Multiscale Modeling of Elastic Modulus across Micro-Meso-Macroscales Based on Grid-Nanoindentation Test for Cementitious Materials
Publication: Journal of Materials in Civil Engineering
Volume 34, Issue 7
Abstract
Estimation of multiscale elastic parameters is of significance for precise design of cementitious material performances, which depends on the materials’ mineral compositions and microstructures. Nanoindentation technology coupling with statistical analysis is an advanced method to probe the mechanical properties of mineral phases, which bridges the equivalent performance of block cementitious materials by upscaling and the microstructures of minerals by downscaling. In this study, grid nanoindentations and mercury intrusion porosimetry (MIP) were performed on cement paste samples with typical water/cement ratios to obtain the elastic modulus of microscopic phases and porosity. Then, upscaling calculation of equivalent elastic modulus was carried out by homogenization methods including dilute method, Mori-Tanaka (M-T) method, self-consistent method, and interaction direct derivation (IDD) method. Comparing calculations with macrotests of elastic modulus, the results are in good agreement with experiment results after considering the effects of capillary pores, especially by the self-consistent method and IDD method. Furtherly, regression analysis using the self-consistent method was employed to obtain the intrinsic elastic modulus of calcium silicate hydrate (CSH) monomers and packing density of CSH clusters, which is in agreement with reported simulation results by molecular dynamics. This work established the relationships quantitatively among gene minerals with special nanostructures, microstructures of cement pastes and macroelastic performances of block cement materials by a multiscale calculation framework across micro-meso-macroscales, offering a foundation for further multiscale design of high-performance construction materials in civil engineering.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request (measured nanoindentation data of cement paste; codes of different homogenization methods).
Acknowledgments
This work was supported by grants from the National Natural Science Foundations of China (Nos. 51308334 and 51479113), which are gratefully acknowledged.
References
Adessina, A., A. Ben Fraj, J. F. Barthelemy, C. Chateau, and D. Garnier. 2019. “Experimental and micromechanical investigation on the mechanical and durability properties of recycled aggregates concrete.” Cem. Concr. Res. 126 (Dec): 105900. https://doi.org/10.1016/j.cemconres.2019.105900.
Bernard, O., F. J. Ulm, and E. Lemarchand. 2003. “A multiscale mictomechanics-hydration model for the early-age elastic properties of cement-based materials.” Cem. Concr. Res. 33 (9): 1293–1309. https://doi.org/10.1016/s0008-8846(03)00039-5.
Chen, X., D. Hou, Y. Han, X. Ding, and P. Hua. 2021. “Clustering analysis of grid nanoindentation data for cementitious materials.” J. Mater. Sci. 56 (21): 12238–12255. https://doi.org/10.1007/s10853-021-05848-8.
Constantinides, G., K. S. R. Chandran, F. J. Ulm, and K. J. Van Vliet. 2006. “Grid indentation analysis of composite microstructure and mechanics: Principles and validation.” Mater. Sci. Eng. A 430 (1–2): 189–202. https://doi.org/10.1016/j.msea.2006.05.125.
Constantinides, G., and F. J. Ulm. 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 (1): 67–80. https://doi.org/10.1016/s0008-8846(03)00230-8.
Constantinides, G., F. J. Ulm, and K. Van Vliet. 2003. “On the use of nanoindentation for cementitious materials.” Mater. Struct. 36 (257): 191–196. https://doi.org/10.1007/bf02479557.
Damien, D., Y. Wang, and Y. Xi. 2019. “Prediction of elastic properties of cementitious materials based on multiphase and multiscale micromechanics theory.” J. Eng. Mech. 145 (10): 04019074. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001650.
Dunn, M. L., and H. Ledbetter. 1995. “Poisson’s ratio of porous and microcracked solids: Theory and application to oxide superconductors.” J. Mater. Res. 10 (11): 2715–2722. https://doi.org/10.1557/jmr.1995.2715.
