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The Influence of Indenter Tip Imperfection and Deformability on Analysing Instrumented Indentation Tests at Shallow Depths of Penetration on Stiff and Hard Materials

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Abstract

We report on the difficulties of extracting plastic parameters from constitutive equations derived by instrumented indentation tests on hard and stiff materials at shallow depths of penetration. As a general rule, we refer here to materials with an elastic stiffness more than 10 % of that of the indenter and a yield strain higher than 1 %, as well as to penetration depths less than ∼ 5 times the characteristic tip defect length of the indenter. We experimentally tested such a material (an amorphous alloy) by nanoindentation. To describe the mechanical response of the test, namely the force-displacement curve, it is necessary to consider the combined effects of indenter tip imperfections and indenter deformability. For this purpose, an identification procedure has been carried out by performing numerical simulations (using Finite Element Analysis) with constitutive equations that are known to satisfactorily describe the behaviour of the tested material. We propose a straightforward procedure to address indenter tip imperfection and deformability, which consists of firstly taking account of a deformable indenter in the numerical simulations. This procedure also involves modifying the experimental curve by considering a truncated length to create artificially the material’s response to a perfectly sharp indentation. The truncated length is determined directly from the loading part of the force-displacement curve. We also show that ignoring one or both of these issues results in large errors in the plastic parameters extracted from the data.

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Abbreviations

E :

Young’s modulus

ν :

Poisson’s ratio

Y c :

Compressive yield strength

\({\epsilon _{y}^{c}}\) :

Compressive yield strain

φ :

Friction angle (Drucker-Prager yield criterion)

P :

Indentation force

δ :

Indentation depth

C :

Indentation loading pre-factor

Δδ :

Indenter truncated length

R :

Indenter tip radius

β :

Indenter equivalent complementary angle

\(\mathcal {L}\) :

Residual of the identification procedure

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Acknowledgments

We acknowledge financial support from the State-Region Plan Contract PRIN2TAN programme for acquisition of the Hysitron nanoindentation apparatus. We would like to thank Prof. Jun Shen (Harbin Institute of Technology, China) for providing the samples, Dr. J.-P. Guin (CNRS, France) for the AFM measurements and Prof. P. Pilvin for advice on the identification procedure. Dr M.S.N. Carpenter post-edited the English style and grammar.

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Authors and Affiliations

  1. University Bretagne Sud, FRE CNRS 3744, IRDL, F-56321, Lorient, France

    V. Keryvin & C. Bernard

  2. University Savoie Mont Blanc, EA 4114, SYMME, F-74000, Annecy, France

    L. Charleux

  3. University Rennes 1, UMR CNRS 6251, IPR, F-35042, Rennes, France

    M. Nivard

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  1. V. Keryvin
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  2. L. Charleux
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  3. C. Bernard
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  4. M. Nivard
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Correspondence to V. Keryvin.

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Keryvin, V., Charleux, L., Bernard, C. et al. The Influence of Indenter Tip Imperfection and Deformability on Analysing Instrumented Indentation Tests at Shallow Depths of Penetration on Stiff and Hard Materials. Exp Mech 57, 1107–1113 (2017). https://doi.org/10.1007/s11340-017-0267-1

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