A finite element analysis of conical indentation in elastic-plastic materials: On strain energy based strategies for an area-independent determination of solids mechanical properties

A systematic finite element analysis (FEA) of conical indentation in different isotropic elastic-plastic bulk solids was realized. In particular, the relation between the indentation Hardness (H)-to-Reduced Elastic Modulus (E-r) ratio and the Elastic (U-e)-to-Total (U-t) strain energy ratio was studied. Results showed a linear dependency between both ratios as predicted by analytical studies, being the proportionality constant mainly dependent on cone semi-angle (theta) and material Poisson's ratio (nu). A well-agreement with experimental data reported in the literature was observed for a wide variety of materials. By a simple analysis of the Oliver & Pharr method and our results, we proposed two analytical equations to calculate the H and E-r parameters overcoming the indenter contact area (A(C)) dependence in indentation data analysis. A(C)-independent analytical procedures can become interesting to simplify the data analysis and overcome considerable uncertainties due to possible pile-up effects associated with different plastic deformation phenomena.