Abstract
At low pressures, of the same order as the strength of the underlying material, the removal of porosity is the dominant aspect controlling the behavior of shock-loaded porous materials. In this chapter, we discuss experimental approaches used in this regime including sample configuration and characterization, instrumentation, and error analyses for the results. We follow this with discussion of modeling approaches utilized at both the continuum and the mesoscale. Building upon these fundamentals, we consider several phenomena that are specific to the low-pressure dynamic behavior of porous materials. Finally, we discuss some of the outstanding issues in the behavior and treatment of porous materials in this regime.
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References
Grady D, Fenton G, Vogler T (2014) Equation of state for shock compression of distended solids. J Phys. Conf Ser 500(11):152007
Fredenburg DA, Koller DD (2014) Interpreting the shock response of porous oxide systems. J Phys Conf Ser 500(11):112025
Nesterenko VF (2001) Dynamics of heterogeneous materials. Springer, New York
Fredenburg DA, Thadhani NN, Vogler TJ (2010) Shock consolidation of nanocrystalline 6061-T6 aluminum powders. Mater Sci Eng A 527:3349–3357
Brown JL, Vogler TJ, Grady DE, Reinhart WD, Chhabildas LC, Thornhill TF (2007) Dynamic compaction of sand. In: Elert M, Furnish MD, Chau R, Holmes N, Nguyen J (eds) Shock compression of condensed matter - 2007. AIP, New York, pp 1363–1366
Vogler TJ, Lee MY, Grady DE (2007) Static and dynamic compaction of ceramic powders. Int J Solids Struct 44:636–658
Sheffield SA, Gustavsen RL, Anderson MU (1997) Shock loading of porous high explosives. In: Davison L, Horie Y, Shahinpoor M (eds) High-pressure shock compression of solids IV: response of highly porous solids to shock loading. Springer, New York, pp 23–61
Trott WM, Baer MR, Castañeda JN, Chhabildas LC, Asay JR (2007) Investigation of the mesoscopic scale response of low-density pressings of granular sugar under impact. J Appl Phys 101:024917
Yang R, Zou R, Yu A (2003) Effect of material properties on the packing of fine particles. J Appl Phys 94:3025–3034
Fredenburg DA, Koller DD, Rigg PA, Scharff RJ (2013) High-fidelity Hugoniot analysis of porous materials. Rev Sci Instrum 84:013903
Borg JP, Vogler TJ (2008) Mesoscale calculations of the dynamic behavior of a granular ceramic. Int J Solids Struct 45:1676–1696
Benson DJ (1995) The calculation of the shock velocity - particle velocity relationship for a copper powder by direct numerical simulation. Wave Motion 21:85–99
Schumaker MG, Kennedy G, Thadhani NN, Hankin M, Stewart ST, Borg JP (2017) Stress and temperature distributions of individual particles in a shock wave propagating through dry and wet sand mixtures. AIP Conf Proc 1793:120016
Jaeger HM (2005) Sand, jams and jets. Phys World 18:34–39
Elliot NE, Staudhammer KP (1992) Effect of internal gas pressure on the shock consolidation of 304 stainless steel powders. Marcel Dekker, New York, pp 371–381
McQueen RG, Marsh SP, Taylor JW, Fritz JN, Carter WJ (1970) The equation of state of solids from shock wave studies. In: Kinslow R (ed) High-velocity impact phenomena. Academic, New York, pp 293–417
Yiannakopoulos G (1990) A review of manganin gauge technology for measurements in the gigapascal range. Tech. Rep. MRL-TR-90-5, Materials Research Labs Ascot Vale, Australia
Bauer F (1982) Behavior of ferroelectric ceramics and PVF2 polymers under shock loading. In: Nellis WJ, Seaman L, Graham RA (eds) Shock waves in condensed matter - 1981. AIP, New York, pp 251–266
Barker LM, Hollenbach RE (1972) Laser interferometry for measuring high velocities for any reflecting surface. J Appl Phys 43:4669–4675
Strand OT, Goosman DR, Martinez C, Whitworth TL, Kuhlow WW (2006) Compact system for high-speed velocimetry using heterodyne techniques. Rev Sci Instrum 77:083108
Eakins DE, Thadhani NN (2009) Shock compression of reactive powder mixtures. Int Mater Rev 54:181–213
