CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
THE SHOCK HUGONIOT OF AN EPOXY RESIN
N. Barnes, N.K. Bourne*, J.C.F. Millett*
AWE, Aldermaston, Reading, Berkshire, RG7 4PR, UK.
*Royal Military College of Science, Cranfield University, Shrivenham, Swindon, SN6 8LA, UK.
Abstract. The Hugoniot of an epoxy resin has been measured using multiple, embedded manganin
stress gauges. In this way, not only is stress measured as a function of particle velocity, but due to
known spacings of the stress gauges, shock velocity has also been determined as an independent
experimental parameter. In both cases, the results have been shown to be similar to those of previous
investigations. However, it has been observed that stresses calculated from the shock velocity-particle
velocity curve tend to be somewhat lower than the directly measured stresses, especially at the higher
end of the stress range studied. It is believed that this may be a reflection of the variation in shear
strength of this material under shock loading.
INTRODUCTION
errors) the Hugoniot curves of all three materials
were the same. They suggested that this indicated
that the variations in cross-linking caused by the
different hardeners had not significant effect on the
compressibility at high stress. Carter and Marsh (7)
investigated epoxy in a wider study on polymeric
materials. Their results showed that in common
with many other polymers, epoxy showed a change
in slope of the shock velocity—particle velocity (Usup) curve at high stress, in this case at ca. 25 GPa.
This they suggested was due to pressure-induced
cross-linking between parallel polymer chains
forming tetragonal carbon-carbon bonds, in a way
analogous to the graphite-diamond transition.
Due to the scarcity of experimental shock data
on epoxy, it is the intention of this investigation to
re-examine the low stress Hugoniot, and to compare
this with existing data.
The response of polymeric materials to shock
loading is becoming of increasing interest, both in
of themselves and as components in inert and
energetic composite systems. However, with the
exception of polymethymethacrylate (PMMA),
which has found application as a window material
for interferometric measurements in shock-wave
experiments (1) the understanding of these
materials under such high strain-rate loading
conditions is limited. More specifically, epoxy
based materials are of interest, as they are used as
the binder phase in composites and as an adhesive
(2) used during assembly of targets for shock wave
experimentation. As such there is an obvious need
to gain an adequate understanding of this material's
behaviour during shock loading.
Perhaps surprisingly, the existing literature
concerning epoxy under shock wave conditions is
not extensive. A number of workers (3-6) have
investigated the shock properties of epoxy when it
has been included as part of a composite material,
but investigations of its response as a bulk material
are less common. Munson and May (3) investigated
three epoxy resin systems, using different hardening
agents, determining that (within experimental
EXPERIMENTAL PROCEDURE
Plate impact experiments were performed on a 50
mm bore, 5 m long single stage gas gun. Flyer
plates of dural (aluminium alloy 6082-T6), copper
and tungsten of thickness 5 and 10 mm were fired at
velocities between 200 and 830 m s"1. Impact
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velocities were measured by the shorting of
sequentially mounted pairs of pins, and the
specimen was aligned to the flyer plate to better
than 1 milliradian by an adjustable specimen mount.
Longitudinal stresses were measured by embedding
a manganin gauge (MicroMeasurements type LMSS-125CH-048) between 10 mm plates of the
epoxy resin. Additionally, a gauge was also
supported on the front surface of the target with a 1
mm plate of the same material as the flyer plate. In
this way, that gauge would experience the same
stress as the embedded gauge whilst the time
difference, A£, and the separation, Aw, of both
gauges (thorough knowledge of the specimen
dimensions is known) could be used to determine
the shock velocity (Us = Aw/Af). Specimen
configurations and gauge placements are shown in
Figure 1.
RESULTS AND DISCUSSION
In Figure 2, typical embedded gauge traces are
presented from this epoxy resin. In this example, a
5 mm copper flyer has been impacted onto the 10
mm target at a velocity of 638 m s"1. Note that in
both traces, the signal rises to its maximum stress
value rapidly, with no evidence of a break in slope
that might indicate an elastic precursor. The rapidity
of the rise is not surprising, since the gauge is
embedded between plates of epoxy, which are
closely matched in impedance to the gauge backing
and the epoxy adhesive used to assemble the
specimen. As such it would be expected that the
gauge response would thus be determined by the
thickness of the manganin gauge element itself, and
thus the signal should rise quickly (ca. 20 ns) as can
be seen from Fig. 2.
