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
EOS DATA OF Ti-6Al-4V TO IMPACT VELOCITIES OF 10.4 KM/S
ON A THREE-STAGE GUN
N. A. Winfree *, L. C. Chhabildas t ? w. D. Reinhartt,
D. E. Carrollt and Q. L Kerley**
*Dominca, Albuquerque, NM, 87111 l
^Sandia National Laboratories, Albuquerque, NM, 87185 2
**Kerley Technical Services, Appomattox, VA 24522
Abstract. Experiments were conducted to acquire Hugoniot data for T16-A1-4V at compress!ve
stresses up to 250 GPa for use as a standard material on the three-stage gun at Sandia. Ti6A1-4V was chosen over several other standards because in previous work on the three-stage
gun it was most readily launched intact and fiat. In each experiment, a graded-density launch
plate travelling at 6.3 or 6.7km/s launches a Ti-6Al-4V flier plate to 9.8 or 10.4 km/s. The
flier impacts a stationary target disk of Ti-6Al-4V. Shorting pins and optical fibers imbedded
in the target serve as time-of-arrival sensors to determine the shock velocity. These also permit
quantification of the bow and tilt of the flier plate, which are found to be comparable to shots
on two-stage guns. Corrections are made for the temperature of the flier in order to calculate
the stress and particle velocity behind the shock.
INTRODUCTION
Existing data for the equation of state (EOS)
behavior of Ti-6Al-4V extend to 202 GPa. This
paper reports two new points at ~230 and
250 GPa, obtained on the Sandia hypervelocity
launcher. This work was detailed in (1), but the
data analysis has changed.
is a 2-4 mm thick stack of plastic (TPX) and
metal disks having densities that increase from
0.81 g/cm3 at the impact face to 16.96 g/cm3 farthest from this face. When this assembly impacts
the flier, it induces a series of gradually increasing compressive shocks in the flier, approximating a "ramp wave." This ramp wave launches the
flier to 10-11.5 km/s with far less shock-induced
heating than if it were launched to the same terminal velocity by a single-density impactor. A
plastic disk on the flier's impacted surface provides additional protection.
Ti-6Al-4V is used for the flier because, compared to other metals, greater success has been
achieved launching it intact and flat from the
third stage. A sacrificial guard ring bears the
worst of the edge effects, leaving the center of
the flier fairly flat.
The flier impacts a Ti-6Al-4V target (Fig. 2)
instrumented with two types of sensors: mechanical pins short when the shock in the target
encounters them, and optical fibers housed in
CONFIGURATION
The Sandia hypervelocity launcher has been
described elsewhere (2, 3). In brief, a two-stage
gun accelerates a graded density impactor to 67.5 km/s. This impactor enters a third stage and
impacts a 17-19 mm diameter x 0.6-1 mm Tir, Fig. 1. The graded density impactor
1
nancy@dominca.com
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the
United States Department of Energy under Contract DEAC04-94AL85000
2
75
Graded
density
impactor
Vl
(a)
Needle
locations
• Flier plate
Target
•Flier plate
•Guard ring
Pin
locations
Impact faceMounting ring-
Guard ring
Dia DB
FIGURE 1. (a) The graded density impactor is
about to strike and launch the flier plate, (b) The
flier plate has been launched and is about to impact
the target. The guard ring, deformed by edge effects,
has separated from the flier. Axis x the common
longitudinal axis of the disks: x = 0 is the impact
interface.
FIGURE 2.
B planeA planeThe target configuration.
cannot be measured. Instead, it is predicted by
CTH simulations: inputs include the velocity V\
of the graded-density impactor, and the thickness and material properties of each layer of the
impactor and flier. This method is justified in
(4): the flier's velocity was determined by interferometry in four tests conducted with no target.
The predicted and measured terminal velocities
agreed within 1%.
Further details are given in (1).
hypodermic needles emit light when the shock
encounters them. Six pins on diameter DA are
inserted from the non-impacted face into flatbottomed holes that end on plane "A" near the
impacted face. Six pins on diameter DB end on
plane "J3," approximately 2 mm behind plane A.
Needles are inserted similarly. The pins and needles provide the transit time of the shock wave
from plane A to plane B, from which the shock
velocity Us in the target is determined to within
2%. An extra pin on the centerline extends to
plane A. Bow and tilt are calculated from the
differences in the time of the shock's arrival at
each sensor on plane A.
