Further investigation on the definition of the representative strain in conical indentation
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Further investigation on the definition of the representative strain in conical indentation was performed in this work. In particular, the representative strains proposed in the work of Cao et al. [J. Mater. Res. 20, 1194 (2005)] and Ogasawara et al. [J. Mater. Res. 20, 2225 (2005)] were discussed in detail. For the method using the energy-based representative strain [Cao et al., J. Mater. Res. 20, 1194 (2005)], it is shown that it can be extended to a wider range of material properties (from nearly fully plastic materials to highly elastic materials). For the stress-state-based definition of the representative strain, we found, in contrast with the results reported in the work of Ogasawara et al. [J. Mater. Res. 20, 2225 (2005)], that similar to the constant representative strain reported by Dao et al. [Acta Mater. 49, 3899 (2001)], it works well only for a limited range of engineering materials. Based on this premise, novel definitions of the representative strain, which can lead to a one-to-one relationship with high level of accuracy between the reduced Young’s modulus, the indentation loading curvature, and the representative stress are further presented. Detailed numerical analysis performed on nine kinds of engineering materials verified the effectiveness of the proposed representative strains and corresponding dimensionless functions. Experimental verification using the data for the ultrafine crystalline Ni further showed that the results reported in this paper have the potential to be applied in practice.
I. INTRODUCTION
Indentation tests have been applied to determine the hardness of materials since the early 1900s.1 During the past three decades, instrumented indentation tests have been developed and are widely used at present to characterize material properties, such as hardness and Young’s modulus,2,3 on a small scale. In recent years, interest has been mounting in the development of systematic methods to extract the local stress–strain relationship of materials from indentation tests. However, the analysis of the indentation response to obtain the mechanical properties, especially plastic properties of elastoplastic materials, is not an easy task. The application of the commercial finite element software, e.g., ABAQUS,4 and the introduction of mathematical skills, e.g., dimensional analysis 5,6 and neural networks method,7–9 provide feasible ways to develop systematic methods to determine elastoplastic properties of materials from indentation tests. Sometimes the application of the concept of the representative strain can significantly
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Address all correspondence to this author. e-mail: [email protected] or [email protected] DOI: 10.1557/JMR.2006.0224 1810
J. Mater. Res., Vol. 21, No. 7, Jul 2006
simplify the analysis of the indentation response and is also the main concern of the present work. The definition of the representative strain in indentation dates back to the work of Tabor in 1950s.10 However, to the authors’ best knowledge, up to the present, this still is a fundamental issue. I
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