Download Optical and mechanical properties of soda lime glass

Transactions on the Built Environment vol 22, © 1996 WIT Press, www.witpress.com, ISSN 1743-3509
Optical and mechanical properties of soda lime
glass under shock compression and release
D.P. Dandekar
U.S. Army Research Laboratory-Materials Directorate,
Aberdeen Proving Ground, MD 21005-5069, USA
Abstract
Previous results of plane shock wave experiments on soda lime glass do not
show a sharp unambiguous cusp in its wave profiles indicating the limit of
elastic deformation i.e., Hugoniot Elastic Limit (HEL). This research was
initiated to determine whether the effect of the change in the refractive index of
the glass on the shift in Doppler frequency can be used to determine its HEL
under shock compression.
Based on the results of a limited number of
experiments performed on soda lime glass, it is inferred that the HEL of soda
lime glass is 3.10 ± 0.06 GPa.
1 Introduction
In the range of stress where finite strength of a solid influences the deformation
mode of the material it is useful to know the stress to which it deforms
elastically. This stress is commonly known as the Hugoniot Elastic Limit
(HEL) of a solid in shock wave literature. Ideally, this is the stress at and below
which a material deforms reversibly under shock compression and release. In
other words, deformation of a solid proceeds in an irreversible manner when this
stress is exceeded under shock wave propagation i.e., shock, release, shock-reshock or shock-release- re-shock paths are no longer the same. While many
solids show unmistakable HEL as a cusp in their shock wave profiles when the
stress exceeds their HELs, there are examples of solids which do not exhibit
such unambiguous cusps.
Examples of such materials are amorphous
materials like fused silica, glass, and polymeric materials like Lucite and
PMMA. Since these materials are also transparent, this work was initiated to
study the feasibility of obtaining information about the HEL of such materials
through measurements of their optical property under plane shock wave loading
and unloading experiments. Such shock wave experiments were performed to
measure the effect of compression on the Doppler shift frequency, in PMMA,
fused silica, and sapphire by Barker and Hollenbach [1]. Measurements on
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440
Structures Under Shock And Impact
PMMA were extended to larger stresses by A say and Hayes [2], and Lee [3].
The change in the refractive index of Lithium fluoride under shock wave
propagation were measured by Lee [3] and Wise and Chhabildas[4]. These
experiments were performed to correct the effect of the refractive index to the
measured particle velocity in the experiments where the above mentioned
materials were used as windows and not for the determination of their HEL.
Gibbons and Aherns [5], measured the refractive index of shock recovered soda
lime glass. In their experiments the glass was subjected to a maximum stress
of 23 GPa and the reversibility of the compression was assumed provided
change in the refractive index was within ±0.0025. Based on this criteria, the
HEL for soda lime glass was reported to be 4.0 GPa.
The present work is the first set of experiments in which the effect of
change in the refractive index on the Doppler frequency of a material under both
compression and release wave propagation on the particle velocity have been
measured. The premise of the work is that the polarizabiliry of a material will
be sensitive to the nature of deformation and it will be possible to determine the
HEL of glass in an unambiguous manner. Further it is expected that the change
in the refractive index of a material is reversible under compression and release
wave propagation provided the magnitude of compressive stress does not exceed
its HEL. In this work results of shock wave experiments are analyzed while the
glass is under shock. A future paper will deal with the full analysis of the
shock and release wave data on the glass.
2 Experiment design
Shock wave experiment configuration was designed to determine the effect of
change in the refractive index resulting from compression of soda lime glass
under plane shock wave propagation on the measured particle velocity. The
actual particle velocity in the glass, under plane wave propagation of a given
magnitude, was determined from the measured values of shock velocity and
known Hugoniot of impactor material and window material used in this work.
The impactor material was either OFHC copper or soda lime glass and the
window material, if used in an experiment, was PMMA. The Hugoniots of the
copper and PMMA are given by McQueen et. al. [6]. In the low particle
velocity range i.e., up to 0.48 km/s, the Hugoniot of PMMA given by Barker
and Hollenbach [1] is used in the analysis of the shock data.