Borg JP, Chapman DJ, Tsembelis K, Proud WG, Cogar JR (2005) Dynamic compaction of porous silica powder. J Appl Phys 98:073509
Dai C, Eakins DE, Thadhani NN (2007) On the applicability of analytical models to predict Hugoniot of nano-sized powder compacts. In: Elert M, Furnish MD, Chau R, Holmes N, Nguyen J (eds) Shock compression of condensed matter - 2007. AIP, New York, pp 35–38
Razorenov SV, Kanel GI, Baumung K, Bluhm HJ (2002) elastic limit and spall strength of aluminum and copper single crystals over a wide range of strain rates and temperatures. In: shock compression of condensed matter - 2001. AIP, New York, pp 503–506
Barker LM, Hollenbach RE (1974) Shock wave study of the alpha to epsilon phase transition in iron. J Appl Phys 45:4872
Fredenburg DA, Koller DD, Coe JD, Kiyanda CB (2014) The influence of morphology on the low- and high-strain-rate compaction response of CeO2 powders. J Appl Phys 115:123511
Barker LM, Hollenbach RE (1970) Shock-wave studies of PMMA, fused silica, and sapphire. J Appl Phys 41:4208–4226
Baer MR, Trott WM (2004) Mesoscale studies of shock loaded tin sphere lattices. In: Furnish MD, Gupta YM, Forbes JW (eds) Shock compression of condensed matter. American Institute of Physics, New York, pp 517–520
Mitchell AC, Nellis WJ (1981) Shock compression of aluminum, copper, and tantalum. J Appl Phys 52:3363–3374
Root S, Haill TA, Lane JMD, Thompson AP, Grest GS, Schroen DG, Mattsson TR (2013) Shock compression of hydrocarbon foam to 200 GPa: experiments, atomistic simulations, and mesoscale hydrodynamic modeling. J Appl Phys 114:103502
Boade RR (1968) Compression of porous copper by shock waves. J Appl Phys 39:5693–5702
Tang Z, Aidun JB (2009) Combined compression and shear plane waves. In: Horie Y (ed) Shock wave science and technology reference library, vol 3. Springer, Berlin, pp 109–167
Sairam S, Clifton RJ (1994) Pressure-shear impact investigation of dynamic fragmentation and flow of ceramics. In: Gilat A (ed) Mechanical testing of ceramics and ceramic composites. AMD, vol 197. ASME, New York, pp 23–40
Vogler TJ, Alexander CS, Thornhill TF, Reinhart WD (2011) Pressure-shear experiments on granular materials. Report SAND2011-6700, Sandia National Laboratories
LaJeunesse JW (2018) Dynamic behavior of granular earth materials subjected to pressure-shear loading. Ph.D. thesis, Marquette University, Department of Mechanical Engineering
Vogler TJ (2015) Shock wave perturbation decay in granular materials. J Dyn Behav Mater 1:370–387
Carton EP, Verbeek HJ, Stuivinga M, Schoonman J (1997) Dynamic compaction of powders by an oblique detonation wave in the cylindrical configuration. J Appl Phys 81:3038–3045
Thadhani NN (1988) Shock compression of powders. Adv Mater Manuf Process 3:493–549
Jin ZQ, Thadhani NN, McGill M, Ding Y, Wang ZL, Chen M, Zeng H, Chakka VM, Liu JP (2005) Explosive shock processing of Pr2Fe14B/α-Fe exchange-coupled nanocomposite bulk magnets. J Mater Res 20:599–609
Sethi G, Myers NS, German RM (2008) An overview of dynamic compaction in powder metallurgy. Int Mater Rev 53:219–234
Nesterenko VF, Meyers MA, Chen HC (1996) Shear localization in high-strain-rate deformation of granular alumina. Acta Mater 44:2017–2026
Shih CJ, Meyers MA, Nesterenko VF (1998) High-strain-rate deformation of granular silicon carbide. Acta Mater 46:4037–4065
Fenton G, Caipen T, Daehn G, Vogler T, Grady D (2009) Shock-less high rate compaction of porous brittle materials. In: Elert ML, Buttler WT, Furnish MD, Anderson WW, Proud WG (eds) Shock compression of condensed matter - 2009. AIP, New York, pp 1337–1340
Herrmann W (1969) Constitutive equations for the dynamic compaction of ductile porous materials. J Appl Phys 40:2490–2499
Carroll M, Holt AC (1972) Suggested modification of the p-alpha model for porous materials. J Appl Phys 43:759–761
Butcher BM, Karnes CH (1969) Dynamic compaction of porous iron. J Appl Phys 40:2967–2976
Carroll M, Holt AC (1974) Shock-wave compaction of porous aluminum. J Appl Phys 45:3864–3875
