Title:
Molecular Material Modeling of Cement Paste Composite in Shock Loading
Author(s):
Ingrid M. Padilla Espinosa, John S. Rivas Murillo, and Ram V. Mohan
Publication:
Materials Journal
Volume:
117
Issue:
6
Appears on pages(s):
89-100
Keywords:
calcium silicate hydrate; equation of state; Grüneisen parameter; isothermal compression; molecular dynamics simulations; nanoscale cement paste
DOI:
10.14359/51728145
Date:
11/1/2020
Abstract:
The effects of molecular features such as phase composition and distribution on the macroscopic behavior of cement paste (CP) subjected to shock waves are still unknown. This study uses molecular dynamics simulations to predict CP’s constitutive material models with different compositions under longitudinal plane shock waves. The CP models are composites of two phases: the main hydrated phase calcium silicate hydrate (CSH) and one unhydrated calcium silicate phase (tricalcium silicate C3S or dicalcium silicate C2S). The Hugoniot pressure parameters are derived from isothermal pressure-specific volume relations, the bulk modulus, and the Grüneisen parameter, relative to phase compositions. These parameters are estimated using an isothermal hydrostatic compression model and thermal variations under constant volume. Further, predicted Birch-Murnaghan equations of state established that the bulk modulus of CP increases with the content of unhydrated phases. Also, the Grüneisen parameter of CP is reported for the first time in this research.
Related References:
1. Sanchez-Silva, M.; Klutke, G.-A.; and Rosowsky, D. V., “Life-Cycle Performance of Structures Subject to Multiple Deterioration Mechanisms,” Structural Safety, V. 33, No. 3, 2011, pp. 206-217. doi: 10.1016/j.strusafe.2011.03.003
2. Davison, L. W., Fundamentals of Shock Wave Propagation in Solids, Springer-Verlag Berlin Heidelberg, Berlin, Germany, 2008.
3. O’Neil, E. F.; Neeley, B. D.; and Cargile, J. D., “Tensile Properties of Very-High-Strength Concrete for Penetration-Resistant Structures,” Shock and Vibration, V. 6, No. 5-6, 1999, pp. 237-245. doi: 10.1155/1999/415360
4. Pavlovic, A.; Fragassa, C.; and Disic, A., “Comparative Numerical and Experimental Study of Projectile Impact on Reinforced Concrete,” Composites. Part B, Engineering, V. 108, 2017, pp. 122-130. doi: 10.1016/j.compositesb.2016.09.059
5. Garboczi, E. J., “Computational Materials Science of Cement-Based Materials,” Materials and Structures, V. 26, No. 4, 1993, pp. 191-195. doi: 10.1007/BF02472611
6. Maekawa, K.; Ishida, T.; and Kishi, T., Multi-Scale Modeling of Structural Concrete, Taylor & Francis, London, UK, 2008.
7. Wu, W.; Al-Ostaz, A.; Cheng, D.; and Song, C. R., “Concrete as a Hierarchical Structural Composite Material,” International Journal for Multiscale Computational Engineering, V. 8, No. 6, 2010, pp. 585-595. doi: 10.1615/IntJMultCompEng.v8.i6.30
8. Jennings, H. M.; Bullard, J. W.; Thomas, J. J.; Andrade, J.; Chen, J. J.; and Scherer, G. W., “Characterization and Modeling of Pores and Surfaces in Cement Paste,” Journal of Advanced Concrete Technology, V. 6, No. 1, 2008, pp. 5-29. doi: 10.3151/jact.6.5
9. Taylor, H. F. W., Cement Chemistry, Thomas Telford, London, UK, 1997.
10. Powers, T. C., “Structure and Physical Properties of Hardened Portland Cement Paste,” Journal of the American Ceramic Society, V. 41, No. 1, 1958, pp. 1-6. doi: 10.1111/j.1151-2916.1958.tb13494.x
11. Illston, J. M., and Domone, P. L. J., Construction Materials: Their Nature and Behaviour, Spon Press, London, UK, 2001.
12. Mehta, P. K., and Monteiro, P. J. M., Concrete: Microstructure, Properties, and Materials, third edition, McGraw-Hill Education, New York, 2006.
