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Collapse of void arrays under stress wave loading

Published online by Cambridge University Press:  13 April 2010

A. B. SWANTEK
Affiliation:
Department of Aerospace Engineering, University of Illinois, Urbana, IL 61801, USA
J. M. AUSTIN*
Affiliation:
Department of Aerospace Engineering, University of Illinois, Urbana, IL 61801, USA
*
Email address for correspondence: jmaustin@illinois.edu

Abstract

The interaction of an array of voids collapsing after passage of a stress wave is studied as a model problem relevant to porous materials, for example, to energy localization leading to hotspot formation in energetic materials. Dynamic experiments are designed to illuminate the hydrodynamic processes of collapsing void interactions for eventual input into device-scale initiation models. We examine a stress wave loading representative of accidental mechanical insult, for which the wave passage length scale is comparable with the void and inter-void length scales. A single void, two-void linear array, and a four-void staggered array are studied. Diagnostic techniques include high-speed imaging of cylindrical void collapse and the first particle image velocimetry measurements in the surrounding material. Voids exhibit an asymmetrical collapse process, with the formation of a high-speed internal jet. Volume and diameter versus time data for single void collapse under stress wave loading are compared with literature results for single voids under shock-wave loading. The internal volume history does not fall on a straight line and is in agreement with simulations, but in contrast to existing linear experimental data fits. The velocity field induced in the surrounding material is measured to quantify a region of influence at selected stages of single void collapse. In the case of multiple voids, the stress wave diffracts in response to the presence of the upstream void, affecting the loading condition on the downstream voids. Both collapse-inhibiting (shielding) and collapse-triggering effects are observed.

