The mechanics of elastic contact with film-covered surfaces

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Abstract
Solutions to the Hertz problem, which predict the contact area between cylindrical or spherical bodies elastically loaded against one another, have frequently been applied to situations in which one of the bodies is coated with a thin film of different material, notably in the analysis of bearings lubricated with thin solid films. In reality the film may often exert a profound influence on the contact area and the Hertzian assumption will be inappropriate. The present work offers approximate analytical solutions for film‐coated cylindrical and spherical contacts, that are valid provided the contact dimensions are large compared to the film thickness and provided also that the Young's modulus of the film material is less than that of the surfaces with which it interacts. It is hoped that the expressions derived here will prove to be particularly useful in the study of lubricant films deposited by such processes as sputtering and ion plating, where a knowledge of the true area of contact is a crucial factor in the understanding of the mechanics involved.

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