Role of flaw statistics in contact fracture of brittle coatings

A flaw statistics analysis is here developed to account for systematic diff erences between experimentally observed and theoretically predicted critica l loads for the initiation of contact-induced radial cracks in brittle coat ings on compliant substrates. Specific attention is drawn to deviations in critical load (P-R) data from ideal quadratic dependence on coating thickne ss (d), i.e. P(R)proportional tod(2), especially at low d values. It is pos tulated that these deviations are attributable to the existence of distribu tions in flaw size and location, in relation to the bell-shaped tensile str ess fields responsible for initiation of the radial cracks at the coating l ower 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 bila yers consisting of glass plates of different thicknesses d bonded to polyca rbonate substrates are used as an illustrative case study. Controlled pre-a brasion flaws are introduced into the lower glass surfaces before joining i nto the bilayer configuration, to enable a priori characterization of distr ibution parameters by image analysis. Finite element modelling is used to d etermine 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)proportional tod(2), relation for designing ceramic coatings fo r failure resistance are considered. (C) 2001 Acta Materialia Inc. publishe d by Elsevier Science Ltd. All rights reserved.