Type
Papers
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Baer, M. R. 2002 Modelling heterogeneous energetic materials at the mesocale. Thermochimica Acta 384, 351367.CrossRefGoogle Scholar
Bailey, M. R., Crum, L. A., Evan, A. P., McAteer, J. A., Williams, J. C., Sapozhnikov, O. A., Cleveland, R. O. & Colonius, T. 2003 Cavitation in shock wave lithotripsy. In Fifth Intl Symp. on Cavitation. Osaka.Google Scholar
Ball, G. J., Howell, B. P., Leighton, T. G. & Schofield, M. J. 2000 Shock-induced collapse of a cylindrical air cavity in water: a free-Lagrange simulation. Shock Waves 10, 265276.CrossRefGoogle Scholar
Bourne, N. K. & Field, J. E. 1990 Collapsing cavities in reactive and non-reactive media. In 19th Intl Congress on High-Speed Photography and Photonics SPIE, vol. 1358, pp. 1046–1055. International Society for Optical Engineering.CrossRefGoogle Scholar
Bourne, N. K. & Field, J. E. 1991 Bubble collapse and the initiation of explosion. Proc. Math. Phys. Sci. 435 (1894), 423435.Google Scholar
Bourne, N. K. & Field, J. E. 1992 Shock-induced collapse of single cavities in liquids. J. Fluid Mech. 244, 225240.CrossRefGoogle Scholar
Bourne, N. K. & Field, J. E. 1999 Explosive ignition by the collapse of cavities. Proc. R. Soc. A 455, 24112426.CrossRefGoogle Scholar
Bourne, N. K. & Milne, A. M. 2003 The temperature of a shock-collapsed cavity. Proc. R. Soc. A 459, 18511861.CrossRefGoogle Scholar
Bowden, F. P. & Yoffe, A. D. 1952 Ignition and Growth of Explosion in Liquids and Solids. Cambridge University Press.Google Scholar
Brennan, C. E. 2005 Fundamentals of Multi-Phase Flow. Cambridge University Press.CrossRefGoogle Scholar
Campbell, A. W. & Travis, J. R. 1985 Shock desensitization of PBX-9404 and composition B-3. In Proc. 8th Symp. (Intl) on Detonation. Albequerque, New Mexico.Google Scholar
Carroll, M. M. & Holt, A. C. 1972 Static and dynamic pore-collapse relations for ductile porous materials. J. Appl. Phys. 43 (4), 16261636.CrossRefGoogle Scholar
Dear, J. P. & Field, J. E. 1988 A study of the collapse of arrays of cavities. J. Fluid Mech. 190, 409425.CrossRefGoogle Scholar
Dear, J. P., Field, J. E. & Walton, A. J. 1988 Gas compression and jet formation in cavities collapsed by a shock wave. Nature 332, 505508.CrossRefGoogle Scholar
Dick, J. J., Hooks, D. E., Menikoff, R. & Martinez, A. R. 2004 Elastic–plastic wave profiles in cyclotetramethylene tetranitramine crystals. J. Appl. Phys. 96 (1), 374379.CrossRefGoogle Scholar
Ding, Z. & Gracewski, S. M. 1996 The behaviour of a gas cavity impacted by a weak or strong shock wave. J. Fluid Mech. 309, 183209.CrossRefGoogle Scholar
Epstein, D. & Keller, J. B. 1972 Expansion and contraction of planar, cylindrical, and spherical underwater gas bubbles. J. Acoust. Soc. Am. 52 (3), 975.Google Scholar
Ferm, E. N., Morris, C. L., Quintana, J. P., Pazuchanic, P., Stacy, H., Zumbro, J. D., Hogan, G. & King, N. 2001 Proton radiography examination of unburned regions in PBX 9502 corner turning experiments. In 12th Am. Phys. Soc. Topical Conf. on Shock Compression of Condensed Matter (ed. Furnish, M. D., Thadhani, N. N. & Horie, Y.), pp. 966969. Georgia.Google Scholar
Haas, J. F. & Sturtevant, B. 1987 Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J. Fluid Mech. 181, 4176.CrossRefGoogle Scholar
Hu, X. Y. & Khoo, B. C. 2004 An interface interaction method for compressible multifluids. J. Comput. Phys. 198 (1), 3564.CrossRefGoogle Scholar
Jaramillo, E., Sewell, T. D. & Strachan, A. 2007 Atomic-level view of inelastic deformation in shock loaded molecular crystal. Phys. Rev. B 76, 6.CrossRefGoogle Scholar
Johnsen, E. & Colonius, T. 2009 Numerical simulations of non-spherical bubble collapse. J. Fluid Mech. 629, 231262.CrossRefGoogle ScholarPubMed
Johnson, J. N., Tang, P. K. & Forest, C. A. 1985 Shock-wave initiation of heterogeneous reactive solids. J. Appl. Phys. 57, 4323.CrossRefGoogle Scholar
Kang, J., Butler, P. B. & Baer, M. R. 1992 A thermochemical analysis of hot spot formation in condensed-phase, energetic materials. Combust. Flame 89, 117139.CrossRefGoogle Scholar
Khasainov, B. A., Borisov, A.A., Ermolaev, B. S. & Korotkov, A. I. 1981 Two phase visco-plastic model of shock initiation of detonation in high density pressed explosives. In Proc. 7th Symp. (Intl) on Detonation. Annapolis, MN.Google Scholar
Kodama, T. & Tomita, Y. 2000 Cavitation bubble behaviour and bubble-shock wave interaction near a gelatin surface as a study of in vivo bubble dynamics. J. Appl. Phys. B 70, 139149.CrossRefGoogle Scholar
Mader, C. L. 1965 Initiation of detonation by the interaction of shocks and density discontinuities. Phys. Fluids 8, 18111816.CrossRefGoogle Scholar
Maiden, D. E. & Nutt, G. L. 1986 A hot-spot model for calculating the threshold for shock initiation of pyrotechnic mixtures. In 11th Intl Pyrotechnics Seminar, pp. 813826. Vail, Colorado.Google Scholar
Menikoff, R. 2001 Compaction wave profiles: simulations of gas gun experiments. J. Appl. Phys. 90 (4), 17541760.CrossRefGoogle Scholar
Menikoff, R. 2003 a Notes on elastic–plastic flow. Tech. Rep. LA-UR-03-0047, Los Alamos National Laboratories, Los Alamos, NM.Google Scholar
Menikoff, R. 2003 b Pore collapse and hot spots in HMX. Am. Phys. Soc. Topical Conf., Shock Compression of Condensed Matter (also LA-UR-03-3113), Portand, OR.Google Scholar
Murphy, M. J. & Adrian, R. J. 2007 Particle response to shock waves in solids: dynamic witness plate/PIV method for detonations. Exper. Fluids 43, 163171.CrossRefGoogle Scholar
Murphy, M. J., Adrian, R. J., Stewart, D. S., Elliott, G. S., Thomas, K. A. & Kennedy, J. E. 2005 Visualization of blast waves created by exploding bridge wires. J. Visual. 8 (2), 125135.CrossRefGoogle Scholar
Nichols, A. & Tarver, C. 2002 A statistical hot spot reactive flow model for shock initiation and detonation of solid high explosives. In Proc. 12th Symp. (Intl) on Detonation. San Diego, CA.Google Scholar
Rattray, M. 1951 Perturbation effects in cavitation bubble dynamics. PhD thesis, California Institute of Technology, Pasadena, California.Google Scholar
Rayleigh, L. 1917 On the pressure developed in a liquid during the collapse of a spherical cavity. Philos. Mag. 34, 9498.CrossRefGoogle Scholar
Sushchikh, S. Y. & Nourgaliev, R. R. 2005 Shock waves and flow patterns in shock-induced bubble collapse. 43rd AIAA Aerospace Sciences Meeting and Exhibit (paper no. 2005-1291), Reno, NV.CrossRefGoogle Scholar
Tarver, C. M., Chidester, S. K. & Nichols, A. L 1996 Critical conditions for impact- and shock-induced hot spots in solid explosives. J. Phys. Chem. 100, 57945799.CrossRefGoogle Scholar
Tarver, C. M., Hallquist, J. O. & Erickson, L. M. 1985 Modelling short shock pulse duration shock initiation of solid explosives. In Proc. 8th Symp. (Intl) on Detonation. Albuquerque, NM.Google Scholar
Tran, L. & Udaykumar, H. 2006 Simulation of void collapse in an energetic material. Part 1: Inert case. J. Propul. Power 22 (5), 947958.CrossRefGoogle Scholar
Turangan, C. K., Jamaluddin, A. R., Ball, G. J. & Leighton, T. G. 2008 Free-Lagrange simulations of the expansion and jetting collapse of air bubbles in water. J. Fluid Mech. 598, 125.CrossRefGoogle Scholar