Abstract
The evolution of spall for a brittle material is investigated under variance of anisotropy, grain boundary fracture energy, and loading. Because spall occurs in the interior of the specimen, fundamental studies of crack nucleation and growth are needed to better understand surface velocity measurements. Within a cohesive approach to fracture, we illustrate that for anisotropic materials, increases in the fracture energy cause a transition in crack nucleation from triple-points to entire grain boundary facets. Analysis of idealized flaws reveals that while crack initiation and acceleration are strong functions of the fracture energy, flaws soon reach speeds on the order of the Rayleigh wave speed. Finally, simulated surface velocities of spalled configurations are correlated with microstructural evolution. These fundamental studies of nucleation, growth, and spall attempt to link atomic separation to the macroscopic spall strength and provide a computational framework to examine the evolution of spall and the impact on the simulated surface velocity field.
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References
Antoun TH, Seaman L, Curran DR, Kanel GI, Razorenov SV, Utkin AV (2003) Spall fracture. Springer, New York
Bakas MP, Greenhut VA, Niesz DE, Quinn GD, McCauley JW, Wereszczak AA, Swab JJ (2004) Anomalous defects and dynamic failure of armor ceramics. Int J Appl Ceram Technol 1: 211–218
Barker LM, Hollenbach RE (1972) Laser interferometry for measuring high velocities for any reflecting surface. J Appl Phys 43: 4669–4675
Cho K, Katz RN (1995) Strength and fracture toughness of hot pressed SiC materials. In: Proceedings of the 19th annual conference on composites, advanced ceramics, materials, and structures–A. The American Ceramic Society, Westerville, Ohio, pp 105–112
Dalton DA, Brewer JL, Bernstein AC, Grigsby W, Milathianaki D, Jackson ED, Adams RG, Rambo P, Schwartz J, Edens A, Geissel M, Smith I, Taleff EM, Ditmire T (2008) Laser-induced spallation of aluminum and Al alloys at strain rates above 2 × 106 s−1. J Appl Phys 104: 013526
Dandekar DP (2004) Spall strength of silicon carbide under normal and simultaneous compression-shear shock wave loading. Int J Appl Ceram Technol 1: 261–268
Dandekar DP, Bartkowski PT (2001) Spall strengths of silicon carbides under shock loading. In: Staudhammer KP, Murr LE, Meyers MA (eds) Fundamental issues and applications of shock-wave and high-strain-rate phenomena. Elsevier, New York, pp 71–77
Espinosa HD, Zavattieri PD (2003a) A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part I: theory and numerical implementation. Mech Mater 35: 323–364
Espinosa HD, Zavattieri PD (2003b) A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part II: numerical examples. Mech Mater 35: 365–394
Forquin P, Denoual C, Cottenot CE, Rota L, Hild F (2000) Experimental approach and modeling of the compressive behaviour of two SiC grades. J de Phys IV 10: 735–740
Foulk JW III, Cannon RM, Johnson GC, Klein PA, Ritchie RO (2007) A micromechanical basis for partitioning the evolution of grain bridging in brittle materials. J Mech Phys Solids 55: 719–743
Foulk JW III, Johnson GC, Klein PA, Ritchie RO (2008) On the toughening of brittle materials by grain bridging: promoting intergranular fracture through grain angle, strength, and toughness. J Mech Phys Solids 56: 2381–2400
Furnish MD, Reinhart WD, Trott WM, Chhabildas LC, Vogler TJ (2009) Determination and interpretation of statistics of spatially resolved waveforms in spalled tantalum from 7 to 13 GPa. Int J Plast 25: 587–602
Gupta V, Yuan J (1993) Measurement of interface strength by the modified laser spallation technique. II. Application to metal/ceramic interfaces. J Appl Phys 74: 2397–2404
Helms KLE, Allen DH, Hurtado LD (1999) A model for predicting grain boundary cracking in polycrystalline viscoplastic materials including scale effects. Int J Fract 95: 175–194
Jung J (2009) Presto 4.11 user’s guide. Tech. Rep. SAND2009-3213, Sandia National Laboratories
Kamitani K, Grimsditch M, Nipko JC, Loong C-K, Okada M, Kimura I (1997) The elastic constants of silicon carbide: a Brillouin-scattering study of 4H and 6H SiC single crystals. J Appl Phys 82: 3152–3154
