Wear due to fatigue initiation

Persson and coauthors have recently proposed an extension of the Rabinowicz idea for fatigue wear at different scales of roughness, where Paris’ crack growth law is applied to ”potential” wear particles. However, Persson’s theory suffers from the fact that initial size of defects is unknown and fatigue life is not entirely due to propagation, so we investigate a different formulation, where a law for initiation of cracks is used for a specimen with initial roughness of engineering interest. We find that results (in particular dependence on amplitude of roughness, and on friction coefficient) are qualitatively similar to the original Persson and coworkers’ theory, but may differ substantially quantitatively. As the assumption of a constant fatigue threshold may be incorrect for short cracks, both fatigue limit and fatigue threshold are made dependent of crack size, using the Murakami formulation as one of the possible alternatives. This makes wear rate be sensitive to the fine scale details of the roughness spectrum, which has an effect on increasing wear rate and small particles emission. The model seems to have qualitative trends in agreement with experiments, but obviously wear is a very complex phenomenon and many factors may be not captured.