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
EVOLUTION OF STRESS RELAXATION STRUCTURES FOR
SEVERAL POLYMERS SUBJECTED TO PLANE SHOCK
COMPRESSION AROUND 0.5 GPA SHOCK STRESS MEASURED BY
PVDF GAUGE
Yasuhito Mori and Kunihito Nagayama
Department of Aeronautics and Astronautics, Faculty of Engineering, Kyushu University,
Hakozaki, Higashiku, Fukuoka 812-8581 Japan
Abstract Impact shock experiments on several polymers have been performed by a PVDF stress
gauge method combined with an optical prism pin to obtain information on shock Hugoniot data and
stress profiles simultaneously. A plane shock wave propagating into the polymers has stress
relaxation structure behind shock front. Data of the evolution of the relaxation structure for the same
shock stress level have been collected by varying the position of the PVDF gauge embedded into a
target assembly. High-density polyethylene (HDPE), low-density polyethylene (LDPE), nylon-6 (N6), and polycarbonate (PC) are used as a specimen. The stress relaxation structures are fitted by
exponential function, and are analyzed in detail by relaxation time i. It is found that the relaxation
structures for these polymers become smaller gradually with increasing the shock stress. It is also
found that the relaxation structure for these polymer specimens can be expressed by one relaxation
time of microsecond order except for PC specimen.
stress profiles for several polymers are measured
simultaneously in the stress region around 0.5 GPa
by a PVDF stress gauge method combined with an
optical prism pin [5,6]. Evolution of the stress
relaxation structure is discussed by varying the
shock propagation distance, i.e., the position of the
PVDF gauge embedded into a target assembly. In
this study, high-density polyethylene (HDPE), lowdensity polyethylene (LDPE), nylon-6 (N-6), and
polycarbonate (PC) are used as a specimen.
INTRODUCTION
Since the dynamical characteristics of polymers
are dominated by strong viscoelasticity and large
compressibility, a plane shock wave propagating
into the polymers has the relaxation structure behind
shock front, in particular, in the relatively low stress
region. [1,2] According to the previous studies, the
relaxation structure for polymethylmethacrylate
(PMMA) and polyethylene (PE) tends to develop
with the shock propagation, and then approaches a
steady state asymptotically [1,2,3,4]. This result
indicates that the polymeric materials are subjected
to the dynamical non-equilibrium conditions, in
particular, for the lower stress region. Therefore, it is
important for polymers to collect the data of the
evolution of relaxation structure for the same shock
stress level as well as the shock parameters.
For this purpose, the Hugoniot data and the shock
EXPERIMENTAL
Single-stage Compressed Gas Gun
All of the experiments have made by a singlestage compressed gas gun, whose launch tube has 40
mm bore diameter and 2 m length [7,8]. A projectile
of 20-250 g mass with a flyer plate is accelerated up
673
to about 50-500 m/s by helium gas. Projectile
velocity is measured by a beam-cut method with
four laser beams [8]. The projectile impacts against
a target assembly without free flight.
Polymer-driver
Polymer-flyer
Symmetric Impact Condition
In case of polymers, it is found that the relaxation
structure behind shock front depends on the shock
propagation distance as mentioned previously [3,4].
Therefore, it is desirable for the final shocked state
to be unchanged with shock propagation. For this
purpose, we have adopted the so-called symmetric
impact condition, in which the flyer plate is made up
of the same material as all of the target plates [5].
We would like to emphasize that this condition is a
very important key in providing a simpler boundary
condition for the study of the relaxation structure of
viscoelastic materials like polymers.
Under this symmetric impact condition, the value
of particle velocity at the impact surface of the target
should be exactly equal to a half of the impact
velocity. The particle velocity should be kept
unchanged during the shock event, even if the
change in the shocked state due to any stress
relaxation mechanisms take place.
Polymer-backer
Ar* Laser
beam
Triangular
prism
PVDF stress gauge
to Recorder
FIGURE 1. Schematic of a target assembly for a PVDF stress
gauge method combined with an optical prism pin.
can be measured simultaneously by using an optical
prism pin. As shown in Fig. 1, an Ar+ laser beam is
used as a light source. When the shock arrives at the
free surface of the polymer-backer, the light intensity of the beam reflected from the prism pin drops
suddenly due to the change in reflectivity. The beam
intensity change can be detected by an avalanche
photodiode (APD). From the obtained shock
velocity, the Hugoniot stress (aH) can be determined
from the conversation law of momentum.