Fredenburg DA, Thadhani NN (2013) On the applicability of the p-alpha and p-lambda models to describe the dynamic compaction response of highly heterogeneous powder mixtures. J Appl Phys 113:043507
Boade RR (1970) Principal Hugoniot, second-shock Hugoniot, and release behavior of pressed copper powder. J Appl Phys 41:4542–4551
Grady DE, Winfree NA, Kerley GI, Wilson LT, Kuhns LD (2000) Computational modeling and wave propagation in media with inelastic deforming microstructure. J Phys IV 10:15–20
Grady DE, Winfree NA (2001) A computational model for polyurethane foam. In: Staudhammer KP, Murr LE, Meyers MA (eds) Fundamental issues and applications of shock-wave and high-strain-rate phenomena. Elsevier, New York, pp 485–491
Fenton G, Grady D, Vogler T (2015) Shock compression modeling of distended mixtures. J Dyn Behav Mater 1:103
Collins GS, Melosh HJ, Wunneman K (2011) Improvements to the 𝜖-α porous compaction model for simulating impacts into high-porosity solar system objects. Int J Impact Eng 38:434–439
Wunnemann K, Collins GS, Melosh HJ (2006) A strain-based porosity model for use in hydrocode simulations of impacts and implications for transient crater growth in porous targets. Icarus 180:514–527
Bland PA, Collins GS, Davison TM, Abreu NM, Ciesla FJ, Muxworthy AR, Moore J (2014) Pressure-temperature evolution of primordial solar systems during impact-induced compaction. Nat Commun 5:5451
Davison TM, Collins GS, Bland PA (2016) Mesoscale modeling of impact compaction of primitive solar system models. Astrophys J 821:68
Benson DJ (1997) The numerical simulation of the dynamic compaction of powders. In: Davison L, Horie Y, Shahinpoor M (eds) High-pressure shock compression of solids IV: response of highly porous solids to shock loading. Springer, New York, pp 233–255
Borg JP, Vogler TJ (2008) Mesoscale simulations of a dart penetrating sand. Int J Impact Eng 35:1435–1440
Dwivedi SK, Teeter RD, Felice CW, Gupta YM (2008) Two dimensional mesoscale simulations of projectile instability during penetration in dry sand. J Appl Phys 104:083502
Homel MA, Herbold EB (2017) On mesoscale methods to enhance full-stress continuum modeling of porous compaction. In: Chau R, Germann T, Oleynik I, Peiris S, Ravelo R, Sewell T (eds) Shock compression of condensed matter - 2015, vol 1793. AIP, New York, p 080010
Borg JP, Vogler TJ (2013) Rapid compaction of granular materials: characterizing two and three-dimensional mesoscale simulations. Shock Waves 23:153–176
Lajeunesse JW, Hankin M, Kennedy GB, Spaulding DK, Schumaker MG, Neel CH, Borg JP, Stewart ST, Thadhani NN (2017) Dynamic response of dry and water-saturated sand systems. J Appl Phys 112:015901
Borg JP, Vogler TJ (2009) Aspects of simulating the dynamic compaction of a granular ceramic. Model Simul Mater Sci Eng 17:045003
Baer MR (2007) Mesoscale modeling of shocks in heterogeneous reactive materials. In: Horie Y (ed) Shock wave science and technology reference library. Springer, Heidelberg, pp 321–356
Benson DJ, Conley P (1999) Eulerian finite-element simulations of experimentally acquired HMX microstructures. Model Simul Mater Sci Eng 7:333–354
Eakins D, Thadhani NN (2007) Discrete particle simulation of shock wave propagation in a binary Ni+Al powder mixture. J Appl Phys 101:043508
McGlaun JM, Thompson SL, Elrick MG (1990) CTH: a three-dimensional shock wave physics code. Int J Impact Eng 10:351–360
Williamson RL (1990) Parametric studies of dynamic powder consolidation using a particle-level numerical model. J Appl Phys 68:1287–1296
Derrick JG, LaJeunesse JW, Davison TM, Borg JP, Collins GS (2018) Mesoscale simulations of shock compaction of a granular ceramic: effects of mesostructure and mixed-cell strength treatment. Model Simul Mater Sci Eng 26:035009
Borg JP, Maines WR, Chhabildas LC (2014) Equation of state and isentropic release of aluminum foam and polyvinylidene fluoride systems. J Appl Phys 115:213515
Dwivedi SK, Pei L, Teeter RD (2015) Two-dimensional mesoscale simulations of shock response of dry sand. J Appl Phys 117:085902