13. Gebbeken, N.; Greulich, S.; and Pietzsch, A., “Hugoniot Properties for Concrete Determined by Full-Scale Detonation Experiments and Flyer-Plate-Impact Tests,” International Journal of Impact Engineering, V. 32, No. 12, 2006, pp. 2017-2031. doi: 10.1016/j.ijimpeng.2005.08.003
14. Tsembelis, K.; Proud, W. G.; Wilmott, G. R.; and Cross, D. L. A., “The Shock Hugoniot Properties of Cement Paste & Mortar up to 18 GPa,” AIP Conference Proceedings, V. 706, No. 1, 2004, pp. 1488-1491. doi: 10.1063/1.1780520
15. Tsembelis, K.; Proud, W. G.; and Field, J. E., “The Dynamic Strength of Cement Paste under Shock Compression,” AIP Conference Proceedings, V. 620, No. 1, 2002, pp. 1414-1418. doi: 10.1063/1.1483804
16. Karinski, Y. S.; Zhutovsky, S.; Feldgun, F. R.; and Yankelevsky, D. Z., “An Experimental Study on the Equation of State of Cementitious Materials Using Confined Compression Tests,” Key Engineering Materials, V. 711, 2016, pp. 830-836. doi: 10.4028/www.scientific.net/KEM.711.830
17. Grote, D. L.; Park, S. W.; and Zhou, M., “Dynamic Behavior of Concrete at High Strain Rates and Pressures: I. Experimental Characterization,” International Journal of Impact Engineering, V. 25, No. 9, 2001, pp. 869-886. doi: 10.1016/S0734-743X(01)00020-3
18. Vu, X. H.; Malecot, Y.; Daudeville, L.; and Buzaud, E., “Experimental Analysis of Concrete Behavior under High Confinement: Effect of the Saturation Ratio,” International Journal of Solids and Structures, V. 46, No. 5, 2009, pp. 1105-1120. doi: 10.1016/j.ijsolstr.2008.10.015
19. Mazzatesta, A. D.; Rosen, M.; Sidhu, H.; and Lindgren, E. A., “Equation of State of Cementitious Materials by Ultrasonic Methodology,” Materials Science and Engineering A, V. 251, No. 1-2, 1998, pp. 121-128. doi: 10.1016/S0921-5093(98)00627-3
20. Nelms, M.; Rajendran, A. M.; Hodo, W.; and Mohan, R., “Shock Wave Propagation in Cementitious Materials at Micro/Meso Scales,” AIP Conference Proceedings, V. 1793, No. 1, 2017, p. 120009 doi: 10.1063/1.4971691
21. Geng, G.; Myers, R. J.; Li, J.; Maboudian, R.; Carraro, C.; Shapiro, D.; and Monteiro, P. J. M., “Aluminum-Induced Dreierketten Chain Cross-Links Increase the Mechanical Properties of Nanocrystalline Calcium Aluminosilicate Hydrate,” Scientific Reports, V. 7, No. 1, 2017, p. 44032. doi: 10.1038/srep44032
22. Moon, J.; Yoon, S.; and Monteiro, P. J. M., “Mechanical Properties of Jennite: A Theoretical and Experimental Study,” Cement and Concrete Research, V. 71, 2015, pp. 106-114. doi: 10.1016/j.cemconres.2015.02.005
23. Cuesta, A.; Rejmak, P.; Ayuela, A.; De la Torre, A. G.; Santacruz, I.; Carrasco, L. F.; Popescu, C.; and Aranda, M. A. G., “Experimental and Theoretical High Pressure Study of Calcium Hydroxyaluminate Phases,” Cement and Concrete Research, V. 97, 2017, pp. 1-10. doi: 10.1016/j.cemconres.2017.03.011
24. Oh, J. E.; Clark, S. M.; Wenk, H.-R.; and Monteiro, P. J. M., “Experimental Determination of Bulk Modulus of 14 Å Tobermorite Using High Pressure Synchrotron X-Ray Diffraction,” Cement and Concrete Research, V. 42, No. 2, 2012, pp. 397-403. doi: 10.1016/j.cemconres.2011.11.004
25. Comboni, D.; Gatta, G. D.; Lotti, P.; Merlini, M.; and Hanfland, M., “Anisotropic Compressional Behavior of Ettringite,” Cement and Concrete Research, V. 120, 2019, pp. 46-51. doi: 10.1016/j.cemconres.2019.03.012
