On the analysis of singular stress fields Part 2: Application to complete slipping contacts

Abstract

The stress state adjacent to the edge of a complete slipping contact has an implied elastic singularity. Using an asymptotic approach the order of this singularity, and hence the spatial distribution of the local stress field, may be found. The region over which it characterizes the full field solution is found by defining a generalized stress intensity factor K*. In practice, this requires a finite element (FE) analysis. However, the use of isoparametric elements leads to convergence problems which may be circumvented by using special singular elements which incorporate the required shape function. Here, these elements are applied to a complete contact problem for which there is an analytical solution, for comparison purposes, i.e. a rigid square-ended punch sliding along an elastic half-plane. It is shown that the singular elements are able to reproduce the singular field accurately, and that they significantly accelerate convergence when compared with a conventional mesh of isoparametric elements. Additionally, a comparison between the asymptotic and FE solutions reveals the domain over which the process (plastic) zone is controlled by the singular solution. The implications of the technique for defining the fretting fatigue strength of complete contacts will be discussed.