Xi CQ, Li QM (2017) Meso-scale mechanism of compaction shock propagation in cellular materials. Int J Impact Eng 109:321–334
Labanda NA, Giusti SM, Luccioni BM (2018) Meso-scale fracture simulation using an augmented Lagrangian approach. Int J Damage Mech 27:138–175
Gunkelmann N, Rosandi Y, Ruestes CJ, Bringa EM, Urbassek HM (2016) Compaction and plasticity in nanofoams induced by shock waves: a molecular dynamics study. Comput Mater Sci 119:27–32
Banlusan K, Strachan A (2016) Shockwave energy dissipation in metal-organic framework MOF-5. J Phys Chem C 120:12463–12471
Cheruka MJ, Germann TC, Kober EM, Strachan A (2014) Shock loading of granular Ni/Al composites. Part I: mechanics of loading. J Phys Chem C 118:26377–26386
Lane JMD, Thompson AP, Vogler TJ (2014) Enhanced densification under shock compression in porous silicon. Phys Rev B 90:134311
Brar NS, Rosenberg Z, Bless SJ (1992) Applying Steinberg’s model to the Hugoniot elastic limit of porous boron carbide specimens. In: Schmidt SC, Dick RD, Forbes JW, Tasker DG (eds) Shock compression of condensed matter. North-Holland, Amsterdam, pp 467–470
Neal WD, Chapman DJ, Proud WG (2012) Shock-wave stability in quasi-mono-disperse granular materials. Eur Phys J Appl Phys 57:31001
Tong W, Ravichandran G (1997) Recent developments in modeling shock compression of porous materials. In: Davison L, Horie Y, Shahinpoor M (eds) High-pressure shock compression of solids IV: response of highly porous solids to shock loading. Springer, New York, pp 177–203
Swegle JW, Grady DE (1985) Shock viscosity and the prediction of shock wave rise times. J Appl Phys 58:692–701
Zhuang S, Ravichandran G, Grady DE (2003) An experimental investigation of shock wave propagation in periodically layered composites. J Mech Phys Solids 51:245–265
Vogler TJ, Borg JP, Grady DE (2012) On the scaling of steady structured waves in heterogeneous materials. J Appl Phys 112:123507
Zel’dovich YaB, Raizer YuP (2002) Physics of shock waves and high-temperature hydrodynamic phenomena. Dover, Mineola, NY
Bakanova AA, Dudoladov IP, Sutulov YN (1974) Shock compressibility of porous tungsten, molybdenum, copper, and aluminum in the low pressure domain. J Appl Mech Tech Phys 15:241–245
Boade RR (1969) Dynamic compression of porous tungsten. J Appl Phys 40:3781–3785
Dandekar DP, Lamothe RM (1977) Behavior of porous tungsten under shock compression at room temperature. J Appl Phys 48:2871–2897
Crockett S (2017) Sesame equation of state 93540. SESAME Database
Grady DE (2010) Length scales and size distributions in dynamic fragmentation. Int J Fract 163:85–99
Davison L, Horie Y, Shahinpoor M (eds) (1997) High-pressure shock compression of solids IV: response of highly porous solids to shock loading. Springer, New York
Krehl POK (2015) The classical Rankine-Hugoniot jump conditions, an important cornerstone of modern shock wave physics: ideal assumptions vs. reality. Eur Phys J H 40:159–204
Meyers MA (1994) Dynamic behavior of materials. Wiley, New York
Lagunov VA, Stepanov VA (1963) Measurements of the dynamic compressibility of sand. Zhurnal Prikladnoi Mekhaniki i Tehknicheskoi Fiziki 4:88–96
Zaretsky E, Asaf Z, Ran E, Aizik F (2012) Impact response of high density flexible polyurethane foam. Int J Impact Eng 39:1–7
Barnes AT, Ravi-Chandar K, Kyriakides S, Gaitanaros S (2014) Dynamic crushing of aluminum foams: part I - experiments. Int J Solids Struct 51:1631–1645
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Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. Los Alamos National Laboratory is managed by Triad National Security, LLC for the U.S. Department of Energy’s NNSA under contract number 89233218CNA000001.
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Fredenburg, D.A., Vogler, T.J. (2019). Low-Pressure Dynamic Compression Response of Porous Materials. In: Vogler, T., Fredenburg, D. (eds) Shock Phenomena in Granular and Porous Materials. Shock Wave and High Pressure Phenomena. Springer, Cham. https://doi.org/10.1007/978-3-030-23002-9_2
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