HAL Id: hal-01520783 https://hal.archives-ouvertes.fr/hal-01520783 Submitted on 18 Jul 2017 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. The Influence of Indenter Tip Imperfection and Deformability on Analysing Instrumented Indentation Tests at Shallow Depths of Penetration on Stiff and Hard Materials Vincent Keryvin, Ludovic Charleux, Cédric Bernard, Mariette Nivard To cite this version: Vincent Keryvin, Ludovic Charleux, Cédric Bernard, Mariette Nivard. The Influence of Indenter Tip Imperfection and Deformability on Analysing Instrumented Indentation Tests at Shallow Depths of Penetration on Stiff and Hard Materials. Experimental Mechanics, Society for Experimental Mechan- ics, 2017, 57 (7), pp.1107-1113. 10.1007/s11340-017-0267-1. hal-01520783
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HAL Id: hal-01520783https://hal.archives-ouvertes.fr/hal-01520783
Submitted on 18 Jul 2017
HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.
The Influence of Indenter Tip Imperfection andDeformability on Analysing Instrumented Indentation
Tests at Shallow Depths of Penetration on Stiff andHard Materials
Vincent Keryvin, Ludovic Charleux, Cédric Bernard, Mariette Nivard
To cite this version:Vincent Keryvin, Ludovic Charleux, Cédric Bernard, Mariette Nivard. The Influence of Indenter TipImperfection and Deformability on Analysing Instrumented Indentation Tests at Shallow Depths ofPenetration on Stiff and Hard Materials. Experimental Mechanics, Society for Experimental Mechan-ics, 2017, 57 (7), pp.1107-1113. �10.1007/s11340-017-0267-1�. �hal-01520783�
24. V. Keryvin, R. Crosnier, R. Laniel, V. H. Hoang, and J.-C. Sangleboeuf, “Indentation and scratching
mechanisms of a ZrCuAlNi bulk metallic glass,” J. Phys. D. Appl. Phys., vol. 41, p. 074029, apr 2008.
625
25. J. Brest, V. Keryvin, P. Longère, and Y. Yokoyama, “Insight into plasticity mechanisms in metallic
glasses by means of a Brazilian test and numerical simulation,” J. Alloys Compd., vol. 586, pp. S236–
S241, feb 2014. 6
26. Y. T. Cheng and C. M. Cheng, “Scaling, dimensional analysis, and indentation measurements,” Mater.
Sci. Eng. R Reports, vol. 44, no. 4-5, pp. 91–150, 2004. 730
27. D. Tabor, “The physical meaning of indentation and scratch hardness,” Br. J. Appl. Phys., vol. 7, no. 5,
p. 159, 1956. 7
28. L. Charleux, V. Keryvin, M. Nivard, J.-P. Guin, J.-C. Sangleboeuf, and Y. Yokoyama, “A method for
measuring the contact area in instrumented indentation testing by tip scanning probe microscopy
imaging,” Acta Mater., vol. 70, pp. 249–258, may 2014.35
29. R. T. Qu, Z. Q. Liu, R. F. Wang, and Z. F. Zhang, “Yield strength and yield strain of metallic glasses and
their correlations with glass transition temperature,” J. Alloys Compd., vol. 637, pp. 44–54, 2015. 7Accep
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Instrumented indentation tests at very low depths on stiff and hard materials 13
30. V. Keryvin, K. Eswar Prasad, Y. Gueguen, J.-C. Sanglebœuf, and U. Ramamurty, “Temperature depen-
dence of mechanical properties and pressure sensitivity in metallic glasses below glass transition,”
Philos. Mag., vol. 88, pp. 1773–1790, apr 2008. 7
31. K. Gadelrab, F. Bonilla, and M. Chiesa, “Densification modeling of fused silica under nanoindenta-
tion,” J. Non. Cryst. Solids, vol. 358, pp. 392–398, jan 2012. 95
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14 V. Keryvin et al.
Yc [MPa] εcy [%] ϕ [°] Residual L (a.u.)
