ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation
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36. R.A. Graham, Impact Techniques for the Study of Physical Properties of Solids under Shock Wave
Loading, J. Basic Eng. (Trans. ASME), Vol 89, 1967, p 911–918
40. E.G. Zukas, Shock-Wave Strengthening, Met. Eng. Q., Vol 6, 1966, p 1–20
45. L.M. Barker and R.E. Hollenbach, Interferometer Technique for Measuring the Dynamic Mechanical
Properties of Materials, Rev. Sci. Instrum., Vol 36, 196, p 1617–1620
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High Velocity Deformation, P.G. Shewmon and V.F. Zackay, Ed., Interscience, 1961, p 409–446
47. G.R. Fowles, Experimental Technique and Instrumentation, Dynamic Response of Materials to Intense
Impulsive Loading, P.C. Chou and A.K. Hopkins, Ed., Air Force Materials Laboratory, Wright Patterson
Air Force Base, 1972, p 405–480
48. P.S. DeCarli and M.A. Meyers, Design of Uniaxial Shock Recovery Experiments, Shock Waves and
High Strain Rate Phenomena in Metals, M.A. Meyers and L.E. Murr, Ed., Plenum, 1981, p 341–373
49. R.G. McQueen and S.P. Marsh, High Explosive Systems for Equation-of-State Studies, Shock Waves in
Condensed Matter—1987, S.C. Schmidt and N.C. Holmes, Ed., Elsevier, 1988, p 107–110
50. M.A. Meyers, Dynamic Behavior of Materials, Wiley Interscience, 1994
51. G.E. Duvall, Shock Waves in the Study of Solids, Appl. Mech. Rev., Vol 15, 1962, p 849–854
52. E.G. Zukas, Shock-Wave Strengthening, Met. Eng. Q., Vol 6 (No. 2), 1966, p 1–20
53. J.N. Fritz and J.A. Morgan, An Electromagnetic Technique for Measuring Material Velocity, Rev. Sci.
Instrum., Vol 44, 1973, p 215–221
54. L.M. Barker and R.E. Hollenbach, Laser Interferometer for Measuring High Velocities of Any
Reflecting Surface, J. Appl. Phys., Vol 43, 1972, p 4669–4675
55. R.G. McQueen, J.W. Hopson, and J.N. Fritz, Optical Technique for Determining Rarefaction Wave
Velocities at Very High Pressures, Rev. Sci. Instrum., Vol 53, 1982, p 245–250
56. J.N. Fritz, C.E. Morris, R.S. Hixson, and R.G. McQueen, Liquid Sound Speeds at Pressure from the
Optical Analyzer Technique, High Pressure Science and Technology 1993, S.C. Schmidt, J.W. Shaner,
G.A. Samara, and M. Ross, Ed., American Institute of Physics, 1994, p 149–152
57. R.J. Clifton, Pressure Shear Impact and the Dynamic Plastic Response of Metals, Shock Waves in
Condensed Matter—1983, J.R. Asay, R.A. Graham, and G.K. Straub, Ed., North-Holland, 1984, p 105–
111
58. R.A. Graham and J.R. Asay, Measurement of Wave Profiles in Shock Loaded Solids, High Temp.—
High Press., Vol 10, 1978, p 355–390
59. G.R. Fowles, G.E. Duvall, J. Asay, P. Bellamy, F. Feistman, D. Grady, T. Michaels, and R. Mitchell,
Gas Gun for Impact Studies, Rev. Sci. Instrum., Vol 41, 1970, p 984–996
60. J.W. Taylor, Experimental Methods in Shock Wave Physics, Metallurgical Effects at High Strain Rates,
R.W. Rohde, B.M. Butcher, J.R. Holland, and C.H. Karnes, Ed., Plenum Press, 1973, p 107–128
61. G.T. Gray III, Deformation Twinning in Aluminum-4.8 wt.% Mg, Acta Metall., Vol 36, 1988, p 1745–
1754
62. G.T. Gray III, P.S. Follansbee, and C.E. Frantz, Effect of Residual Strain on the Substructure
Development and Mechanical Response of Shock-Loaded Copper, Mater. Sci. Eng. A, Vol 111, 1989, p
9–16
63. D.L. Paisley, Laser-Driven Miniature Flyer Plates for Shock Initiation of Secondary Explosives, Shock
Compression of Condensed Matter—1989, S.C. Schmidt, J.N. Johnson, and L.W. Davidson, Ed.,
Elsevier, 1990, p 733–736
64. D.E. Mikkola and R.N. Wright, Dislocation Generation and Its Relation to the Dynamic Plastic
Response of Shock Loaded Metals, Shock Waves in Condensed Matter—1983, J.R. Asay, R.A. Graham,
and G.K. Straub, North-Holland, 1984, p 415–418
