Modelling the hardness response of coated systems: the plate bending approach

In order to design the hard coating best suited to engineer the surface of a given substrate for a particular application, it is important that we have a clear picture of the mechanisms by which thin hard coated systems work. In this paper we describe a quantitative model designed to explore the increase in systems' hardness attributable to stresses created on the coating by the upthrust of substrate. material flowing plastically in response to indentation. Thus the model considers how the upwelling of displaced substrate material creates an upward pressure on the coating inducing elastic flexure which, in turn, resists the substrate deformation. The influence of this flexure has been investigated using a combination of existing analytical solutions (e.g. plate theory) to determine the overall effect on the indentation response of coated systems. The resulting model is critically compared with previous work. Experimental verification is provided by diverse experimental data from indentation tests on thin (1-24 μm) coatings of TiN and Cr on various metal substrates, sugar on chocolate substrates and other results drawn from the literature. The model helps to identify Eh³/d³H₀ as a dimensionless parameter which provides a means of condensing all available data onto a single "master" curve. Further developments are discussed.