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.

Automated summary

The study conducted systematic finite element analysis of conical indentation in various isotropic elastic-plastic bulk solids, and found a linear relationship between the indentation hardness-to-reduced elastic modulus ratio and the elastic-to-total strain energy ratio, with the proportionality constant mainly influenced by the material's Poisson's ratio and cone semi-angle. Analytical equations were proposed to calculate the hardness and elastic modulus parameters independently of the indenter contact area, offering a potential solution to simplify data analysis and reduce uncertainties associated with plastic deformation phenomena.