Fang, G., and M. Zhang. 2020. “Multiscale micromechanical analysis of alkali-activated fly ash-slag paste.” Cem. Concr. Res. 135 (Sep): 106141. https://doi.org/10.1016/j.cemconres.2020.106141.
Gao, X., Y. Wei, and W. Huang. 2017. “Effect of individual phases on multiscale modeling mechanical properties of hardened cement paste.” Constr. Build. Mater. 153 (Oct): 25–35. https://doi.org/10.1016/j.conbuildmat.2017.07.074.
Goebel, L., C. Bos, R. Schwaiger, A. Flohr, and A. Osburg. 2018. “Micromechanics-based investigation of the elastic properties of polymer-modified cementitious materials using nanoindentation and semi-analytical modeling.” Cem. Concr. Compos. 88 (Apr): 100–114. https://doi.org/10.1016/j.cemconcomp.2018.01.010.
Hill, R. 1965. “A self-consistent mechanics of composite materials.” J. Mech. Phys. Solids 13 (4): 213–222. https://doi.org/10.1016/0022-5096(65)90010-4.
Honorio, T., L. Brochard, and B. Bary. 2018. “Statistical variability of mechanical fields in thermo-poro-elasticity: Multiscale analytical estimations applied to cement-based materials at early age.” Cem. Concr. Res. 110 (Aug): 24–41. https://doi.org/10.1016/j.cemconres.2018.05.010.
Hu, C. L. 2014. “Microstructure and mechanical properties of fly ash blended cement pastes.” Constr. Build. Mater. 73 (Dec): 618–625. https://doi.org/10.1016/j.conbuildmat.2014.10.009.
Hu, C. L., and Z. J. Li. 2015. “A review on the mechanical properties of cement-based materials measured by nanoindentation.” Constr. Build. Mater. 90 (Aug): 80–90. https://doi.org/10.1016/j.conbuildmat.2015.05.008.
Jennings, H. M. 2004. “Colloid model of C-S-H and implications to the problem of creep and shrinkage.” Mater. Struct. 37 (265): 59–70. https://doi.org/10.1007/bf02481627.
Jennings, H. M. 2008. “Refinements to colloid model of C-S-H in cement: CM-II.” Cem. Concr. Res. 38 (3): 275–289. https://doi.org/10.1016/j.cemconres.2007.10.006.
Jennings, H. M., J. J. Thomas, J. S. Gevrenov, G. Constantinides, and F. J. Ulm. 2007. “A multi-technique investigation of the nanoporosity of cement paste.” Cem. Concr. Res. 37 (3): 329–336. https://doi.org/10.1016/j.cemconres.2006.03.021.
Jiang, L., C. Hu, Y. Zhang, and Z. Li. 2012. “Calculation of elastic modulus of early-age cement paste.” Adv. Cem. Res. 24 (4): 193–201. https://doi.org/10.1680/adcr.11.00002.
Liang, S., Y. Wei, and Z. Wu. 2017. “Multiscale modeling elastic properties of cement-based materials considering imperfect interface effect.” Constr. Build. Mater. 154 (Nov): 567–579. https://doi.org/10.1016/j.conbuildmat.2017.07.196.
Mori, T., and K. Tanaka. 1973. “Average stress in matrix and average elastic energy of materials with misfitting inclusions.” Acta Metall. 21 (5): 571–574. https://doi.org/10.1016/0001-6160(73)90064-3.
Nemecek, J., V. Smilauer, and L. Kopecky. 2011. “Nanoindentation characteristics of alkali-activated aluminosilicate materials.” Cem. Concr. Compos. 33 (2): 163–170. https://doi.org/10.1016/j.cemconcomp.2010.10.005.
Oliver, W. C., and G. M. Pharr. 1992. “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments.” J. Mater. Res. 7 (6): 1564–1583. https://doi.org/10.1557/jmr.1992.1564.
Oliver, W. C., and G. M. Pharr. 2004. “Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology.” J. Mater. Res. 19 (1): 3–20. https://doi.org/10.1557/jmr.2004.19.1.3.
