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 DEVIATORIC RESPONSE OF AN EPOXY RESIN
TO ONE-DIMENSIONAL SHOCK LOADING
N.K. Bourne, J.C.F. Millett, N. Barnes*, I. Belcher*
Royal Military College of Science, Cranfield University, Shrivenham, Swindon, SN6 8LA, UK.
*AWE, Aldermaston, Reading, Berkshire, RG7 4PR, UK.
Abstract. In a previous paper, it was shown that an experiment might be designed to
simultaneously measure the stress-particle velocity and the shock velocity-particle velocity
properties of an impacted solid. It was shown that in an epoxy, the Hugoniot and the hydrostat
diverged which was suggested might be due to variations in shear strength with increasing
longitudinal stress. In this paper, this issue is investigated further by embedding manganin
stress gauges in such orientation that they are sensitive to the lateral component of the stress
during the one-dimensional shock loading. From measured lateral and known longitudinal
stresses, shear strengths are calculated. Results show that this increases with increasing shock
stress amplitude. It has also been noticed that behind the shock front at higher stresses, there is
a significant decrease in lateral stress. Such behaviour has been observed before in
polymethylmethacrylate where it was suggested that this was due to the viscoeleastic/plastic
nature of the material. It would thus seem likely that epoxy resins behave in a similar fashion.
INTRODUCTION
within errors, the Hugoniot curves of three different
epoxies using different hardeners were identical.
They took this as an indication that the degree of
cross-linking according to the different hardeners
had little effect upon the compressibility at high
stresses. Carter and Marsh (7) also showed that, in
common with many other polymers, epoxy
underwent a change in slope in the shock
velocity-particle velocity (£/s-«p), in this case at ca.
25 GPa.
In a previous paper (8), the Hugoniot of an
epoxy system was investigated, measuring both
stress and shock velocities. It was shown that the
Hugoniots determined in stress-particle velocity
and shock velocity-particle velocity space were,
within errors, effectively identical to previous
investigations (7). One interesting feature occurred
when comparison of the directly measured
Hugoniot (stress-particle velocity) to the
hydrodynamic curve was attempted. The
hydrodynamic curve was calculated from the shock
velocity from the relation,
The response of polymeric materials to highstrain-rate and shock loading has been of increasing
interest over the past few years. They are used as
binder systems for both inert composites used as
structural materials in the aerospace and automotive
industries and in reactive materials such as polymer
bonded explosives. In the latter situation, these
materials need to be understood as they can
experience temperature cycling during their
operation lifetime, and sudden loading due to
accidents during handling.
With the exception of polymethylmethacrylate
(PMMA) (1), which is used as a window material
for interferometric measurements in shock
experiments, the behaviour of polymers, under
shock loading is not well understood. Epoxies have
been investigated as binders in composite systems
by a number of workers (2-5), but the available data
on the shock properties of bulk epoxies is not
extensive. Munson and May (6) demonstrated, that
649
of 0.33. The shock parameters (CQ and S) were 2.58
mm jis"1 and 1.47 (7).
(1)
where crx is the stress and p0 is the density, clear
differences were noted between the Hugoniot and
hydrodynamic curve, as particle velocity increased.
In that work, it was suggested that this may be due
to an increase in shear strength (T), since this
defines the offset of the Hugoniot from the
hydrostrat (P), thus,
ax=p+-r.
3
Ffyer
(2)
It is the intention of this paper to investigate this
hypothesis by directly measuring the shear strength
through the direct measurement of the lateral stress.
FIGURE 1. Specimen configuration and gauge placement.
EXPERIMENTAL
RESULTS AND DISCUSSION
Plate impact experiments were performed on a
5 m long, 50 mm bore, single-stage gas gun.
Specimens were aligned to better than 1 mrad using
an adjustable specimen mount. Impact velocities
were measured to an accuracy of ca. 0.1% by the
shorting of sequentially mounted pairs of pins.
Lateral stresses were measured by sectioning 75
mm x 75 mm x 10 mm thick tiles of epoxy and
introducing manganin stress gauges (MicroMeasurements type J2M-SS-380SF-025) 2 mm
from the impact face. The sample was reassembled
using a low viscosity epoxy adhesive, and holding
in a specimen jig for approximately 12 hours. The
impact face of each sample was lapped flat to
within 5 optical fringes. Lateral stresses were
determined from the raw gauge data using the
methods of Rosenberg and Partom (9), using a
modified analysis that does not require prior
knowledge of the impact stress (10). 5 mm flyer
plates of dural (aluminium alloy 6082-T6) and
copper were impacted onto the targets at such
velocities so as to induce stresses in the range 0.5 to
3.5 GPa. The specimen configuration and gauge
placement are shown in Fig. 1.
The material properties of the epoxy
investigated in this paper were- density 1.14 g cm"3,
longitudinal sound speed (CL) 2.38 mm jas"1, shear
sound speed (cs) 1.20 mm us"1 and a Poisson's ratio
The measured Hugoniot and the hydrodynamic
curve of this epoxy are shown in Fig. 2. It has been
included so that it may act as a reference for the
following deductions.
