On determination of material parameters from loading and unloading responses in nanoindentation with a single sharp inde
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This paper quantitatively describes the loading-unloading response in nanoindentation with sharp indenters using scaling analyses and finite element simulations. Explicit forward and inverse scaling functions for an indentation unloading have been obtained and related to those functions for the loading response [L. Wang et al., J. Material Res. 20(4), 987–1001 (2005)]. The scaling functions have been obtained by fitting the large deformation finite element simulations and are valid from the elastic to the full plastic indentation regimes. Using the explicit forward functions for loading and unloading, full indentation responses for a wide range of materials can be obtained without use of finite element calculations. The corresponding inverse scaling functions allow one to obtain material properties from the indentation measurements. The relation between the work of indentation and the ratio between hardness and modulus has also been studied. Using these scaling functions, the issue of nonuniqueness of the determination of material modulus, yield stress, and strain-hardening exponent from nanoindentation measurements with a single sharp indenter has been further investigated. It is shown that a limited material parameter range in the elastoplastic regime can be defined where the material modulus, yield stress, and strain-hardening exponent may be determined from only one full indentation response. The error of such property determination from scattering in experimental measurements is determined.
I. INTRODUCTION
Instrumented micro- and nanoindentation has found widespread application in measurement of mechanical properties of materials on a small scale.1–5 Because of the very complex nature of the indentation process, numerical simulation is essential in relating material properties to measurable indentation parameters. Simulations of load-displacement indentation response during loading and unloading have been performed in several comprehensive studies using finite element analysis (FEA).6–11 To formulate general relations between measurable indentation and material parameters and to reduce the number of governing variables, a dimensional analysis has been applied to obtain scaling relations for conical indentation in elastoplastic solids.7,12–15 The scaling analysis has been extended to include the cone angle using similarity analysis.16
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2006.0130 J. Mater. Res., Vol. 21, No. 4, Apr 2006
Young’s modulus and indentation hardness are traditionally determined by inverse analysis of the indentation loading and unloading responses based on the elastic solution.1–3 These inverse methods usually misestimate the modulus because of material plasticity.8,17 To take into account the plastic behavior of materials, direct inversion of the FEA model by fitting the loading and unloading force-displacement nanoindentation responses has been proposed.6,9,18,19 Another approach is to obtain a set of empirical nonlinear relations between in
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