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A data analysis procedure for phase identification in nanoindentation results of cementitious materials

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Abstract

Measuring accurately phase properties is essential for a realistic mesoscale modeling of materials, and nanoindentation is a popular technique regarding mechanical properties. Given the statistical nature of the grid indentation method, where large arrays of indents are performed blindly, the identification of phases from the distributions of measured properties is an essential step. Many biases can be introduced at that stage when the phases do not have very distinct properties as is often the case for cementitious materials, since many indentation tests may also be in effectively heterogeneous areas. It is proposed in the present work to analyze statistical indentation results on cementitious materials with a hierarchical clustering algorithm making use of enriched information, including the spatial coordinates of the indent. It is shown that it allows to reduce potential biases of the method by eliminating tests in potentially heterogeneous areas and performing model independent identification of the different phases.

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References

  1. 1.

    Mondal P, Shah SP, Marks LD (2009) Nanomechanical properties of interfacial transition zone in concrete. In: Nanotechnology in construction, vol 3, Springer, Berlin, pp 315–320. https://doi.org/10.1007/978-3-642-00980-8_42

  2. 2.

    Zhu W, Bartos PJM (2000) Application of depth-sensing microindentation testing to study of interfacial transition zone in reinforced concrete. Cem Concr Res 30:1299–1304. https://doi.org/10.1016/S0008-8846(00)00322-7

  3. 3.

    Constantinides G, Ulm F-J (2004) The effect of two types of C–S–H on the elasticity of cement-based materials: results from nanoindentation and micromechanical modeling. Cem Concr Res 34:67–80. https://doi.org/10.1016/S0008-8846(03)00230-8

  4. 4.

    Han J, Pan G, Sun W, Wang C, Cui D (2012) Application of nanoindentation to investigate chemomechanical properties change of cement paste in the carbonation reaction. Sci China Technol Sci 55:616–622. https://doi.org/10.1007/s11431-011-4571-1

  5. 5.

    Frech-Baronet J, Sorelli L, Charron J-P (2017) New evidences on the effect of the internal relative humidity on the creep and relaxation behaviour of a cement paste by micro-indentation techniques. Cem Concr Res 91:39–51. https://doi.org/10.1016/j.cemconres.2016.10.005

  6. 6.

    Pichler Ch, Lackner R (2009) Identification of logarithmic-type creep of calcium-silicate-hydrates by means of nanoindentation. Strain 45:17–25. https://doi.org/10.1111/j.1475-1305.2008.00429.x

  7. 7.

    Vandamme M, Ulm F-J (2013) Nanoindentation investigation of creep properties of calcium silicate hydrates. Cem Concr Res 52:38–52. https://doi.org/10.1016/j.cemconres.2013.05.006

  8. 8.

    Zhang Q, Le Roy R, Vandamme M, Zuber B (2014) Long-term creep properties of cementitious materials: comparing microindentation testing with macroscopic uniaxial compressive testing. Cem Concr Res 58:89–98. https://doi.org/10.1016/j.cemconres.2014.01.004

  9. 9.

    Constantinides G, Ulm F-J, Vliet KV (2003) On the use of nanoindentation for cementitious materials. Mater Struct 36:191–196. https://doi.org/10.1007/BF02479557

  10. 10.

    Hughes JJ, Trtik P (2004) Micro-mechanical properties of cement paste measured by depth-sensing nanoindentation: a preliminary correlation of physical properties with phase type. Mater Charact 53:223–231. https://doi.org/10.1016/j.matchar.2004.08.014

  11. 11.

    Mondal P, Shah SP, Marks L (2007) A reliable technique to determine the local mechanical properties at the nanoscale for cementitious materials. Cem Concr Res 37:1440–1444. https://doi.org/10.1016/j.cemconres.2007.07.001

  12. 12.

    Velez K, Maximilien S, Damidot D, Fantozzi G, Sorrentino F (2001) Determination by nanoindentation of elastic modulus and hardness of pure constituents of Portland cement clinker. Cem Concr Res 31:555–561. https://doi.org/10.1016/S0008-8846(00)00505-6

  13. 13.

    Wei Y, Liang S, Gao X (2017) Phase quantification in cementitious materials by dynamic modulus mapping. Mater Charact 127:348–356. https://doi.org/10.1016/j.matchar.2017.02.029

  14. 14.

    Bernard O, Ulm F-J, Lemarchand E (2003) A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials. Cem Concr Res 33:1293–1309. https://doi.org/10.1016/S0008-8846(03)00039-5

  15. 15.

