Fracture mode transitions in brittle coatings on compliant substrates as a function of thickness

The fundamentally changing nature of fracture in brittle coatings on compliant substrates with diminishing coating thickness is examined. Attention is focused on cracking induced by concentrated loading with a spherical indenter at the top surface. It is shown that the fracture mode undergoes transitions, from top-surface ring cracking around the contact (thick-coating region) to bottom-surface radial cracking at the lower ceramic surface (intermediate region) and, finally, back to surface ring cracking (thin-coating region). These transitions reflect a progressively changing stress field in the layer structures and highlight the differences in failure mechanism that may be anticipated at the large- and small-scale levels. Simple fracture relations are derived for each mode, expressing critical loads in terms of coating thickness relative to contact or sphere radius, coating strength and coating/substrate modulus mismatch. Data from finite element simulations and contact experiments on model ceramic/polymer bilayer systems are used to validate the basic elements of the analytical relations and to quantify deviations. Implications of the transitional behavior in relation to the strength of brittle coating/film systems are discussed.