Abstract
This article describes two techniques used to characterize intact and damaged soda-lime glass at pressures up to ∼2 GPa: triaxial compression and confined sleeve. The results of the characterization experiments are described for intact and damaged glass as a function of confinement pressure and interpreted in terms of two pressure-dependent constitutive models, Drucker-Prager and Mohr-Coulomb. An observation is that the slopes of the two models appear to be independent of the degree of damage (intact, predamaged and severely damaged specimens). It is also observed that there is a maximum strength for the damaged glass, i.e., there is a cap on the strength. The compressive response of soda-lime glass is compared to that of a borosilicate glass, and to flyer-plate impact data.
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Notes
Technically, the specimens that were initially intact and then failed could also carry a load, but failure is so catastrophic that the plastic sleeve is ripped apart and the comminuted specimen is dispersed in the hydraulic fluid.
Many of the analysis procedures, particularly for the confined sleeve test, were developed during characterization of the Borofloat glass. Analysis of the Starphire data used a refined procedure.
The hydrostatic pressure is larger than the confinement pressure since the hydrostatic pressure is a combination of the confinement pressure and the axial load.
Bourne et al. , show uncertainty (“error”) bars of approximately 0.5 GPa centered on their data values. For clarity, we have omitted these error bars.
For convenience, for this discussion of flyer-plate impact, we assume that the stress is positive in compression.
Presumably, the glass remains elastic below the HEL, but fails upon reaching the HEL.
References
Chocron S, Anderson CE Jr, Nicholls A, Dannemann K (2010) Characterization of confined intact and damaged borosilicate glass. J Am Ceram Soc 93(10):3390–3398
Chocron S, Anderson CE Jr (2009) Predictive modeling of dynamic processes: a tribute to Klaus Thoma, chapter 10, Numerical simulations of the penetration of glass using two pressure-dependent constitutive models. Springer Science+Business Media LLC, New York, pp 167–187
Behner Th, Anderson CE Jr, Orphal DL, Hohler V, Moll M, Templeton DW (2008) Penetration and failure of lead and borosilicate glass against rod impact. Int J Impact Eng 35(6):447–456
Patel P, Matoya M (2005) US Army Research Laboratory, Aberdeen, MD, personal communication
Desai CS, Siriwardane HJ (1984) Constitutive laws for engineering materials with emphasis on geologic materials. Prentice-Hall, Englewood Cliffs, NJ 07632
Dannemann KA, Chocron S, Nicholls AE, Anderson CE Jr (2008) Compressive damage development in confined borosilicate glass. Mater Sci Eng A Struct 478:340–350
Dannemann KA, Jr. Anderson CE, Chocron S, Spencer JF (2011) Damage development in confined borosilicate and soda-lime glasses. J A Ceram Soc 1–9
Chocron S, Walker JD, Nicholls AE, Dannemann KA, Anderson CE Jr (2008) Analytical model of the confined compression test used to characterize brittle materials. J Appl Mech Trans ASME 75:021006–1–021006–7
Chocron S, Dannemann KA, Walker JD, Nicholls AE, Anderson CE Jr (2007) Constitutive model for damaged borosilicate glass under confinement. J Am Ceram Soc 90(8):2549–2555
Timoshenko S, Goodier JN (1951) Theory of elasticity. Mc. Graw-Hill, New York
Curran DR, Shockey DA, Simons JW (2008) Mesomechanical constitutive relations for glass and ceramic armor. In 32nd Int. Conf. on Advanced Ceramics and Composites, Daytona Beach, January 2008
Peter KW (1970) Densification and flow phenomena of glass in indentation experiments. J Non-Cryst Solids 5:103–115
Ernsberger FM (1977) Mechanical properties of glasses. J Non-Cryst Solids 25:293–321
Lankford J, Anderson CE Jr, Nagy AJ, Walker JD, Nicholls AE, Page RA (1998) Inelastic response of confined aluminum oxide under dynamic loading conditions. J Mat Sci 33:1619–1625
Holmquist TJ, Johnson GR (2005) Characterization and evaluation of silicon carbide for high velocity impact. J Appl Phys 97:093502
Holmquist TJ, Johnson GR (2008) The failed strength of ceramics subjected to high-velocity impact. J Appl Phys 104(013533):013533–1–013533–11
Drucker DC, Prager W (1952) Soil mechanics and plastic analysis of limit design. Q Appl Math 10(2):157–175
Nedderman RM (1992) Statics and kinematics of granular materials. Cambridge University Press, The Edinburgh Building, Cambridge CB2 2RU, UK
Beissel SR, Holmquist TJ, Johnson GR (2012) Influence of the third invariant in the ballistic impact of silicon carbide. International Journal of Impact Engineering 45:52–59
Jaeger JC, Cook NGW (1969) Fundamentals of rock mechanics. Chapman and Hall, Ltd. and Science Paperbacks
Anderson CE Jr, Chocron S, Bigger RP (2011) Time-resolved penetration into glass: experiments and computations. Int J Impact Eng 38(8–9):723–731
Brar NS, Bless SJ, Rosenberg Z (1991) Impact-induced failure waves in glass bars and plates. J Appl Phys 59(26):3396–3398
Bourne N, Millett J, Rosenbergand Z, Murray N (1998) On the shock induced failure of brittle solids. J Mech Phys Solid 46(10):1887–1908
Bourne NK, Millet JCF, Field JE (1999) On the strength of shocked glasses. Proc R Soc Lond A 455:1275–1282
Alexander CS, Chhabildas LC, Templeton DW (2007) The hugoniot elastic limit of soda-lime glass. In CP955, Shock Compression of Condensed Matter-2007, pp 733–738. American Institute of Physics
Alexander CS, Chhabildas LC, Reinhart WD, Templeton DW (2008) Changes to the shock response of fused quartz due to glass modification. In press, Int J Impact Eng doi:10.1016/j.ijimpeng.2008.07.019
Rosorenov SV, Kanel GI, Fortov VE (1991) The fracture of glass under high pressure impulsive loading. High Press Res 6:225–232
Holmquist TJ, Johnson GR, Grady DE, Lopatin CM, Jr Hertel ES (1995) High strain rate properties and constitutive modeling of glass. In Proceedings 15th International Symposium on Ballistics, Jerusalem, Israel, pp 237–244
Acknowledgements
The authors would like to thank Dr. Doug Templeton from TARDEC for funding this work, and Mr. Rick Rickert of TARDEC for the administrative support provided during this program. The authors are also grateful to Parimal Patel and colleagues at the Army Research Laboratory for ultrasonic modulus measurements of intact samples. Mr. Jim Spencer (SwRI) is acknowledged for his skillful assistance in sectioning and evaluation of glass specimens following testing. Appreciation is also extended to Mr. Bill Livermore for assistance with schematics and figures.
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Chocron, S., Anderson, C.E., Dannemann, K.A. et al. Pressure Effects on the Compressive Response of Confined Intact and Damaged Soda-Lime Glass. Exp Mech 53, 77–89 (2013). https://doi.org/10.1007/s11340-012-9632-2
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DOI: https://doi.org/10.1007/s11340-012-9632-2