Research Papers

Constitutive Stiffness Characteristics of Cement Paste as a Multiphase Composite System—A Molecular Dynamics-Based Model

[+] Author and Article Information
Ingrid M. Padilla Espinosa

Nanoengineering Department,
Joint School of Nanoscience
and Nanoengineering,
North Carolina A&T State University,
2907 E Gate City Boulevard,
Greensboro, NC 27401
e-mail: impadill@aggies.ncat.edu

Wayne Hodo

Engineering Research and Development Center,
3909 Halls Ferry Road,
Vicksburg, MS 39180
e-mail: Wayne.d.hodo@usace.army.mil

John S. Rivas Murillo

Nanoengineering Department,
Joint School of Nanoscience
and Nanoengineering,
North Carolina A&T State University,
2907 E Gate City Boulevard,
Greensboro, NC 27401
e-mail: jrmurill@ncat.edu

A. M. Rajendran

Department of Mechanical Engineering,
University of Mississippi,
Oxford, MS 38677
e-mail: raj@olemiss.edu

Ram V. Mohan

Nanoengineering Department,
Joint School of Nanoscience
and Nanoengineering,
North Carolina A&T State University,
2907 E Gate City Boulevard,
Greensboro, NC 27401
e-mail: rvmohan@ncat.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received October 3, 2016; final manuscript received March 30, 2017; published online May 25, 2017. Assoc. Editor: Hareesh Tippur.

J. Eng. Mater. Technol 139(4), 041007 (May 25, 2017) (7 pages) Paper No: MATS-16-1282; doi: 10.1115/1.4036588 History: Received October 03, 2016; Revised March 30, 2017

Cement paste is a material with heterogeneous composite structure consisting of hydrated and unhydrated phases at all length scales that varies depending upon the degree of hydration. In this paper, a method to model cement paste as a multiphase system at molecular level for predicting constitutive properties and for understanding the constitutive mechanical behavior characteristics using molecular dynamics is presented. The proposed method creates a framework for molecular level models suitable for predicting constitutive properties of heterogeneous cement paste that could provide potential for comparisons with low length scale experimental characterization techniques. The molecular modeling method followed two approaches: one involving admixed molecular phases and the second involving clusters of the individual phases. In particular, in the present study, cement paste is represented as two-phase composite systems consisting of the calcium silicate hydrate (CSH) phase combined with unhydrated phases tricalcium silicate (C3S) or dicalcium silicate (C2S). Predicted elastic stiffness constants based on molecular model representations employed for the two phases showed that, although the individual phases have anisotropic characteristics, the composite system behaves as an isotropic material. The isotropic characteristics seen from two-phase molecular models mimic the isotropic material nature of heterogeneous cement paste at engineering scale. Further, predicted bulk modulus of the composite system based on molecular modeling is found to be high compared to the elastic modulus, which concurs with the high compression strength of cement paste seen at engineering length scales.

