3D versus 2D finite element simulation of the effect of surface roughness on nanoindentation of hard coatings

Indentation with a spherical indenter tip into CrN coatings with an arithmetic surface roughness (Ra) ranging between 2.6 and 11.1 nm is modelled with the finite element method. Results are compared for a 2D axisymmetric model (published earlier) and a true 3D model for three different coatings within that roughness range. Both models predict a significant underestimation of the evaluated Young's modulus due to the effect of surface roughness. They give comparable results for Ra < 3 nm, but differ considerably for higher roughness values. The axisymmetric setup of the 2D model leads to increased scatter of the load–displacement data and higher stiffness on average compared to the 3D model and therefore a 3D simulation seems preferable.