A numerical approach to evaluation of elastic modulus using conical indenter with finite tip radius

Geometrical self-similarity is a feature of mathematically sharp indenters such as conical and Berkovich indenters. However, self-similarity is considered inappropriate for practical use because of inevitable indenter tip blunting. In this study, we analyze the load–depth curves of conical indenters with various tip radii via finite element analyses. Based on the numerical data, we propose a method of restoring the Kick’s law coefficient C of finite tip-radius indenter to that of zero tip-radius indenter, thereby retaining the self-similarity of the sharp indenter. We then regress the unloading slope for the evaluation of elastic modulus in several ways. Finally, we establish a method to evaluate elastic modulus, which successfully provides the value of the elastic modulus with a maximum error of less than 5%, regardless of tip radius and material properties of both indenter and specimen.