Fracture mechanics analysis of transverse cracks in thin coatings under spherical indentation

The competition between transverse cracks originating from the surface and sub-surface of a thin, hard coating bonded by a delamination resistant adhesive to a polycarbonate substrate due to spherical indentation is investigated in real-time as a function of coating thickness and indenter radius. Fine (Y-TZP) and intermediate (alumina) size grain polycrystalline ceramics as well as pre-abraded amorphous glass are used for the coating. As the coating thickness is reduced, the familiar star-shape sub-surface damage is completely suppressed, leaving the surface ring crack to dominate the fracture. In the transition range, the sub-surface damage occurs as a set of off-axis circumferential cracks. This observation provides the basis for our simplified treatment of the sub-surface damage as a cylindrical crack. A linear fracture mechanics approach is used to predict the onset of transverse fracture in the coating. In consistency with the tests, the damage on the surface as well as the sub-surface of the coating is assumed as a cylindrical crack. The interactive effect of the coating thickness, indenter radius, crack length and contact radius is explored using a large-strain FEM contact code. In consistency with its polycrystalline nature, the coating is assumed to contain a distribution of cracks. The least fracture load among all permissible crack lengths that is obtained from the analysis is taken as the critical load. The numerical predictions from this analysis compare well with the tests results. The analysis also helps identify the applicability range of a relatively simple critical stress criterion in terms of the system parameters.