Volumes sampled for hardness and for modulus of elasticity during nanoindentation testing
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In this article, the sizes of the volumes sampled by nanoindentation tests for hardness and modulus measurements are studied using finite element simulations. The zones of influence for hardness and modulus in single-phase systems are determined by modeling a hemispherical particle in a matrix, with properties close to those of each other, and monitoring the deviation of the measured values from those of the particle. It is found that, for hardness testing of elastic-perfectly plastic materials, the intrinsic hardness of the particle is measured as long as the plastic region is still within the particle, i.e., the contact radius is one half or less of the particle radius. Thus, in a hardness test of a single-phase material, all of the plastically deforming material, and only the plastically deforming material, contributes to the hardness measured. In contrast, the zone influencing the modulus is not restricted to a specific volume near the indenter. The modulus measured from the elastic response at the indentation point is dependent upon the entire specimen. A relationship is developed to describe the observed behavior of the measured modulus, that holds true for both sink-in and pile-up material behavior and for different indenter cone angles.
I. INTRODUCTION
The raw data from a quasistatic nanoindentation test consist of continuous load versus displacement data obtained during the loading of an indenter with known geometry into a specimen, followed by data obtained during unloading. Oliver and Pharr1 applied Sneddon’s solution for elastic indentation to analyze the initial portion of the unloading process and developed a relation between the slope of the unloading curve and the area of contact. This enabled measurement of the hardness and the elastic modulus of specimens by nanoindentation. When indenting into a homogeneous bulk of material with a sharp pyramidal indenter, it is expected that both the hardness and modulus would be independent of the depth of penetration; however, if the sample were not a semi-infinite, homogeneous, isotropic, scale-independent continuum with uniform mechanical properties, the measured properties would be a function of depth of penetration, as observed in nanoindentation on thin film systems. There are numerous articles that address the mechanics of nanoindentation on thin films. For measurement of the hardness of thin films, the ‘10% rule’ is typically used, i.e., the maximum depth of penetration is kept below 10% of the thickness of the film; however, “for measurement of elastic modulus, influence from the substrate is unavoidable”.2 Lichinchi et al.3 carried out 3D simulation of nanoindentation of hard films a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2012.107 J. Mater. Res., Vol. 27, No. 12, Jun 28, 2012
on a soft substrate using a Berkovich indenter. They concluded for the titanium nitride-coated high speed steels (TiN/HSS) system, the critical depth at which the substrate begins to deform is 15% of the thickness of the film. Their
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