65. S. Larouche, E.T. Marsh, and D.E. Mikkola, Strengthening Effects of Deformation Twins and
Dislocations Introduced by Short Duration Shock Pulses in Cu-8.7Ge, Metall. Trans. A, Vol 12, 1981 p
1777–1785
66. D.L. Paisley, Laser-Driven Miniature Plates for One-Dimensional Impacts at 0.5-ε6 km/s, Shock-Wave
and High-Strain-Rate Phenomena in Materials, M.A. Meyers, L.E. Murr, and K.P. Staudhammer, Ed.,
Marcel Dekker, 1992, p 1131–1141
67. D.L. Paisley, R.H. Warnes, and R.A. Kopp, Laser-Driven Flat Plate Impacts to 100 GPa with Sub-
Nanosecond Pulse Duration and Resolution for Material Property Studies, Shock Compression of
Condensed Matter—1991 S.C. Schmidt, R.D. Dick, J.W. Forbes, and D.G. Tasker, Ed., Elsevier, 1992,
p 825–828
68. J.H. Shea, A. Mazzella, and L. Avrami, Equation of State Investigation of Granular Explosives Using a
Pulsed Electron Beam, Proc. Fifth Symp. (Int.) on Detonation, Office of Naval Research, Arlington,
Virginia, 1970, p 351–359
69. F. Cottet and J.P. Romain, Formation and Decay of Laser-Generated Shock Waves, Phys. Rev. A, Vol
25, 1982, p 576–579
70. F. Cottet, J.P. Romain, R. Fabbro, and B. Faral, Measurements of Laser Shock Pressure and Estimate of
Energy Lost at 1.05μm Wavelength, J. Appl. Phys., Vol 55, 1984, p 4125–4127
71. F. Cottet and M. Boustie, Spallation Studies in Aluminum Targets Using Shock Waves Induced by
Laser Irradiation at Various Pulse Durations, J. Appl. Phys., Vol 66, 1989, p 4067–4073
72. T. de Rességuier and M. Hallouin, Stress Relaxation and Precursor Decay in Laser Shock-Loaded Iron,
J. Appl. Phys., Vol 84, 1998, p 1932–1938
73. T. de Rességuier and M. Deleignies, Spallation of Polycarbonate under Laser Driven Shocks, Shock
Waves, Vol 7, 1997, p 319–324
74. C.E. Ragan, Equation-of-State Experiments using Nuclear Explosions, Proc. Int. Symp. on Behaviour of
Condensed Matter at High Dynamic Pressures, Commissariat à l'Energie Atomique, Saclay, Paris,
1978, p 477
75. C.E. Ragan III, Shock Compression Measurements at 1 to 7 TPa, Phys. Rev. A, Vol 25, 1982, p 3360–
3375
76. R.F. Trunin, Shock Compressibility of Condensed Materials in Strong Shock Waves Generated by
Underground Nuclear Explosions, Physics Usp., Vol 37, 1994, p 1123–1145
Shock Wave Testing of Ductile Materials
George T. (Rusty) Gray III, Los Alamos National Laboratory
Design of Shock Recovery and Spallation Fixtures
The structure/property relationships in materials subjected to shock wave deformation are very difficult to
conduct and complex to interpret due to the dynamic nature of the shock process and the very short time of the
test. Due to these imposed constraints, the majority of real-time shock process measurements are limited to
studying the interactions of the transmitted wave arrival at the free surface or at target-window interfaces. To
augment these in situ wave profile measurements, shock recovery techniques were developed in the late 1950s
to experimentally assess the residual effects of shock wave compression, release, and shock-induced fracture
events on materials. The object of soft recovery experiments is to examine the terminal structure-property
relationships of a material that has been subjected to a known uniaxial shock history then returned to ambient
conditions without experiencing radial release tensile wave loading or collateral recovery strains. Tensile wave
interactions may be mostly mitigated by surrounding the sample with tightly fitting material of the same (or
nearly the same) shock impedance, both laterally and axially around the sample. This technique, termed
momentum trapping, has continued to evolve to prevent large radial release waves from entering the sample and
to prevent Hopkinson fracture (spallation) for a variety of sample configurations and shock-loading methods.
