Predictive model to estimate the stress–strain curves of bulk metals using nanoindentation

Many studies have shown that finite element modeling (FEM) can be used to fit experimental load–displacement data from nanoindentation tests. Most of the experimental data are obtained with sharp indenters. Compared to the spherical case, sharp tips do not directly allow the behavior of tested materials to be deduced because these produce a nominally-constant plastic strain impression. The aim of this work is to construct with FEM an equivalent stress–strain response of a material from a nanoindentation test, done with a pyramidal indenter. The procedure is based on two equations which link the parameters extracted from the experimental load–displacement curve with material parameters, such as Young's modulus E, yield stress Y 0 and tangent modulus E T. We have already tested successfully the relations on well-known pure metallic surfaces. However, the load–displacement curve obtained using conical or pyramidal indenters cannot uniquely determine the stress–strain relationship of the indented material. The non-uniqueness of the solution is due to the existence of a characteristic point ( ε c, σ c); for a given elastic modulus, all bilinear stress–strain curves that exhibit the same true stress σ c at the specific true strain ε C lead to the same loading and unloading indentation curve. We show that the true strain ε c is constant for all tested materials (Fe, Zn, Cu, Ni), with an average value of 4.7% for a conical indenter with a half-included angle θ=70.3°. The ratio σ c/ ε c is directly related to the elastic modulus of the indented material and the tip geometry.