Pressure-shear plate impact experiment on soda-lime glass at a pressure of 30 GPa
and strain rate of 4·10
7
s
–1
Christian Kettenbeil
, Michael Mello
, Tong Jiao
, Rodney J. Clifton
, and
Guruswami Ravichandran
Citation:
AIP Conference Proceedings
1979
, 070019 (2018); doi: 10.1063/1.5044828
View online:
https://doi.org/10.1063/1.5044828
View Table of Contents:
http://aip.scitation.org/toc/apc/1979/1
Published by the
American Institute of Physics
Pressure-Shear Plate Impact Experiment on Soda-Lime
Glass at a Pressure of 30 GPa and Strain Rate of 4
·
10
7
s
−
1
Christian Kettenbeil
1,a)
, Michael Mello
1,b)
, Tong Jiao
2,c)
, Rodney J. Clifton
2,d)
and
Guruswami Ravichandran
1,e)
1
California
Institute
of
Technology,
1200
E
California
Blvd
Pasadena,
CA
91125
, USA
2
School
of
Engineering,
Brown
University,
182
Hope
St
Providence,
RI
02912
, USA
a)
Corresponding author: ckb@caltech.edu
b)
mello@caltech.edu
c)
tong
jiao@brown.edu
d)
rodney
clifton@brown.edu
e)
ravi@caltech.edu
Abstract.
Recent modifications of a powder gun facility at Caltech have enabled pressure-shear plate impact (PSPI) experiments
in a regime of pressures and strain rates that were previously unaccessible. A novel heterodyne di
ff
racted beam photonic Doppler
velocimeter (DPDV) has also been developed for simultaneous measurement of the normal and transverse particle velocity histories
using the
±
1
st
order di
ff
racted beams produced by a 400 lines
/
mm di
ff
raction grating deposited onto the polished rear surface of the
impacted target plate. We present and interpret the results of a PSPI experiment conducted on a 5
μ
m thick soda-lime glass sample
subjected to a normal stress of 30 GPa and a shear strain rate of 4
·
10
7
s
−
1
. Transverse particle velocity measurements reveal a peak
shear stress level of 1
.
25 GPa up to a shear strain value of 2
.
2, followed by a precipitous drop in stress and complete loss of shear
strength.
INTRODUCTION
The shearing resistance of materials depends on a number of parameters, such as the strain rate [1, 2] and pressure [3]
that a material experiences during loading. Pressure-induced phase transformations add another level of complexity to
characterizing the strength of materials, as structural changes on an atomistic scale may lead to very di
ff
erent material
behavior. Hence, experiments have to be carried out over a wide range of conditions to develop reliable models for
the simulation of dynamic loading events.
Gleason et al. [4] conducted laser-induced shock experiments on amorphous silica and observed a phase transfor-
mation towards a dense, crystalline phase called stishovite at pressures beyond 18.9 GPa. PSPI experiments constitute
an excellent technique to investigate the e
ff
ect of the stishovite phase transformation on the strength of silica glasses
due to their well-characterized one-dimensional plane wave loading [1]. However, current PSPI setups rely on single-
stage gas guns to accelerate their projectile and are limited to maximum normal stresses of approximately 20 GPa.
Recent modifications of a powder gun at Caltech have enabled PSPI experiments at normal stresses of up to 75 GPa
and shear strain rates approaching 10
8
s
−
1
. This capability is employed to explore the dynamic strength of soda-lime
glass under the conditions conducive to the reported phase transformation in [4].
EXPERIMENTAL SETUP
The PSPI technique requires a slotted gun barrel to prevent rotation of the sabot after alignment of the flyer and target
plates. A 38 mm diameter powder gun barrel containing a broached rectangular keyway (3
.
2 mm width, 1
.
9 mm depth,
1
.
5 mm corner radii) permits the acceleration of sabots with inclined flyer plates to velocities ranging between 200 and
Shock Compression of Condensed Matter - 2017
AIP Conf. Proc. 1979, 070019-1–070019-5; https://doi.org/10.1063/1.5044828
Published by AIP Publishing. 978-0-7354-1693-2/$30.00
070019-1
FIGURE 1.