When ideally trapped, the residual strain, ε
res
, in the recovered sample (defined here as the final sample
thickness divided by the initial sample thickness) should be on the order of only a few percent. Since the
inception of shock recovery studies, the use of momentum trapping techniques has been successfully applied to
a large number of metallic systems and a more limited number of brittle solids.
Several review papers chronicle the development and design of shock recovery techniques (Ref 25, 26, 34, 40,
48, 77,and 78). To correctly assess the influence of shock wave deformation on ductile material structure and
properties, it is crucial to systematically control the experimental loading parameters and design the shock
fixtures to recover the test sample with minimum residual strain. With higher peak pressures (from 10 GPa, or
1.5 × 10
6
psi, upward) however, recovery of shock-loaded samples becomes increasingly difficult. For low-
pressure shocks, for example, a few times the Hugoniot elastic limit of the material, shock recovery is
straightforward independent of whether the shock is generated via HE, launcher impact, or radiation
impingement. At pressures in excess of 50 to 60 GPa (7.3 × 10
6
to 8.7 × 10
6
psi) recovery of bulk metallic
samples that have not been seriously compromised by significant shock heating and/or radial release strains is
nearly impossible. At shock pressures greater than 100 GPa (14.5 × 10
6
psi) recovery of samples is essentially
impossible. The techniques described below have been used for both HE- and launcher-driven shock recovery
experiments.
References cited in this section
25. G.T. Gray III, Influence of Shock-Wave Deformation on the Structure/Property Behavior of Materials,
High-Pressure Shock Compression of Solids, J.R. Asay and M. Shahinpoor, Ed., Springer-Verlag, 1993,
p 187–216
26. D.G. Doran and R.K. Linde, Shock Effects in Solids, Solid State Phys., Vol 19, 1966, p 230–290
34. G.T. Gray III, Shock Experiments in Metals and Ceramics, Shock-Wave and High-Strain-Rate
Phenomena in Materials, M.A. Meyers, L.E. Murr, and K.P. Staudhammer, Ed., Marcel-Dekker, 1992,
p 899–912
40. E.G. Zukas, Shock-Wave Strengthening, Met. Eng. Q., Vol 6, 1966, p 1–20
48. P.S. DeCarli and M.A. Meyers, Design of Uniaxial Shock Recovery Experiments, Shock Waves and
High Strain Rate Phenomena in Metals, M.A. Meyers and L.E. Murr, Ed., Plenum, 1981, p 341–373
77. R.N. Orava and R.H. Wittman, Techniques for the Control and Application of Explosive Shock Waves,
Proc. of Fifth Int. Conf. on High Energy Fabrication, University of Denver, 1975, p 1.1.1
78. M.A. Mogilevskii, Shock-Wave Loading of Specimens with Minimum Permanent Set, Combust.
Explos. Shock Waves, Vol 21, 1985, p 639–640
Shock Wave Testing of Ductile Materials
George T. (Rusty) Gray III, Los Alamos National Laboratory
Design Parameters for Flyer-Plate Experiments
The variation of the shock parameters (peak pressure and pulse duration) for recovery experiments can be
calculated using several simple formulations. Equations have been developed by Orava and Wittman (Ref 77)
for the design of recovery assemblies to achieve a given peak pressure and pulse duration and to protect the
sample from significant radial release and possible subsequent spallation. Design of the target-flyer variables to
achieve a given set of shock parameters in a shock recovery experiment is typically started by fixing the desired
peak shock pressure or true transient strain. This is linked to the fact that changes in peak shock pressure are
known to produce the most significant variation in post shock material structure-property relations (Ref 24, 25,
26, 28, 29, 30, 40, 42, 44, and 46). When the flyer plate and target assembly are the same material, called
symmetric impact, the material velocity behind the shock is exactly one half of the projectile velocity (Ref 77,
79):
V
p
= + = 2U
p
(Eq 1)
where V
p
is the projectile velocity and U
p
is the particle velocity partitioned between the driver plate, , and
the target, . Symmetric impact is generally preferred because it is most easily analyzed. In the case of
dissimilar materials, the particle velocity is divided according to the Hugoniot equations of each by the
impedance matching method (Ref 6). In this situation, complex release behavior is typical. Hugoniot data for a
wide range of materials can be found tabulated in Ref 79. The total equivalent or effective transient strain
induced in the sample due to this impact (encompassed as a sum of both the elastic and plastic compression and
elastic and plastic release portions of the shock process), ε
t
