The deformation of the substrate during indentation into superhard coatings: Bückle's rule revised

• Deformation of substrate under superhard coatings studied by non-linear finite elements modeling
• The indentation depth must be much smaller than 10% of coatings' thickness.
• Compound hardness of superhard coatings and soft substrate determined
• Good agreement with experimental data found

We use non-linear finite element modeling (FEM) to study the deformation of softer substrate during the indentation into hard and superhard coatings, and its influence on the measured compound hardness of the system coating-substrate. It is shown that the “Bückle rule”, according to which correct hardness of hard coatings on a softer substrate is obtained when the indentation depth does not exceed 10% of the coating thickness, does not apply generally. Depending on the hardness of the coating and of the substrate, the ratio of the thickness of the coatings to the indentation depth, where the deformation of the substrate may be neglected, increases with increasing hardness of the coatings much more than what would be expected from Bückle's rule. In the case of superhard coatings on steel, the deformation of the substrate occurs already for indentation depth of less than 3% of the coating thickness. We present quantitative data which allow one to estimate the minimum thickness needed for correct measurement of the hardness of superhard coatings on substrates made of steel, silicon and cemented carbide. When correct hardness of ultrahard (H ≥ 80 GPa) coating should be measured without substrate deformation at high load, the coatings would have to be tens of micrometers thick. It is experimentally very difficult or, because of biaxial compressive stress in the coatings even impossible to prepare such coatings. Therefore we present non-linear FEM calculations of the compound hardness of the ultrahard coatings on softer substrates vs. maximum applied load up to 1000 mN to show a very good agreement with the previously reported experimental data.