26. Clark, S. M.; Colas, B.; Kunz, M.; Speziale, S.; and Monteiro, P. J. M., “Effect of Pressure on the Crystal Structure of Ettringite,” Cement and Concrete Research, V. 38, No. 1, 2008, pp. 19-26. doi: 10.1016/j.cemconres.2007.08.029
27. Moon, J.; Yoon, S.; Wentzcovitch, R. M.; Clark, S. M.; and Monteiro, P. J. M., “Elastic Properties of Tricalcium Aluminate from High-Pressure Experiments and First-Principles Calculations,” Journal of the American Ceramic Society, V. 95, No. 9, 2012, pp. 2972-2978. doi: 10.1111/j.1551-2916.2012.05301.x
28. Remy, C.; Guyot, F.; and Madon, M., “High Pressure Polymorphism of Dicalcium Silicate Ca2SiO4. A Transmission Electron Microscopy Study,” Physics and Chemistry of Minerals, V. 22, No. 7, 1995, doi: 10.1007/BF00200319
29. Remy, C.; Andrault, D.; and Madon, M., “High-Temperature, High-Pressure X-Ray Investigation of Dicalcium Silicate,” Journal of the American Ceramic Society, V. 80, No. 4, 1997, pp. 851-860. doi: 10.1111/j.1151-2916.1997.tb02914.x
30. Rivas Murillo, J. S.; Hodo, W.; Mohamed, A.; Mohan, R. V.; Rajendran, A.; and Valisetty, R., “A Molecular Dynamics Investigation of Hydrostatic Compression Characteristics of Mineral Jennite,” Cement and Concrete Research, V. 99, 2017, pp. 62-69. doi: 10.1016/j.cemconres.2017.05.004
31. Rivas Murillo, J.; Mohan, R.; and Mohamed, A., “Constitutive Material Models for High Strain Rate Behavior of Cementitious Materials from Material Chemistry—Molecular Dynamics Modeling Methodology with Illustrative Application to Hydrated Calcium Silicate Hydrate Jennite,” Blast Mitigation Strategies in Marine Composite and Sandwich Structures, S. Gopalakrishnan and Y. Rajapakse, eds., 2018, pp. 423-442.
32. Moon, J.-H.; Oh, J. E.; Balonis, M.; Glasser, F. P.; Clark, S. M.; and Monteiro, P. J. M., “Pressure Induced Reactions Amongst Calcium Aluminate Hydrate Phases,” Cement and Concrete Research, V. 41, No. 6, 2011, pp. 571-578. doi: 10.1016/j.cemconres.2011.02.004
33. Manzano, H.; Ayuela, A.; Telesca, T.; Monteiro, P. J. M.; and Dolado, J. S., “Ettringite Strengthening at High Pressures Induced by the Densification of the Hydrogen Bond Network,” The Journal of Physical Chemistry C, V. 116, No. 30, 2012, pp. 16138-16143. doi: 10.1021/jp301822e
34. Lin, W.; Zhang, C.; Fu, J.; and Xin, H., “Dynamic Mechanical Behaviors of Calcium Silicate Hydrate under Shock Compression Loading Using Molecular Dynamics Simulation,” Journal of Non-Crystalline Solids, V. 500, 2018, pp. 482-486. doi: 10.1016/j.jnoncrysol.2018.09.007
35. Padilla Espinosa, I. M.; Hodo, W.; Rivas Murillo, J. S.; Rajendran, A. M.; and Mohan, R. M., “Constitutive Stiffness Characteristics of Cement Paste as a Multiphase Composite System—A Molecular Dynamics-Based Model,” Journal of Engineering Materials and Technology, V. 139, No. 4, 2017, p. 041007 doi: 10.1115/1.4036588
36. Chen, J. J.; Thomas, J. J.; Taylor, H. F. W.; and Jennings, H. M., “Solubility and Structure of Calcium Silicate Hydrate,” Cement and Concrete Research, V. 34, No. 9, 2004, pp. 1499-1519. doi: 10.1016/j.cemconres.2004.04.034
37. Richardson, I., “Model Structures for C-(A)-S-H(I),” Acta Crystallographica. Section B, Structural Crystallography and Crystal Chemistry, V. 70, No. 6, 2014, pp. 903-923.
