journal article·2022-09-14

Self-calibration in compliance and indenter tip defect for instrumented indentation

D. Chicot, A. Mejias, F. Roudet, A. Montagne, D. Betrancourt, T. Coorevits

Journal of Materials Research· Volume 37· Issue 17
Publisher page

Abstract

The accuracy in the determination of the mechanical properties by instrumented indentation strongly depends on the indenter/material contact area, the corrective compliance, and the indenter tip defect. For the calibration, we suggest to combine 3 functions: (i) a Force-function, where only the corrective compliance term is the unknown parameter, (ii) an Area-function, allowing the estimation of the tip defect knowing the corrective compliance, and finally (iii) a Martens-function, to determine the Martens hardness. The proposed methodology is validated on a series of experiments performed between 2006 and 2015 on ceramics and metals using the same indentation instrument and the same Vickers indenter having undergone different blunts. As a main result, the Young’s moduli are found very close to that available in literature if a β-factor is introduced into the Area-function and Force-function. In addition, both the instrumented hardness and Martens hardness do not vary with the indentation force.Graphical abstract
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Research context

OpenAlex topics: Metal and Thin Film Mechanics · Advanced Surface Polishing Techniques · Adhesion, Friction, and Surface Interactions

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (50)

Show source-provided references
1. Y.T. Cheng, C.M. Cheng, Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng. R R44, 91–149 (2004). https://doi.org/10.1016/j.mser.2004.05.00110.1016/j.mser.2004.05.001 ↗
2. D. Chicot, E.S. Puchi-Cabrera, A. Iost, M.H. Staia, X. Decoopman, F. Roudet, G. Louis, Analysis of the indentation size effect in copper and its alloys. Mater. Sci. Technol. 29–7, 868–879 (2013). https://doi.org/10.1179/1743284713Y.000000021310.1179/1743284713Y.0000000213 ↗
3. S.J. Bull, T.F. Page, E.H. Yoffe, An explanation of the identification size effect in ceramics. Phil. Mag. Lett. 59–6, 281–288 (1989). https://doi.org/10.1080/0950083890820635610.1080/09500838908206356 ↗
4. H. Li, R.C. Bradt, The microhardness indentation load/size effect in rutile and cassiterite single crystals. J. Mater. Sci. 28, 917–926 (1993). https://doi.org/10.1007/BF0040087410.1007/BF00400874 ↗
5. K. Sangwal, B. Surowska, P. Blaziak, Analysis of the indentation size effect in the microhardness measurement of some cobalt-based alloys. Mater. Chem. Phys. 77, 511–520 (2002). https://doi.org/10.1016/S0254-0584(02)00086-X10.1016/S0254-0584(02)00086-X ↗
6. W.D. Nix, H. Gao, Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Sol. 46, 411–425 (1998). https://doi.org/10.1016/S0022-5096(97)00086-010.1016/S0022-5096(97)00086-0 ↗
7. A. Iost, R. Bigot, Indentation size effect: reality or artefact? J. Mater. Sci. 31–13, 3573–3577 (1996). https://doi.org/10.1007/BF0036076410.1007/BF00360764 ↗
8. Y. Sun, S. Zheng, T. Bell, J.F. Smith, Indenter tip radius and load frame compliance calibration using nanoindentation loading curves. Phil. Mag. Lett. 79–9, 649–658 (1999). https://doi.org/10.1080/09500839917669810.1080/095008399176698 ↗
9. C. Ullner, E. Reimann, H. Kohlhoff, A. Subaric-Leitis, Effect and measurement of the machine compliance in the macro range of instrumented indentation test. Meas. 43, 216–222 (2010). https://doi.org/10.1016/j.measurement.2009.09.00910.1016/j.measurement.2009.09.009 ↗
