Instrumented indentation methods, which provide a continuous record of the variation of indentation load, P, as a function of the depth of penetration, h, into the indented specimen, have been the topics of considerable attention in recent years. Such interest can be attributed to the following possible applications of the methods. (1) Properties such as Young’s modulus, yield strength, and strain hardening exponent [1], as well as fracture toughness (e.g. [2]) of materials can be estimated by recourse to continuous indentation. (2) The magnitude and sign of any preexisting residual stresses can be assessed, in some cases, from indentation of surfaces [3]. (3) To the extent that continuum analyses adequately characterize indentation, the mechanical properties and residual stresses can be probed at different size scales by the appropriate choice of commercially available instrumentation, as well as indenter load, size and shape. (4) In materials with spatially varying composition, microstructure or dislocation density, the “inverse problem” of the determination of gradients in Young’s modulus and yield strength can be accomplished, in some cases, by means of instrumented indentation (e.g. [4,5]). Most of these applications of instrumented indentation are limited, however, by complications in clearly interpreting the indentation results. Such a complication arises from the “pile-up” or “sink-in” of the material around the indenter, which is primarily affected by the plastic properties of the material [6]. In a low-strain-hardening alloy, plastically displaced material tends to flow up to (and pile-up against) the faces of the indenter due to the incompressibility of plastic deformation. The result is a “barrel-shaped” impression due to pile-up around the sharp polygonal indenter, as shown in Fig. 1(a). On the other hand, for high-strain-hardening materials, the plastically deformed region is pushed out from the indenter with the imprint sinking below the initial surface level. The result is a “pin-cushionlike” impression around the sharp indenter, as shown in Fig. 1(b). Methods which properly account for pile-up or sink-in around the indenter are essential for the interpretation of the plastic properties of materials by recourse to instrumented indentation. As a consequence of pile-up or sink-in, large differences may arise between the true contact area (which is influenced by the pile-up and sink-in of the materials and which is often difficult to assess in-situ during indentation) and the apparent contact area which is usually observed after indentation. A knowledge of the relationship between the indentation load and the true (projected) contact area, however, is essential to extract the mechanical properties from instrumented indentation. This difficulty can be overcome if explicit expressions, relating the true contact area A and the depth of penetration of the indenter h into the material being tested, are known a priori for different indenter geometries. Pergamon Scripta Materialia, Vol. 40, No. 10, pp. 1191–1198, 1999 Elsevier Science Ltd Copyright © 1999 Acta Metallurgica Inc. Printed in the USA.
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