A general configuration of the experiments performed on soda lime glass is
shown in Figure 1 (a). The associated stress-particle velocity diagram is shown
in Figure 1 (b). Variation of the configuration included : (i) symmetric impact
experiments i.e., experiments in which impactor was also glass, with or without
PMMA as the window, and (ii) experiments in which a copper impacted glass
target without PMMA window. The main effect of these variations is to change
the associated stress-particle velocity diagram. These changes will be pointed
out later, if necessary.
Figure l(b) shows the associated stress - particle velocity diagram
corresponding to the experimental configuration in Figure 1 (a). For simplicity,
the compression and release loci of copper, glass and PMMA are shown to be
linear. The impactor is assumed to be thick enough so that the release wave
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Structures Under Shock And Impact 441
s,
a
6
To VISAR
(a) Experimental configuration
Glass
0
(b) Stress- particle velocity diagram
Figure 1. Configuration and associated stress - particle velocity diagram for the
described shock wave experiment in soda lime glass.
from the free (back) surface of the impactor does not effect shock wave
interactions occurring between copper, glass and PMMA due to the impact of
copper on glass. As indicated, upon impact of copper on glass, shock waves in
copper and glass travel away from the impact surface. The magnitude of stress
and particle velocity generated due to the impact is denoted by coordinate 1 in
this figure. The shock wave propagating in glass when it arrives at the glass PMMA interface, due to impedance mismatch between the glass and PMMA,
induces a shock wave of magnitude denoted by coordinate 2. This wave then
propagates in PMMA away from the interface and a release wave of the same
magnitude 2 to propagates in glass towards the impact surface. The interaction
between the release wave and shocked state of the copper at the impact surface
induces release waves to propagate back into the copper and a release wave to
propagate in the glass towards the glass - PMMA interface. The common state
reached at the impact surface in glass and copper is denoted by 3. Finally, this
release interacting with the shocked state of PMMA leads to a shock propagating
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Structures Under Shock Ami Impact
back in glass towards the impact surface and release propagating in PMMA
away from the glass - PMMA interface. The common stress - particle velocity
state attained in glass and PMMA due to this final interaction is denoted by 4.
Thus if the change in the refractive index of the glass did not effect the measured
particle velocities, particle velocity profile observed at the impact surface will
show a jump to a value of Uj lasting for the duration of transit time
corresponding to the initial shock and release wave velocities in glass specimen
of a given thickness and then jump to a new value of u, corresponding to the
state 3. On the other hand, the particle velocity profile observed at the glass PMMA interface will show a jump to a magnitude of u% corresponding to the
state 2 from a stationary state, after a time corresponding to the transit time of the
shock wave in glass, and then drop from that value to u* after a duration
corresponding to the time taken by the second release and the final shock waves
to transverse the thickness of the glass target When PMMA is not used in an
experiment the states observed are 1 and a stress free state on the abscissa. For
the configuration shown in Figure 1 (a), this state is u^. For the symmetric
impact experiments i.e., when glass is used as an impactor, the above statement
holds.
Few such experiments were performed for checking the internal
consistency of the particle velocity measurements to be discussed in the section
dealing with the results in this paper.
Shock wave experiments were performed on a 10 cm diameter single stage
gas gun. Impact velocity of the impactor on the glass specimen / target was
measured by shorting four charged pins at pre-measured separations of about 2
cm ahead of the target impact surface. The uncertainty in impact velocity
measurement was less than 0.5 %. The planarity of impact was of the order of
0.5 to 1 mrad.
The shock wave response of soda lime glass, both mechanical and optical,
was determined by means of a four beam VISAR at the Army Research
Laboratory. Precision of particle velocity measurements by means of the four
beam VISAR was 1 %.
The copper discs, used as an impactor were lapped and polished to surface
roughness of 0.05 |im. Glass specimens were polished and flat to 10 jim. A
thin aluminium coating of less than 0.2 Jim was vacuum deposited on the
desired surface of the glass specimens to provide a reflective surface for
measuring particle velocity by means of the VISAR. The aluminium coatings
were 5-8 |im in diameter and were located in a staggered configuration and at
least 25 mm from the lateral edge of a glass specimen. These staggered coating
locations on the discs of soda lime glass permitted simultaneous measurements
of particle velocities at various depths of the glass target in a given experiment.
