Abstract
Molecular-level modeling and simulations are employed to study room-temperature micro-structural and mechanical response of soda-lime glass when subjected to high (i.e., several giga-Pascal) uniaxial-strain stresses/pressure. The results obtained revealed the occurrence of an irreversible phase-transformation at ca. 4 GPa which was associated with a (permanent) 3-7% volume reduction. Close examination of molecular-level topology revealed that the pressure-induced phase transformation in question is associated with an increase in the average coordination number of the silicon atoms, and the creation of two- to fourfold (smaller, high packing-density) Si-O rings. The associated loading and unloading axial-stress versus specific-volume isotherms were next converted into the corresponding loading Hugoniot and unloading isentrope axial-stress versus specific-volume relations. These were subsequently used to analyze the role of the pressure-induced phase-transformation/irreversible-densification in mitigating the effects of blast and ballistic impact loading onto a prototypical glass plate used in monolithic and laminated transparent armor applications. The results of this part of the study revealed that pressure-induced phase-transformation can provide several beneficial effects such as lowering of the loading/unloading stress-rates and stresses, shock/release-wave dispersion, and energy absorption associated with the study of phase-transformation.
Similar content being viewed by others
References
E. Strassburger, P. Patel, W. McCauley, and D.W. Templeton, Visualization of Wave Propagation and Impact Damage in a Polycrystalline Transparent Ceramic-AlON, Proceedings of the 22 nd International Symposium on Ballistics, November 2005, Vancouver, Canada
AMPTIAC Quarterly: Army Materials Research: Transforming Land Combat Through New Technologies, 8 (No. 4), 2004
E. Strassburger, P. Patel, J.W. McCauley, C. Kovalchick, K.T. Ramesh, and D.W. Templeton, High-Speed Transmission Shadowgraphic and Dynamic Photoelasticity Study of Stress Wave and Impact Damage Propagation in Transparent Materials and Laminates Using The Edge-on Impact Method, Proceedings of the 23rd International Symposium on Ballistics, Spain, April 2007
D.Z. Sun, F. Andreiux, and A. Ockewitz, Modeling of the Failure Behavior of Windscreens and Component Tests, 4th LS-DYNA Users’ Conference, Bamberg, Germany, 2005
L.V. Woodcock, C.A. Angell, and P. Cheeseman, Molecular Dynamics Studies of the Vitreous State: Simple Ionic Systems and Silica, J. Chem. Phys., 1976, 65, p 1565–1577
R.G.D. Valle and E. Venuti, High-Pressure Densification of Silica Glass: A Molecular-Dynamics Simulation, Phys. Rev. B, 1996, 54(6), p 3809–3816
K. Trachenko and M.T. Dove, Densification of Silica Glass Under Pressure, J. Phys. Condens. Matter, 2002, 14, p 7449–7459
Y. Liang, C.R. Miranda, and S. Scandolo, Mechanical Strength and Coordinate Defects in Compressed Silica Glass: Molecular Dynamics Simulations, Phys. Rev. B, 2007, 75, p 024205
B. Nghiem, PhD thesis, University of Paris 6, France 1998
C. Denoual and F. Hild, Dynamic Fragmentation of Brittle Solids: A Multi-scale Model, Eur. J. Mech. Solids A, 2002, 21, p 105–120
M. Yazdchi, S. Valliappan, and W. Zhang, A Continuum Model for Dynamic Damage Evolution of Anisotropic Brittle Materials, Int. J. Numer. Methods Eng., 1996, 39, p 1555–1583
