Micromechanical Model and Associated Validation for Dynamic Failure of Brittle Materials Containing Pores and Slit-Like Flaws
Publication: Journal of Engineering Mechanics
Volume 141, Issue 10
Abstract
Characterizing dynamic failure is critically important to a number of applications, among others including armor, material fragmentation, and structural blast. In brittle materials, this failure is driven by crack growth from pre-existing flaws in the material microstructure. Structural scale models that explicitly address the cracks associated with each individual flaw are computationally infeasible; therefore, a model that accurately links flaw population to dynamic failure strength provides a much-needed connection between the microscale and macroscale. The current paper introduces a micromechanical model that addresses the effects of both air-entrained pores and slit-like flaws on the strain-rate dependent uniaxial compressive strength of the material. In particular, four variants of the model are addressed: a two-dimensional (2D) model with only pore flaws, a 2D model with both pores and slit-like flaws, a pseudo-three-dimensional (3D) model with only pore flaws, and a pseudo-3D model with both pores and slit-like flaws. To demonstrate the relative success of each of these approaches, the model is based on microstructural characterization and subsequent Kolsky bar tests on air-entrained mortar. Air-entrained mortar provides an excellent model material for this study, since the pore population introduced by air-entrainment is characterized relatively easily and the slit-like flaw population is deduced from the sand gradation. Furthermore, the sample sizes used in the Kolsky bar set-up are larger than the length scale of the microstructure of mortar, so that the samples are reasonably representative and provide a good basis of comparison with the micromechanics model. The micromechanics model is shown to provide reasonable agreement with experimentally obtained uniaxial compressive dynamic strength of air-entrained mortar.
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Acknowledgments
The authors are extremely grateful to Prof. Robert McMeeking at the University of California, Santa Barbara and to Prof. K. T. Ramesh and Matthew Shaeffer at Johns Hopkins University, for their insights, notes and experimental support that made much of this work possible. This material is based on work supported by the National Science Foundation under Grants No. 0969972 and 0801471, and through a Cooperative Agreement between the Materials in Extreme Dynamic Environments (MEDE) Consortium and U.S. Army Research Lab (Contract number W911NF-12-2-0022). Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation or the Army Research Lab.
References
Ashby, M. F., and Hallam, S. D. (1986). “The failure of brittle solids containing small cracks under compressive stress states.” Acta Metallurgica, 34(3), 497–510.
Basista, M., and Gross, D. (1998). “The sliding crack model of brittle deformation: an internal variable approach.” Int. J. Solids Struct., 35(5–6), 487–509.
Batdorf, S. B., and Crose, J. G. (1974). “A statistical theory for the fracture of brittle structures subjected to non-uniform poly-axial stresses.” J. Appl. Mech., 41(2), 459–464.
Bazant, Z. P. (1997). “Scaling of quasibrittle fracture: Hypothesis of invasive and lacunar fractality, their critique and Weibull connection.” Int. J. Fract., 83(1), 41–65.
Budiansky, B., and O’Connell, R. (1976). “Elastic moduli of a cracked solid.” Int. J. Solids Struct., 12(2), 81–97.
Deshpande, V. S., and Evans, A. G. (2008). “Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model.” J. Mech. Phys. Solids, 56(10), 3077–3100.
Deshpande, V. S., Nell Gamble, E. A., Compton, B. G., McMeeking, R. M., Evans, A. G., and Zok, F. W. (2011). “A constitutive description of the inelastic response of ceramics.” J. Am. Ceram. Soc., 94(S1), s204–s214.
Evans, A. G., and Jones, R. L. (1978). “Evaluation of a fundamental approach for the statistical analysis of fracture.” J. Am. Ceram. Soc., 61(3–4), 157–160.
Graham-Brady, L. L. (2010). “Statistical characterization of meso-scale uniaxial compressive strength in brittle materials with randomly occurring flaws.” Int. J. Solids Ceram., 47(18–19), 2398–2413.