Particle velocities were measured at least in two locations. These locations were
the impact surface or at some distance from the impact surface, or at the glass PMMA interface or at the free surface. PMMA discs, when used in an
experiment, did not need any surface preparation. The diameters or the lateral
dimensions of the discs, copper, glass and PMMA, used in an experiment were
nearly the same and exceeded 65 mm.
Soda lime glass used in this work was provided by Dr. Brar, University of
Dayton, Ohio. The measured density of the material is 2.491 ± 0.006 Mg/m\
The values of longitudinal and shear wave velocities measured by a pulse
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Table 1. Summary of shock wave experiments in soda lime glass.
Configuiration
number
317
332
C->G1 + PMMA
C->G1 + G2 +
G3+G4 -f PMMA
333
C >G1 + G2 +
PMMA
420
G->G1 + G2
Target
thickness
(mm)
5.644
3.21 to
3.22
3. 17 and
3.2
Impact
velocity
(km/s)
0.303 ±
0.001
0.501 ±
0.002
0.6356 ±
0.0002
Interface
Measured panicle velocity at states (knVs)*
1
2
3
4
C/G1
Gl/P
0.244 (0.2166)
G1/G2
G2/G3
G3/G4
0.400 (0.3634)
0.400 (0.3634)
0.393 (0.3634)
G1/G2
G2/P
0.475 (0.4639) 0.693 (0L7055) 0.573
0.7041S(0.7055)
0.290
0335 (C1.3434)
0.260
0.523
0.573
5.65 and
0.422 ±
G/G1
0.235 (0.2105)
3.18
0.002
G2/F
0.420
425
C >G1 + G2 +
3.17(2)
0.602 ±
G1/G2
0.466 (0.4391)
G3
and 11.32 0.009
G2/G3
0.464 (0.4391)
527
G >G1 + G2
3. 18 and 0.2004 ± G1/G2
0.121 (0.1002) 0.200
1.47
0.0004
G2/F
070? (0.2004)
..._ ....^^^^. ,„ ^vm jiiuv 5iaoo v/i wntn ucc auiwLc vciuciues are measured ana tne state
2 in these cases corresponds to a totally stress free state in the glass. Numbers in parenthesis are the calculated values of particle
velocities based on shock and release wave velocities. See the text.
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444
Structures Under Shock And Impact
overlap ultrasonic technique are 5.82 ±0.01, and 3.45 ± 0.03 km/s, respectively.
The value of its refractive index at 514.5 nm wave length was determined to be
1.5240.
3 Results
A summary of shock wave experiments performed on soda lime glass including
their respective configurations is given in Table 1. Copper, glass, PMMA, and
free surface are denoted by C, G, P, and F, respectively in this table. If more
than one discs of soda lime glass were used in an experiment, each disc is
represented by GX, where X is a numeral. Numeral 1 indicates that the disc
was impacted by the impactor. A glass impactor is simply represented by G.
Finally, an interface between two adjoining specimens, say between copper
impactor (Q and the target material (Gl) at the impact surface, is denoted by C/
Gl in this table. The thicknesses of copper impactors and PMMA windows are
not given in this table because the particle velocity measurements made in these
experiments are not affected by their thickness.
Six experiments were
performed on soda lime glass. A maximum stress of 6.4 GPa was generated in
these experiments.
