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Estimating fracture toughness of C–S–H using nanoindentation and the extended finite element method

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Abstract

In this paper, an approach to integrating nanoindentation testing and finite element simulations is introduced to compute the fracture toughness of cementitious materials. Calcium silicate hydrate (C–S–H) was synthesized using the standard procedure of mixing calcium oxide (CaO) and silicate (SiO2) at a mixture ratio of 1.5. C–S–H powder was filtered, dried to a relative humidity of 11%, and then compacted at 400 MPa. Nanoindentation tests incorporating dwell time were performed on polished C–S–H specimens using a Berkovich indenter tip. The reduced elastic moduli of the C–S–H specimens were extracted from the nanoindentation measurements. Viscoelastic and viscoelastic-plastic finite element models with creep and cracking capabilities were developed to simulate the nanoindentation tests and to extract the fracture energy. The viscoelastic-plastic model utilized the extended finite element method (XFEM) to describe cracking and evaluate the cracking surface of C–S–H. The analysis showed that the proposed approach could fairly predict the fracture energy release rate and thus fracture toughness of C–S–H. The calculated fracture toughness was in agreement with the fracture toughness values reported in the literature.

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References

  1. Taylor, H.F.W.: Cement Chemistry, 2nd ed., Thomas Telford Publishing (1997)

  2. Jennings, H.M.: A model for the microstructure of calcium silicate in cement paste. Cem. Concr. Res. 30, 855–863 (2000)

    Article  Google Scholar 

  3. Beaudoin, J.J., Feldman, R.F.: Dependence of degree of silica polymerization and intrinsic mechanical properties of C–S–H on C/S ratio. In: 8th International Congress on the Chemistry of Cement, Brazil, vol. 3, pp. 337–342 (1986)

  4. Alizadeh, R., Beaudoin, J.J., Raki, L.: Mechanical properties of calcium silicate hydrates. Mater. Struct. 44, 13–28 (2010)

    Article  Google Scholar 

  5. Kim, J.J., Foley, E.M., Reda Taha, M.M.: Nano-mechanical characterization of synthetic calcium–silicate–hydrate (C–S–H) with varying CaO/SiO2 mixture ratios. Cem. Concr. Compos. 36, 65–70 (2013)

    Article  Google Scholar 

  6. Constantinides, G., Ulm, F.J.: The effect of two types of C–S–H on the elasticity of cement based materials: results from nanoindentation and micro modeling. Cem. Concr. Res. 34, 67–80 (2004)

    Article  Google Scholar 

  7. Sugiyama, D.: Chemical alteration of calcium silicate hydrate (C–S–H) in sodium chloride solution. Cem. Concr. Res. 38, 1270–1275 (2008)

    Article  Google Scholar 

  8. Foley, E.M., Kim, J.J., Reda Taha, M.M.: Synthesis and nano-mechanical characterization of C–S–H with a 1.5 C/S ratio. Cem. Concr. Res. 42, 1225–1232 (2012)

    Article  Google Scholar 

  9. Lodeiro, I.G., Macphee, D.E., Palomo, A., Fernández-Jiménez, A.: Effect of alkalis on fresh C–S–H gels. FTIR analysis. Cem. Concr. Res. 39, 147–153 (2009)

    Article  Google Scholar 

  10. Higgins, D.D., Bailey, J.E.: Fracture measurements on cement paste. J. Mater. Sci. 11(11), 1995–2003 (1976)

    Article  Google Scholar 

  11. Jenq, Y.S., Shah, S.P.: A fracture toughness criterion for concrete. Eng. Fract. Mech. 21(5), 1055–1069 (1985)

    Article  Google Scholar 

  12. Hillemeier, B., Hilsdorf, H.K.: Fracture mechanics studies on concrete compounds. Cem. Concr. Res. 7(5), 523–535 (1977)

    Article  Google Scholar 

  13. Dwivedi, V. S., Pratt, P. L.: Strength, fracture and deformation behaviour of Portland cement paste. In: ICF6, New Delhi (India) 1984