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Garboczi, E. J. , 1995, “ Microstructure and Transport Properties of Concrete,” Performance Criteria for Concrete Durability, J. Kropp and H. K. Hilsdorf , eds., RILEM, London.
Garboczi, E. J. , and Bentz, D. P. , 1998, “ Concrete: A Multi-Scale Interactive Composite,” International RILEM Conference, Haifa, Israel, Mar. 8–12, pp. 43–50.
Garboczi, E. J. , and Bentz, D. P. , 1996, “ Multi-Scale Picture of Concrete and Its Transport Properties: Introduction for Non-Cement Researchers,” National Institute of Standards and Technology, Gaithersburg, MD, Report No. NISTIR 5900.
Powers, T. C. , 1958, “ Structure and Physical Properties of Hardened Portland Cement Paste,” J. Am. Ceram. Soc., 41(1), pp. 1–6. [CrossRef]
American Concrete Institute, and A. C. I. Committee 225, 1999, “ 225R-99: Guide to the Selection and Use of Hydraulic Cements,” American Concrete Institute, Farmington Hills, MI, Report No. ACI 225R-99.
Mehta, P. K. , and Monteiro, P. J. M. , 2006, Concrete: Microstructure, Properties, and Materials, 3rd ed., McGraw Hill Professional, McGraw-Hill Education, New York.
Richardson, I. G. , 2000, “ The Nature of the Hydration Products in Hardened Cement Pastes,” Cem. Concr. Compos., 22(2), pp. 97–113. [CrossRef]
Richardson, I. G. , Skibsted, J. , Black, L. , and Kirkpatrick, R. J. , 2010, “ Characterisation of Cement Hydrate Phases by TEM, NMR and Raman Spectroscopy,” Adv. Cem. Res., 22(4), pp. 233–248. [CrossRef]
Taylor, R. , Richardson, I. G. , and Brydson, R. M. D. , 2007, “ Nature of C-S-H in 20 Year Old Neat Ordinary Portland Cement and 10% Portland Cement-90% Ground Granulated Blast Furnace Slag Pastes,” Adv. Appl. Ceram., 106(6), pp. 294–301. [CrossRef]
Odler, I. , 1998, “ 6—Hydration, Setting and Hardening of Portland Cement A2—Hewlett, Peter C.,” Lea's Chemistry of Cement and Concrete, 4th ed., P. C. Hewlett , ed., Butterworth-Heinemann, Oxford, UK, pp. 241–297.
Taylor, H. F. W. , 1997, Cement Chemistry, Thomas Telford, London.
Haecker, C. , Garboczi, E. J. , Bullard, J. W. , Bohn, R. B. , Sun, Z. , Shah, S. P. , and Voigt, T. , 2005, “ Modeling the Linear Elastic Properties of Portland Cement Paste,” Cem. Concr. Res., 35(10), pp. 1948–1960. [CrossRef]
Bernard, O. , Ulm, F.-J. , and Lemarchand, E. , 2003, “ A Multiscale Micromechanics-Hydration Model for the Early-Age Elastic Properties of Cement-Based Materials,” Cem. Concr. Res., 33(9), pp. 1293–1309. [CrossRef]
Smilauer, V. , and Bittnar, Z. , 2006, “ Microstructure-Based Micromechanical Prediction of Elastic Properties in Hydrating Cement Paste,” Cem. Concr. Res., 36(9), pp. 1708–1718. [CrossRef]
Sanahuja, J. , Dormieux, L. , and Chanvillard, G. , 2007, “ Modelling Elasticity of a Hydrating Cement Paste,” Cem. Concr. Res., 37(10), pp. 1427–1439. [CrossRef]
Hain, M. , and Wriggers, P. , 2008, “ Numerical Homogenization of Hardened Cement Paste,” Comput. Mech., 42(2), pp. 197–212. [CrossRef]
Pichler, B. , Hellmich, C. , and Eberhardsteiner, J. , 2009, “ Spherical and Acicular Representation of Hydrates in a Micromechanical Model for Cement Paste: Prediction of Early-Age Elasticity and Strength,” Acta Mech., 203(3–4), pp. 137–162. [CrossRef]
Ghabezloo, S. , 2010, “ Association of Macroscopic Laboratory Testing and Micromechanics Modelling for the Evaluation of the Poroelastic Parameters of a Hardened Cement Paste,” Cem. Concr. Res., 40(8), pp. 1197–1210.
Hua, C. , Ehrlacher, A. , and Acker, P. , 1997, “ Analyses and Aodels of the Autogenous Shrinkage of Hardening Cement Paste—2: Modelling at Scale of Hydrating Grains,” Cem. Concr. Res., 27(2), pp. 245–258. [CrossRef]
Shahzamanian, M. M. , Tadepalli, T. , Rajendran, A. M. , Hodo, W. D. , Mohan, R. , Valisetty, R. , Chung, P. W. , and Ramsey, J. J. , 2013, “ Representative Volume Element Based Modeling of Cementitious Materials,” ASME J. Eng. Mater. Technol., 136(1), p. 011007. [CrossRef]
