CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
2002 American Institute of Physics 0-7354-0068-7
THE USE OF THE TAYLOR TEST IN EXPLORING AND
VALIDATING THE LARGE-STRAIN, HIGH-STRAIN-RATE
CONSTITUTIVE RESPONSE OF MATERIALS
Joseph C. Foster, Jr.1
Martin Gilmore2
L.L. Wilson3
]
Air Force Research laboratory/Munitions Directorate (AFRL/MN)
EglinAFB,FL
2
Defense Science and Technology Laboratory (DSTL-UK)
Exchange Scientist @ AFRL/MN
3
Science Application Incorporated (SAIC)
EglinAFB,FL
Abstract: The characterization of the mechanical response of materials to high rate loading is an
experimental challenging task. As the load rate becomes high, the engineering analysis of the results of
the experiment places more and more emphasis on understanding the influence of the method of test on
the data recovered from the experiment. At very high rates, the inertia of the test specimen dominants
the load.1 Impact testing techniques combined with judicious specimen design provides access to a
unique range of strain, strain-rate, and load conditions that have a broad range of engineering
applications. This more general interpretation of the classical Taylor test 2 provides opportunities to
characterize a variety of materials in a unique range of conditions.
INTRODUCTION
materials to high-rate loads drives the test design
naturally to impact test techniques. Controlled
impact tests to measure the high rate mechanical
response of materials have been used in the
community for a number of years. The tests provide
data in the 104"5 /sec strain rate regime directly
above that accessible via Hopkinson bar techniques
and below shock experimentation. We have
expanded upon the definition of a Taylor test by
adopting the spirit of Taylor's 1945 James Forrest
Lecture. Experiments designed to study the
mechanical response of materials subjected to highrates of loading where the load cycle is controlled
by the inertia of the specimen are herein termed
generalized Taylor tests. This more general
interpretation of the classical Taylor test 2 provides
opportunities to characterize materials in a variety
Taylor characterized the difficulty of designing
material testing machines as a function of load rates
in a James Forrest Lecture in 1945.1 He concluded
that at very high rates of loading "...the inertia of
the specimen itself gives rise to changes of stress
along its length, which must be taken into account
when seeking to interpret experimental results." In
essence, the inertia of the specimen is controlling
the load cycle and the stress-state is nonequilibrium. This characterization remains valid. It
is interesting to note that he focused on the
difficulties associated with applying the load
quickly as opposed to the high rate deformation
response of the materials being tested. The
measurement of the mechanical response of
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The EOM combined with an assumption that the
material passing through the plastic wave front
comes to zero velocity in a short distance forms the
basis to assess the dynamic yield stress based on the
geometry of the deformed specimen. The stress is
determined from the experimental measurement of
the specimen's final overall length after impact (Lf)
compared to its original length (L0) and the length
of the un-deformed section (lf) using the measured
impact velocity (v) and specimen density (p)
according to
of test conditions that are difficult to obtain via
other techniques.
THE EXPERIMENT
Historical
One standard approach used is the impact
of a right circular cylinder on either a massive anvil
or a receptor rod of identical material, an
experiment commonly called a Taylor test after G.I.
Taylor.
Figure 1 depicts the basic set of
experimental parameters recovered from the
original experiment.
=pv
assuming uniform deceleration of the un-deformed
specimen length.
A first order correction is provided by
Figure 1. Geometry of the rod-on-anvil experiment together
with basic parameters measured from the post-test specimen.
that addresses the non-uniform deceleration of the
un-deformed specimen length
The strength of this original formulation of
the experiment is the relative ease of conducting the
experiment and reducing the experimental
measurements to mechanical properties data.
The goal of the experiment was to "extract
as much information as possible from
measurements of the recovered projectile
(specimen)" The experiment is used to measure a
property associated with a material's plastic
response characterized as the dynamic yield stress.
The load cycle in the experiment is controlled by
the equation of motion (EOM) of the un-deformed
section of the specimen. The original EOM was
arrived at via an analysis of the elastic ring down of
the specimen from the initial impact velocity
yielding
Modernization-The Experiment
The Taylor test has survived for the last
fifty-five years because it provides data in a unique
region of mechanical response that is unobtainable
by any other simple test technique. Additions to the
fundamental basis of the experiment fall into a.)
advanced equations of motion 4'5'6'7'8) b.) alternate
approaches to interpreting the results of the
experiment9'10'11'12 and c.) improved test techniques.
