Methods of correction for analysis of depth-sensing indentation test data for spherical indenters
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Depth-sensing indentation testing has proven extremely useful in the determination of mechanical properties of thin films and small volumes of material. However, the validity of the results obtained depend largely on the corrections made to the experimentally recorded data to account for initial penetration depth, nonuniformities in indenter shape, and compliance of the loading frame. The present work examines each of these issues and presents potential methods of correction for them. The present work also highlights limitations inherent in the data analysis methods and the significance of these in terms of experimental test parameters.
I. INTRODUCTION
Submicron indentation tests using either spherical or pyramidal indenters have proven extremely useful in the determination of mechanical properties of thin films and small volumes of material.1–3 Experimental readings of indenter load and depth of penetration given an indirect measure of the area of contact from which the mean contact pressure, and thus hardness, may be estimated. Elastic modulus of the test specimen may also be obtained from the elastic unloading portion of the test. The test procedure, for both spheres and pyramidal indenters, usually involves an elastic–plastic loading sequence followed by an unloading. Doerner and Nix1 observed that, for tests with a Berkovich indenter, the initial unloading curve is linear for a wide range of test materials, which is similar to that which would be observed for the elastic unloading of a cylindrical punch. Oliver and Pharr2 extended this treatment to account for observed changes in the area of contact during initial unloading by treating the elastic unloading in terms of both a cone and a paraboloid of revolution. Field and Swain3 developed a similar treatment for the special case of contact with spherical indenters. All of these analysis methods assume that the unloading portion of the indentation test is elastic, and they thus rely on the so-called “Hertz” equations4 that describe the contact of elastic solids of revolution.
a)
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J. Mater. Res., Vol. 16, No. 8, Aug 2001 Downloaded: 14 Mar 2015
Hertz showed that the relationship between the radius of the circle of contact and the indenter load for contacting spheres is given by a3 =
3 PR 4E*
.
(1)
E* is the combined modulus of the indenter and specimen, and R is the relative radius of curvature of the contacting surfaces. The distance of mutual approach between the indenter and specimen is given by ␦=
a2 . R
(2)
For the special case of a perfectly rigid indenter, this is also the value of the depth of penetration beneath the specimen free surface, he in Fig. 1. Substituting Eq. (2) into Eq. (1) and using he for ␦, we obtain E* =
3 P . 4 ahe
(3)
In previous work,5 it was shown that the specimen undergoes identical deformations whether loaded with an elastic indenter of radius R or a perfectly rigid indenter of a larger radius den