, is determined from the measured Hugoniot data,
which is the dynamic compressibility of the material as a function of pressure where V
0
and V are the initial and
final volumes of the material during the peak of the shock. Assuming that the residual strain remaining in the
sample after the shock release is zero (Ref 80), the transient or equivalent total strain imparted to the sample
due to the shock-loading impulse and release is given by:
(Eq 2)
In Fig. 4, a time-distance diagram of a symmetric impact by a driver plate with the target backed by a spall
plate is presented that ignores strength in the sample. The symmetry of impact is reflected in the similar slope
of the shock velocity, labeled U
s
, into the driver and target starting at time zero. The length of time the sample
remains at pressure is determined by combining the shock wave and release wave transit times through the
flyer. When the rarefaction wave reaches the flyer-target interface the pressure in the sample is released. The
release process is stretched in time in the form of a “rarefaction fan” due to the variation in longitudinal and
bulk wave speeds as a function of pressure. The pulse duration time, t
p
, at the front of the sample is
approximated by (Ref 77):
(Eq 3)
where d
D
is the driver plate thickness, is the shock velocity in the driver in shock, and are density of
driver at ambient pressure and under shock, respectively, and C
D
is the bulk sound speed in the compressed
(shocked-state) driver.
Fig. 4 Time-distance diagram of a symmetric shock wave impact
To assure the recovery specimen experiences uniaxial strain, that is, one-dimensional strain, in nature during
both loading and unloading it is necessary to protect the sample from radial release prior to uniaxial release.
Figure 4 schematically represents the time distance for a symmetric impact and the commensurate particle-
velocity time history, which would be visible to an interferometer, such as a VISAR, looking at the rear surface
of the sample assembly. If the driver plate and target assembly have the same dimension, then immediately
after the target assembly is impacted by the driver, radial release waves will be directed toward the interior of
the target assembly from the driver edges. In order to mitigate these lateral release waves, the sample within the
target assembly is surrounded by momentum traps comprised of rings or rails of material similar to the sample.
The width of the momentum trapping necessary must be sufficient to contain the total shock event in the flyer
and target of time, t
s
(Ref 77).
Given simple centered flow conditions where the driver, target, and momentum trapping materials are the same,
the minimum trapping width w is given by (Ref 77):
(Eq 4)
After the shock has traversed the sample, if it is not obstructed, it will reflect off the back surface of the
specimen as a release wave. This further complicates the loading history of the sample, indeed, if the rear
surface release wave is allowed to interact with the forward-moving release wave propagating in from the
driver that releases the sample to ambient pressure. In this case the two tensile release fans will meet and cause
spall fracture when the amplitude is above the dynamic tensile strength of the material. To prevent this from
occurring in the sample intended for postshock characterization, a spall plate is placed behind the sample to
isolate the release wave interactions in the spall plate, thereby protecting the sample spallation (Fig. 4). The
release time, t
R
, must be greater than or equal to the shock time. To protect the sample from spall interactions,
the spall plate thickness must equal or exceed the dimension (Ref 77):
(Eq 5)
As an example, a 10 GPa (1.5 × 10
6
psi), 1 μs pulse shock in a 5 mm (0.2 in.) thick high-purity copper sample
(symmetric impact, C
0
= 3.94 mm/μs, C = 4.425 mm/μs, U
s
= 4.326 mm/μs, and V/V
0
= 0.94) requires an
impactor traveling at 0.518 mm/μs (U
p
= 0.259 mm/μs) using a 2.25 mm (0.09 in.) thick copper impactor or
driver plate. The minimum momentum trapping and spall plate requirements are then calculated to be 10.45
mm (0.41 in.) and 10.56 mm (0.42 in.), respectively. While Eq 4 and 5 pertaining to the momentum trapping
and spallation requirements can be corrected for nonsymmetrical impact, this is not usually done. Internal
impedance mismatching within the assembly will cause additional wave reflections that compromise the simple
compression loading history of the sample. In instances where symmetric assembly design is impossible, as is
typically the case for most brittle solids, other techniques are necessary.
