In this paper, three-scale stochastic elastic finite element analyses are made for recycled aggregate concrete (RAC) based on nano-indentation digital images. The elastic property of RAC contains uncertainties across scales. It has both theoretical and practical values to model and predict its mechanical performance. Based on homogenization theory, effective stochastic elastic moduli of RAC at three different scales are obtained using moving window technique, nano-indentation digital images, and Monte-Carlo method. It involves the generation of a large number of random realizations of microstructure geometry based on different volume fraction of the inclusions and other parameters. The mean value, coefficient of variation and probability distribution of the effective elastic moduli are computed considering the material multiscale structure. The microscopic randomness is taken into account, and correlations of RAC among five phases are investigated. The effective elastic properties are used to obtain the global behavior of a composite structure. It is indicated that the response variability can be considerably affected by replacement percentage of recycled aggregates.
Xiao J, Sun C, Jiang X. Flexural behavior of recycled aggregate concrete graded slabs. Structural Concrete, 2014, 16(2): 249–261 https://doi.org/10.1002/suco.201400008
2
Li T, Xiao J, Zhu C, Zhong Z. Experimental study on mechanical behaviors of concrete with large-size recycled coarse aggregate. Construction & Building Materials, 2016, 120: 321–328 https://doi.org/10.1016/j.conbuildmat.2016.05.110
3
Waseem S A, Singh B. Shear transfer strength of normal and high-strength recycled aggregate concrete—An experimental investigation. Construction & Building Materials, 2016, 125: 29–40 https://doi.org/10.1016/j.conbuildmat.2016.08.022
4
Vinay Kumar B M, Ananthan H, Balaji K V A. Experimental studies on utilization of coarse and finer fractions of recycled concrete aggregates in self compacting concrete mixes. Journal of Building Engineering, 2017, 9: 100–108 https://doi.org/10.1016/j.jobe.2016.11.013
5
Xiao J, Li W, Liu Q. Meso-level numerical simulation on mechanical properties of modeled recycled concrete under uniaxial compression. Journal of Tongji University—Natural Science, 2011, 39(6): 791–797
6
Li W, Xiao J, Yuan J. Stress distribution characteristics of modeled recycled aggregate concrete under uniaxial compression. Journal of Tongji University—Natural Science, 2012, 40(6): 906–913
7
Peng Y, Chu H, Pu J. Numerical simulation of recycled concrete using convex aggregate model and base force element method. Advances in Materials Science and Engineering, 2016, (1): 1–10
8
Hughes J J, Trtik P. Micro-mechanical properties of cement paste measured by depth-sensing nanoindentation: A preliminary correlation of physical properties with phase type. Materials Characterization, 2004, 53(2-4): 223–231 https://doi.org/10.1016/j.matchar.2004.08.014
9
Wu Y, Kang L, Li H. Determination of elastic-plastic and creep of calcium-silicate-hydrate gel. Chinese Journal of Materials Research, 2010(2):123–128
10
Li W, Xiao J, Huang L, Shah S P. Experimental study on mechanical properties of interracial transition zones in recycled aggregate concrete. Journal of Hunan University—Natural Sciences, 2014, 41(12): 31–39 https://doi.org/10.3724/SP.J.1238.2013.00031
11
Sorelli L, Constantinides G, Ulm F J, Toutlemonde F. The nano-mechanical signature of ultra high performance concrete by statistical nanoindentation techniques. Cement and Concrete Research, 2008, 38(12): 1447–1456 https://doi.org/10.1016/j.cemconres.2008.09.002
12
Němeček J, Králík V, Vondřejc J. Micromechanical analysis of heterogeneous structural materials. Cement and Concrete Composites, 2013, 36(3): 85–92 https://doi.org/10.1016/j.cemconcomp.2012.06.015
13
Silva W R L D, Němeček J, Štemberk P. Application of multiscale elastic homogenization based on nanoindentation for high performance concrete. Advances in Engineering Software, 2013, 62-63(8): 109–118 https://doi.org/10.1016/j.advengsoft.2013.04.007
14
Němeček J, Šmilauer V, Kopecký L. Nanoindentation characteristics of alkali-activated aluminosilicate materials. Cement and Concrete Composites, 2011, 33(2): 163–170 https://doi.org/10.1016/j.cemconcomp.2010.10.005
15
Pharr W. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. Journal of Materials Research Home, 2011, 7(6): 1564–1583
16
Kamiński M, Kleiber M. Perturbation based stochastic finite element method for homogenization of two-phase elastic composites. Computers & Structures, 2000, 78(6): 811–826 https://doi.org/10.1016/S0045-7949(00)00116-4
17
Povirk G L. Incorporation of microstructural information into models of two-phase materials. Acta Metallurgica et Materialia, 1995, 43(8): 3199–3206 https://doi.org/10.1016/0956-7151(94)00487-3
18
Gusev A A. Representative volume element size for elastic composites: A numerical study. Journal of the Mechanics and Physics of Solids, 1997, 45(9): 1449–1459 https://doi.org/10.1016/S0022-5096(97)00016-1
19
Zaitsev Y B, Wittmann F H. Simulation of crack propagation and failure of concrete. Materials and Structures, 1981, 14(5): 357– 365
20
Walraven J C. Aggregate interlock: A theoretical and experimental analysis. Delft: Delft University Press, 1980
21
Voigt W. Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper. Annalen der Physik, 1889, 274(12): 573–587 (in German) https://doi.org/10.1002/andp.18892741206
22
Reuss A. Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. Journal of Applied Mathematics and Mechanics, 1929, 9(1): 49–58 (in German) https://doi.org/10.1002/zamm.19290090104
23
Savvas D, Stefanou G, Papadrakakis M. Determination of RVE size for random composites with local volume fraction variation. Computer Methods in Applied Mechanics and Engineering, 2016, 305: 340–358 https://doi.org/10.1016/j.cma.2016.03.002
24
Vu-Bac N, Lahmer T, Zhang Y, Zhuang X, Rabczuk T. Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs). Composites. Part B, Engineering, 2014, 59: 80–95 https://doi.org/10.1016/j.compositesb.2013.11.014
25
Hamdia K M, Msekh M A, Silani M, Vu-Bac N, Zhuang X, Nguyen-Thoi T, Rabczuk T. Uncertainty quantification of the fracture properties of polymeric nanocomposites based on phase field modeling. Composite Structures, 2015, 133: 1177–1190 https://doi.org/10.1016/j.compstruct.2015.08.051
26
Vu-Bac N, Silani M, Lahmer T, Zhuang X, Rabczuk T. A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites. Computational Materials Science, 2015, 96: 520–535 https://doi.org/10.1016/j.commatsci.2014.04.066
27
Vu-Bac N, Rafiee R, Zhuang X, Lahmer T, Rabczuk T. Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters. Composites. Part B, Engineering, 2015, 68: 446–464 https://doi.org/10.1016/j.compositesb.2014.09.008
28
Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31 https://doi.org/10.1016/j.advengsoft.2016.06.005