Kikuchi H, Kalia RK, Branicio PS, Shimojo F (2005) Brittle dynamic fracture of crystalline cubic silicon carbide (3C-SiC) via molecular dynamics simulation. J Appl Phys 98: 103524
Klein PA, Foulk JW, Chen EP, Wimmer SA, Gao HJ (2001) Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods. Theor Appl Fract Mech 37: 99–166
Kraft RH, Molinari J-F (2008) A statistical investigation of the effects of grain boundary properties on transgranular fracture. Acta Mater 56: 4739–4749
Kraft RH, Molinari J-F, Ramesh KT, Warner DH (2008) Computational micromechanics of dynamic compressive loading of a brittle polycrystalline material using a distribution of grain boundary properties. J Mech Phys Solids 56: 2618–2641
Maiti S, Geubelle PH (2004) Mesoscale modeling of dynamic fracture of ceramic materials. Comput Model Eng Sci 5: 91–101
Maiti S, Rangaswamy K, Geubelle PH (2005) Mesoscale analysis of dynamic fragmentation of ceramics under tension. Acta Mater 53: 823–834
Merala TB, Chan HW, Howitt DG, Kelsey PV, Korth GE, Williamson RL (1988) Dislocation microstructures in explosively deformed hard materials. Mater Sci Eng A 105: 293–298
Needleman A (1987) A continuum model for void nucleation by inclusion debonding. J Appl Mech 54: 525–531
Needleman A (1990) An analysis of tensile decohesion along an interface. J Mech Phys Solids 38: 289–324
Nittur PG, Maiti S, Geubelle PH (2008) Grain-level analysis of dynamic fragmentation of ceramics under multi-axial compression. J Mech Phys Solids 56: 993–1017
Nye JF (1985) Physical properties of crystals, their representation by tensors and matrices. Clarendon Press, Oxford
Rose JH, Ferrante J, Smith JR (1981) Universal binding energy curves for metals and bimetallic interfaces. Phys Rev Lett 47: 675–678
Trott WM, Castaûeda JN, O’Hare JJ, Knudson MD, Chhabildas LC, Baer MR, Asay JR (2001) Examination of the mesoscopic scale response of shock compressed heterogeneous materials using a line-imaging velocity interferometer. In: Staudhammer KP, Murr LE, Meyers MA (eds) Fundamental issues and applications of shock-wave and high-strain-rate phenomena. Elsevier, New York, pp 647–654
Tvergaard V, Hutchinson JW (1988) Microcracking in ceramics induced by thermal expansion or elastic anisotropy. J Am Ceram Soc 71: 157–166
Tvergaard V, Hutchinson JW (1990) Effect of fiber debonding in a whisker-reinforced metal. Mater Sci Eng A125: 203–213
Tvergaard V, Hutchinson JW (1992) The relation between crack growth resistance and fracture process parameters in elastic-plastic solids. J Mech Phys Solids 40: 1377–1397
Tvergaard V, Hutchinson JW (1993) The influence of plasticity on mixed mode interface toughness. J Mech Phys Solids 41: 1119–1135
Vogler TJ, Clayton JD (2008) Heterogeneous deformation and spall of an extruded tungsten alloy: plate impact experiments and crystal plasticity modeling. J Mech Phys Solids 56: 297–335
Vogler TJ, Trott WM, Reinhart WD, Alexander CS, Furnish MD, Knudson MD, Chhabildas LC (2008) Using the line-VISAR to study multi-dimensional and meso-scale impact phenomena. Int J Impact Eng 35: 1435–1440
Zavattieri PD, Espinosa HD (2001) Grain level analysis of crack initiation and propagation in brittle materials. Acta Mater 49: 4291–4311
Zavattieri PD, Espinosa HD (2003) An examination of the competition between bulk behavior and interfacial behavior of ceramics subjected to dynamic pressure-shear loading. J Mech Phys Solids 51: 607–635
Zavattieri PD, Raghuram PV, Espinosa HD (2001) A computational model of ceramic microstructures subjected to multi-axial dynamic loading. J Mech Phys Solids 49: 27–68
Zhou XW, Zimmerman JA, Reedy ED Jr, Moody NR (2008) Molecular dyanmics simulation based cohesive surface representation of mixed-mode fracture. Mech Mater 40: 832–845
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Foulk, J.W., Vogler, T.J. A grain-scale study of spall in brittle materials. Int J Fract 163, 225–242 (2010). https://doi.org/10.1007/s10704-010-9470-0
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DOI: https://doi.org/10.1007/s10704-010-9470-0