10. T. Coorevits, S. Kossman, D. Chicot, F. Hennebelle, A. Montagne, A. Iost, Virtual machine concept applied to uncertainties estimation in instrumented indentation testing. J. Mater. Res. 34–14, 2501–2516 (2019). https://doi.org/10.1557/jmr.2019.20310.1557/jmr.2019.203 ↗
11. W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 6–6, 1564–1583 (1992). https://doi.org/10.1557/JMR.1992.156410.1557/JMR.1992.1564 ↗
12. G.M. Pharr, W.C. Oliver, F.R. Brotzen, On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. J. Mater. Res 7, 613–617 (1992). https://doi.org/10.1557/JMR.1992.061310.1557/JMR.1992.0613 ↗
13. NF EN ISO 14577:2015, Metallic materials—instrumented indentation test for hardness and other materials parameters—part 1: test method—part 2: verification and calibration of the testing machine—part 3: calibration of reference test pieces, October 2003 and part 4: test Method for Metallic and Non-Metallic Coatings, October (2005)
14. D. Chicot, P. De Baets, M.H. Staia, E.S. Puchi-Cabrera, G. Louis, Y. Perez Delgado, J. Vleugels, Influence of tip defect and indenter shape on the mechanical properties determination by indentation of a TiB2–60%B4C ceramic composite. Int. J. Refract. Met. Hard Mater. 38, 102–110 (2013). https://doi.org/10.1016/j.ijrmhm.2013.01.00610.1016/j.ijrmhm.2013.01.006 ↗
15. J.L. Loubet, M. Bauer, A. Tonck, S. Bec, B. Gauthier-Manuel, Nanoindentation with a surface force apparatus, in Mechanical properties and deformation behavior of materials having ultra-fine microstructures, vol. 233, ed. by M. Nastasi, D. Parkin, H. Gleiter (Springer, Dordrecht, 1993), pp. 429–447. https://doi.org/10.1007/978-94-011-1765-4_2810.1007/978-94-011-1765-4_28 ↗
16. S. Bec, A. Tonck, J.M. Georges, E. Georges, J.L. Loubet, Improvements in the indentation method with a surface force apparatus. Phil. Mag. A 74–5, 1061–1072 (1996). https://doi.org/10.1080/0141861960823970710.1080/01418619608239707 ↗
17. G. Hochstetter, A. Jimenez, J.L. Loubet, Strain-rate effects on hardness of glassy polymers in the nanoscale range. Comparison between quasi-static and continuous stiffness measurements. J. Macromol. Sci. B 38(5–6), 681–692 (1999). https://doi.org/10.1080/0022234990824813110.1080/00222349908248131 ↗
18. G. Guillonneau. Nouvelles techniques de nanoindentation pour des conditions expérimentales difficiles : très faibles enfoncements, surfaces rugueuses, température. Thèse de doctorat. Ecole Centrale de Lyon (2012). https://tel.archives-ouvertes.fr/tel-00800426
19. C.A. Klein, G.F. Cardinale, Young’s modulus and Poisson’s ratio of CVD diamond. Diam. Rel. Mater. 2(5–7), 918–923 (1993). https://doi.org/10.1016/0925-9635(93)90250-610.1016/0925-9635(93)90250-6 ↗
20. K. Herrmann, N.M. Jennett, W. Wegener, J. Meneve, K. Hasche, R. Seemann, Progress in determination of the area function of indenters used for nanoindentation. Thin Solids Films 377–378, 394–400 (2000). https://doi.org/10.1016/S0040-6090(00)01367-510.1016/S0040-6090(00)01367-5 ↗
21. A.C. Fischer-Cripps, Critical review of analysis and interpretation of nanoindentation test data. Surf. Coat. Technol. 200(14–15), 4153–4165 (2006). https://doi.org/10.1016/j.surfcoat.2005.03.01810.1016/j.surfcoat.2005.03.018 ↗
22. K. Herrmann, K. Hasche, F. Pohlenz, R. Seemann, Characterisation of the geometry of indenters used for the micro-And nanoindentation method. Measurement 29–3, 201–207 (2001). https://doi.org/10.1016/S0263-2241(00)00039-710.1016/S0263-2241(00)00039-7 ↗
