Dynamic compression of composite materials is of scientific interest because the mechanical mismatch between internal phases challenges continuum theories. Typical assumptions about steady wave propagation and quasi-instantaneous state changes require reexamination along with the need for time-dependent models. To that end, data and models are presented for the shock compression of an idealized particulate composite. To serve as a generic representative of this material class, a polymer matrix was filled with tungsten particles, ranging from 1 to 50 vol. %. This creates a simple microstructure containing randomly scattered particles with an extreme impedance mismatch to the binding matrix. These materials were parallel plate impact loaded by Al flyers traveling at 1.8–5.0 km/s. Velocimetry provided records of the equilibrium state and the compression wave structure for each case with trends quantified by an empirical fit. The same quantities were also studied as a function of the wave's propagation distance. A homogenized viscoelastic model then made it possible to progress from cataloging trends to making predictions. Starting from a Mie–Gruneisen equation of state, additional time varying terms were added to capture the transient response. After calibration, accurate predictions of the steady wave structure were possible.
REFERENCES
1.
J.
Wackerle
, “Shock-wave compression of quartz
,” J. Appl. Phys.
33
, 922
–937
(1962
). 2.
L. M.
Barker
and R. E.
Hollenbach
, “Shock-wave studies of pmma, fused silica, and sapphire
,” J. Appl. Phys.
41
, 4208
–4226
(1970
). 3.
X.
Chen
, N.
Chandra
, and A. M.
Rajendran
, “Analytical solution to the plate impact problem of layered heterogeneous material systems
,” Int. J. Solids Struct.
41
, 4635
–4659
(2004
). 4.
M. B.
Rauls
and G.
Ravichandran
, “Shock wave structure in particulate composites
,” in Proceedings of the 2015 Hypervelocity Impact Symposium
, edited by W. P.
Schonberg
(Elsevier Science
, Amsterdam
, 2015
), Vol. 103, pp. 515
–521
.5.
D.
Grady
, “Scattering as a mechanism for structured shock waves in metals
,” J. Mech. Phys. Solids
46
, 2017
–2032
(1998
). 6.
M. U.
Anderson
, D. E.
Cox
, S. T.
Montgomery
, and R. E.
Setchell
, “Initial temperature effects on the shock compression and release properties of different alumina-filled epoxy compositions
,” in Shock Compression of Condensed Matter, 2007, Pts. 1 and 2
, edited by M.
Elert
, M. D.
Furnish
, R.
Chau
, N. C.
Holmes
, and J.
Nguyen
(American Institute of Physics
, Melville
, 2007
), Vol. 955, pp. 683
–686
.7.
D. B.
Bober
, J.
Lind
, and M.
Kumar
, “In situ observation of material flow in composite media under shock compression
,” Phys. Rev. Mater.
3
, 073603
(2019
). 8.
E. B.
Herbold
, M. A.
Homel
, J
. Lind
, R.
Crum
, R. C.
Hurley
, B. J.
Jensen
, A. J.
Iverson
, C. T.
Owens
, C. A.
Carlson
, and M. C.
Akin
, “Microscale investigation of dynamic impact of dry and saturated glass powder
,” in Shock Compression of Condensed Matter—2017
, edited by R.
Chau
, T. C.
Germann
, J. M. D.
Lane
, E. N.
Brown
, J. H.
Eggert
, and M. D.
Knudson
(American Institute of Physics
, Melville
, 2018
), Vol. 1979.9.
D. B.
Bober
, M.
Rhee
, N.
Barton
, and M.
Kumar
, “Observation of tungsten particle deformation inside shock compressed polymer
,” in 21st Biennial Conference of the APS Topical Group on Shock Compression of Condensed Matter, edited by M. Armstrong, T. Germann, and M. Lane (2020).10.
G. E.
Duvall
and S. M.
Taylor
, “Shock parameters in a two component mixture
,” J. Compos. Mater.
5
, 130
–139
(1971
). 11.
Y. F.
Alekseev
, L. V.
Al’tshuler
, and V. P.