  14. Beaudoin, J.J., Gu, P., Myers, R.E.: The fracture of CSH and CSH/CH mixtures. Cem. Concr. Res. 28(3), 341–347 (1998)

    Article  Google Scholar 

  15. Cotterell, B., Mai, Y.W.: Crack growth resistance curve and size effect in the fracture of cement paste. J. Mater. Sci. 22(8), 2734–2738 (1987)

    Article  Google Scholar 

  16. Hoover, C.G., Ulm, F.J.: Experimental chemo-mechanics of early-age fracture properties of cement paste. Cem. Concr. Res. 75, 42–52 (2015)

    Article  Google Scholar 

  17. Bauchy, M., Laubie, H., Qomi, M.A., Hoover, C.G., Ulm, F.J., Pellenq, R.M.: Fracture toughness of calcium–silicate–hydrate from molecular dynamics simulations. J. Non-Cryst. Solids 419, 58–64 (2015)

    Article  Google Scholar 

  18. Bauchy, M., Wang, B., Wang, M., Yu, Y., Qomi, M.J.A., Smedskjaer, M.M., Bichara, C., Ulm, F., Pellenq, R.: Fracture toughness anomalies: viewpoint of topological constraint theory. Acta Mater. 121, 234–239 (2016)

    Article  Google Scholar 

  19. Fisher-Cripps, A.C.: Nanoindentation. Springer, New York (2004)

    Book  Google Scholar 

  20. Kumar, R., Narasimhan, R.: Analysis of spherical indentation of linear viscoelastic materials. Curr. Sci. 87, 1088–1095 (2004)

    Google Scholar 

  21. Oyen, M.L.: Sensitivity of polymer nanoindentation creep measurements to experimental variables. Acta Mater. 55(11), 3633–3639 (2007)

    Article  Google Scholar 

  22. Fischer-Cripps, A.C.: A simple phenomenological approach to nanoindentation creep. Mater. Sci. Eng., A 385(1), 74–82 (2004)

    Article  Google Scholar 

  23. Lu, H., Wang, B., Ma, J., Huang, G., Viswanathan, H.: Measurement of creep compliance of solid polymers by nanoindentation. Mech. Time Depend. Mater. 7(3), 189–207 (2003)

    Article  Google Scholar 

  24. Tweedie, C.A., Van Vliet, K.J.: Contact creep compliance of viscoelastic materials via nanoindentation. J. Mater. Res. 21(06), 1576–1589 (2006)

    Article  Google Scholar 

  25. Němeček, J.: Creep effects in nanoindentation of hydrated phases of cement pastes. Mater. Charact. 60(9), 1028–1034 (2009)

    Article  Google Scholar 

  26. Harding, D.S., Oliver, W.C., Pharr, G.M.: Cracking during nanoindentation and its use in the measurement of fracture toughness. In: Materials Research Symposium Proceedings. Houston, USA, pp. 663–668 (1995)

  27. Field, J.S., Swain, M.V., Dukino, R.D.: Determination of fracture toughness from the extra penetration produced by indentation-induced pop-in. J. Mater. Res. 18, 1412–1419 (2003)

    Article  Google Scholar 

  28. Chen, J., Bull, S.J.: Indentation fracture and toughness assessment for thin optical coatings on glass. J. Appl. Phys. 40, 5401–5417 (2007)

    Google Scholar 

  29. Bolshakov, A., Oliver, W.C., Pharr, G.M.: Influences of stress on the measurement of mechanical properties using nanoindentation: Part II. Finite element simulations. J. Mater. Res. 11, 760–768 (1996)

    Google Scholar 

  30. Lichinchi, M., Lenardi, C., Haupt, J., Vitali, R.: Simulation of Berkovich nanoindentation experiments on thin films using finite element method. Thin Solid Films 312, 240–248 (1998)

    Article  Google Scholar 

  31. Bressan, J.D., Tramontin, A., Rosa, C.: Modeling of nanoindentation of bulk and thin film by finite element method. Wear 258, 115–122 (2005)

    Article  Google Scholar 

  32. Walter, C., Antretter, T., Daniel, R., Mitterer, C.: Finite element simulation of the effect of surface roughness on nanoindentation of thin films with spherical indenters. Surf. Coat. Technol. 202, 1103–1107 (2007)

    Article  Google Scholar 

  33. Sarris, E., Constantinides, G.: Finite element modeling of nanoindentation on C–S–H: effect of pile-up and contact friction. Cem. Concr. Compos. 36, 78–84 (2013)