    Constantinides G, Ravichandran KS, Ulm FJ, Vanvliet KJ (2006) Grid indentation analysis of composite microstructure and mechanics: principles and validation. Mater Sci Eng, A 430:189–202. https://doi.org/10.1016/j.msea.2006.05.125

  16. 16.

    Ulm F-J, Vandamme M, Bobko C, Alberto Ortega J, Tai K, Ortiz C (2007) Statistical indentation techniques for hydrated nanocomposites: concrete, bone, and shale. J Am Ceram Soc 90:2677–2692. https://doi.org/10.1111/j.1551-2916.2007.02012.x

  17. 17.

    Chen JJ, Sorelli L, Vandamme M, Ulm F-J, Chanvillard G (2010) A coupled nanoindentation/SEM-EDS study on low water/cement ratio portland cement paste: evidence for C–S–H/Ca(OH)2 nanocomposites. J Am Ceram Soc 93:1484–1493. https://doi.org/10.1111/j.1551-2916.2009.03599.x

  18. 18.

    Krakowiak KJ, Wilson W, James S, Musso S, Ulm F-J (2015) Inference of the phase-to-mechanical property link via coupled X-ray spectrometry and indentation analysis: application to cement-based materials. Cem Concr Res 67:271–285. https://doi.org/10.1016/j.cemconres.2014.09.001

  19. 19.

    Wilson W, Sorelli L, Tagnit-Hamou A (2018) Automated coupling of nanoindentation and quantitative energy-dispersive spectroscopy (NI-QEDS): a comprehensive method to disclose the micro-chemo-mechanical properties of cement pastes. Cem Concr Res 103:49–65. https://doi.org/10.1016/j.cemconres.2017.08.016

  20. 20.

    Trtik P, Münch B, Lura P (2009) A critical examination of statistical nanoindentation on model materials and hardened cement pastes based on virtual experiments. Cem Concr Compos 31:705–714. https://doi.org/10.1016/j.cemconcomp.2009.07.001

  21. 21.

    Ulm F-J, Vandamme M, Jennings HM, Vanzo J, Bentivegna M, Krakowiak KJ, Constantinides G, Bobko CP, Van Vliet KJ (2010) Does microstructure matter for statistical nanoindentation techniques? Cem Concr Compos 32:92–99. https://doi.org/10.1016/j.cemconcomp.2009.08.007

  22. 22.

    Lura P, Trtik P, Münch B (2011) Validity of recent approaches for statistical nanoindentation of cement pastes. Cem Concr Compos 33:457–465. https://doi.org/10.1016/j.cemconcomp.2011.01.006

  23. 23.

    Trtik P, Dual J, Muench B, Holzer L (2008) Limitation in obtainable surface roughness of hardened cement paste: ‘virtual’ topographic experiment based on focussed ion beam nanotomography datasets. J Microsc 232:200–206. https://doi.org/10.1111/j.1365-2818.2008.02090.x

  24. 24.

    Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7:1564–1583. https://doi.org/10.1557/JMR.1992.1564

  25. 25.

    Sneddon IN (1965) The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int J Eng Sci 3:47–57. https://doi.org/10.1016/0020-7225(65)90019-4

  26. 26.

    Bushby AJ (2001) Nano-indentation using spherical indenters. Nondestruct Test Eval 17:213–234. https://doi.org/10.1080/10589750108953112

  27. 27.

    Dempster AP, Laird NM, Rubin DB (1976) Maximum likelihood from incomplete data via the EM algorithm. https://dash.harvard.edu/handle/1/3426318. Accessed 1 Feb 2018

  28. 28.

    Randall NX, Vandamme M, Ulm F-J (2009) Nanoindentation analysis as a two-dimensional tool for mapping the mechanical properties of complex surfaces. J Mater Res 24:679–690. https://doi.org/10.1557/jmr.2009.0149

  29. 29.

    Hu C, Han Y, Gao Y, Zhang Y, Li Z (2014) Property investigation of calcium–silicate–hydrate (C–S–H) gel in cementitious composites. Mater Charact 95:129–139. https://doi.org/10.1016/j.matchar.2014.06.012

  30. 30.

    Hu C, Li Z (2015) A review on the mechanical properties of cement-based materials measured by nanoindentation. Constr Build Mater 90:80–90. https://doi.org/10.1016/j.conbuildmat.2015.05.008

  31. 31.

    Moevus M, Godin N, R’Mili M, Rouby D, Reynaud P, Fantozzi G, Farizy G (2008) Analysis of damage mechanisms and associated acoustic emission in two SiC$_f/$[Si–B–C] composites exhibiting different tensile behaviours. Part II: unsupervised acoustic emission data clustering. Compos Sci Technol 68:1258–1265

  32. 32.