Many researchers have expanded on the way in
which the data is interpreted in terms of a more
complete description of the mechanical response of
the specimen material. 13'14
dv _ <TQ
~dt~~~^
where: <TO = dynamic yield stress
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There remains significant benefit in the
analysis of the post-test specimen. Improved
measurements equipment can be used to accurately
map the entire profile of the post-test specimen
geometry. Figure 2 is a set of precision profile data
taken on the 3.4 hard copper {Rf=103} being used
as the driver material in our 'sleeved' Taylor tests.15
Knowledge of the Lagrangian position and the final
position permit the construction of the axial
displacement
and the strain
_dUz
822
~ dZ
Precision Profile Data
(3/4 Hard Copper [VHN=103])
Z,.-Z M
0.4-
The post-test profile data can now be presented as
displacement and incremental strain in the
Lagrangian coordinates of the specimen. (Reference
figure 3 and figure 4)
I
o
to
8
4S
|
S
°-°H
Zf-ZM
161 m/sec
172 m/sec
185 m/sec
200 m/sec
130 m/sec
Axial Lagrangian Displacement
(3/4 Hard Copper [ VHN=103])
-0.2-
—
—
— ——
——
-0.4-
I
0.0
I
I
I
0.5
1.0
1.5
Distance from Anvil (inches)
I
2.0
161 m/sec
172 m/sec
185 m.sec
130 m/sec
200 m/sec
Figure 2. Precision profile data taken from post-test 3A hard
copper specimens at a variety of impact velocities.
This type of data is recovered from the post-test
specimen using precision optical scanning
techniques. The measurements data can be used to
reconstruct the original specimen geometry from
the deformed geometry using an approximation that
plane sections remain plane.
0.0
\
I
I
I
I
0.5
1.0
1.5
2.0
2.5
Lagriangian Position (inches)
Figure 3. Experimental Lagrangian displacement calculated
from the precision profile measurements data on the post-test
specimen configuration.
Jz.-Z.
jVjL( z .-z. T D 2 + D 2 + D . D .
v
i
i-l' 4 12 v i
i-ll i
i-l
i i-l
The (Di, zO data are the data from the optical
scanner and Zj is the axial coordinate in the original
specimen which is the referential or Lagrangian
coordinates for the experiment.16 Then, the
algorithm for constructing the Lagrangian
coordinates from the precision measurements data
is
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Lagrangian Strain Distribution
3/4 Hard Copper [VHN=103]
O.O-i
— - 161 m/sec
— - 172 m/sec
— - 185 m/sec
200 m/sec
130 m/sec
0.0
I
0.5
I
1.0
I
1.5
I
2.0
I
2.5
Lagrangian Position (inches)
Figure 5. Back-lite high-speed camera data on deforming
urethane specimen
Figure 4. Lagrangian strain distribution calculated from
precision profile measurements data on post-test annealed copper
specimens at various impact velocities.
The data base provided by the high-speed
photography can be differentiated across
intermediate phases of the deformation process that
represent quasi-steady deformation.18
Many modelers find this data useful in combination
with continuum mechanics codes to develop the
constants associated with more complicated
constitutive relations describing the yield behavior
of the material. The simple geometry of the
experiment yields to analysis using continuum
codes without burdening the developer with lengthy
cycle times in the machine.
Beyond the accumulation of measurements
data from the post-test specimen, ultra-high speed
photography yields time-resolved deformation
states.17 (Reference figure 5) The time-resolved
experimental techniques provide the capability to
capture highly transient deformation states such as
those in visco-elastic materials that cannot be
obtained from post-test measurements. Figure 5
illustrates photographic data taken with a Cordin
330 rotating mirror camera that provides 84 frames
of continuous access. The data from the camera can
be subject to dimensional analysis similar to that
conducted on the post-test specimens albeit with
less resolution.
TEST PROTOCOL AND GENERALIZATION
In
addition to the physical
measurements data recovered from the
experiment, if appropriate test protocol is
followed, significant data can be can be
obtained on the micro-structural changes in the
material. Johnson 19 has prescribed a standard
materials test protocol for measuring structural
response of materials to loads where the
instrumentation is unable to time resolve the
information. These include:
1.) Pre-load micro-structure characterization
2.) Real-time continuum observation
3.) Post-load micro-structure characterization
This data generally includes one or more of the
following: optical microscopy, scanning electron
microscopy, and x-ray diffraction studies
When testing energetic materials we have
modified Johnson's protocol to read:
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research projects at the Munitions Directorate of the
Air Force Research Laboratory. The researchers are
indebted to numerous technicians who provide
outstanding support of the research objectives at the
Advanced Warheads Experimentation Facility .
