A fracture toughness model for brittle coating on ductile substrate under indentation loading

This paper presents an analytical fracture toughness model for brittle coating/ductile substrate systems. The model considers a well-developed radial/median crack of semi-elliptical shape in proximity of the coating/substrate interface. It incorporates three critical factors to correct Lawn et al.’s formalism for monolithic materials: (i) an elliptical crack shape factor introduced by adopting Borodachev’s solution for an elliptical crack under a concentrated force at the crack center, which represents the residual plastic component due to expansion of the plastic zone under indentation; (ii) an interface correction factor obtained by analyzing Noda et al.’s results for an elliptical crack near a bi-material interface, which expresses explicitly its dependence on the distance ratio, h/a, and Young’s modulus ratio, Es/Ec, and (iii) the composite system hardness incorporated in the formula to take into account the influence of the substrate material. Overall, the model shows a non-linear relationship between the radial crack length, c3/2, and indentation load, P, for brittle coating on ductile substrate systems. A series of indentation experiments have been carried out on a WC/10Co/4Cr coating/1080 low carbon steel substrate system to validate the model.