Grechka, V., and Kachanov, M. (2006). “Effective elasticity of rocks with closely spaced and intersecting cracks.” Geophysics, 71(3), D85–D91.
Horii, H., and Nemat-Nasser, S. (1986). “Brittle failure in compression: Splitting, faulting, and brittle ductile transition.” Philos. Trans. R. Soc. London, Ser. A, 319(1549), 337–374.
Hu, G. (2013). “The failure of brittle materials under dynamic multiaxial loading.” Ph.D. thesis, Dept. of Mechanical Engineering, Johns Hopkins Univ., Baltimore.
Hu, G., Liu, J., Graham-Brady, L. L., and Ramesh, K. T. (2015). “A 3D mechanistic model for brittle materials containing evolving flaw distributions under dynamic multiaxial loading.” J. Mech. Phys. Solids, 78, 269–297.
Huang, C., and Subhash, G. (2003). “Influence of lateral confinement on dynamic damage evolution during uniaxial compressive response of brittle solids.” J. Mech. Phys. Solids, 51(6), 1089–1105.
Huang, C., Subhash, G., and Vitton, S. (2002). “A dynamic damage growth model for uniaxial compressive response of rock aggregates.” Mech. Mater., 34(5), 267–277.
Katcoff, C. Z. (2013). “Modeling high-strain-rate loading in brittle materials with a self-consistent model focused on circular voids.” Ph.D. thesis, Johns Hopkins Univ., Baltimore.
Katcoff, C. Z., and Graham-Brady, L. L. (2014). “Modeling dynamic brittle behavior of materials with circular flaws or pores.” Int. J. Solids Struct., 51(3–4), 754–766.
Kimberley, J., Ramesh, K. T., and Daphalapurkar, N. P. (2013). “A scaling law for the dynamic strength of brittle solids.” Acta Materialia, 61(9), 3509–3521.
Mayercsik, N. P., Felice, R., Ley, M. T., and Kurtis, K. E. (2014). “A probabilistic technique for entrained air void analysis in hardened concrete.” Cem. Concr. Res., 59, 16–23.
Mayercsik, N. P., Shaeffer, M., Graham-Brady, L. L., and Kurtis, K. E. (2015). “Analysis of Portland cement mortar under impact: A combined material characterization, micromechanics modeling, and dynamic testing approach.” Cem. Concr. Res., 73, 190–206.
Nemat-Nasser, S., and Horii, H. (1982). “Compression-induced nonplanar crack extension with application to splitting, exfoliation, and rockburst.” J. Geophys. Res., 87(B8), 6805–6821.
Nemat-Nasser, S., and Obata, M. (1988). “Microcrack model of dilatancy in brittle materials.” J. Appl. Mech., 55(1), 24–35.
Paliwal, B., and Ramesh, K. T. (2008). “An interacting microcrack damage model for failure of brittle materials under compression.” J. Mech. Phys. Solids, 56(3), 896–923.
Rasband, W. S. (2013). Image J, U.S. National Institutes of Health, Bethesda, MD.
Ravichandran, G., and Subhash, T. (1995). “A micromechanical model for high strain rate behavior of ceramics.” Int. J. Solids Struct., 32(17-18), 2627–2646.
Sammis, C., and Ashby, M. (1986). “The failure of brittle porous solids under compressive stress states.” Acta Metallurgica, 34(3), 511–526.
Sarva, S., and Nemat-Nasser, S. (2001). “Dynamic compressive strength of silicon carbide under uniaxial compression.” Mater. Sci. Eng., 317(1–2), 140–144.
Tonge, A. L., Kimberley, J., and Ramesh, K. T. (2012). “The mechanism of compressive unloading failure in single crystal quartz and other brittle solids.” Int. J. Solids Struct., 49(26), 3923–3934.
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Published In
Journal of Engineering Mechanics
Volume 141 • Issue 10 • October 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Aug 28, 2014
Accepted: Jan 8, 2015
Published online: May 7, 2015
Published in print: Oct 1, 2015
Discussion open until: Oct 7, 2015
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