4
3.5
Typical Error
3
£2.5
1
0.5
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Particle Velocity (mm ys"1)
Figure 2. The shock Hugoniot of this epoxy resin. The curve is
the hydrodynamic curve constructed from equation 1, with
measured values of c0 and S of 2.6 mm ^is"1 and 1.5.
As has been noted in the introduction, the
hydrodynamic curve (calculated from equation 1 is
significantly lower than the data itself, especially at
650
impact stress. This has been calculated using
equation 3, with the lateral stress taken from the
gauge traces at the arrows shown in Fig 3.
higher stresses. It has been suggested previously (8)
that this is due to an increasing shear strength.
As an independent measurement of the shear
strength as a function of stress, lateral gauges were
embedded to track the shock. Lateral stress gauge
traces are shown in Fig. 3.
0.5
1
1.5
2
2.5
3
3.5
Longitudinal Stress (GPa)
J/T 0.48 G
0.5" l" 1.
.5
2
2.5
3
FIGURE 4. Shear strength of epoxy resin. The straight line fit
represents the elastic behaviour according to equation 4.
3.5
Time (ps)
The straight line is an elastic trend deduced
using the relations
FIGURE 3. Lateral gauge traces in epoxy resin.
The histories at the two lower stress have a
rather shorter pulse length than the upper two since
5 mm dural flyer plates were used compared to the
higher traces where 5 mm copper flyers (with a
lower wave speed) were used. All the traces rise in
ca. 100 ns which is to be expected given their active
width of 240 urn. Also observe that at 1.95 GPa and
above, lateral stress drops significantly behind the
shock front before the arrival of the release wave.
This may be interpreted as strengthening behind the
shock front given the shear strength is expressed in
terms of the longitudinal (crx) and lateral stresses
ayy
=
- _
1-v
1-v
(4)
It can be seen that all but the lower datum point lay
below the predicted behaviour according to the
elastic response defined by equation 4. However,
there is still a significant increase in shear strength
with increasing longitudinal stress. Similar
behaviour has been noted in PMMA (12, 13) as
well, and thus needs explanation. Such behaviour is
also common in metallic systems, where dislocation
generation has been proposed as a mechanism (14).
Thus it is possible that some sort of microstructural
rearrangement such as increased cross-linking
between the polymer chains may be responsible.
However, a precise explanation of the hardening
mechanism in this and other polymers has yet to be
determined, and as such further work is necessary.
(Oy),
(3)
Such behaviour has been observed before in
PMMA, both by Gupta and Gupta (11), and Millett
and Bourne (12) who noted that this occurred both
above and below the quoted Hugoniot Elastic Limit
(HEL) of 0.75 GPa. Here it was suggested that this
was a manifestation of the viscoelastic/viscoplastic
behaviour of PMMA. Thus it would appear that
epoxy is showing similar features.
Finally, in Fig. 4, the shear strength of epoxy,
measured in this manner, is plotted against the
CONCLUSIONS
The shear strength of an epoxy resin has been
determined with the use of laterally mounted
manganin stress gauges. At higher stresses, it has
been observed that lateral stress decreases
651
10. Millett, J.C.F., Bourne, N.K. and Rosenberg, Z. J.
Phys. D, Applied Physics 29 (1996) 2466-2472.
11. Gupta, S.C. and Gupta, Y.M. J. Appl Phys. 57 (1985)
2464-2473.
12. Millett, J.C.F. and Bourne, N.K. J. Appl, Phys, 88
(2000) 7037-7040.
13. Bat'kov, Y.V., Novikov, S.A. and Fishman, N.D.,, in
Shock Compression of Condensed Matter 1995, S.C.
Schmidt and W.C. Tao, Editors. 1996, AIP Press: Seattle,
WA. p. 577-580.
14. Miliett, J.C.F., Bourne, N.K. and Rosenberg, Z.
J.Appl Phys 81 (1997) 2579-2583.
significantly behind the shock front, and thus the
shear strength increases, in a manner similar to
PMMA. It would seem possible that this is in
response to the viscoplastic nature of the material. It
has also been observed that shear strength increases
markedly with increasing impact stress. This agrees
with the comparison of the measured Hugoniot
stresses and the hydrostatic pressures. An
increasing difference between the hydrodynamic
curve and the Hugoniot as particle velocity
increases, suggests that the offset of the Hugoniot
from the hydrostat (the shear strength) is also
increasing.
The mechanisms that give rise to these observed
effects remain to be fully elucidated. The decrease
in lateral stress under the higher impact conditions
of this experiment suggests a recovery which may
be due to the rotation of polymer units in the
shocked polymer.
The effects that give rise to hardening behaviour
are more difficult to consider. One possible cause
may be the pressure and temperature dependence of
the shear modulus. Such measurements are planned
in further work to elucidate the operating
mechanisms.
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