Velez, K. , Maximilien, S. , Damidot, D. , Fantozzi, G. , and Sorrentino, F. , 2001, “ Determination by Nanoindentation of Elastic Modulus and Hardness of Pure Constituents of Portland Cement Clinker,” Cem. Concr. Res., 31(4), pp. 555–561. [CrossRef]
Constantinides, G. , and 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(1), pp. 67–80. [CrossRef]
Acker, P. , 2004, “ Swelling, Shrinkage and Creep: A Mechanical Approach to Cement Hydration,” Mater. Struct., 37(268), pp. 237–243. [CrossRef]
Xu, J. , Corr, D. J. , and Shah, S. P. , 2015, “ Nanomechanical Properties of C-S-H Gel/Cement Grain Interface by Using Nanoindentation and Modulus Mapping,” J. Zhejiang Univ.-Sci. A, 16(1), pp. 38–46. [CrossRef]
Howind, T. , Hughes, J. , and Zhu, W. , 2014, “ Mapping of Mechanical Properties of Cement-Based Materials at Micro/Nano-Scale,” J. Innovative Eng., 2(1), p. 2.
Constantinides, G. , Ulm, F. , and Van Vliet, K. , 2003, “ On the Use of Nanoindentation for Cementitious Materials,” Mater. Struct., 36(257), pp. 191–196. [CrossRef]
Neubauer, C. M. , Bergstrom, T. B. , Sujata, K. , Xi, Y. , Garboczi, E. J. , and Jennings, H. M. , 1997, “ Drying Shrinkage of Cement Paste as Measured in an Environmental Scanning Electron Microscope and Comparison With Microstructural Models,” J. Mater. Sci., 32(24), pp. 6415–6427. [CrossRef]
Laugesen, J. L. , 2005, “ Density Functional Calculations of Elastic Properties of Portlandite, Ca(OH)(2),” Cem. Concr. Res., 35(2), pp. 199–202. [CrossRef]
Wu, W. , Al-Ostaz, A. , Cheng, A. H. D. , and Song, C. R. , 2011, “ Computation of Elastic Properties of Portland Cement Using Molecular Dynamics,” J. Nanomech. Micromech., 1(2), pp. 84–90. [CrossRef]
Mishra, R. K. , Flatt, R. J. , and Heinz, H. , 2013, “ Force Field for Tricalcium Silicate and Insight Into Nanoscale Properties: Cleavage, Initial Hydration, and Adsorption of Organic Molecules,” J. Phys. Chem. C, 117(20), pp. 10417–10432. [CrossRef]
Hou, D. , Zhu, Y. , Lu, Y. , and Li, Z. , 2014, “ Mechanical Properties of Calcium Silicate Hydrate (C–S–H) at Nano-Scale: A Molecular Dynamics Study,” Mater. Chem. Phys., 146(3), pp. 503–511.
Pellenq, R. J. M. , Kushima, A. , Shahsavari, R. , Van Vliet, K. J. , Buehler, M. J. , Yip, S. , and Ulm, F.-J. , 2009, “ A Realistic Molecular Model of Cement Hydrates,” Proc. Natl. Acad. Sci. U. S. A., 106(38), pp. 16102–16107. [CrossRef] [PubMed]
Manzano, H. , Dolado, J. S. , and Ayuela, A. , 2009, “ Elastic Properties of the Main Species Present in Portland Cement Pastes,” Acta Mater., 57(5), pp. 1666–1674. [CrossRef]
Gmira, A. , Zabat, M. , Pellenq, R. J. M. , and Van Damme, H. , 2004, “ Microscopic Physical Basis of the Poromechanical Behavior of Cement-Based Materials,” Mater. Struct., 37(265), pp. 3–14. [CrossRef]
Hajilar, S. , and Shafei, B. , 2015, “ Nano-Scale Investigation of Elastic Properties of Hydrated Cement Paste Constituents Using Molecular Dynamics Simulations,” Comput. Mater. Sci., 101, pp. 216–226. [CrossRef]
Taylor, H. F. W. , 1986, “ Proposed Structure for Calcium Silicate Hydrate Gel.,” J. Am. Ceram. Soc., 69(6), pp. 464–467. [CrossRef]
Murillo, J. S. R. , Mohamed, A. , Hodo, W. , Mohan, R. V. , Rajendran, A. , and Valisetty, R. , 2016, “ Computational Modeling of Shear Deformation and Failure of Nanoscale Hydrated Calcium Silicate Hydrate in Cement Paste: Calcium Silicate Hydrate Jennite,” Int. J. Damage Mech., 25(1), pp. 98–114. [CrossRef]
Downs, R. T. , and Hall-Wallace, M. , 2003, “ The American Mineralogist Crystal Structure Database,” Am. Mineral., 88(1), pp. 247–250.
Bonaccorsi, E. , Merlino, S. , and Taylor, H. F. W. , 2004, “ The Crystal Structure of Jennite, Ca9Si6O18(OH)6·8H2O,” Cem. Concr. Res., 34(9), pp. 1481–1488. [CrossRef]
Golovastikov, N. I. , Matveera, R. G. , and Belov, N. V. , 1975, “ Crystal Structure of the Tricalcium Silicate 3CaO.SiO2=C3S,” Kristallografiya, 20, pp. 721–729.
Tsurumi, T. , Hirano, Y. , Kato, H. , Kamiya, T. , and Daimon, M. , 1994, “ Crystal Structure and Hydration of Belite,” Ceram. Trans., 40, pp. 19–25.
Dassault Systèmes BIOVIA, 2015, “ Materials Studio Modeling Environment, Release 6.0,” Dassault Systèmes, San Diego, CA.