Figure 5 illustrates an example of a soft shock recovery fixture positioned on a shock support or impact
assembly for conducting shock recovery experiments on a gas- and/or propellant-driven launcher. Following
release of the shock through the sample, the two opposing release waves are designed to interact within the
spall plate, thereby isolating the sample from the high tensile stresses resulting from the overlap of the two
release fans. The central opening in the impact is thereafter utilized to facilitate the escape of the sample
assembly into the recovery catch tank area for deceleration. This central passageway additionally serves as a
mechanism to separate the sample assembly from the continued forward momentum on the projectile.
Inadequate assembly design to ensure a one-dimensional shock loading and release sequence has been shown to
alter the sample shock history and subsequent structure-property response due to the additional plastic work
imposed on the sample due to late-time radial release effects (Ref 80, 81). Careful attention to momentum
trapping of samples during shock recovery experimentation is therefore required if the structure-property
effects quantified in postmortem recovered samples are to be correlated to processes occurring during shock
loading.
Fig. 5 Schematic of a soft shock recovery fixture used on a gas/powder launcher assembly
References cited in this section
6. R.G. McQueen and S.P. Marsh, Equation of State for Nineteen Metallic Elements from Shock-Wave
Measurements to Two Megabars, J. Appl. Phys., Vol 31, 1960, p 1253–1269
24. C.S. Smith, Metallographic Studies of Metals after Explosive Shock, Trans. Metall. Soc. AIME, Vol
214, 1958, p 574–589
25. G.T. Gray III, Influence of Shock-Wave Deformation on the Structure/Property Behavior of Materials,
High-Pressure Shock Compression of Solids, J.R. Asay and M. Shahinpoor, Ed., Springer-Verlag, 1993,
p 187–216
26. D.G. Doran and R.K. Linde, Shock Effects in Solids, Solid State Phys., Vol 19, 1966, p 230–290
28. W.C. Leslie, Microstructural Effects of High Strain Rate Deformation, Metallurgical Effects at High
Strain Rates, R.W. Rhode, B.M. Butcher, J.R. Holland, and C.H. Karners, Ed., Plenum Press, 1973, p
571
29. L.E. Murr, Residual Microstructure—Mechanical Property Relationships in Shock-Loaded Metals and
Alloys, Shock Waves and High Strain Rate Phenomena in Metals, M.A. Meyers and L.E. Murr, Ed.,
Plenum, 1981, p 607–673
30. L.E. Murr, Metallurgical Effects of Shock and High-Strain-Rate Loading, Materials at High Strain
Rates, T.Z. Blazynski, Ed., Elsevier Applied Science, 1987, p 1–46
40. E.G. Zukas, Shock-Wave Strengthening, Met. Eng. Q., Vol 6, 1966, p 1–20
42. G.T. Gray III, Shock-Induced Defects in Bulk Materials, Materials Research Society Symp. Proc., Vol
499, 1998, p 87–98
44. S. Mahajan, Metallurgical Effects of Planar Shock Waves in Metals and Alloys, Phys. Status Solidi (a),
Vol 2, 1970, p 187–201
46. G.E. Dieter, Metallurgical Effects of High-Intensity Shock Waves in Metals, Response of Metals to
High Velocity Deformation, P.G. Shewmon and V.F. Zackay, Ed., Interscience, 1961, p 409–446
77. R.N. Orava and R.H. Wittman, Techniques for the Control and Application of Explosive Shock Waves,
Proc. of Fifth Int. Conf. on High Energy Fabrication, University of Denver, 1975, p 1.1.1
79. S.P. Marsh, LASL Shock Hugoniot Data, University of California Press, 1980
80. G.T. Gray III, P.S. Follansbee, and C.E. Frantz, Effect of Residual Strain on the Substructure
Development and Mechanical Response of Shock-Loaded Copper, Mater. Sci. Eng. A, Vol 111, 1989, p
9–16
81. A.L. Stevens and O.E. Jones, Radial Stress Release Phenomena in Plate Impact Experiments:
Compression-Release, J. Appl. Mech. (Trans. ASME), Vol 39, 1972, p 359–366
Shock Wave Testing of Ductile Materials
George T. (Rusty) Gray III, Los Alamos National Laboratory
Shock Recovery and Spallation Studies of Ductile Materials
As described previously, shock wave research includes analysis of samples subjected to an impact excursion to
examine the postmortem signature of the shock prestraining on the substructure and mechanical behavior of a
material in addition to damage evolution of a ductile material when subjected to a spallation uniaxial strain
loading history. A few examples of the types of experimental data and post mortem characterization results
typically quantified for both shock recovery and spallation research are introduced below.
