Determination of mechanical properties by nanoindentation independently of indentation depth measurement
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Guillaume Kermouche Ecole Nationale d’Ingénieurs de Saint-Etienne, Université de Lyon, Laboratoire de Tribologie et Dynamique des Systèmes, UMR 5513 CNRS/ECL/ENISE, 42000 Saint-Etienne, France
Sandrine Bec and Jean-Luc Loubet Ecole Centrale de Lyon, Université de Lyon, Laboratoire de Tribologie et Dynamique des Systèmes, UMR 5513 CNRS/ECL/ENISE, 69134 Ecully, France (Received 20 April 2012; accepted 18 July 2012)
A new technique based on the detection of the amplitude of the second harmonic was described in a previous paper. To compute the elastic modulus and the hardness of materials, the technique uses only the derivative of the contact radius with respect to the indentation depth. For this reason, this method is applicable only to homogeneous materials. In this paper, the method is extended to any materials with constant Young modulus. The indentation depth value is not needed at all, thus eliminating uncertainties related to the displacement measurement, which are very influent at small penetration depths. Furthermore, we also explain how to compute the indentation depth from the detection of the amplitude of the second harmonic. This new measurement technique was tested on three samples: fused silica, Poly(methyl methacrylate) (PMMA), and calcite, which is expected to exhibit indentation size effect. The obtained results show that mechanical properties and the indentation depth can be determined with good accuracy for penetration depths between 25 and 100 nm using this method.
I. INTRODUCTION
The nanoindentation technique is widely used to measure the hardness H and the reduced elastic modulus E9* of materials at the nanometer scale. The first hardness tests were realized by Brinell, who used a hard steel sphere to indent samples (see Tabor1). Other hardness tests were developed later, such as the Vickers test or the Knoop test, which differ in the indenter geometry.2 To measure hardness, the load and the projected contact area have to be known. For these tests, the load is imposed, and the contact area is measured after the test with an optical microscope. At a smaller scale, optical measurement of the contact area is not precise enough, so instrumented indentation testing has been developed. With instrumented nanoindentation testing, the load P and the displacement hm are measured continuously during the test. With this technique, which is based on load and displacement measurement, Bulychev et al.3 showed that the reduced elastic modulus of the material can be obtained from the unloading curve. A great number of authors have contributed to a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2012.261 J. Mater. Res., Vol. 27, No. 19, Oct 14, 2012
the understanding of the loading–unloading curves with new methods of analysis.4–10 The past 20 years or so have seen the development of a dynamic technique called Continuous Stiffness Measurement (CSM).6 The principle is to superimpose a small oscillation amplitude on the displacement (or load) signal and to measur
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