    Article  Google Scholar 

  34. Asroun, N., Asroun, A.: Simulation of viscoelastic and plastic deformation of C–S–H of cement paste at very low (w/c) mass ratio. In: 1st International Symposium on Innovative Technologies in Engineering And Science. Sakarya, Turkey, pp. 575–583 (2013)

  35. Perzyński, K., Madej, Ł.: Numerical modeling of fracture during nanoindentation of the TiN coatings obtained with the PLD process. Bull. Polish Acad. Sci. Tech. Sci. 61, 973–978 (2013)

    Google Scholar 

  36. Csanádi, T., Németh, D., Lofaj, F.: Mechanical properties of hard WC coating on steel substrate deduced from nanoindentation and finite element modeling. Exp. Mech. 1–13 (2016). doi:10.1007/s11340-016-0190-x

  37. Bažant, Z.P., Hauggaard, A.B., Baweja, S., Ulm, F.J.: Microprestress-solidification theory for concrete creep. I: aging and drying effects. J. Eng. Mech. 123(11), 1188–1194 (1997)

    Article  Google Scholar 

  38. ASTM Standard E 104-02: Standard Practice for maintaining constant relative humidity by means of aqueous solution. ASTM International (2007)

  39. Kim, J.J., Rahman, M.K., Reda Taha, M.M.: Examining microstructural composition of hardened cement paste cured under high temperature and pressure using nanoindentation and 29Si MAS NMR. Appl. Nanosci. 2(4), 445–456 (2012)

    Article  Google Scholar 

  40. Aboubakr, S.H., Begaye, M.L., Soliman, E., Reda Taha, M.M.: Correlating microstructural features, elastic, and viscoelastic characteristics of synthetic CSH. ACI Spec. Publ. 312, 1–12 (2016)

    Google Scholar 

  41. Miller, M., Bobko, C., Vandamme, M., Ulm, F.J.: Surface roughness criteria for cement paste nanoindentation. Cem. Concr. Res. 38(4), 467–476 (2008)

    Article  Google Scholar 

  42. Vandamme, M., Ulm, F.J.: Nanoindentation investigation of creep properties of calcium silicate hydrates. Cem. Concr. Res. 52, 38–52 (2013)

    Article  Google Scholar 

  43. Oliver, W.C., Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564–1583 (1992)

    Article  Google Scholar 

  44. Kabele, P., Davydov, D., Jůn, P., Němeček, J., Jirásek, M.: Study of micromechanical behavior of cement paste by integration of experimental nanoindentation and numerical analysis. Creep, shrinkage and durability mechanics of concrete and concrete structures: Proceedings of the CONCREEP, 8, pp. 89–96 (2008)

  45. Pichler, C., Lackner, R.: Identification of logarithmic-type creep of calcium–silicate–hydrates by means of nanoindentation. Strain 45(1), 17–25 (2009)

    Article  Google Scholar 

  46. Němeček, J.: Nanoindentation of heterogeneous structural materials. Habilitační práce, CTU Reports, 14 (2010)

  47. Grasley, Z. C., Jones, C. A., Li, X., Garboczi, E. J., Bullard, J. W.: Elastic and viscoelastic properties of calcium silicate hydrate. In: 4th International Symposium on Nanotechnology in Construction, 2012

  48. Resapu, R. R., Bradshaw, R. D.: Analysis of berkovich indentation of viscoelastic materials using finite element analysis. In: Proceedings of the XI International Congress and Exposition June 2–5, 2008 Orlando, Florida USA

  49. Bower, A. F.: Applied mechanics of solids. CRC Press (2009)

  50. Kim, Y. R., Guddati, M. N., Underwood, B. S., Yun, T. Y., Subramanian, V., Savadatti, S.: Development of a multiaxial viscoelastoplastic continuum damage model for asphalt mixtures (No. FHWA-HRT-08-073), 2009

  51. Penny, R.K., Marriott, D.L.: Design for Creep. Springer, Dordrecht (2012)

    Google Scholar 

  52. Goodall, R., Clyne, T.W.: A critical appraisal of the extraction of creep parameters from nanoindentation data obtained at room temperature. Acta Mater. 54(20), 5489–5499 (2006)

