions.