A Fractional Time-Derivative Model for Severe Wear: Hypothesis and Implications

Based on the example of wear of polymers, which exhibit a power-law time variation of the wear loss under constant loading conditions, a fractional time-derivative wear equation has been introduced. The wear contact problem with a fixed contact zone is solved using the known method of separation of spatial and time variables. It is shown that during the wear process, the contact pressure approaches a uniform distribution over the contact area, which is termed as a quasi-steady-state solution, since the mean volumetric wear rate does not tend to become constant. It is of interest that the contact pressure variation displays a decaying oscillatory nature in the case of severe wear, when the mean volumetric wear rate increases with time.