Self-similarity in abrasiveness of hard carbon-containing coatings

The abrasiveness of hard carbon-containing thin films such as diamond-like carbon (DLC) and boron carbide (nominally B4C) towards steel is considered here. First, a remarkably simple experimentally observed power-law relationship between the abrasion rate of the coatings and the number of cycles is described. This relationship remains valid over at least 4 orders of magnitude of the number of cycles, with very little experimental scatter. Then possible models of wear are discussed. It is assumed that the dominant mechanism of steel wear is its mechanical abrasion by nano-scale asperities on the coating that have relatively large attack angles, i.e. by the so-called sharp asperities. Wear of coating is assumed to be mainly due to physical/chemical processes. Finally, models of the abrasion process for two basic cases are presented, namely a coated ball on a flat steel disk and a steel ball on a coated flat disk. The nominal contact region can be considered as constant in the former case, while in the latter case, the size of the region may be enlarged due to wear of the steel. These models of the abrasion process are based on the assumption of self-similar changes of the distribution function characterizing the statistical properties of patterns of scattered surface sharp asperities. It is shown that the power-law relationship for abrasion rate follows from the models