When hard rough surfaces slide repeatedly on softer half-spaces, systems of protective residual stresses may be developed in the near surface layers of the softer material which enable loads sufficiently large to cause plastic deformation in the early cycles of loading to be accommodated purely elastically in the later stages of component life. This is the process of shakedown and limits on the intensity of the allowable Hertzian pressures consistent with the eventual cessation of plastic deformation for uniform half-spaces are now well established. In this paper, we produce shakedown maps for coated or treated surfaces, choosing principally to carry out the numerical calculations on a system which models the behavior of ceramic coatings on steel substrates. In addition to the relative hardnesses of coating and the substrate, important system parameters are shown to be the normalized thickness of the coating and the strength or integrity of the bond at the interface between the coating and substrate. It is quite possible for the production of a coating of less than the critical thickness, or one displaying poor adhesion, to reduce the shakedown performance to lower values than would be the case for an unprotected surface. Design curves are produced which illustrate how the improvement in shakedown performance of such coated surfaces varies with the normalized depth of coating and the strength of the interlayer bond.

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