Limiting shape of profiles in fretting wear

Fretting wear in the displacement- and load-controlled settings is considered. The axisymmetric wear contact problem with stick and slip zones is studied under the assumption that the contacting bodies are elastically similar and their stress-strain states can be modeled by half-space approximations. It is shown that in the presence of a stick zone, the worn shape of profiles in contact tends to some limiting shape which is determined solely by the solution of a certain frictionless normal contact problem. In the both cases, it has been proved that the value of the limiting stick-zone radius corresponds to that of the initial stick zone, and the limiting shape of profiles is obtained in a closed form involving one quadrature. The novelty of this work is in study of the limiting shapes in load controlled fretting wear situations.