    Tenenbaum JB, de Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290:2319–2323. https://doi.org/10.1126/science.290.5500.2319

  33. 33.

    Lee JA, Verleysen M (2007) Nonlinear dimensionality reduction. Springer, New York. http://www.springer.com/us/book/9780387393506. Accessed 11 Oct 2018

  34. 34.

    Jain AK, Murty MN, Flynn PJ (1999) Data clustering: a review. ACM Comput Surv 31:264–323. https://doi.org/10.1145/331499.331504

  35. 35.

    Ward J Jr (1963) Hierarchical grouping to optimize an objective function. J Am Stat Assoc 58:236–244

  36. 36.

    Davies DL, Bouldin DW (1979) A cluster separation measure. IEEE Trans Pattern Anal Mach Intell 2:224–227. https://doi.org/10.1109/tpami.1979.4766909

  37. 37.

    Aili A (2017) Shrinkage and creep of cement-based materials under multiaxial load: poromechanical modeling for application in nuclear industry. PhD Thesis, Université Paris-Est. https://pastel.archives-ouvertes.fr/tel-01682129/document. Accessed 13 Feb 2018

  38. 38.

    Marshall DB (1984) Geometrical effects in elastic/plastic indentation. J Am Ceram Soc 67:57–60. https://doi.org/10.1111/j.1151-2916.1984.tb19148.x

  39. 39.

    Suganuma M (1999) Spherical and Vickers indentation damage in Yttria-stabilized tetragonal zirconia polycrystals. J Am Ceram Soc 82:3113–3120. https://doi.org/10.1111/j.1151-2916.1999.tb02210.x

  40. 40.

    Durst K, Göken M, Pharr GM (2008) Indentation size effect in spherical and pyramidal indentations. J Phys Appl Phys 41:074005. https://doi.org/10.1088/0022-3727/41/7/074005

  41. 41.

    Trtik P, Diaz A, Guizar-Sicairos M, Menzel A, Bunk O (2013) Density mapping of hardened cement paste using ptychographic X-ray computed tomography. Cem Concr Compos 36:71–77. https://doi.org/10.1016/j.cemconcomp.2012.06.001

  42. 42.

    Cuesta A, De la Torre ÁG, Santacruz I, Diaz A, Trtik P, Holler M, Lothenbach B, Aranda MAG (2019) Quantitative disentanglement of nanocrystalline phases in cement pastes by synchrotron ptychographic X-ray tomography. IUCrJ 6:473–491. https://doi.org/10.1107/s2052252519003774

  43. 43.

    Ukrainczyk N, Koenders EAB, van Breugel K (2013) Representative volumes for numerical modeling of mass transport in hydrating cement paste. In: Multi-scale modeling and characterization of infrastructure mater, Springer, Dordrecht, pp 173–184. https://doi.org/10.1007/978-94-007-6878-9_13

  44. 44.

    Yio MHN, Wong HS, Buenfeld NR (2017) Representative elementary volume (REV) of cementitious materials from three-dimensional pore structure analysis. Cem Concr Res 102:187–202. https://doi.org/10.1016/j.cemconres.2017.09.012

  45. 45.

    Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V, Vanderplas J, Passos A, Cournapeau D, Brucher M, Perrot M, Duchesnay É (2011) Scikit-learn: machine learning in python. J Mach Learn Res 12:2825–2830

  46. 46.

    Trtik P, Kaufmann J, Volz U (2012) On the use of peak-force tapping atomic force microscopy for quantification of the local elastic modulus in hardened cement paste. Cem Concr Res 42:215–221. https://doi.org/10.1016/j.cemconres.2011.08.009

  47. 47.

    Laugesen JL (2005) Density functional calculations of elastic properties of portlandite, Ca(OH)2. Cem Concr Res 35:199–202. https://doi.org/10.1016/j.cemconres.2004.07.036

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Acknowledgements

This work has been carried out in the framework of the CEA-EDF-Framatome agreement. The author thanks S. Poyet (CEA) for discussions regarding the manuscript.

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Correspondence to Fabien Bernachy-Barbe.

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Bernachy-Barbe, F. A data analysis procedure for phase identification in nanoindentation results of cementitious materials. Mater Struct 52, 95 (2019). https://doi.org/10.1617/s11527-019-1397-y

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Keywords

  • Nanoindentation
  • Micromechanics
  • Cementitious materials
  • Unsupervised clustering