A new method for interpreting Vickers indentation measurements

Abstract

A new method for interpreting Vickers microindentation data is proposed, based on continuum mechanics and, more precisely, the Gradient Elasticity framework. The main feature is the elastic properties’ calculation from the initial (elastic) region of the load vs. depth indentation data, which makes the calculation independent of the maximum indentation depth. This approach deviates significantly from the semi-empirical method of Oliver and Pharr, which calculates the material properties (such as elastic modulus and hardness) from the elastic unloading region, with the calculated values of the elastic modulus and hardness being strongly dependent on the indentation depth and, therefore, giving rise to the so-called indentation size effect (ISE). The proposed framework considers the Vickers indentation as a compression test with a complex geometry, as the pyramidal indenter tip applies load to directions perpendicular to its four faces. An elastic displacement field is initially assumed following Boussinesq’s solution before an indent is made, while afterwards the displacement of the material in contact with the tip is assumed to follow the Vickers tip’s geometry. The respective von Mises equivalent strain calculated through a continuum mechanics approach can qualitatively capture thin film delamination micrographs and shear band formation, showing the potential of the present formulation to model such micro-deformation problems. The traction vector calculated on each of the four sides of the Vickers tip, leads to the generation of load-displacement data, which compare well with experimental indentation data, with the elastic properties (i.e. elastic modulus) thus calculated being in accordance with the corresponding literature values.