Sun, H. , Ren, P. , and Fried, J. R. , 1998, “ The COMPASS Force Field: Parameterization and Validation for Phosphazenes,” Comput. Theor. Polym. Sci., 8(1–2), pp. 229–246. [CrossRef]
Sun, H. , and Rigby, D. , 1997, “ Polysiloxanes: Ab Initio Force Field and Structural, Conformational and Thermophysical Properties,” Spectrochim. Acta Part A-Mol. Biomol. Spectrosc., 53(8), pp. 1301–1323. [CrossRef]
Zhao, L. F. , Liu, L. C. , and Sun, H. , 2007, “ Semi-Ionic Model for Metal Oxides and Their Interfaces With Organic Molecules,” J. Phys. Chem. C, 111(28), pp. 10610–10617. [CrossRef]
Hub, J. S. , de Groot, B. L. , Grubmüller, H. , and Groenhof, G. , 2014, “ Quantifying Artifacts in Ewald Simulations of Inhomogeneous Systems With a Net Charge,” J. Chem. Theory Comput., 10(1), pp. 381–390. [CrossRef] [PubMed]
Payne, M. C. , Teter, M. P. , Allan, D. C. , Arias, T. A. , and Joannopoulos, J. D. , 1992, “ Iterative Minimization Techniques for Ab Initio Total-Energy Calculations: Molecular Dynamics and Conjugate Gradients,” Rev. Mod. Phys., 64(4), pp. 1045–1097. [CrossRef]
Parrinello, M. , and Rahman, A. , 1980, “ Crystal Structure and Pair Potentials: A Molecular-Dynamics Study,” Phys. Rev. Lett., 45(14), pp. 1196–1199. [CrossRef]
Ray, J. R. , Moody, M. C. , and Rahman, A. , 1986, “ Calculation of Elastic-Constants Using Isothermal Molecular-Dynamics,” Phys. Rev. B, 33(2), pp. 895–899. [CrossRef]
Theodorou, D. N. , and Ulrich, W. S. , 1986, “ Atomistic Modeling of Mechanical Properties of Polymeric Glasses,” Macromolecules, 19(1), pp. 139–154. [CrossRef]
Skrzypek, J. J. , and Ganczarski, A. W. W. , 2015, Mechanics of Anisotropic Materials, Springer International Publishing, Cham, Switzerland.
Brown, J. M. , 2015, “ Determination of Hashin-Shtrikman Bounds on the Isotropic Effective Elastic Moduli of Polycrystals of Any Symmetry,” Comput. Geosci., 80, pp. 95–99. [CrossRef]
Hill, R. , 1952, “ The Elastic Behaviour of a Crystalline Aggregate,” Proc. Phys. Soc. Sec. A, 65(5), p. 349. [CrossRef]
Chawla, K. K. , 2006, “ Metal Matrix Composites,” Materials Science and Technology, Springer, New York.
Boumiz, A. , Sorrentino, D. , Vernet, C. , and Tenoudji, F. C. , 1997, “ Modelling the Development of the Elastic Moduli as a Function of the Hydration Degree of Cement Pastes and Mortars,” Second International RILEM Symposium on Hydration and Setting, pp. 295–316.
Shahsavari, R. , Buehler, M. J. , Pellenq, R. J. M. , and Ulm, F. J. , 2009, “ First-Principles Study of Elastic Constants and Interlayer Interactions of Complex Hydrated Oxides: Case Study of Tobermorite and Jennite,” J. Am. Ceram. Soc., 92(10), pp. 2323–2330. [CrossRef]
Dharmawardhana, C. C. , Misra, A. , Aryal, S. , Rulis, P. , and Ching, W. Y. , 2013, “ Role of Interatomic Bonding in the Mechanical Anisotropy and Interlayer Cohesion of CSH Crystals,” Cem. Concr. Res., 52, pp. 123–130. [CrossRef]


Grahic Jump Location
Fig. 1

Unit cell molecular structure of (a) CSH—jennite, (b) C3S, and (c) C2S

Grahic Jump Location
Fig. 5

Bulk modulus of two-phase cement paste composite systems: (a) CSH + C3S and (b) CSH + C2S

Grahic Jump Location
Fig. 4

Isotropy relations of the stiffness constants for two-phase structures of CSH and C2S: (a) C11 ≈ C22 ≈ C33, (b) C12 ≈ C13 ≈ C23, and (c) C44 ≈ (C11 − C12)/2. The dotted lines show a linear trend of the constants, short dashed correspond to approach A and long dashed correspond to approach B.

Grahic Jump Location
Fig. 3

Isotropy relations of the stiffness constants for two-phase structures of CSH and C3S: (a) C11 ≈ C22 ≈ C33, (b) C12 ≈ C13 ≈ C23, and (c) C44 ≈ (C11 − C12)/2. The dotted lines show a linear trend of the constants, short dashed correspond to approach A and long dashed correspond to approach B.

Grahic Jump Location
Fig. 2

Schematic representation of the methods used to create the two-phase cement paste molecular structures used in this study: (a) approach A and (b) approach B




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