'
I
1
Gauge
-Flyer
Impact
Position
£
Target
Plate
0
FIGURE 1. Specimen configuration and gauge placement.
The acoustic properties were measured using 5
MHz quartz transducers, connected to a
Panametrics 500 PR pulse receiver.
Time (jus)
FIGURE 2. Representative embedded gauge traces at 0 mm from
impact (i.e. between coverplate and specimen) and 10 mm from
impact. 5 mm copper flyer at 638 m s""1
One would expect any separation between the
elastic and inelastic parts of the shock wave to be
clearly discernable in the trace at 10 mm. However,
in other polymers such as PMMA, such a difference
has been attributed to the non-linear relationship
between shock and particle velocity (1,8), which in
turn has been ascribed to the viscoelastic/
viscoplastic nature of the material. Thus it would
seem possible that epoxy displays a similar
response to shock-loading conditions.
MATERIAL PROPERTIES
The epoxy studied in this investigation had a
density (po) of 1.14 g cm"3, a longitudinal sound
speed (CL) of 2.38 mm fis"1, a shear wave speed (cs)
of 1.20 mm jis"1 and a Poisson's ratio, v, calculated
using the previous elastic wavespeeds and the initial
density was 0.333. The transducer for velocity
measurement operated at 5 MHz.
136
— This Investigation
o Carter and Marsh (7)
—— U s =2.58+1.47u
— - U = 2.65+1.60i^
o
-This Investigation
Carter and Marsh (7)
I
0.2
0.4
0.6
0.8
-/v
Particle Velocity (mm jus')
0.2
0.4
0.6
Particle Velocity (mm
0.8
FIGURE 3. Shock velocity vs. particle velocity for epoxy resin.
Best fit values for CQ and S given.
FIGURE 4. Shock Hugoniot of epoxy in stress-particle velocity
space. Fit is according to equation 1.
A complete summary of experimental
conditions and results is given in table 1.
In Fig. 4, the shock Hugoniot of this epoxy
resin, is plotted in stress-particle velocity space. As
a comparison, the same data from Carter and Marsh
(7) over a similar stress range is included. As
expected from the shock velocity results shown in
Fig. 3, and the work of Munson and May (3), there
is close agreement between the two sets of data.
The other feature of note in this figure is the plotted
of the material, using c0 and S fitted from the
measured shock velocity plots shown in Fig. 3.
Here it has been assumed that the longitudinal stress
(<7X) can be calculated from the shock velocity (LQ
- particle velocity (up) curve thus,
Table 1. Summary of Experimental Results.
Aw
up
At
Us
Ok
(mm us'1)
(mm jus ) (GPa)
(mm)
(US)
10.06
0.44
3.49
2.88
0.178
0.424
3.17
10.06
3.17
1.40
3.14
10.06
3.20
2.00
0.493
10.07
2.87
3.51
0.571
2.60
3.50
2.72
10.01
3.68
0.735
10.04
3.65
0.734
3.00
2.75
At - time between gauge traces
Aw - distance between gauges
cr =
In figure 3, a plot of shock velocity versus
particle velocity for this epoxy is presented. As a
comparison, the previous work of Carter and Marsh
(7) is also included. Us was calculated from
t/ s =Aw/A* (see table 1), and up from standard
impedance matching techniques. Note that there is a
clear similarity between the two sets of data, with
that of Carter and Marsh (7) lying within the error
bars of our own. Thus it is likely that any
differences between the two could be ascribed to
variations in differently sourced material. Also, as
has been commented on previously, Munson and
May (3), in examining the shock behaviour of
epoxies using different hardeners also observed the
same results over the range of their materials. Note
that Carter and Marsh used a different range of
shock loading apparatus to that used here.
where
O)
and c0 and S are the conventional shock parameters.
