When a hard rough surface slides repeatedly on a softer half-space a s
ystem of protective residual stresses may be developed in the near sur
face layers of the softer material which enable loads sufficiently lar
ge to cause plastic deformation in the early cycles of loading to be a
ccommodated purely elastically in the later stages of the component li
fe. This is the process of shakedown and limits on the intensity of th
e allowable Hertzian pressures consistent with the eventual cessation
of plastic deformation for uniform half-spaces are now well establishe
d. Many practical techniques of surface engineering rely on the deposi
tion of a well-bonded hard coat on a softer substrate and, in this sit
uation, both the elastic and the plastic properties of the coat differ
from those of the underlying material; these differences present diff
iculties in formulating the corresponding shakedown limits for such co
ated systems. In addition to the relative hardness and stiffness of th
e coating compared to that of the substrate, important system paramete
rs are the thickness of the coating (in comparison to the characterist
ic dimension of surface roughness) the integrity of the bond between t
he coating and the substrate and the coefficient of friction between t
he coated component and the surface against which it slides. In this i
nvestigation these parameters have been varied in order to study their
effect on the resulting shakedown limits and the results of the study
are displayed in the form of a number of non-dimensional shakedown ma
ps.