Schematic of PSPI setup with experimental parameters. DPDV (simultaneous normal and transverse particle velocity
measurement) with independent PDV diagnostic (normal particle velocity measurement) and PDV impact velocity measurement
1800 m
/
s. A maximum impact velocity of 1800 m
/
s translates to a normal stress of
≈
75 GPa using high impedance,
pure WC flyer and anvil plates.
A schematic of the PSPI experimental setup is shown in Fig. 1. The flyer and target (anvil) plates were made from
pure WC and inclined at an angle of 18
◦
relative to the direction of approach. The pure WC anvil plates sandwich
a5
μ
m thick vapor deposited layer of soda-lime glass, covered by a 200 nm thick SiO
2
coating which was added to
prevent moisture absorption. A 400 lines
/
mm gold di
ff
raction grating was applied to the polished rear surface of the
anvil plate assembly to e
ffi
ciently di
ff
ract a normally incident
λ
=
1550 nm laser beam into a 0
th
and
±
1
st
order beams
used by the PDV and DPDV arrangement depicted in Fig. 2. The 0
th
order and
±
1
st
order di
ff
racted beams are each
collected using custom fiber-optic probes specifically designed to address the anticipated loss of light at higher impact
velocities. Symmetrically di
ff
racted
±
1
st
order beams are directed to the DPDV diagnostic for combined measurement
of normal and transverse particle velocities, while the 0
th
order beam is interfered by a PDV to obtain an independent
measurement of the normal particle velocity [5]. A shifted-window discrete Fourier transform (DFT) algorithm is
applied to extract the signal frequency variation from the acquired DPDV fringe records, which are then appropriately
combined and scaled to obtain the normal and transverse velocity profiles [5]. Low transverse velocities in PSPI ex-
ĐŽƵƉůĞƌ
ĞƚĞĐƚŽƌ
ĐŽƵƉůĞƌ
ĐŽƵƉůĞƌ
ĞƚĞĐƚŽƌ
нϭ
Ɛƚ
Ͳϭ
Ɛƚ
ŝĨĨƌĂĐƚĞĚĞĂŵWs
;WsͿ
ĞƚĞĐƚŽƌ
ŝƌĐƵůĂƚŽƌ
ZĞĨĞƌĞŶĐĞ>ĂƐĞƌ
;ĂĚũƵƐƚĂďůĞǁĂǀĞůĞŶŐƚŚͿ
WsͲEŽƌŵĂů
/ŶƚĞƌĨĞƌŽŵĞƚƌLJ
߮
ƌŝǀĞ>ĂƐĞƌ
ߣൌͳͷͷͲ
Ŷŵ
KƐĐŝůůŽƐĐŽƉĞ
Ϭ
ƚŚ
FIGURE 2.
Schematic of PDV and DPDV diagnostic system, which relies on the interference of the 0
th
and
±
1
st
order di
ff
racted
beams with an adjustable wavelength reference laser for frequency conversion
periments produce correspondingly low signal frequencies that are impossible to analyze by a shifted-window DFT
070019-2
algorithm while providing a su
ffi
cient temporal resolution for PSPI experiments. The heterodyne scheme overcomes
this challenge by shifting the signal frequency at zero velocity to 1.3 GHz, which enables the accurate determination
of normal and transverse particle velocities with nanosecond time resolution [6] and provides automatic, unambigu-
ous detection of velocity reversals. The e
ff
ective DPDV measurement sensitivity to transverse velocity is controlled
by the grating pitch and theoretically equivalent to that of a transverse displacement interferometer (TDI) [7]. The
measurement sensitivity to normal velocity is increased by 1
.
78
×
compared to the sensitivity of the PDV using the 0
th
order (reflected) beam [5].
EXPERIMENTAL RESULTS
The normal and transverse rear surface particle velocity profiles acquired from the DPDV fringe records are shown in
Fig. 3(a). Corresponding normal and shear stresses on the glass sample interface, plotted in Fig. 3(b), were obtained
using an experimentally validated strength model calibrated to stress levels exceeding the Hugoniot elastic limit (HEL)
of pure WC [8]. The normal stress plot in Fig. 3(b) reveals the HEL of the WC anvil plates at 5.8 GPa, which is close
to the pressure range (6.1-7.1 GPa) reported in other studies [9]. This is followed by a sharp rise to a stress level of 30
GPa as shown in Fig. 3(b). The shear stress curve exhibits a rapid climb to a peak value of 1.25 GPa and is followed
by a sudden and rapid loss in shear strength.