38. Carpenter, A. B.; Chalmers, R. A.; Gard, J. A.; Speakman, K.; and Taylor, H. F. W., “Jennite, A New Mineral,” The American Mineralogist, V. 51, No. 1-2, 1966, pp. 56-74.
39. Bonaccorsi, E.; Merlino, S.; and Kampf, A. R., “The Crystal Structure of Tobermorite 14 A (Plombierite), a C-S-H Phase,” Journal of the American Ceramic Society, V. 88, No. 3, 2005, pp. 505-512. doi: 10.1111/j.1551-2916.2005.00116.x
40. Merlino, S.; Bonaccorsi, E.; and Armbruster, T., “The Real Structure of Tobermorite 11A: Normal and Anomalous Forms, OD Character and Polytypic Modifications,” European Journal of Mineralogy, V. 13, No. 3, 2001, pp. 577-590. doi: 10.1127/0935-1221/2001/0013-0577
41. Merlino, S.; Bonaccorsi, E.; and Armbruster, T., “Tobermorites: Their Real Structure and Order-Disorder (OD) Character,” The American Mineralogist, V. 84, No. 10, 1999, pp. 1613-1621. doi: 10.2138/am-1999-1015
42. Gard, J. A., and Taylor, H. F. W., “Crystal Structure of Foshagite (Ca4Si3O9(OH)2),” Nature, V. 183, No. 4655, 1959, pp. 171-173. doi: 10.1038/183171b0
43. Richardson, I. G., “The Calcium Silicate Hydrates,” Cement and Concrete Research, V. 38, No. 2, 2008, pp. 137-158. doi: 10.1016/j.cemconres.2007.11.005
44. Taylor, H. F. W., “726. Hydrated Calcium Silicates. Part I. Compound Formation at Ordinary Temperatures,” Journal of the Chemical Society (Resumed), 1950, pp. 3682-3690.
45. Copeland, L. E., Kantro, D. L.; and Verbeck. G., “Chemistry of Hydration of Portland Cement,” Chemistry of Cement, Fourth International Symposium, U. S. Department of Commerce, Washington, DC, 1960.
46. Richardson, I. G., “Tobermorite/Jennite- and Tobermorite/Calcium Hydroxide-Based Models for the Structure of C-S-H: Applicability to Hardened Pastes of Tricalcium Silicate, β-Dicalcium Silicate, Portland Cement, and Blends of Portland Cement with Blast-Furnace Slag, Metakaolin, or Silica Fume,” Cement and Concrete Research, V. 34, No. 9, 2004, pp. 1733-1777. doi: 10.1016/j.cemconres.2004.05.034
47. Bentz, D. P., “CEMHYD3D: A Three-Dimensional Cement Hydration and Microstructure Development Modeling Package. Version 3.0,” NISTIR 7232, National Institute of Standards and Technology, Gaithersburg, MD, 2005.
48. Richardson, I. G., and Groves, G. W., “Models for the Composition and Structure of Calcium Silicate Hydrate (C-S-H) Gel in Hardened Tricalcium Silicate Pastes,” Cement and Concrete Research, V. 22, No. 6, 1992, pp. 1001-1010. doi: 10.1016/0008-8846(92)90030-Y
49. Taylor, H. F. W., “Proposed Structure for Calcium Silicate Hydrate Gel,” Journal of the American Ceramic Society, V. 69, No. 6, 1986, pp. 464-467. doi: 10.1111/j.1151-2916.1986.tb07446.x
50. Bonaccorsi, E.; Merlino, S.; and Taylor, H. F. W., “The Crystal Structure of Jennite, Ca9Si6O18(OH)6·8H2O,” Cement and Concrete Research, V. 34, No. 9, 2004, pp. 1481-1488. doi: 10.1016/j.cemconres.2003.12.033
51. Downs, R. T., and Hall-Wallace, M., “The American Mineralogist Crystal Structure Database,” The American Mineralogist, V. 88, No. 1, 2003, pp. 247-250.
