E
I.
<
58A//39§-Q334!
--
-
,-
r,
15th
International
Symposium
on
Ballistics
Jerusalem, Israel,
21-24
May,
1995
-
HIGH
STRAIN
UTE
PROPERTIES
AND
CONSTITu?TvE
MO13ELNG
OF
GLASS
Tim J. Holmquist
(l),
Gordon
R.
Johnson
(l),
Dennis
E.
Grady
(2),
Craig M."Lopatin
(1)
and Eugene
S.
Hertel Jr.
(2)
(1)
Alliant Techsystems Inc.,
600
2nd St.
NE.,
Hopkins,
MN,
USA
(2)
Sandia National Laboratto$,
P.
0.
Box
5800,
Albuquerque,
NM,
USA
This
paper presents experimental data and computational modeling for a
well-defined glass material. The experimental data cover a wide range of
strains, strain rates, and pressures that are obtained fiom quasi-static
compression and tension tests, split Hopkinson pressure bar compression
tests, explosively driven flyer plate impact tests, and depth of penetration
ballistic tests. The test data
are
used
to obtain constitutive model constants
for the improved Johnson-Holmquist (JH-2) brittle material model. The
model and constants are then used to perform computations of the various
tests.
INTRODUCTION
Recently, much effort has been directed at understanding and niodeling brittle materials
subjected to impact conditions. Under these conditions brittle materials experience large
strains, high strain rates,
and
high pressures; and under certain conditions may also exhibit
bulking
or
dilatation effects
[l].
This paper presents experimental
data,
for
a
well-defined
glass material, over a wide range of strains, strain rates, and pressures. The data are used to
obtain constitutive model constants for the improved Johnson-Holimquist
(JH-2)
model
[2].
The technique
used
to
obtain model constants is discussed
and
computations of
the
flyer plate
impact and ballistic tests are presented.
TEST DATA
The float glass used for
all
experiments is the same material that was
used
for the ballistic
penetration tests performed previously
[3].
The chemical composition and density are
presented in Table
1.
Table
1.
Float Glass Chemical Composition ant1 Density
I
L(tp
Percent Chemical Composition Density
Si02
Na20
.
CaO
MgO
A1203
73.7
10.6
9.4
3.1
1.8
1.1
The results of
16
tests performed on the float glass are summazized
in
Table
2.
Tests
1
through
11
are compression and tension tests at
two
strain rates. These tests were performed
on cylindrical specimens where the
z-axis
is the
axis
of
symmeny. Tests
1
through 4 are
quasi-static uniaxial compression tests. Tests
5
through
8
are Cynamic compression tests
performed using a split Hopkinson pressure bar. Tests 9 through
11
are
quasi-static tension
tests where
the
test technique (radial loading) is similar to that used to determine the tensile
strength
in
concrete
[4].
For tests
1
through
11
the stress state at failure
(O~,CJ~,O~,T)
is
rovided, as well as the equivalent
stress,
0,
pressure,
P,
and average equivalent
stran
rate,
i.
mz
u
OISTAI~~UTION
OF
THIS
LUGUMENC
Is
uN'iMITED
This
WOA
WZIS
SupDorted
by
the
United
States
Department
of
Energy
under
TI4929
Contract
DE-ACQ4
-
94&85QQQ,
DISCLAIMER
This report was prepared as an account of work sponsored
by an agency of the United States Government. Neither the
United States Government nor any agency thereof, nor any
of their employees, make any warranty, express or implied,
or assumes any legal liability or responsibility for the
accuracy, completeness, or usefulness of any information,
apparatus, product, or process disclosed, or represents that
its use would not infringe privately owned rights. Reference
herein to any specific commercial product, process, or
service by trade name, trademark, manufacturer, or
otherwise does not necessarily constitute
cir
imply
its
endorsement, recommendation, or favoring
by
the United
States Government or any agency thereof. The views and
opinions of authors expressed herein do not necessarily
state or reflect those of the United States Government or
any agency thereof.
DISCLAIMER
Portions
of
this document may be ililegible
in
electronic
image
products. Images are
produced from the best available original
document.
I
,
Table
2.
Summary of Test
Data
for FIoat
Glass
Compression and Tension
Tests
Three flyer plate impact experiments were performed (tests
12,
13,
and
14)
to
determine the
Hugoniot Elastic Limit
(HEL),
the Hugoniot stress state, and the particle velocity-time history
wave profiles. The volumetric strain
is
defined as
eV
=
v/vo-l where
v
and
vo
are
the
compressed volume and initial volume, respectively. The
HEL,
and Hugoniot states are
presented in Table
2
and
the
wave profiles are presented
in
Figure
I.
Ballistic penetration experimental results were reported
by
Anderson et.
al.
[3].
Tungsten
penetrators impacting float glass targets at
two
velocities were investigated. The
final
depths
of penetration are provided
in
Table
2.
DETERMINATION
OF
CONSTANTS FOR THE
JH-2
MODEL
The
JH-2
model
is
summarized
in
Figures
2
and
3.
The strength of the material is described
by
a
smoothly varying function of the intact strength, fractured. strength, strain rate,
and
damage. The normalized strength is given
by
O*
=
O*i
-
D(O*i
-
O*f)
(1)
where
O*i
is the normalized intact strength,
o*f
is the normalized fiactwed strength, and
D
is
the damage
(OSD11.0).
The
normalized equivalent stresses
(o*,
O*i
,
o*f)
have the general
form,
G*
=
~GHEL,
where
(T
is the actual equivalent stress and
o~m
is
the
equivalent stress
at the
HEL.
The normalized intact strength is given
by
o*i
=
A(P*
+
T*)N
(1
+
C*ln&*)
(2)
T14929
15OC
1W
h
+
u
0
.I
I
0
0
1
1
Test
12
(VO
=
1990
m/s)
5
Test
13
(VO
=
2380
m/~>
Test
Configurations
Test12&l3
25.4mm
4
1
1
Test
14
(Vo
=
1940
m/s)
2.0
4.0
0
2.0
4.0
6.0
Time
(p)
Figure
1.
Flyer Plate Impact
Tests
for
Float
Glass
and the normalized fractured strength is given by
.
cT*f
=
B(P*)M
(I
+
C*lnk*)
(3)
where
the
material constants
are
A,
By
C,
M,
N,
and
SFMAX.
SFMAX
is
an
optional fracture
strength parameter that allows the normalized fracture strength to be
limited
by
cT*f
I
SFMAX.
The normalized pressure
is
P*
=
P/PHEL,
where
P
is the actual pressure and
PEL
is
the pressure at the
HEL.
The normalized maximum tensile hydrostatic pressure
is
T*
=
T/PHEL,
where
T
is
the maximum
tensile
hydrostatic pressure the material can
withstand. The dimensionless
strain
rate
is
k*
=
t%,,
where
k
is. the actual strain rate and
&
=
1.0
s-1
is
the
reference strain rate.
The damage for fracture
is
accumulated and is given by
D
=
A&phpf
where
to fracture under a constant pressure,
P.
The
specific expression
is
;given by
is
the plastic strain during a cycle of integration and
E$
=
f(P)
is
&e
plastic strain
~~f=
Dl(P*
+
T*)D2
where
D1
and
D2
are constants and
P*
and
T*
are
as defined previously in equation
(2).
The hydrostatic pressure is given by
TI4929