Defect Generation during Shock Loading as Quantified Using Shock Recovery Experiments. In an ideal
isotropic homogeneous material, the passage of an elastic shock through a bulk material should leave behind no
lattice defects or imperfections. In practice, the severe loading path conditions imposed during a shock induce a
high density of defects in most materials (i.e., dislocations, point defects, and/or deformation twins). In
addition, during the shock process some materials may undergo a pressure-induced phase transition that affects
the material response. If the high-pressure phase persists upon release of pressure to ambient conditions
(although metastable) the postmortem substructure and mechanical response will also reflect the high-pressure
excursion. Interpretation of the results of shock wave effects on materials must therefore address all of the
details of the shock-induced deformation substructure in light of the operative metallurgical strengthening
mechanisms in the material under investigation and the experimental conditions under which the material was
deformed and recovered.
Microstructural examinations of shock-recovered samples have characterized the differing types of lattice
defects (dislocations, point defects, stacking faults, deformation twins, and, in some instances, high-pressure
phase products) generated during shock loading. The specific type of defect or defects activated and their
density and morphology within the shock-recovered material have, in turn, been correlated to the details of the
starting material chemistry, microstructure, and initial mechanical behavior or hardness, and the postmortem
mechanical behavior of the shock-prestrained material. Several in-depth reviews have summarized the
microstructural and mechanical response of shock-recovered metals and alloys (Ref 24, 25, 26, 28, 29, 30, 40,
42, 44, and 46). In general, the deformation substructures resulting from modest shock loading (up to 40 GPa,
or 6 × 10
6
psi) in metals are observed to be very uniformly distributed on a grain-to-grain scale.
The specific type of substructure developed in the shock in a given metal (e.g., dislocation cells, twins, or
faults) has been shown to critically depend on a number of factors. These include the crystal structure of the
metal or alloy, the relevant strengthening and deformation mechanisms in the material (such as alloying, grain
size, second phases, and interstitial content), temperature, stacking fault energy, and the shock-loading
parameters and experimental conditions. The overall substructure, while macroscopically uniform, can vary
within single grains. The substructure can consist of homogeneously distributed dislocation tangles or cells,
coarse planar slip, stacking faults, or twins (i.e., be locally heterogeneous). The type of substructure formed
depends on the deformation mechanisms operative in the specific material under the specific shock conditions.
These shock-induced microstructural changes in metallic systems in turn correlate with variations in the
postmortem mechanical properties. For example, the formation of deformation twins is facilitated in many
materials due to the very high strain rate during shock loading (Ref 61).
Shock loading in most metals and alloys has been shown to manifest greater hardening than quasi-static
deformation for the same total strain, particularly if the metal undergoes a polymorphic phase transition, such as
is observed in pure iron (Ref 42). Figure 6 compares the stress-strain response of annealed copper and annealed
tantalum samples that have been quasi-statically loaded with the quasi-static reloading responses of the samples
that have been shock prestrained. The shock-loaded stress-strain curves are plotted offset at the approximate
total transient shock strains, calculated as ; 1n (V/V
0
) for the shock (where V and V
0
are the compressed
volumes during the shock and the initial volumes, respectively). The offset curve for copper shows that the
reload behavior of the shock-prestrained sample (compared at an equivalent strain level) exhibits a reload flow
stress considerably higher than the unshocked copper. Other face-centered cubic metals and alloys (e.g., copper,
nickel, and aluminum) have been seen to exhibit similar behavior (Ref 24, 25, 26, 28, 29, 30, 40, 42, 44, and
46). On the contrary, the reload stress-strain response of tantalum shock prestrained to 7 and 20 GPa (1 and 3 ×
10
6
psi) is observed to display essentially no enhanced shock hardening in comparison to quasi-static loading to
an equivalent plastic strain.
Fig. 6 Stress-strain response of tantalum and copper illustrating the varied effect of shock prestraining
on postshock mechanical behavior
Spallation “Hopkinson Fracture” Studies of Ductile Materials. Spallation is the failure in a material due to the
action of tensile stresses developed in the interior of a sample or component through the overlap of two release
waves. Since the early work of Hopkinson (Ref 14), numerous researchers have studied this phenomena (Ref
15, 16, 20, 22, and 82). Early work by Rinehart (Ref 16), through systematic studies on a range of engineering
metals and alloys, demonstrated that a critical shock stress is needed to produce scabbing in a material. The
characteristic nature of this material quantity, as well as its importance to understanding interactions between
shock and the structure, continues to make spallation research of primary scientific and engineering interest. A
systematic representation of the idealized process of release wave overlap driving a material into a dynamic
tension, uniaxial strain, loading state is shown in Fig. 4. The elastic wave in this figure is assumed to be
negligible compared to the plastic I wave; no additional waves, such as a phase transition plastic II wave, are
present.
