A note on the crack analogue fretting fatigue model with varying normal load

The crack analogue model was developed to interpret various experimental observations of damage and cracking in fretting fatigue. This method assumes infinite friction at the interface and defines the oscillatory stress-intensity factor at the contact edge when the tangential load cyclically varies while the normal force is constant. However, practical engineering systems are subject to periodic loading in both the normal and shear directions, so that the contact area is not constant any more. Recently, Ciavarella and Berto suggested a crude extension to the crack analogue model in order to include the case of varying normal load, which is still not immediate to use since the singularities move in space and have no equivalent to fatigue from a crack. In this paper, we shall investigate the validity of the proposed model. For this, we shall establish an exact solution for a full stick contact problem with harmonic loading in normal and tangential directions. Here, this solution shows that there is a moving singularity at the edge of the contact area as unloading proceeds. The magnitude of the moving singularity depends on the tangential force difference between unloading and loading curve at constant normal force and the instantaneous value of the contact semi-width. Also, this solution shows that there is a logarithmic singularity which does not move.