Compensating for elastic deformation of the indenter in hardness tests of very hard materials
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Compensating for elastic deformation of the indenter in hardness tests of very hard materials Roger Yu Lo and David B. Bogya) Computer Mechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, California 94720 (Received 26 August 1998; accepted 5 March 1999)
The current method of analysis for hardness measurements by indentation is examined. Although the method is based on Sneddon’s solution for an elastic stress field within a homogeneous half space indented by an elastically deformable indenter, it implicitly assumes a fixed indenter geometry. Therefore, if indentations are made on materials whose hardness or elastic modulus are close to those of the indenter, this method underestimates the contact area and, thus, overestimates the hardness and modulus values of the indented materials. A new method, based on the Hertz contact theory, is proposed that accounts for the elastic deformation of the indenter and provides a simple way to calculate the tip radius. The restrictions of this method are also indicated and discussed. Finally, the hardness and modulus for two recently developed films are measured by this method, and the results are compared with published finite element method (FEM) results.
I. INTRODUCTION
The demand for higher areal storage density for disk drives has driven the development of thinner and harder protective films for disks and sliders. Nanoindentation tests have been widely adopted to study the mechanical properties, such as hardness and modulus of these films. The modified Sneddon solution for an elastic field within a homogeneous half space indented by a solid of revolution is usually used to analyze the load/displacement curves obtained from experiments. Indenters are implicitly treated as rigid bodies by using a fixed tip shape function. (This point will be explained in detail later in this section.) When indenting on materials with hardnesses of 50 GPa or lower a diamond indenter can be treated as a rigid body and no appreciable errors will be introduced. However, if indentations are made on much harder materials such as, for example, the recently developed cathodic-arc amorphous carbon films, the diamond indenter deforms during the indentation processes. As the demand for higher performance protective films for disk drives continues, even harder materials will be developed. The current method of analysis will then fail to predict the right hardness and modulus values. A new technique is needed to compensate for the diamond indenter deformation during indentation. The new method proposed here is based on the Hertz contact theory for elastic solids. The hardness values for the cathodic-arc amorphous carbon films calculated by this method are compared with the values predicted a)
Address all correspondence to this author. Current address: 5146 Etcheverry Hall, Berkeley, California 94720. e-mail: [email protected]
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http://journals.cambridge.org
J. Mater. Res., Vol. 14, No. 6, Jun 1999
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