1.) Pre-load micro-structure characterization
2.) Real-time continuum observation near
threshold
3.) Post-load micro-structure characterization
REFERENCE
Taylor, G.I. I Inst. of Civil Engng. 26, 486
Taylor, G.I. Proc. R. Soc. London Ser. A 194, 289
G. I. Barenblatt and A. I. Islinskii, Prikladnaya
Matematika I Mekhanika 26, 497 (1962)
T.C.E. Ting, . J. Appl. Mech. Trans. ASME 33, 505
(1966)
J.B. Hawkyard, D. Eaton and W. Johnson, Int. J.
Mech.Sci. 10,929(1968)
J.B. Hawkyard. Int. J. Mech. Sci. 11, 313 (1969)
Jones, S.E., Gillis, P.P. and Foster Jr., J.C., J. Appl.
Phys. 61,499-502(1987)
J.C. Foster, Jr,, P. J. Maudlin, and S.E. Jones, "On
the Taylor test: A continuum analysis of plastic
wave propagation" in Shock Compression of
Condensed Matter-1995 by S. C. Schmidt and W.C.
Tao, AIP Press 1996 pp 291
10. S.E. Jones, P.J. Maudlin and J.C. Foster, Jr, Int.
Jour. Imp. Engng. 19, no. 2, p. 95 (1997)
11. P. J. Maudlin, S. E. Jones, and J. C. Foster, Jr.,
InternationalJournal of Impact Engineering, 19, no.
3, pp. 231-256, 1997.
12. S.E. Jones, Jeffery A. Drinkard, W.K. Rule and L.L.
Wilson, Int, J. Impact Engng., Vol 21, Nos.l pp 113 (1998)
13. Johnson Gordon R. and Holmquist 1988, J. Appl.
Phys. 64 (S), 15 October
1 4. William K. Rule and S.E. Jones, , Int. J. Impact
Engng. Vol. 21, No. 8 pp. 609-624 (1998)
15 Martin Gilmore, Joseph C. Foster, L.L. Wilson, lan
Cullis, "Dynamic Fracture Studies using Sleeved
Taylor Specimens" in 2001 Proceeding of the APS
Shock Compression of Condensed Matter Topical
Subgroup 24-29 June, 2001
16. Malvern, Lawrence, Introduction to the Mechanics
of a Continuous Medium, Prentice-Hall Inc. 1969,
pg.138-141
17 Wilson, L. L., House, J. W. and Nixon. M. E.I 989
,Time Resolved Deformation from the Cylinder
Impact Test, Air Force Armament Laboratory
Report AFATL-TR-89-76
18. J.W. House, B. Aref, J.C. Foster, Jr., and P.P. Gillis,
J. of Strain Analysis, Vol. 34, No. 5, pp. 337-345
19. Johnson, J.N., "Micromechanical Considerations in
Shock Compression of Solids," in High-Pressure
Shock Compression of Solids, edited by James R
Asay and Mohsen Shahinpoor, Springer- Verlag,
New York,
Figure 6 Pre-test and post-test scanning electron
micrographs of PBXN-109 impacted at 69 m/sec
using a rod-on-rod test configuration
This same protocol has been used doing dynamic
fracture studies with sleeved Taylor specimens
where the threshold of interest is now the fracture
threshold.15
The sleeved Taylor test is basic on our
interpretation of Taylor's James Forrest Lecture in
that the inertia properties of a well-characterized
material (the core) are being exploited to measure
the mechanical response of a material of interest
(the sleeve). This generalization of test
methodology for characterization of the mechanical
response of materials to high load rates suggests a
variety of geometric configurations that might be
used depending on the required data. The
combination of test design, test protocol, and
formulation of EOM for the design which can be
used to describe the load cycle are the fundamental
elements of what we have termed herein as
'generalized Taylor tests.'
ACKNOWLEDGMENTS
The work presented in this paper has been
funded by a variety of in-house exploratory
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