Measurements of the spall strength are based on analysis of the one-dimensional motion of compressible,
contiguous, condensed matter following the reflection of the shock pulse from the surface of the sample or
component. Figure 4 shows the shock trajectory that a sample undergoes during the path in a spallation
experiment. The shock that is imparted into the target through the jump in particle velocity upon impact with
the driver plate (or impactor) is thereafter unloaded through the release wave originating (in one dimension)
from the rear surface of the driver plate that diminishes the free surface velocity. If the impactor is sufficiently
thin, the rarefaction will overtake the shock because the release wave is traveling into the precompressed solid
and, therefore, its wave speed is higher than the shock velocity. In this case, the rarefaction will attenuate the
shock. This unloading wave is actually a fan of characteristics, which erodes the shock down toward ambient
pressure. This reduces the particle velocity from the peak Hugoniot State achieved by the imposed shock. For
thicker impactors, as in Fig. 4, the release fan arrives at the rear surface of the target well after the arrival of the
main shock. At the free rear surface of the target, the shock wave is reflected as an unloading wave that travels
back toward the interior of the target. Overlap of the release fans causes the material in the overlap region to be
loaded in tension. The maximum tensile stress is reached in the central area of the overlap of the two release
fans, termed the spall plane.
If the maximum tensile stress achieved exceeds the local fracture, strength damage is initiated in the target.
Fracture of the material at the spall plane causes the tensile stress to decrease rapidly to zero. As a result, a
compression wave forms in the matter adjacent to the spall plane region. These waves propagate in each
direction away from the spall plane. At the rear surface of the target, as in Fig. 4 where the particle velocity is
monitored, this compression wave is manifested as a jump in velocity. When the target spalls, a stress wave is
trapped between the spall plane and the rear of the target. Later reverberations of this stress wave lead to a
damped oscillation in the particle velocity record. This “ringing,” or period of oscillations, can be used to
determine the thickness of the spalled layer or scab produced.
Monitoring of the rear surface velocity of the sample or of the sample-window interface using a manganin
pressure gage or VISAR quantifies the sample particle velocity history. A representation of the correlation
between the spallation process within a sample and its manifestation on the sample rear surface or sample-
window surface is shown on the right side of Fig. 4. Measurements of the wave profile of a sample driven to
spall provides information on the time-dependent wave propagation and intersection processes leading to
damage evolution in a material if the tensile stresses are sufficiently high. Shock studies designed to study
spallation in a material therefore use the wave profile and, specifically, the details of the magnitude of the “pull-
back” signal to quantify the energy necessary to nucleate and propagate damage. Figure 7 presents a VISAR
wave profile of high-purity zirconium subjected to spall loading (Ref 83). The arrow A identifies the Hugoniot
elastic limit for this material and the pull-back signal documents that this shock amplitude is sufficient to cause
damage evolution in this material; in this case, however, no scab was formed but rather only incipient spall.
Fig. 7 Rear surface velocity shock wave profile (developed using VISAR interferometry) showing
spallation in zirconium. Source: Ref 83
Profiles such as Fig. 7 provide quantitative data to compare with one-dimensional wave propagation finite-
difference and finite-volume code calculations that model dynamic fracture. Additional insight into the physics
and materials science controlling the process of spallation can be provided through examining the postshocked
and damaged samples, just as Hopkinson did in his first steel studies. Figure 8 shows a metallographic cross
section through an incipiently spalled high-purity tantalum sample following impact loading. In this example,
nearly spherical ductile voids are observed to have nucleated and grown, as a function of position from the
central fracture plane, and begun to coalesce under the imposed tensile stress history. Given sufficient tensile
stress amplitude and appropriate geometry, damage can lead to scab formation and, therefore, complete
separation of the sample into multiple pieces. Identification of the final fracture modes manifesting complete
separation can be obtained by soft recovering the scab formed and then examining its fracture surface. Figure 9
presents an example of a fracture surface of a spalled Ta-10W sample illustrating cleavage fracture behavior.