23. J. Thurn, R.F. Cook, Simplified area function for sharp indenter tips in depth-sensing indentation. J. Mater. Res. 17–5, 1143–1146 (2002). https://doi.org/10.1557/JMR.2002.016910.1557/JMR.2002.0169 ↗
24. M. Troyon, L. Huang, Comparison of different analysis methods in nanoindentation and influence on the correction factor for contact area. Surf. Coat. Technol. 201(3–4), 1613–1619 (2006). https://doi.org/10.1016/j.surfcoat.2006.02.03310.1016/j.surfcoat.2006.02.033 ↗
25. A.R. Franco Jr., G. Pintaude, A. Sinatora, C.E. Pinedo, A.P. Tschiptschin, The use of a Vickers indenter in depth sensing indentation for measuring elastic modulus and Vickers hardness. J. Mater. Res. 7–3, 483–491 (2004). https://doi.org/10.1590/S1516-1439200400030001810.1590/S1516-14392004000300018 ↗
26. H. Bei, E.P. George, J.L. Hay, G.M. Pharr, Influence of indenter tip geometry on elastic deformation during nanoindentation. Phys. Rev. Lett. 95, 045501 (2005). https://doi.org/10.1103/physrevlett.95.04550110.1103/physrevlett.95.045501 ↗
27. J.M. Antunes, A. Cavaleiro, L.F. Menezes, M.I. Simoes, J.V. Fernandes, Ultra-microhardness testing procedure with Vickers indenter. Surf. Coat. Technol. 149–1, 27–35 (2002). https://doi.org/10.1016/S0257-8972%2801%2901413-X10.1016/S0257-8972%2801%2901413-X ↗
28. L.A. Berla, A.M. Allen, S.M. Han, W.D. Nix, A physically based model for indenter tip shape calibration for nanoindentation. J. Mater. Res. 25, 735–745 (2010). https://doi.org/10.1557/JMR.2010.009810.1557/JMR.2010.0098 ↗
29. D. Chicot, M. YetnaNjock, E.S. Puchi-Cabrera, A. Iost, M.H. Staia, G. Louis, G. Bouscarrat, R. Aumaitre, A contact area function for Berkovich nanoindentation: case study on TiHfCN thin film. Thin Solids Films 558, 259–266 (2014). https://doi.org/10.1016/j.tsf.2014.02.04410.1016/j.tsf.2014.02.044 ↗
30. M. Yetna Njock, D. Chicot, J.M. Ndjaka, J. Lesage, X. Decoopman, F. Roudet, A. Mejias, A criterion to identify sinking-in and piling-up in indentation of materials. Int. J. Mech. Sci. 90, 145–150 (2015). https://doi.org/10.1016/j.ijmecsci.2014.11.00810.1016/j.ijmecsci.2014.11.008 ↗
31. D. Chicot, J. Mendoza, A. Zaoui, G. Louis, V. Lepingle, F. Roudet, J. Lesage, Mechanical properties of magnetite (Fe3O4), hematite (–Fe2O3) and goethite (–FeO.OH) by molecular dynamic analysis and depth-sensing micro-indentation. Mater. Chem. Phys. 129–3, 862–870 (2011). https://doi.org/10.1016/j.matchemphys.2011.05.05610.1016/j.matchemphys.2011.05.056 ↗
32. S.I. Bulychev, V.P. Alekhin, M.K. Shorshorov, A.P. Ternovskij, G.D. Shnyrev, Determination of Young modulus by the hardness indentation diagram. Zavod. Lab. 41, 1137–1140 (1975)
33. J.M. Antunes, L.F. Menezes, J.V. Fernandes, Three-dimensional numerical simulation of Vickers indentation tests. Int. J. Sol. Struct. 43–3(4), 784–806 (2006). https://doi.org/10.1016/j.ijsolstr.2005.02.04810.1016/j.ijsolstr.2005.02.048 ↗
34. J.C. Hay, A. Bolshakov, G. Pharr, A critical examination of the fundamental relations used in the analysis of nanoindentation data. J. Mater. Res. 14–6, 2296–2305 (1999). https://doi.org/10.1557/JMR.1999.030610.1557/JMR.1999.0306 ↗
35. G.D. Quinn, P.L. Patel, I. Lloyd, Effect of loading rate upon conventional ceramic microindentation hardness. J. Res. Natl. Inst. Stand. Technol. 107, 299–306 (2002). https://doi.org/10.6028/jres.107.02310.6028/jres.107.023 ↗
36. ASTM E92 - 17 Standard Test Methods for Vickers Hardness and Knoop Hardness of Metallic Materials, (Originally approved in 1952) 1–27. https://doi.org/10.1520/E0092-1710.1520/E0092-17 ↗