(a) 5200 2.31 20 15
(b) 1835 0.816 41 26
(c) 5120 2.28 8 13
(d) 3690 1.64 22 0.6
Table 1. Results of the four different identification procedures in terms of material parameters. Yc (com-pressive strength) and ϕ (friction angle) are the identified plastic parameters (see Eq. (1)); εc
y = Yc/E is thecompressive yield strain; L is the residual of the identification procedure (see Eq. (2)). Case (a) is when takinginto account neither the indenter tip defect nor its deformability. Case (b) is when taking into account only theindenter deformability. Case (c) is when taking into account only the tip defect. Case (d) is when taking intoaccount the indenter tip defect and its deformability. Note that both E,Young’s modulus, and ν, Poisson’s ratiowere kept constant at 225 GPa and 0.337, respectively.
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Instrumented indentation tests at very low depths on stiff and hard materials 15
0 50 100 150 200Displacement, δ [nm]
0
2
4
6
8
10
Forc
e,P[m
N]
Test 1Test 2
Test 3Test 4
Test 5
Fig. 1. Force-displacement curves of the Fe-base metallic glass under a nanoindentation test (five tests).
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16 V. Keryvin et al.
0 50 100 150 200Displacement, δ [nm]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Squa
rero
otof
forc
e,p P[m
N1 2]
Truncated length ∆δ = b/a ∼ 15 nm
∆δ
Experiment, for Pm = 10 mN
Fit,p
P(δ) = a*δ + b, for δ > 50 nm
Fig. 2. Evolution of the square root of the force versus the indentation depth during the loading stageof a 10 mN indentation test on the Fe-base glass. A linear fit for depths higher than 50 nm (for which we are inthe similitude regime) is extrapolated down to the x-axis to give the tip defect in terms of a truncated length ∆δ∼ 15 nm.
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Instrumented indentation tests at very low depths on stiff and hard materials 17
β
β
td = R1− cos β
cos βr
z
O
C
T
R
zt = R (1− cos β)
Fig. 3. Schematic of a blunted indenter modelled as sphero-conical. The spherical part (in red) and theconical part (in blue) are joined so that they have the same slope at point T. The tip defect length (td) is given bythe radius of the spherical tip (R) and the angle between the horizontal axis and the conical part (β). The verticaldistance between the horizontal axis and point T is zt
.
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18 V. Keryvin et al.
0 50 100 150 200 250 300 350Displacement, δ [nm]
0
5
10
15
20
25
Forc
e,P[m
N]
Indentation with rounded tip
Sharp indentation at maximum depth + ∆δIndentation with rounded tip shifted by ∆δ
0 10 20 30 40 50
Fig. 4. Numerical simulations (force-displacement curves) with a rounded tip of 260 nm (in accordancewith AFM measurements) at a given arbitrary penetration depth δm = 292nm and a perfectly sharp tip (at apenetration depth δm +∆δ, where ∆δ is the truncated length (found by fitting the loading stage of the roundedtip simulation, here 15 nm). The results from the rounded tip simulation, shifted by ∆δ to higher penetrationdepths, overlap those with the perfect tip. The inset indicates furthermore that this is only valid for δ greater than∼ 40 nm that is ∼ 2-3 times ∆δ.
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Instrumented indentation tests at very low depths on stiff and hard materials 19
0 50 100 150 200Displacement, δ [nm]
0
2
4
6
8
10
12
14
Forc
e,P[m
N]
Experiment shifted by ∆δ=15 nm
Simulation (deformable indenter) with fitted parameters
Simulation (rigid indenter) with fitted parameters
Fig. 5. Results of the identification procedure (d). The force-displacement curve obtained from numeri-cal simulations with the parameters found in Table 1 (d), taking into account the indenter deformability matchesthe experimental curve (shifted by the truncated length ∆δ = 15 nm). The results of a direct simulation withthe same material parameters but with a rigid indenter are also shown to highlight the dramatic influence if theindenter deformability for hard and stiff materials.
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20 V. Keryvin et al.
0.0
2.5
5.0
7.5
10.0
Experiment Numerical simulation
0 50 100 150 2000.0
2.5
5.0
7.5
10.0
0 50 100 150 200Displacement, δ [nm]
Forc
e,P[m
N] (a)
�Tip Defect
� Deformability
(b)
�Tip Defect
2� Deformability
(c)
2�Tip Defect
� Deformability
(d)
2�Tip Defect
2� Deformability
Fig. 6. Results of the four different identification procedures in terms of force-displacement curves (ex-periment versus numerical simulation). Case (a) is when taking into account neither the indenter tip defect norits deformability. Case (b) is when taking into account only the indenter deformability. Case (c) is when takinginto account only the tip defect. Case (d) is when taking into account the indenter tip defect and its deformability.