Wave profiles obtained in experiment 317 at the impact surface of the glass
target i.e., C/G1 interface and at the Gl/P interface are shown in Figure 2. The
profile recorded at the impact surface shows that the particle velocity
corresponding to state 1 is attained upon impact, undergoes a discontinuous
reduction in its value at the time the shock wave reaches the Gl/P interface, and
finally attains a magnitude corresponding to the state 3 discontinuously from its
preceding value as a result of interaction between the release wave arriving at the
interface from the Gl/P interface and the shock state 1 at C/G1 interface. The
profile at the Gl/P interface, which is unaffected by the change in the refractive
index of glass due to shock compression, shows a discontinuous increase in the
particle velocity corresponding to the state 2 and remained there for the duration
of time corresponding to that required by the release waves to travel back and
forth in the glass leading to a change in the particle velocity at the Gl/P interface
corresponding to the state 4. It should be noted that the discontinuous decrease
in the particle velocity at the C/ G1 interface preceding to one corresponding to
the state 3, is simply due to a change in the refractive index of the glass resulting
from the change in the stress state of the glass from the state 1 to state 2. Thus,
this intermediate change is purely due to the optical condition of the glass even
though no change in the stress-particle velocity state has taken place at the C/G1
interface.
It is clear from the above observations that the duration for which state 1 is
maintained corresponds to the time required by the shock wave to transverse the
thickness of the glass specimen, and arrive at the Gl/P interface from the impact
surface of the glass. Similarly, the duration for which the intermediate state
between states 1 and 3, represented by l' in Figure 2 , corresponds to the time
required by the release wave to transverse the glass specimen. Thus, these
measured durations combined with the measured thickness of the glass target
permit calculations of shock and release wave velocities in the glass. The results
of such calculations are given in Table 2. This table shows that the values of
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Structures Under Shock And Impact 445
350
y^V^.s,^ ^v^vv^V-V^^V^vV*^
^
A
State 2
:
Glass/PMMA interface
300
State 3
250
\
State 4
State 1
!
>>
I
15
t>
-S 150
State 1'
Imp actor /glass interface
100
50
0
0
0.5
1
1.5
2
2.5
3.5
Time (jis)
Figure 2. Particle velocity profiles recorded at C/G1 and Gl/P interfaces in
experiment 317.
Table 2. Measured Lagrangian shock and release wave velocities, impact
stress, and associated particle velocity in soda lime glass.
Experiment
Impact stress Particle velocity
Velocity (km/s)
Shock
(GPa)
(km/s)
Release
0,2166
317
3..14
5.82 ±0.06
5.76 ± 0..06
0,2105
3..04
420
5.81 ± 0.03
5.78 ± 0..06
0..3634
332
5.65 ± 0.20
5..09
5.62 ±0.12
0.4639
6..43
5.57 ± 0.06
5.38 ± 0.20
333
0,1002
1,,45
5.82 ±0.06
5.76 ± 0.06
527*
* Shock and release velocities are those obtained from experiments 317 and 420.
Since the specimen thickness appropriate for such calculations was 1.743 mm,
the time duration accuracy of better than 7 ns was required to obtain reliable
values of these velocities.
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Structures Under Shock And Impact
shock wave velocities obtained in the above manner tend to decline with an
increase in the impact stress. Its magnitude equals the measured ultrasonic
longitudinal wave for the impact stress of 3.09 ± 0.05 GPa but its magnitude at
Table 3. Values of impact stress, particle velocity, Av/v, and refractive
index (n) in soda lime glass.
Experiment
Impact
stress (GPa )
317
420
332
332
332
333
425
527
3.14
3.04
5.09
5.09
5.09
6.43
6.09
1.45
Particle
velocity
(km/s)
0.2166
0.2105
0.3634
0.3634
0.3634
0.4639
0.4391
0.1002
Refractive
index (n)
0.1265
0.1164
0.1008
0.1008
0.0816
0.0239
0.0613
0.2076
1.5394
1.5394
1.5533
1.5533
1.5546
1.5695
1.5636
1.5296
Soda lime glass (Presen t work)
Fused silica ( Barker &Hollenbach)
•
o
0.2
Av/v
0.15
>
1
i
0.1
\
0
o
0.05
\
o
CD
i
*
. i . . . .i i . 1 1 1 1 1 1 1
0
(
)
0.1
0.2
0.3
0.4
0.5
0.
Particle velocity (km/s)
Figure 3. Av/v as a function of particle velocity in soda lime glass and fused
silica.
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5 GPa and above is less than the longitudinal wave velocity of 5.82 ± 0.01 km/s.
