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The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed on three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained. I. INTRODUCTION

In recent studies, interest has been intensifying in the development of indentation-based methods to extract material elastic-plastic properties. In those studies, the elastic-Hollomon power-law hardening hypothesis was generally adopted, in which the uniaxial true stress-true strain (s
e) curves of materials are assumed to be expressible in the form
s ¼ Ee; for e  ey ; ð1Þ n s ¼ Ee1
n e ; for e  ey y where E is the elastic modulus, sy is the yield stress, n is the strain-hardening exponent, and ey is equal to the ratio of yield stress to elastic modulus. This material model has also been used in the present study, and the indenter was assumed to be rigid. In recent years, some investigations have shown that the stress-strain curve cannot be uniquely determined from loading and unloading curve produced by a single sharptipped indenter.1,2 Subsequently, several methods using multiple sharp-tipped indenters have been developed to extract plastic properties,3–8 although these methods still present a degree of inconvenience when operating with these indenters. In changing to spherical indentation, various authors have demonstrated that, by analyzing the force-depth curves, it is possible to determine material plastic properties.9–24 However, most of these proposed a)

Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0108 J. Mater. Res., Vol. 24, No. 3, Mar 2009

methods depend on estimates of the contact area under the spherical indenter tip,9–19 the estimates being difficult to obtain especially when “piling-up” occurs. For some methods, additional problems are created by repetitive loading and unloading, such as the method proposed by Kucharski and Mroz17 and that by Huber and Tsakmkis.23 Later, the work of Nayebi et al.24 demonstrated the feasibility in determining plastic properties by using a single spherical indentation curve, but it is only applicable to steels. In a recent study, by extending the representative strain (a