Krupnikova
, “Shock compression of two-component paraffin-tungsten mixtures
,” J Appl. Mech. Technol. Phys.
12
, 624
–627
(1974
). 12.
A. N.
Dremin
and I. A.
Karpukhin
, “Method for determining shock adiabats of dispersed substances
,” Prikl. Mekh. Tekh. Fiz
3
, 184
–188
(1960
).13.
O. E.
Petel
and F. X.
Jette
, “Comparison of methods for calculating the shock hugoniot of mixtures
,” Shock Waves
20
, 73
–83
(2010
). 14.
L. M.
Barker
, “A model for stress wave propagation in composite materials
,” J. Compos. Mater.
5
, 140
–162
(1971
). 15.
T. J.
Vogler
, C. S.
Alexander
, J. L.
Wise
, and S. T.
Montgomery
, “Dynamic behavior of tungsten carbide and alumina filled epoxy composites
,” J. Appl. Phys.
107
, 043520
(2010
). 16.
E. B.
Herbold
, V. F.
Nesterenko
, D. J.
Benson
, J.
Cai
, K. S.
Vecchio
, F.
Jiang
, J. W.
Addiss
, S. M.
Walley
, and W. G.
Proud
, “Particle size effect on strength, failure, and shock behavior in polytetrafluoroethylene-Al-W granular composite materials
,” J. Appl. Phys
. 104
, 103903
(2008
). 17.
J. L.
Borges
, On Exactitude in Science. A Universal History of Infamy
(Penguin Books
, Middlesex
, 1970
).18.
G. I.
Kanel
, M. F.
Ivanov
, and A. N.
Parshikov
, “Computer simulation of the heterogeneous materials response to the impact loading
,” Int. J. Impact Eng.
17
, 455
–464
(1995
). 19.
B. D.
Coleman
, M. E.
Gurtin
, and I. R.
Herrera
, “The velocity of one-dimensional shock and acceleration waves
,” Arch. Ration. Mech. Anal.
19
, 1
–19
(1965
). 20.
D. E.
Munson
, R. R.
Boade
, and K. W.
Schuler
, “Stress-wave propagation in Al2O3-epoxy mixtures
,” J. Appl. Phys.
49
, 4797
–4807
(1978
). 21.
B. R.
Gafarov
, A. V.
Utkin
, S. V.
Razorenov
, A. A.
Bogach
, and E. S.
Yushkov
, “Front structure of a weak shock wave in dense composites
,” J Appl. Mech. Technol. Phys.
40
, 501
–506
(1999
). 22.
O. T.
Strand
, D. R.
Goosman
, C.
Martinez
, T. L.
Whitworth
, and W. W.
Kuhlow
, “Compact system for high-speed velocimetry using heterodyne techniques
,” Rev. Sci. Instrum
. 77
, 083108
(2006
). 23.
D. B.
Bober
, Y.
Toyoda
, B.
Maddox
, E.
Herbold
, Y.
Gupta
, and K.
Kumar
, “Shock compression response of model polymer/metal composites
,” in Society for Experimental Mechanics
, edited by K. B.
Zimmerman
(Springer
, 2018
), Vol. 1.24.
D. R.
Bland
, “On shock structure in a solid
,” IMA J. Appl. Math
. 1
, 56
–75
(1965
). 25.
J. W.
Swegle
and D. E.
Grady
, “Shock viscosity and the prediction of shock-wave rise times
,” J. Appl. Phys.
58
, 692
–701
(1985
). 26.
A. C.
Mitchell
and W. J.
Nellis
, “Shock compression of aluminum, copper, and tantalum
,” J. Appl. Phys.
52
, 3363
–3374
(1981
). 27.
S. S.
Batsanov
, Effects of Explosions on Materials: Modification and Synthesis Under High-Pressure Shock Compression
(Springer-Verlag
, New York
, 1994
).28.
R. E.
Winter
, G.
Whiteman
, G. S.
Haining
, D. A.
Salisbury
, and K.
Tsembelis
, “Measurement of equation of state of silicone elastomer
,” AIP Conf. Proc.
