Matching the slip condition at two types of contact

This paper develops a methodology to match the contact edge conditions between a plane-receded contact and a Hertzian contact, under oscillatory loading. This provides a route by which the edge conditions in a complicated contact configuration may be reproduced in a standard Hertzian experiment. A receded contact is formed by pressing an elastic layer against an elastically similar half-plane and then subjecting it to small fluctuations of load. From this analysis, we can describe the stress state at the contact edges in terms of stress intensity factors. By matching these descriptions to a Hertzian contact, we reproduce the leading near-edge stress and slip descriptors of the receded contact. The method provides an edge-equivalent configuration for subsequent fretting fatigue experiments. The advantage of using the equivalent Hertzian geometry is that the same local edge quantities can be generated in a simpler, well-defined contact configuration, using at most a two-actuator test machine.