(a)
0.8 1 1.2 1.4 1.6 1.8
0
100
200
300
400
500
600
700
0
10
20
30
40
50
60
70
(b)
0.8 1 1.2 1.4 1.6 1.8
0
5
10
15
20
25
30
0
0.2
5
0.5
0.7
5
1
1.2
5
1.5
1.7
5
2
FIGURE 3.
(a) Normal and transverse free surface velocity profiles measured by the DPDV diagnostic. (b) Inferred normal and
shear stresses using an experimentally calibrated strength model for pure WC anvil plates [8]
Figure 4(a) compares the shear stress versus time profile obtained in the present experiment with two nearly
identical experiments conducted by Jiao et al. [10] at lower normal stresses of approximately 9 GPa and shear strain
rates of 8
·
10
6
s
−
1
. Plots of the shear stress as a function of accumulated shear strain for each of these experiments
are depicted in Fig. 4(b). Although the peak shear stress observed in our experiment is reached in a shorter amount of
time, the total shear strain is comparable to the strain reported by Jiao et al. [10]. A shear strain value of 1
.
5
−
2
.
2at
peak shear stress, as depicted in Fig. 4(b), has also been observed in previously reported experiments and is attributed
to a bond-switching mechanism between covalent Si-O bonds in this range of shear strain [11, 12].
Figure 5(a) provides an expanded view of the normal velocity profile measured by the DPDV diagnostic super-
imposed upon an independently measured normal velocity profile obtained by the PDV using the 0
th
order reflected
beam. Close examination of the two nearly perfectly superimposed curves reveals an inflection, which occurred at
approximately 0
.
93
μ
s as the particle velocity crossed the 350 m
/
s threshold. Finite element simulations using the
aforementioned strength model of WC revealed that this wave structure can be attributed to the interaction between
070019-3
(a)
1.3 1.4 1.5 1.6 1.7 1.8
0
0.25
0.5
0.75
1
1.25
(b)
01234
0
0.25
0.5
0.75
1
1.25
FIGURE 4.
Comparison of shear stress as a function of (a) time and (b) shear strain in the present experiment with two experiments
conducted by Jiao et al. [10] at lower normal stresses of 9 GPa and shear strain rates of 8
·
10
6
s
−
1
the reflection of the elastic precursor from the rear surface of the target assembly and the plastic wave before reach-
ing the free surface. Figure 5(b) depicts the corresponding normal stress profiles that follow from the experimentally
validated strength model.
(a)
0.84 0.86 0.88 0.9 0.92 0.94 0.96
0
100
200
300
400
500
600
(b)
0.84 0.86 0.88 0.9 0.92 0.94 0.96
0
5
10
15
20
25
FIGURE 5.
Detailed view of the (a) normal velocity profile in Fig. 3(a) measured independently with PDV and DPDV diagnostics
and (b) inferred normal stress based on the PDV and DPDV measurement. A wave structure between the elastic and final plastic
wave, associated with the interaction of the elastic precursor and plastic wave, is observed at an inferred normal stress of 18 GPa
070019-4
CONCLUSIONS
Results are presented from a PSPI experiment conducted on a 5
μ
m thick soda-lime glass sample conducted at an
unprecedented pressure (30 GPa) and strain rate (4
·
10
7
s
−
1
). Normal and transverse particle velocities were measured
using a newly developed heterodyne di
ff
racted beam photonic Doppler velocimeter (DPDV) and a complimentary
PDV arrangement, which provided an independent measurement of the normal particle velocity. Normal and shear
stress profiles were inferred using an experimentally calibrated strength model of the pure WC anvil plates [8], which
sandwiched the thin glass specimen. The shear stress observed in the experiment quickly reached its maximum value
of 1
.
25 GPa after which a sudden loss of shear strength occurred. Comparisons to previous experiments conducted at
lower pressures by Jiao et al. [10] showed a similar shear strain level (1
.
5
−
2) at which this maximum shear stress is
achieved.
ACKNOWLEDGMENTS
The authors are grateful for support from the O
ffi
ce of Naval Research (Award No. N00014-16-1-2839) for the devel-
opment of the PSPI capability at high pressures and the Air Force O
ffi
ce of Scientific Research (Award No. FA9550-
12-1-0091) for development of the PDV-DPDV interferometer system.
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