706
, 679
–684
(2004
). 29.
S. P.
Marsh
, LASL Shock Hugoniot Data
(University of California Press
, Berkeley
, 1980
).30.
31.
R. E.
Setchell
and M. U.
Anderson
, “Shock-compression response of an alumina-filled epoxy
,” J. Appl. Phys
. 97
, 083518
(2005
). 32.
R. E.
Setchell
, M. U.
Anderson
, and S. T.
Montgomery
, “Compositional effects on the shock-compression response of alumina-filled epoxy
,” J. Appl. Phys.
101
, 083527
(2007
). 33.
J. C. F.
Millett
, N. K.
Bourne
, and D.
Deas
, “The equation of state of two alumina-filled epoxy resins
,” J. Phys. D Appl. Phys.
38
, 930
–934
(2005
). 34.
J. L.
Jordan
, L.
Ferranti
, and R. A.
Austin
, “Equation of state of aluminum-iron oxide-epoxy composite
,” J. Appl. Phys.
101
, 093520
(2007
). 35.
L.
Ferranti
, J. L.
Jordan
, R. D.
Dick
, and N. N.
Thadhani
, “Shock hugoniot behavior of particle reinforced polymer composites
,” in Shock Compression of Condensed Matter—2007, Pts. 1 and 2
, edited by M.
Elert
, M. D.
Furnish
, R.
Chau
, N. C.
Holmes
, and J.
Nguyen
(American Institute of Physics
, Melville
, 2007
), Vol. 955, p. 123
.36.
J. L.
Jordan
, D. M.
Dattelbaum
, G.
Sutherland
, D. W.
Richards
, S. A.
Sheffield
, and R. D.
Dick
, “Shock equation of state of a multi-phase epoxy-based composite (Al-MnO2-epoxy)
,” J. Appl. Phys.
107
, 103528
(2010
). 37.
J. L.
Jordan
, E. B.
Herbold
, G.
Sutherland
, A.
Fraser
, J.
Borg
, and D. W.
Richards
, “Shock equation of state of multi-constituent epoxy-metal particulate composites
,” J. Appl. Phys.
109
, 013531
(2011
). 38.
K. W.
Schuler
, “Propagation of steady shock waves in polymethyl methacrylate
,” J. Mech. Phys. Solids
18
, 277
–293
(1970
). 39.
B. D.
Coleman
and M. E.
Gurtin
, “On the growth and decay of one-dimensional acceleration waves
,” Arch. Ration. Mech. Anal.
19
, 239
–265
(1965
). 40.
C. D.
Lundergan
, “Discussion of transmitted waveforms in a periodic laminated composite
,” J. Appl. Phys.
42
, 4148
–4155
(1971
). 41.
L. M.
Barker
, C. D.
Lundergan
, P. J.
Chen
, and M. E.
Gurtin
, “Nonlinear viscoelasticity and the evolution of stress waves in laminated composites: A comparison of theory and experiment
,” J. Appl. Mech.
41
, 1025
–1030
(1974
). 42.
P. J.
Chen
and M. E.
Gurtin
, “On the propagation of one-dimensional acceleration waves in laminated composites
,” J. Appl. Mech.
40
, 1055
–1060
(1973
). 43.
C.
Noble
, A.
Anderson
, N.
Barton
, J.
Bramwell
, A.
Capps
, M.
Chang
, J.
Chou
, D.
Dawson
, E.
Diana
, T.
Dunn
, D.
Faux
, A.
Fisher
, P.
Greene
, I.
Heinz
, Y.
Kanarska
, S.
Khairallah
, B.
Liu
, J.
Margraf
, A.
Nichols
, and J.
White
, ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code, Lawrence Livermore National Laboratory, Livermore, CA, 2017
.44.
S. J.
Ali
, R. G.
Kraus
, D. E.
Fratanduono
, D. C.
Swift
, and J. H.
Eggert
, “An iterative forward analysis technique to determine the equation of state of dynamically compressed materials
,” J. Appl. Phys.
121
, 195901
(2017
). © 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
