Analysis of the tip roundness effects on the micro- and macroindentation response of elastic-plastic materials
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work, the effects of indenter tip roundness on the load–depth indentation curves were analyzed using finite element modeling. The tip roundness level was studied based on the ratio between tip radius and maximum penetration depth (R/hmax), which varied from 0.02 to 1. The proportional curvature constant (C), the exponent of depth during loading (a), the initial unloading slope (S), the correction factor (b), the level of piling-up or sinking-in (hc/hmax), and the ratio hmax/hf are shown to be strongly influenced by the ratio R/hmax. The hardness (H) was found to be independent of R/hmax in the range studied. The Oliver and Pharr method was successful in following the variation of hc/hmax with the ratio R/hmax through the variation of S with the ratio R/hmax. However, this work confirmed the differences between the hardness values calculated using the Oliver–Pharr method and those obtained directly from finite element calculations; differences which derive from the error in area calculation that occurs when given combinations of indented material properties are present. The ratio of plastic work to total work (Wp/Wt) was found to be independent of the ratio R/hmax, which demonstrates that the methods for the calculation of mechanical properties based on the indentation energy are potentially not susceptible to errors caused by tip roundness. I. INTRODUCTION
The instrumented indentation technique (IIT), frequently called nanoindentation, is today one of the most commonly used techniques to measure mechanical properties of films and small volumes. The IIT uses high-resolution instrumentation for control and measurement of loads and depths of indenter penetration, when it is applied to and withdrawn from the studied material, in a cycle of loading and unloading. These tests are usually conducted with indenters that have deviations from the ideal geometry, because of manufacturing tolerances and wearing off due to excessive use. Therefore, many works have focused on the calibration of area functions to determine the precise geometry of the indenters.1–3 These geometrical deviations seriously affect the values of hardness when measurements are conducted at penetration depths with magnitude similar to the indenter radius.4–6 In these cases, the changes in the shape of the loading curve can also be confused with those caused by the material work hardening,7 which leads to errors in the calculation of the work-hardening coefficient. Furthermore, significant changes on the correction factor b,
II. INDENTATION VARIABLES
a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0078
Figure 1 shows a typical curve of load as a function of penetration depth (P–h), obtained during instrumented
J. Mater. Res., Vol. 24, No. 3, Mar 2009
http://journals.cambridge.org
used to adjust Sneddon’s equations,8–12 have been recently observed due to indenter tip roundness. Therefore, indenter tip radius may affect not only hardness and elastic modulus calculations, but also other variables of
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