Mechanical Properties of Nanometre Volumes of Material: use of the Elastic Response of Small Area Indentations
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MECHANICAL PROPERTIES OF NANOMETRE VOLUMES OF MATERIAL: USE OF THE ELASTIC RESPONSE OF SMALL AREA INDENTATIONS
J.B.PETHICA* AND W.C.OLIVER**
*Department of Metallurgy and Science of Materials, Parks Road, Oxford OX1 3PH, England **Oak Ridge National Laboratory, P.O.Box M, Oak Ridge, TN 37832
ABSTRACT A new, differential method for determining the stiffness of a sub-micron indentation
contact area is presented. This allows measurement of elastic modulus as well as plastic hardness, continuously during a single indentation, and without the need for discrete unloading cycles. Some of the new experiments that become possible with this technique, especially at the
nanometre scale, are described. We show quantitatively that electropolished tungsten reproducibly exhibits the ideal theoretical lattice strength at small indentation loads.
INTRODUCTION In recent years there has been a considerable increase ininterest inthe mechanical properties of small volumes of materials. This is motivated partly by interest ininherently small structures such as thin films, interfaces and composites, and partly by newly available methods of directly measuring local mechanical properties. Prominent amongst these is sub-micron indentation. By sensing the depth of indentation as a function of the applied load, it has been shown that both plastic hardness and elastic modulus of volumes a few hundred nm across can be obtained, [1,2,3,4] There is no need to go through the difficult process of imaging the nanometre scale indentations. In this paper we present a significant further development inthe scale at which these tests can be made, and a means of further simplifying the calculation of hardness. We show that at the smallest scale, inherent atomic lattice properties can be observed. Two problems have to date made it difficult to use depth sensing tests at extremely low loads and depths. The fLrst is the risk of thermal drift in the apparatus, which being unknown, gives uncertainty in the plastic depth. The second is the accuracy with which the shape of the indenter is known, which in turn limits the knowledge of the true contact area. The key to reducing these problems lies in determining the stiffness (or spring constant) of the contact between indenter and surface. For an indenter load P and displacement x of indenter normal to the surface, the stiffness S = DP/Dx. The utility of S comes from the fact that for a very wide range of stress distributions under the indenter, S is given by [5,6]
Mat. Res. Soc. Symp. Proc. Vol. 130.
1989 Materials Research Society
14
S
=
A E 'Contactaa
where
1 E
l
(1)
+ E2
V2 2
E2
E being the Young's modulus and v the Poisson's ratio of the indenter and surface (suffices 1 & 2 respectively). The constant A varies at most between 2/(4Jc) for a flat punch or a spherical (Hertzian) contact, and (47r)/2 for some intermediate stress fields. It has been noted elsewhere [1,3] that S is often constant for a significant part of the unloading process; that is, the indenter plus its 'cap' of plasticall
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