A similar trend is observed in the release wave velocities. However, it can be
said that the magnitudes of shock and release at given impact stress are equal to
one another.
These values of compression and release velocities are utilized in the
calculations of particle velocities in the glass for the shock and release states
which are in turn used to calculate the magnitudes of relative change in the
frequency (Av/v) due to change in the refractive index and the values of
refractive index in the soda lime glass under shock. The results of the above
mentioned calculations are given in Table 3. The precision of the values of
Av/v is ± 0.009. A plot of Av/v as function of particle velocity for soda lime
glass and fused silica from the work of Barker & Hollenbach [1] is shown in
Figure 3. This figure shows that the relative change in the values of Av/v for
soda lime glass is larger than for fused silica. However in the cases of both
materials the magnitudes are larger at smaller particle velocities than at the larger
velocities. In addition, change of Av/v with the particle velocity in the soda lime
glass shows a break around 0.2 km/s in the glass. The variation in the value of
1.57
1.56
*G
X.
•§
1.55
I
2 1.54
1.53
1.52
o
0.1
0.2
0.3
0.4
Particle velocity (km/s)
Figure 4. Refractive index versus particle velocity in soda lime glass.
0.5
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Structures Under Shock Ami Impact
Av/v is highly nonlinear at the higher particle velocities in the glass. Therefore,
the average value of the particle velocities in Experiments 317 and 420, i.e.,
0.2136 km/s is taken to correspond to the HEL of the glass. The value of HEL
obtained from this particle velocity and the measured shock impedance (14.5 ±
0.17 Gg/mls) of the glass is 3.10 ± 0.06 GPa. Rosenberg et. al.[7] reported the
HEL to be 6.4 GPa for presumably similar soda lime glass.
It is of interest to note that the the values of refractive index as a function of
stress or particle velocity vary smoothly and there is no discernible break in the
slope of refractive index with stress or particle velocity in contrast to the variation
of Av/v with the particle velocity in the soda lime glass. The described variation
of refractive index of glass is shown in Figure 4.
4 Conclusion and future work
This work shows that in transparent material if the change in its refractive index
does not follow Gladstone-Dale behavior, it is possible to design shock wave
experiments to yield information pertaining to shock and release wave
propagation velocities, HEL for the material with no discernible cusp in the
particle wave velocity profile, refractive index of material both under
compression and release through the measurements of particle velocity profiles
at pertinent locations by means of multi-beam VISAR or a similar
interferometer. Additional experiments in the stress range of 3.5-4.5 GPa will
be performed on soda lime glass in the near future to determine whether the
magnitude of HEL i.e., 3.10 ± 0.06 GPa reported in this work needs to be
revised.
Acknowledgment
Author thanks P. Beaulieu for performing the shock experiments on glass.
References
1. Barker, L. M. & Hollenbach, R. E. Shock wave studies of PMMA, fused
silica, and sapphire, Journal of Applied Physics, 1970, 41, 4208-4226.
2. Asay, J. R. & Hayes, D. B. Shock compression and release behavior near
melt states in aluminum, Journal of Applied Physics, 1975, 46,4789-4800.
3. Lee, L. M. Shock induced index of refraction variations in PMMA, sapphire
and lithium fluoride, Ktech Corp. Report TR-76-04, 1976.
4. Wise, J. L. & Chhabildas, L. C. Laser interferometer measurements of
refractive index in shock compressed materials, in Shock waves in condensed
matter (ed. Y. M. Gupta), pp. 441-454, Plenum, New York, 1986.
5. Gibbons, R. V. & Ahrens, T. J. Shock metamorphism of silicate glasses,
Journal of Geophysical Research, 1971, 76, 5489-5498.
6. McQueen, R. G., Marsh, S. P., Taylor, J. W., and Carter, W. J. , The equation
of state of solids from shock wave studies, Chapter VII, High - Velocity Impact
Phenomena, ed R. Kinslow, pp 293-417, and pp 515-568, Academic, New
York and London, 1970.
7. Rosenberg, Z., Yaziv, D., and Bless, S. Spall strength of shock-loaded glass,
Journal of Applied Physics, 1985, 58, 3249-3251.