Polymeric Specimens
In this study, high-density polyethylene (HOPE),
low-density polyethylene (LDPE), nylon-6 (N-6),
and polycarbonate (PC) are used as polymer
specimens. Initial density of the samples are 0.9601,
0.9205, 1.121, and 1.179 g/cm3, respectively.
Longitudinal sound velocity is measured to be about
2.44, 2.01, 2.52, and 2.20 km/s, respectively.
Very Sensitive Shock Wave Detection
To measure both the Hugoniot data and the shock
wave profiles simultaneously in the stress region
around 0.5 GPa, we had developed a very sensitive
shock detection method. This method based on total
internal reflection by triangular prisms has been
combined with a streak photographic method
[8,9,10] or a PVDF stress gauge method [5,6]. We
have also modified this prism method as a very
sensitive shock sensor for liquids like water [11,12].
RESULTS AND DISCUSSION
High-density Polyethylene (HDPE)
Figure 2 shows the obtained shock stress profiles
for HDPE in the Hugoniot stress of about 0.2, 0.4
and 0.8 GPa. The shock propagation distance in each
experiment, i.e., the thickness of the polymer-driver
specimen, is expressed. It is found that these profiles
have the stress relaxation structure behind shock
front.
We have evaluated the relaxation structure by
fitting the stress profile with exponential functions.
First, the origin of time axis for each profile is
defined as a maximum slope point of the shock rise.
Next, as shown in Fig. 3, one can obtain a part of the
stress relaxation structure by subtracting the
normalized stress profile from a step function.
Target Assembly
Figure 1 shows a schematic of a target assembly
for a PVDF stress gauge method combined with an
optical prism pin [5,6]. After a plane shock wave
propagated into a polymer-driver specimen, a shock
stress profile can be directly recorded by an inmaterial PVDF stress gauge (Dynasen Co., PVF211-.125-EK) connected with a charge integrator
(Dynasen Co., CI-50-0.1) [13]. The active area of
about 10 mm2 of the PVDF gauge has the thickness
of about 60 jam sandwiched between Kapton
insulated films.
Shock velocity inside a polymer-backer specimen
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0.8
0.6
(c) 0.46GPa
4.90mm
(d)0.42GPa
10.11mm
0.4
(b)0.20GPa 10.00mm
(a)0.18GPa
4.18mm
0.2
CO
JJ
0.0
5
FIGURE 4. The evolution of the relaxation time for HDPE for
three stress levels of about 0.2, 0.4, and 0.8 GPa obtained by
varying the shock propagation distance.
Time [1 ps /div]
FIGURE 2. The obtained shock stress profiles for HDPE. The
Hugoniot stress and the shock propagation distance in each
experiment are expressed.
iiiiliiii
10
Distance [mm]
HDPE
i i i I , i • r-ri-r-i-ri | i 1-1 i | . . . .
HDPE,0.46GPa ;
•8 0.4
(0
» 0.2 •
v______J
ffi
1°
£ -0.2
0.2
0.4
0.6
0.8
1.0
Shock Stress [GPa]
:
z
FIGURE 5. The dependence of the relaxation time on the shock
stress in the propagation distance of about 10 mm for HDPE.
-04
-0.5
0
0.5
1
1.5
Time [microsec]
2
2.5
FIGURE 3. A part of the stress relaxation structure obtained by
subtracting the normalized stress profile of 0.46 GPa shown as
(c) in Fig. 2 from a step function.
HDPE. Figure 6 shows the evolution of the
relaxation time T for LDPE for the same stress level
by varying the shock propagation distance. The
relaxation time for LDPE is larger than that for
HDPE. The asymptotic tendency of the evolution is
not clear in the distance range up to about 10 mm.
Relaxation structure becomes larger with shock
stress similar to the case of HDPE.
Finally, the data of t > 0 in Fig. 3 are fitted by
exponential functions. It is found from this fitting
that the relaxation structure for HDPE can be
expressed by one relaxation time r except for the
region of shock rise.
Figure 4 shows the evolution of the relaxation
time rfor HDPE for the same stress level by varying
the shock propagation distance. It is found that the
relaxation time develops gradually with increasing
the propagation distance, then tends to approach to
the steady state asymptotically.
Figure 5 shows the stress dependence of the
relaxation time r obtained from three profiles in Fig.
2 for about 10 mm in distance for HDPE. It is found
that for the lower shock stress, the relaxation
structure is larger.
