Power-law characteristics of damage and failure of ceramic coating systems under three-point bending

• The crack and damage evolution of nanostructured, conventional, thin, and thick ceramic coatings under in-situ three-point bending were statistically studied.
• An analytic model on damage and catastrophic failure of ceramic coatings based on the Taylor's expansion was developed.
• The experimental results are in agreement with the theoretical predictions, and the power law characteristics of damage of ceramic coatings are proposed.

Damage and failure of ceramic coatings bonded on alloy substrates was studied by observing crack evolution in the coating systems under in situ three-point bending tests with corresponding load–displacement curves. A damage and catastrophic failure model on the ceramic coatings was proposed based on our experimental results and the Taylor expansion of the controlling variable. The results indicate that the damage increases with increasing stress and obeys the power-law characteristics with the power exponent of 0.5, and the damage is 1 as the stress reaches the critical point corresponding to the failure of the coating systems. The damage rate increases rapidly when the stress is near the failure point and shows a power law singularity of − 0.5. The experimental results of thin, thick, nanostructured, and conventional micrometer-scale microstructured coatings are all in agreement with the predictions based on the model.