37. ASTM E384 - 17 Standard Test Method for Microindentation Hardness of Materials, (Originally approved in 1969) 1–40. https://doi.org/10.1520/E0384-1710.1520/E0384-17 ↗
38. Z. Chen, U. Gandhi, J. Lee, R.H. Wagoner, Variation and consistency of Young’s modulus in steel. J. Mater. Proc. Technol. 227, 227–243 (2016). https://doi.org/10.1016/j.jmatprotec.2015.08.02410.1016/j.jmatprotec.2015.08.024 ↗
39. E. Österlund, J. Kinnunen, V. Rontu, A. Torkkeli, M. Paulasto-Kröckel, Mechanical properties and reliability of aluminum nitride thin films. J. All. Comp. 772, 306–313 (2019). https://doi.org/10.1016/j.jallcom.2018.09.06210.1016/j.jallcom.2018.09.062 ↗
40. A. Khan, J. Philip, P. Hess, Young’s modulus of silicon nitride used in scanning force microscope cantilevers. J. Appl. Phys. 95–4, 1667–1672 (2004). https://doi.org/10.1063/1.163888610.1063/1.1638886 ↗
41. O. Pabst, M. Schiffer, E. Obermeier., T. Tekin, K. D. Lang, H-D. Ngo. Measurement of Young’s modulus and residual stress of thin SiC layers for MEMS high temperature applications. Conference Paper in Microsystem Technologies. April 2011. https://doi.org/10.1117/12.88645310.1117/12.886453 ↗
42. B. Hähnlein, J. Kovac Jr., J. Pezoldt, Size effect of the silicon carbide Young’s modulus. Appl. Mater. Sci. 214–4, 1600390 (2017). https://doi.org/10.1002/pssa.20160039010.1002/pssa.201600390 ↗
43. T. Savaskhan, S. Murphy, Mechanical properties and lubricated wear of Zn-25Al-based alloys. Wear 116–2, 211–224 (1987). https://doi.org/10.1016/0043-1648(87)90234-110.1016/0043-1648(87)90234-1 ↗
44. F. Kramer, M. Roellig, R. Metasch, J. Ahmar, K. Meier, S. Wiese, Experimental determination of the Young’s modulus of copper and solder materials for electronic packaging. Microelec. Rel. 91–2, 251–256 (2018). https://doi.org/10.1109/eurosime.2017.792623910.1109/eurosime.2017.7926239 ↗
45. J.H. Baek, Y.P. Kim, W.S. Kim, Y.T. Kho, Effect of temperature on the charpy impact and CTOD values of type 304 stainless steel pipeline for LNG transmission. KSME Int. J. 16, 351–357 (2002). https://doi.org/10.1007/BF0298401510.1007/BF02984015 ↗
46. S. Laasri, M. Taha, E.K. Hlil, A. Laghzizil, A. Hajjaji, Manufacturing and mechanical properties of calcium phosphate biomaterials. C.R. Mécanique 340, 715–720 (2012). https://doi.org/10.1016/j.crme.2012.09.00510.1016/j.crme.2012.09.005 ↗
47. D. Chicot, A. Tricoteaux, J. Lesage, A. Leriche, M. Descamps, E. Rguiti-Constantin, Mechanical properties of porosity-free beta tricalcium phosphate (β-TCP) ceramic by sharp and spherical indentations. New J. Glass Ceram. 3, 16–28 (2013). https://doi.org/10.4236/njgc.2013.3100410.4236/njgc.2013.31004 ↗
48. S. Wu, S. Wu, G. Zhang, W. Zhang, Hardness and elastic modulus of titanium nitride coatings prepared by pirac method. Surf. Rev. Lett. 25–1, 1850040 (2018). https://doi.org/10.1142/S0218625X1850040310.1142/S0218625X18500403 ↗
49. H.R. Kulkarni, S.N. Shukla, M.B. Dongare, Determination of young’s modulus of aluminium, copper, iron, brass and steel alloys by using double exposure holographic interferometry (DEHI) technique. Mater. Sci. Res. India. 14–2, 128–132 (2017). https://doi.org/10.13005/msri/14020710.13005/msri/140207 ↗
50. Z.A. Yasar, R.A. Haber, Evaluating the role of uniformity on the properties of B4C–SiC composites. Ceram. Int. 47–4, 4838–4844 (2021). https://doi.org/10.1016/j.ceramint.2020.10.05510.1016/j.ceramint.2020.10.055 ↗