A model for compressive coating stresses in the scratch adhesion test

Despite the widespread use of the scratch adhesion test, there is no model available to determine the critical coating stress for initiating interfacial failure, so that ranking the coating–substrate adhesion of coated systems with different mechanical properties is impossible. In this study, a mathematical model is developed to calculate the distribution of compressive stresses in a thin coating induced by a scratch indenter. For ease of use in practice, a simple equation, σSm=0.15 (PcHf/H)0.5 Ef0.3 E0.2/R, is then derived from the model, where σSm is the critical mean compressive stress in the coating for interfacial failure, Pc is the critical normal load measured from the scratch adhesion test, Hf and Ef are the hardness and Youngʹs modulus of the coating, H and E are the hardness and Youngʹs modulus of the substrate, and R is the indenter radius. This equation is useful for ranking the coating–substrate adhesion of different coated systems, or, for estimating the critical mean coating stress for interfacial failure.