Effect of penetration depth on indentation response of soft coatings on hard substrates: a finite element analysis

The nanoindentation process of a soft coating on a harder substrate has been simulated by the finite element method. The frequently used three-face Berkovich indenter was simulated by an axisymmetric conical indenter with the same projected area-depth function. The present paper discusses the critical indentation depth below which the substrate has negligible effect on the indentation response of layered systems. The influence of the yield strength ratio of the soft coating to the harder substrate and the indenter tip radius in the critical depth has been analysed. Two distinctly different relationships between the critical depth and the yield strength ratio of the coating to the substrate have been noted. In the yield strength ratio range of 0.2–0.8, the critical depth increases approximately linearly with decreasing yield strength ratio. When the yield strength ratio is below 0.2, an abrupt increase in the critical depth occurs. Further analysis reveals that these two different regimes are derived from the two dominant substrate effects on indentation response, i.e. the initiation and propagation of plastic deformation in the substrate, and the enhanced material pile-up around the indenter.