The effect of a thin compliant protective coating on Hertzian contact stresses

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Abstract
When a brittle material is loaded by a blunt indenter a Hertzian cone crack may form in its surface. This crack weakens the material and can lead to material removal. In many practical situations a thin compliant coating may be applied either to deliberately reduce this type of damage or for some other reason. The author models abrasion and impact on the coated system by the contact of a rigid sphere. The results of simple analyses for the stresses within the coating are used to determine how the tensile stresses in the surface of the material, which would lead to Hertzian fracture in the absence of the coating, are modified by the presence of the coating. The two extreme cases of rigid and zero adhesion of the coating to the substrate are directly compared. The stresses are most sensitive to the coating adhesion, Poisson's ratio and thickness while the modulus of the coating material is only of secondary importance. For optimum protection by the coating, it should be rigidly adhering to the substrate, that it should be nearly incompressible and that the coating thickness should be approximately 20% of the radius of the contact between the coating and the sphere. These criteria allow a protective coating to be designed using theoretical arguments rather than to be developed empirically.

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