    Article  Google Scholar 

  53. Dean, J., Bradbury, A., Aldrich-Smith, G., Clyne, T.W.: A procedure for extracting primary and secondary creep parameters from nanoindentation data. Mech. Mater. 65, 124–134 (2013)

    Article  Google Scholar 

  54. Simulia. ABAQUS analysis user’s manual guide. Abaqus 6.14 Documentation, pp. 22–22 (2014)

  55. Lubliner, J., Oliver, J., Oller, S., Onate, E.: A plastic-damage model for concrete. Int. J. Solids Struct. 25(3), 299–326 (1989)

    Article  Google Scholar 

  56. Bažant, Z.P.: Concrete fracture models: testing and practice. Eng. Fract. Mech. 69(2), 165–205 (2002)

    Article  Google Scholar 

  57. Jirasek, M., Rolshoven, S., Grassl, P.: Size effect on fracture energy induced by non-locality. Int. J Numer. Anal. Met. 28(7–8), 653–670 (2004)

    Article  MATH  Google Scholar 

  58. Nguyen, G. D.: A thermodynamic approach to constitutive modelling of concrete using damage mechanics and plasticity theory. Ph.D. dissertation, University of Oxford, Oxford, UK, 2005

  59. Allison, P., Moser, R.D., Chandler, M.Q., Rushing, T.S., Williams, B.A., Cummins, T.K.: Nanomechanical structure–property relations of dynamically loaded reactive powder concrete. Mater. Charact. V, 287–298 (2011)

    Google Scholar 

  60. Asroun, N., Asroun, A.: The visco-elasto-plastic behavior of cement paste at nanoscale. Int. J. Eng. Res. Technol. 2(6) (2013)

  61. Pellenq, R.J.M., Kushima, A., Shahsavari, R., Van Vliet, K.J., Buehler, M.J., Yip, S., Ulm, F.J.: A realistic molecular model of cement hydrates. Proc. Natl. Acad. Sci. 106(38), 16102–16107 (2009)

    Article  Google Scholar 

  62. Manzano, H., Pellenq, R.J., Ulm, F.J., Buehler, M.J., van Duin, A.C.: Hydration of calcium oxide surface predicted by reactive force field molecular dynamics. Langmuir 28(9), 4187–4197 (2012)

    Article  Google Scholar 

  63. Hou, D., Zhu, Y., Lu, Y., Li, Z.: Mechanical properties of calcium silicate hydrate (C–S–H) at nano-scale: a molecular dynamics study. Mater. Chem. Phys. 146(3), 503–511 (2014)

    Article  Google Scholar 

  64. Hou, D., Zhao, T., Wang, P., Li, Z., Zhang, J.: Molecular dynamics study on the mode I fracture of calcium silicate hydrate under tensile loading. Eng. Fract. Mech. 131, 557–569 (2014)

    Article  Google Scholar 

  65. Shah, S.P.: Fracture toughness of cement-based materials. Mater. Struct. 21, 145–150 (1988)

    Article  Google Scholar 

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Acknowledgements

The experimental work performed herein was supported by the National Science Foundation (NSF) Award #1131369. The authors acknowledge this financial support. Additional support to the authors by the University of New Mexico, USA and Assiut University, Egypt to conduct the computational work presented herein is greatly appreciated. Special thanks to Ms. Elisa Borowski for her detailed editorial review of the manuscript.

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Authors and Affiliations

  1. Department of Civil Engineering, Assiut University, Assiut, 71516, Egypt

    Eslam M. Soliman

  2. Department of Civil Engineering, University of New Mexico, Albuquerque, NM, 87131, USA

    Sherif H. Aboubakr & Mahmoud M. Reda Taha

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  1. Eslam M. Soliman
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  2. Sherif H. Aboubakr
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Correspondence to Mahmoud M. Reda Taha.

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Soliman, E.M., Aboubakr, S.H. & Reda Taha, M.M. Estimating fracture toughness of C–S–H using nanoindentation and the extended finite element method. Int J Adv Eng Sci Appl Math 9, 154–168 (2017). https://doi.org/10.1007/s12572-017-0191-8

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