F. Hild, C. Denoual, P. Forquin, and X. Brajer, On the Probabilistic and Deterministic Transition Involved in a Fragmentation Process of Brittle Materials, Comput. Struct., 2003, 81, p 1241–1253
M. Grujicic, B. Pandurangan, N. Coutris, B.A. Cheeseman, C. Fountzoulas, P. Patel, and E. Strassburger, A Ballistic Material Model for Starphire®, A Soda-lime Transparent Armor Glass, Mater. Sci. Eng. A, 2008, 492(1), p 397–411
M. Grujicic, B. Pandurangan, W.C. Bell, N. Coutris, B.A. Cheeseman, C. Fountzoulas, and P. Patel, An Improved Mechanical Material Model for Ballistic Soda-Lime Glass, J. Mater. Eng. Perform., 2009, 18(8), p 1012–1028
M. Grujicic, B. Pandurangan, N. Coutris, B.A. Cheeseman, C. Fountzoulas, and P. Patel, A Simple Ballistic Material Model for Soda-Lime Glass, Int. J. Impact Eng., 2009, 36, p 386–401
T.J. Holmquist, D.W. Templeton, and K.D. Bishnoi, Constitutive Modeling of Aluminum Nitride for Large Strain High-strain Rate, and High-pressure Applications, Int. J. Impact Eng., 2001, 25, p 211–231
G.T. Camacho and M. Ortiz, Computational Modeling of Impact Damage in Brittle Materials, Int. J. Solids Struct., 1996, 33(20–22), p 2899–2938
W.D. Kingery, H.K. Bowen, and D.R. Uhlmann, Introduction to Ceramics, 2nd ed., Wiley, New York, 1976, p 91–124
http://www.accelrys.com/mstudio/msmodeling/amorphouscell.html
H. Sun, COMPASS: An ab Initio Force-Field Optimized for Condensed-Phase Applications Overview with Details on Alkane and Benzene Compounds, J. Phys. Chem. B, 1998, 102, p 7338–7364
H. Sun, P. Ren, and J.R. Fried, The COMPASS Force Field: Parameterization and Validation for Phosphazenes, Comput. Theor. Polym. Sci., 1998, 8(1/2), p 229–246
M. Grujicic, Y.-P. Sun, and K. Koudela, The Effect of Covalent Functionalization of Carbon Nanotube Reinforcements on the Atomic-Level Mechanical Properties of Poly-Vinyl-Ester-Epoxy, Appl. Surf. Sci., 2007, 253, p 3009–3021
S. Nose, A Unified Formulation of the Constant Temperature Molecular Dynamics Methods, J. Chem. Phys., 1984, 81, p 511–519
M. Grujicic, B. Pandurangan, C.D. Angstadt, K.L. Koudela, and B.A. Cheeseman, Ballistic Performance Optimization of a Hybrid Carbon Nanotube/E-Glass Reinforced Poly-Vinyl-Ester-Epoxy Matrix Composite Armor, J. Mater. Sci., 2007, 42, p 5347–5349
D.E. Grady and L.C. Chhabildas, Shock-wave Properties of Soda-lime Glass, Report No: SAND96-2571C, 1996
C.S. Alexander, L.C. Chhabildas, W.D. Reinhart, and D.W. Templeton, Changes to the Shock Response of Fused Quartz due to Glass Modification, Int. J. Impact Eng., 2008, 35, p 1376–1385
L. Davison, Fundamentals of Shock-wave Propagation in Solids. Shock-wave and High Pressure Phenomena, Springer, Berlin, Heidelberg, 2008
Y. Sato and O.L. Anderson, A Comparison of the Acoustic and Thermal Gruneisen Parameters for Three Glasses at Elevated Pressure, J. Phys. Chem. Solids, 1980, 41(4), p 401–410
Cambridge Engineering Selector, http://www.grantadesign.com/
Acknowledgments
The material presented in this paper is based on study supported by the U.S. Army/Clemson University Cooperative Agreements W911NF-04-2-0024 and W911NF-06-2-0042 and by an ARC-TARDEC research contract.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Grujicic, M., Bell, W.C., Glomski, P.S. et al. Multi-Length Scale Modeling of High-Pressure-Induced Phase Transformations in Soda-Lime Glass. J. of Materi Eng and Perform 20, 1144–1156 (2011). https://doi.org/10.1007/s11665-010-9774-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11665-010-9774-2