Whilst it can be seen that the hydrodynamic
curve lies within the errors of the measured stress
data, it appears that it does lie some distance below
those stress points, with the difference increasing
with increasing particle velocity. There are two
possible explanations for this. Firstly, it could be
due to simple experimental error. The Hugoniot of
the epoxy should be raised above the hydrostat by a
term including the shear strength r. Clearly the
diverging data suggests that there is an increasing
strength value in this offset which remains to be
explained. Clearly, the two should be different since
the material has an HEL but this could not be
measured using normal techniques as discussed
above and thus assumed that it was too low to have
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a significant effect upon the results. However, if
this assumption is incorrect, then failure to take
account of the elastic behaviour of epoxy could
cause an underestimate in the stress when using
shock velocity data alone. The second more likely
cause concerns the shear strength (T) of the
material. During one-dimensional shock loading of
a target with finite strength, the longitudinal stress
during impact can be defined as a function of the
hydrostatic pressure (P) and the shear strength,
= P+ -T.
agreement with data already in the literature. It also
agrees with the observations of Munson and May
(3) who showed that the Hugoniot of epoxies was
effectively insensitive to changes in the hardener.
When the shock stress was calculated from the
measured shock velocities, it was observed that
there was a small but noticeable difference between
that and the measured stress. It has been suggested
that this may be the effect of an increase in shear
strength with increasing shock stress, and is the
subject of ongoing research.
The issue of how a thermoset may 'harden' (in
the traditional sense of the word) is problematic
when considered from a mechanistic point of view.
This is a conceptual difficulty that appears general
in the field when considering polymer shock
compression and it is a question one that future
work will aim to address.
(2)
Also, it should be realised that in using
equations 1 and 2 to predict the Hugoniot in stress
and particle velocity space, one is making the
assumption that shear strength (that is the offset of
the Hugoniot from the hydrostat), is constant.
However this is not always the case. For example,
in polymethylmethacrylate (PMMA), a number of
workers (9, 10) have observed that the shear
strength actually increases with increasing shock
stress, and therefore this would explain the
increasing discrepancy between the measured and
calculated stresses. It remains a challenge to
measure the shear strength as a function of impact
stress directly in order to resolve these issues. A
summary of the shock parameters for this epoxy,
and as a comparison, those of Carter and Marsh (7),
are shown in table 2.
REFERENCES
1. Barker, L.M. and Hollenbach, R.E., J. Appl Phys. 41,
4208-4226(1970).
2. Feng, R. and Gupta, Y.M., in High Pressure Science
and Technology 1993, (ed. S.C. Schmidt, et al.)9 New
York: American Institute of Physics, pp. 1127-1130,
(1994).
3. Munson, D.E. and May, R.P., J. Appl Phys. 43, 962971 (1972).
4. Zhuk, A.Z., Kanet, G.I. and Lash, A.A., J, Phys. IV
France Colloq. C8 4, 403-408 (1994).
5. Plastinin, A.V. and Silvestrov, V.V., Mech. Compos,
Mater, 31,549-553(1995).
6. Thissell, W.R., Zurek, A.K. and Addessio, F., in
Shock Compression of Condensed Matter 1995, (ed. S.C.
Schmidt and W.C. Tao), Woodbury, New York:
American Institute of Physics, pp. 551-554, (1996).
7. Carter, WJ. and Marsh, S.P., (1995), Hugoniot
equation of state of polymers, Los Alamos Report, LA12006-MS.
8. Schuler, K.W. and Nunziato, J.W., J. Appl. Phys, 47,
2995-2998 (1976).
9. Batkov, Y.V., Novikov, S.A. and Fishman, N.D., in
Shock Compression of Condensed Matter 1995, (ed. S.C.
Schmidt and W.C. Tao), Woodbury, New York:
American Institute of Physics, pp. 577-580, (1996).
10. Millett, J.C.F. and Bourne, N.K., Journal of Applied
Physics 88, 7037-7040 (2000).
TABLE 2. Shock Parameters derived for Epoxy Resin.
Material
This investigation
Carter and Marsh (7)
c0 (mm us )
2.6±0.1
1.5±0.2
2.65______1.60
CONCLUSIONS
The shock Hugoniot for an epoxy resin has been
measured using multiple embedded stress gauges.
The technique is novel since it measures the shock
velocity and the stress in a single experiment. It
however, assumes that the shock velocity is
constant with distance through the target which is a
topic under investigation at present. These results,
both in shock velocity-particle velocity and
stress-particle velocity space, show close
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