In the friction of a hard coating the maximum tensile stress in the sliding direction generated at the friction surface is important for predicting crack propagation in the coating. The finite element method is employed to evaluate the stress field in the hard coating and the substrate under frictional loads, and the ratio between the values of maximum tensile stress and the maximum contact pressure is calculated under various contact conditions. Finally, a simple equation is introduced for the calculation of the maximum tensile stress at the friction surface. This equation is a function of friction coefficient, maximum contact pressure, coating thickness, contact width and elastic moduli of coating and substrate, and gives the value of the maximum tensile stress which is affected by the existence of the substrate.
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