Differential application of wear models to fractional thin films

Global application of bulk wear models, originally developed for monolithic bodies, to pre-deposited thin films and coatings can lead to the paradoxical prediction of wear removal rates exceeding the rate of film introduction into the tribological contact. A thin-film wear model is developed which resolves this paradox through differential wear model application, coupled with the fractional nature of such thin films which may exist as they are worn through and the corresponding fractional normal load that film supports. The model predicts the state of the wearing film as a function of position within the contact. A corresponding description of friction coefficient of contacts of such wearing fractional thin films is also developed, for purely sliding as well as combined rolling/sliding contacts. Furthermore, it is demonstrated that prediction of film state through the contact, from inlet to exit, enables subsequent prediction of the evolving global wear and friction behavior with time. The model is compared to examples of experimental friction data for thin films taken from the literature. The manuscript closes with a discussion of extension of the model to cases where such thin films are continuously replenished, such as in vapor phase lubrication.