Papadopoulos, V., and M. Impraimakis. 2017. “Multiscale modeling of carbon nanotube reinforced concrete.” Compos. Struct. 182 (Dec): 251–260. https://doi.org/10.1016/j.compstruct.2017.09.061.
Pellenq, R. J. M., A. Kushima, R. Shahsavari, K. J. Van Vliet, M. J. Buehler, S. Yip, and F. J. Ulm. 2009. “A realistic molecular model of cement hydrates.” Proc. Natl. Acad. Sci. U.S.A. 106 (38): 16102–16107. https://doi.org/10.1073/pnas.0902180106.
Randall, N. X., M. Vandamme, and F. J. Ulm. 2009. “Nanoindentation analysis as a two-dimensional tool for mapping the mechanical properties of complex surfaces.” J. Mater. Res. 24 (3): 679–690. https://doi.org/10.1557/jmr.2009.0149.
Sanahuja, J., L. Dormieux, and G. Chanvillard. 2007. “Modelling elasticity of a hydrating cement paste.” Cem. Concr. Res. 37 (10): 1427–1439. https://doi.org/10.1016/j.cemconres.2007.07.003.
Shaanxi Academy of Architectural Sciences. 2009. Standard for test method of basic properties of construction mortar. JGJ/T 70-2009, 34–36. Beijing: China Architecture & Building Press.
Stefaniuk, D., P. Niewiadomski, M. Musial, and D. Lydzba. 2019. “Elastic properties of self-compacting concrete modified with nanoparticles: Multiscale approach.” Arch. Civ. Mech. Eng. 19 (4): 1150–1162. https://doi.org/10.1016/j.acme.2019.06.006.
Tennis, P. D., and H. M. Jennings. 2000. “A model for two types of calcium silicate hydrate in the microstructure of portland cement pastes.” Cem. Concr. Res. 30 (6): 855–863. https://doi.org/10.1016/s0008-8846(00)00257-x.
Ulm, F. J., M. Vandamme, C. Bobko, and J. A. Ortega. 2007. “Statistical indentation techniques for hydrated nanocomposites: Concrete, bone, and shale.” J. Am. Ceram. Soc. 90 (9): 2677–2692. https://doi.org/10.1111/j.1551-2916.2007.02012.x.
Vandamme, M., and F. J. Ulm. 2013. “Nanoindentation investigation of creep properties of calcium silicate hydrates.” Cem. Concr. Res. 52 (Oct): 38–52. https://doi.org/10.1016/j.cemconres.2013.05.006.
Velez, K., S. Maximilien, D. Damidot, G. Fantozzi, and F. Sorrentino. 2001. “Determination by nanoindentation of elastic modulus and hardness of pure constituents of portland cement clinker.” Cem. Concr. Res. 31 (4): 555–561. https://doi.org/10.1016/s0008-8846(00)00505-6.
Xu, J., B. Wang, and J. Zuo. 2017. “Modification effects of nanosilica on the interfacial transition zone in concrete: A multiscale approach.” Cem. Concr. Compos. 81 (Aug): 1–10. https://doi.org/10.1016/j.cemconcomp.2017.04.003.
Zaoui, A. 2002. “Continuum micromechanics: Survey.” J. Eng. Mech. 128 (8): 808–816. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:8(808).
Zhang, Y., Z. G. Yan, J. W. Ju, H. H. Zhu, and Q. Chen. 2017. “A multi-level micromechanical model for elastic properties of hybrid fiber reinforced concrete.” Constr. Build. Mater. 152 (Oct): 804–817. https://doi.org/10.1016/j.conbuildmat.2017.07.024.
Zheng, Q. S., and D. X. Du. 2001. “An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution.” J. Mech. Phys. Solids 49 (11): 2765–2788. https://doi.org/10.1016/s0022-5096(01)00078-3.
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Received: Jul 22, 2021
Accepted: Oct 29, 2021
Published online: Apr 22, 2022
Published in print: Jul 1, 2022
Discussion open until: Sep 22, 2022
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