52. Jeffery, J. W., “The Crystal Structure of Tricalcium Silicate,” Acta Crystallographica, V. 5, No. 1, 1952, pp. 26-35. doi: 10.1107/S0365110X52000083
53. Mumme, W. G.; Hill, R. J.; Bushnell-Wye, G.; and Segnit, E. R., “Rietveld Crystal Structure Refinements, Crystal Chemistry and Calculated Powder Diffraction Data for the Polymorphs of Dicalcium Silicate and Related Phases,” Neues Jahrbuch für Mineralogie. Abhandlungen, V. 169, No. 1, 1995, pp. 35-68.
54. Bigaré, M.; Guinier, A.; Mazières, C.; Regourd, M.; Yannaquis, N.; Eysbl, W.; Hahn, T. H.; and Woermann, E., “Polymorphism of Tricalcium Silicate and Its Solid Solutions,” Journal of the American Ceramic Society, V. 50, No. 11, 1967, pp. 609-619. doi: 10.1111/j.1151-2916.1967.tb15009.x
55. Urabe, K.; Shirakami, T.; and Iwashima, M., “Superstructure in a Triclinic Phase of Tricalcium Silicate,” Journal of the American Ceramic Society, V. 83, No. 5, 2000, pp. 1253-1258. doi: 10.1111/j.1151-2916.2000.tb01363.x
56. Chen, Y.-L.; Shih, P.-H.; Chiang, L.-C.; Chang, Y.-K.; Lu, H.-C.; and Chang, J.-E., “The Influence of Heavy Metals on the Polymorphs of Dicalcium Silicate in the Belite-Rich Clinkers Produced from Electroplating Sludge,” Journal of Hazardous Materials, V. 170, No. 1, 2009, pp. 443-448. doi: 10.1016/j.jhazmat.2009.04.076
57. Bridge, T. E., “Bredigite, Larnite and Gamma Dicalcium Silicates from Marble Canyon,” American Mineralogist, V. 51, No. 11-1, 1966, pp. 1766-1774.
58. Sakurada, R.; Singh, A. K.; Briere, T.; Uzawa, M.; and Kawazoe, Y., “Crystal Structure Analysis of Dicalcium Silicates by AB-Initio Calculation,” 32nd Our World in Concrete and Structures (OWICs), Singapore Concrete Institute, Singapore, 2007.
59. Golovastikov, N. I.; Matveera, R. G.; and Belov, N. V., “Crystal Structure of the Tricalcium Silicate 3CaO.SiO2=C3S,” Kristallografiya, V. 20, 1975, pp. 721-729.
60. Midgley, C. M., “The Crystal Structure of Beta-Dicalcium Silicate,” Acta Crystallographica, V. 5, No. 3, 1952, pp. 307-312. doi: 10.1107/S0365110X52000964
61. Jost, K. H.; Ziemer, B.; and Seydel, R., “Redetermination of the Structure of Beta-Dicalcium Silicate,” Acta Crystallographica. Section B, Structural Crystallography and Crystal Chemistry, V. 33, No. 6, 1977, pp. 1696-1700. doi: 10.1107/S0567740877006918
62. Tsurumi, T.; Hirano, Y.; Kato, H.; Kamiya, T.; and Daimon, M., “Crystal Structure and Hydration of Belite,” Ceramic Transactions, V. 40, 1994, pp. 19-25.
