Limits of using bilinear stress–strain curve for finite element modeling of nanoindentation response on bulk materials

Abstract For 10 years, finite element modeling (FEM) has been widely used to simulate elastic and plastic deformations beneath a pointed indenter. Hardness measurement with a sharp pyramidal indenter, such as Berkovich or Vickers, is one of the most complex mechanical problems. This is due to the 3D dimensional phenomenon associated with elastic and plastic deformations, with large strain field. Nowadays FEM is used to extract the true hardness of thin coatings, from the composite hardness measurements. The first step consists in assuming that the film and substrate behavior can be modeled with a bilinear law. Two parameters for the layer are extracted from the simulation fit of experimental load displacement curves: the yield strength, Y 0 , at the plastic strain of 0.2% and Young's modulus, E . The aim of this work is to show on bulk pure metals the limits of the bilinear model. We show that the bilinear model does not define correctly the first step of strain hardening, which results in an overestimation of the yield stress or one need to adjust the target modulus at each indentation depth. Moreover we prove the strong influence of the indenter tip on the load–displacement curve. Finally, we propose a method to determine the tip radius, R , of the equivalent conical indenter used for FEM, to approximate the real Berkovich indenter geometry.