SHAKEDOWN LIMITS IN SLIDING CONTACTS ON A SURFACE-HARDENED HALF-SPACE

Most work on the mechanics of shakedown has been on half-spaces which have strength properties invariant with depth. In this paper we extend the shakedown analysis to a half-space whose surface has been heat-treated or case-hardened so that hardness and yield strength vary with depth. The results of the analysis show that the shakedown limit (i.e. the load that can be carried purely elastically in the steady state) is a function of the surface or case hardness, the core or bulk hardness and the depth of the hardened layer. As the case hardness increases, so there is improvement in the shakedown limit. Increasing the depth of hardening with respect to the size of a typical asperity contact has a similar effect. The analysis also indicates that as the thickness of the hardened case decreases, so finer surface finishes are needed to provide a given improvement in shakedown performance.