63. Grady, D. E., “Shock-Wave Compression of Brittle Solids,” Mechanics of Materials, V. 29, No. 3-4, 1998, pp. 181-203. doi: 10.1016/S0167-6636(98)00015-5
64. Sun, H., “COMPASS: An Ab Initio Force-Field Optimized for Condensed-Phase Applications - Overview with Details on Alkane and Benzene Compounds,” The Journal of Physical Chemistry B, V. 102, No. 38, 1998, pp. 7338-7364. doi: 10.1021/jp980939v
65. Yang, J.; Ren, Y.; Tian, A.-M.; and Sun, H., “COMPASS Force Field for 14 Inorganic Molecules, He, Ne, Ar, Kr, Xe, H-2, O-2, N-2, NO, CO, CO2, NO2, CS2, and SO2, in Liquid Phases,” The Journal of Physical Chemistry B, V. 104, No. 20, 2000, pp. 4951-4957. doi: 10.1021/jp992913p
66. Hub, J. S.; de Groot, B.; Grubmüller, H.; and Groenhof, G., “Quantifying Artifacts in Ewald Simulations of Inhomogeneous Systems with a Net Charge,” Journal of Chemical Theory and Computation, V. 10, No. 1, 2014, pp. 381-390. doi: 10.1021/ct400626b
67. Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T. A.; and Joannopoulos, J. D., “Iterative Minimization Techniques for Ab Initio Total-Energy Calculations: Molecular Dynamics and Conjugate Gradients,” Reviews of Modern Physics, V. 64, No. 4, 1992, pp. 1045-1097. doi: 10.1103/RevModPhys.64.1045
68. Parrinello, M., and Rahman, A., “Crystal Structure and Pair Potentials: A Molecular-Dynamics Study,” Physical Review Letters, V. 45, No. 14, 1980, pp. 1196-1199. doi: 10.1103/PhysRevLett.45.1196
69. Anderson, O. L., “Evidence Supporting the Approximation γρ = Const for the Grüneisen Parameter of the Earth’s Lower Mantle,” Journal of Geophysical Research. Solid Earth, V. 84, 1979, pp. 3537-3542. doi: 10.1029/JB084iB07p03537
70. Gospodinov, V., ““Volume Dependence of the Grüneisen Ratio for Shock-Wave Equation-of-State Studies,” International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics,” Applied Physics (Berlin), V. 28, No. 28, 2014
71. Birch, F., “Finite Elastic Strain of Cubic Crystals,” Physical Review, V. 71, No. 11, 1947, pp. 809-824. doi: 10.1103/PhysRev.71.809
72. Murnaghan, F. D., “The Compressibility of Media under Extreme Pressures,” Proceedings of the National Academy of Sciences of the United States of America, V. 30, No. 9, 1944, pp. 244-247. doi: 10.1073/pnas.30.9.244
73. Theodorou, D. N., and Suter, U. W., “Atomistic Modeling of Mechanical Properties of Polymeric Glasses,” Macromolecules, V. 19, No. 1, 1986, pp. 139-154. doi: 10.1021/ma00155a022
74. Wong, H. S., and Buenfeld, N. R., “Determining the Water-Cement Ratio, Cement Content, Water Content and Degree of Hydration of Hardened Cement Paste: Method Development and Validation on Paste Samples,” Cement and Concrete Research, V. 39, No. 10, 2009, pp. 957-965. doi: 10.1016/j.cemconres.2009.06.013
75. Kim, Y.-Y.; Lee, K.-M.; Bang, J.-W.; and Kwon, S.-J., “Effect of W/C Ratio on Durability and Porosity in Cement Mortar with Constant Cement Amount,” Advances in Materials Science and Engineering, V. 2014, 2014, p. 1 doi: 10.1155/2014/273460
76. Walter, H. P., “Factors Influencing Concrete Strength,” ACI Journal Proceedings, V. 47, No. 2, Feb. 1951, pp. 417-432.
77. Speziale, S.; Reichmann, H. J.; Schilling, F. R.; Wenk, H. R.; and Monteiro, P. J. M., “Determination of the Elastic Constants of Portlandite by Brillouin Spectroscopy,” Cement and Concrete Research, V. 38, No. 10, 2008, pp. 1148-1153. doi: 10.1016/j.cemconres.2008.05.006
78. Riedel, W.; Wicklein, M.; and Thoma, K., “Shock Properties of Conventional and High Strength Concrete: Experimental and Mesomechanical Analysis,” International Journal of Impact Engineering, V. 35, No. 3, 2008, pp. 155-171. doi: 10.1016/j.ijimpeng.2007.02.001