Relation between the reduced and unreduced hardness in nanomicroindentation tests

Bulychev, S. I.

doi:10.1134/1.1259346

Cited by 16 publications

(11 citation statements)

References 10 publications

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“…Bulychev, 1999). Hingegen bedeuten ν i und E i die äquivalenten Materialparameter des Eindringkörpers.…”

Section: Einflüsse Auf Die Härtemessungunclassified

Charakterisierung der Kratzanfälligkeit von Gläsern im Bauwesen

Schula¹

2015

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“…Bulychev, 1999). Hingegen bedeuten ν i und E i die äquivalenten Materialparameter des Eindringkörpers.…”

Section: Einflüsse Auf Die Härtemessungunclassified

Charakterisierung der Kratzanfälligkeit von Gläsern im Bauwesen

Schula¹

2015

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“…The investigation of the link between the unloading slope S and the elasticity properties of the indented material is more recent, requiring depth sensing indentation techniques that provide a continuous record of the P-h curve during loading and unloading in an indentation test (Tabor, 1951;Doerner and Nix, 1986;Oliver and Pharr, 1992;Bulychev, 1999). Application of such techniques in indentation analysis confirmed the link provided by classical contact mechanic solutions (Hertz, 1882;Boussinesq, 1885;Love, 1939;Galin, 1961;Sneddon, 1965;Borodich and Keer, 2004) between the indentation modulus and the elasticity properties of the indented material.…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic solutions for conical indentation

Vandamme

Ulm

2006

International Journal of Solids and Structures

143

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International audienceThe aim of indentation analysis is to link indentation data, typically an indentation force vs. indentation depth curve, P–h, to meaningful mechanical properties of the indented material. While well established for time independent behavior, the presence of a time dependent behavior can strongly affect both the loading and the unloading responses. The paper presents a framework of viscoelastic indentation analysis based on the method of functional equations, developed by Lee and Radok [1960, The contact problem for viscoelastic bodies, J. Appl. Mech. 27, 438–444]. While the method is restricted to monotonically increasing contact areas, we show that it remains valid at the very beginning of the unloading phase as well. Based on this result, it is possible to derive closed form solutions following the classical procedure of functional formulations of viscoelasticity: (1) the identification of the indentation creep function, which is the indentation response to a Heaviside load; and (2) a convolution integral of the load history over the indentation creep function. This is shown here for a trapezoidal loading by a conical indenter on three linear isotropic viscoelastic materials with deviator creep: the 3-parameter Maxwell model, the 4-parameter Kelvin–Voigt model and the 5-parameter combined Kelvin–Voigt–Maxwell model. For these models, we derive closed form solutions that can be employed for the back-analysis of indentation results from the loading and holding period and for the definition of unloading time criteria that ensure that viscous effects are negligible in the unloading response

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“…It will be assumed in the following that the unloading curve can be described by this relationship, which is supported by the observations by Bulychev. 51 The deviation of the exponent from 2 will mainly arise at lower loads/depth, and thus, even though a fit might result in a changed exponent, this deviation at small loads and depths will only result in a minor change of the elastic energy.…”

Section: Dissipated Energymentioning

confidence: 98%

Indentation load–displacement curve, plastic deformation, and energy

Malzbender

2002

J. Mater. Res.

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Various methods to access indentation data are considered on the basis of the load P-displacement h curve, its derivative, or its integral. This paper discusses and extends the various analytical models to estimate the indentation P-h curve, the slope, and the dissipated energy to aid the development of a concise methodology to analyze indentation data. Special consideration is given to the effect of pile-up and sink-in. Relationships for sharp and spherical indenters are presented and in addition for sharp indenters with a rounded tip. An overview over analytic expressions for the P-h curve is given and compared to finite element simulations and experimental data. An expression derived for the representative strain at the onset of yield under sharp and spherical indenters compares well with literature results. The effect of a rounded tip on the yielding under a sharp indenter is discussed. The ratio of loading to unloading slope and the ratio of the plastically dissipated energy to the total energy is related to hardness and elastic modulus. In combination these ratios can be used to determine the strain-hardening coefficient.

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Relation between the reduced and unreduced hardness in nanomicroindentation tests

Cited by 16 publications

References 10 publications

Charakterisierung der Kratzanfälligkeit von Gläsern im Bauwesen

Charakterisierung der Kratzanfälligkeit von Gläsern im Bauwesen

Viscoelastic solutions for conical indentation

Indentation load–displacement curve, plastic deformation, and energy

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