1.6
LDPE
1.4
1.2
1
-°
0.8
0.6
o.4
0.2
0.0. e
5
10
Distance [mm]
FIGURE 6 The evolution of the relaxation time for LDPE for
three stress levels of 0.11, 0.32, and 0.53 GPa obtained by
varying the shock propagation distance.
Low-density Polyethylene (LDPE)
It is found that the relaxation structure for LDPE
can be expressed by one relaxation time as well as
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Nylon-6 (N-6)
CONCLUSION
Three shots for N-6 had been made in the propagation distance of about 10 mm. It is found that the
relaxation structure can be expressed by one relaxation time, and that the stress dependence of the
relaxation time is the almost same as that for HDPE.
It should be emphasized that it is necessary for
the study of the shock properties of polymers to
discuss the Hugoniot curves, the shock wave profiles,
and the evolution of the profiles. For this purpose, a
PVDF stress gauge method combined with an
optical prism pin has been adopted here. The
relaxation structures behind shock front have been
discussed for HOPE, LDPE, N-6, and PC. As a
consequence, it is found for three of 4 polymers
tested in this study that the lower the shock stress is,
the larger the relaxation structure is. This tendency
differs from the relaxation structure of the particle
velocity reported for PMMA [1,2]. It is also found
that the relaxation structure for these polymers
tested in this study can be expressed by one
relaxation time of microsecond order except for PC
specimen. Details of the interesting shock properties
for polymers will be revealed by further studies.
Polycarbonate (PC)
As shown in Fig. 7, three shots for polycarbonate
(PC) had been made in the different shock stress in
the propagation distance of about 10 mm. These
stress profiles could not be fitted by one relaxation
time. In case of PC, two kinds of the relaxation time
seem to be necessary for good fitting. These two
relaxation time are plotted against the shock stress in
Fig. 8. The evaluated values equal to be about 0.1
and 0.5 jus over the distance range up to about 10
mm. The shock rise for the shot of 0.219 GPa,
however, is very long as shown in Fig. 7. Therefore
the evaluated relaxation time for this shot might be
unreliable. It is therefore concluded that the stress
relaxation structure for PC is obviously different
from that for HDPE, LDPE, and N-6.
1. Barker, L.M., and Hollenbach, R.E., J. Appl Phys., 41,
4208-26 (1970).
2. Schuler, K.W., and Nunziato, J.W., Int. J. Solids
Structures, 9, 1237-81 (1973).
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Pressure Sci. Technol, 7, 858-860 (1998).
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Processing TechnoL, 85, 20-24 (1999).
5 Mori, Y., Hidaka, K., and Nagayama, K., Rev. Sci.
Instrum., 71, 6,2492-96 (2000).
6. Mori, Y., and Nagayama, K, Shock Compression of
Condensed Matter-1999, 69-72 (2000).
7. Nagayama, K., "Shock Waves in Material Science",
Springer-Verlag, Tokyo, 1993, Chap. 9, pp. 195-224.
8. Mori, Y., and Nagayama, K., Proc. 2nd Symposium on
High Speed Photography and Photonics, Tohoku
University, Sendai, Japan, 159-193 (1996).
9. Mori, Y., and Nagayama, K., Shock Compression of
Condensed Matter-1997, 875-878 (1998).
10. Mori, Y, Tamura, T., and Nagayama K., Rev. Sci.
Instrum., 69,4,1730-34 (1998).
11 Mori, Y., Shimada, K., Nakahara, M, and Nagayama,
K., Rev. Sci. Instrum., 72,4,2123-27 (2001).
12 Nagayama, K, Mori, Y., Shimada, K., and Nakahara,
M., Shock Compression of Condensed Matter-1999,
65-68 (2000).
13 Charest, J.A., and Lynch, C.S., Shock Compression of
Condensed Matter-1989, 797-800 (1990).
PC-
0.486 GPa
b K> !* o> oo
O
'
•
.
0.21 9 GPa -
0 0 0 0
Shock Stress [GPa]
0.710 GPa
REFERENCES
I
i
i
i
i
i
i
Time [1 ps /div]
FIGURE 7. The obtained stress profiles for polycarbonate (PC).
i i i — i — i — i —| , , ,
i i i
PC,1()mm
"o"
|
0.8
.2
£0.6
<D
E
P
0.4
m—^'-"""•I
—^
»
•B
8
•f °'2
•
nn
0.0
0.2
9-9———
0.4
0.6
0.8
Shock Stress [GPa]
FIGURE 8. The dependence of the relaxation time on the shock
stress in the propagation distance of about 10 mm for PC.
676