Role of flaw statistics in contact fracture of brittle coatings

A flaw statistics analysis is here developed to account for systematic differences between experimentally observed and theoretically predicted critical loads for the initiation of contact-induced radial cracks in brittle coatings on compliant substrates. Specific attention is drawn to deviations in critical load ( P R) data from ideal quadratic dependence on coating thickness ( d), i.e. P R∝ d 2, especially at low d values. It is postulated that these deviations are attributable to the existence of distributions in flaw size and location, in relation to the bell-shaped tensile stress fields responsible for initiation of the radial cracks at the coating lower surface. A statistics-based expression is derived for the mean values of P R in terms of flaw density and size distribution. Data from model bilayers consisting of glass plates of different thicknesses d bonded to polycarbonate substrates are used as an illustrative case study. Controlled pre-abrasion flaws are introduced into the lower glass surfaces before joining into the bilayer configuration, to enable a priori characterization of distribution parameters by image analysis. Finite element modelling is used to determine the tensile stress distribution at the coating lower surface. The predicted statistics-based P R( d) function is shown to fit the data within uncertainty bounds. Implications concerning the continued usefulness of the ideal, P R∝ d 2 relation for designing ceramic coatings for failure resistance are considered.