The diameter of each plate is much greater
than its thickness to ensure that waves emanating from the lateral surfaces do not reach the
sensors during the duration of the experiment.
Likewise, the radial distance between the diameters DA and DB is appreciably greater than the
distance between planes A and B so that disturbances caused by the outer detectors would not
reach the inner detectors.
The velocity V\ of the graded density impactor
is determined to within 2% by detecting the
times at which it breaks five beams of laser light
spaced at ~57 mm increments.
With the target in place, the flier's velocity VQ
RESULTS AND ANALYSIS
Two shots were conducted, Table 1. We assume that the x — t diagram of Fig. 3 represents
the response of the target and the flier. Continuity and conservation of momentum require that
particle velocity and stress must be continuous
across the impact interface. Across the discontinuities that propagate into the flier and target,
continuity and conservation of momentum impose the jump conditions
=p ,
(i)
(2)
where 7 = (pQ - p)/p and 7' = (p'Q - p')/p'As one bound, assume "symmetric impact,"
i.e., that the target and flier have identical densities and temperatures at impact, and that their
responses are identical. We impose U's = Us, p'$ =
po> and p1 ~ p in (1) and (2), then solve for P,
76
TABLE 1. Impact parameters in second stage, calculated terminal velocity VQ of flier launched
from second stage, measured shock velocities Us in third stage, and tilt and bow in third stage.
Impactor thicknesses, mm
V\
VQ
Us
Tilt
Bow
Shot
TPX/Mg/Al/Ti/Cu/Ta
km/s km/s Sensors
km/s
mrad
ns
HVLTi7-P
HVLTi8-P
.978/.617/.483/.371/.315/1.089
.874/..493/..407/..328/.258/.809
6.28
6.69
up, and p. The results are included in Table 2
and Figures 4 to 6.
The preceding analysis does not account for
shock-induced heating of the flier during launch.
To correct for this, we first need the temperature in the flier. Therefore we conducted experiments with no target, monitoring the flier's
free surface with infrared pyrometry. These suggested that its temperature did not exceed 650 K
when launched to 9.8 km/s, or 850 K when
launched to 10.8 km/s. Linearly extrapolating VQ
for HVLTi7-P and interpolating for HVLTi8-P
produces the upper temperature bounds given
in Table 2.
We find the density of the flier at the elevated
temperatures from p'Q = p0/(!+.<*AT)3, where a
is the coefficient of linear expansion measured between room temperature (assumed to be 298 K)
and the elevated temperature. The results are
given in Table 2.
Finally, we assume that the propagation velocities U's and Us are related to the jump in
particle velocity across them by the same linear
9.77
10.4
Pins
Needles
Pins
Needles
10.616
10,.564
10..983
11..074
4..27
2 .90
5..30
8,.22
10
10
4.,7
5.8
!~
«
relation:
(3)
From (l)-(3) we can find
+ 5(F0 - 2up))(VQ - Up) . (4)
All quantities except up and S in (4) are known.
We found that varying 5 from 0.9 to 1.4 produced less than 0.1% change in up, P, and p. Existing data for up > 1.8 km/s are well-described
by Us = cQ + Sup with S « 1.1, so we chose
5=1.1. Substituting for 5 in (4), we solve for up,
then use (1) and (3) to find the other unknowns.
The results are given in Table 2 and Figures 4
to 6.
CLOSING REMARKS
The Sandia hypervelocity launcher has been
used to acquire two new data points for the equation of state (EOS) behavior of Ti-6Al-4V above
220 GPa. The data were first analyzed without
accounting for thermal expansion in the flier
caused by shock-induced heating during launch.
Then, the maximum temperature of the flier was
bounded by pyrometry, and the data analyzed
using the density of Ti-6Al-4V at this temperature. The results of the two analyses are nearly
identical, and suggest that Ti-6Al-4V stiffens
considerably at these high pressures.
Flier
p',up,P
x
ACKNOWLEDGEMENT
The authors are grateful to T. K. Bergstresser
for assistance in pyrometry.
FIGURE 3. x-t diagram of the flier and target impact. The initial density in the target is
PQ =4.418 g/cm3 and the discontinuity propagates
at speed Us- Behind the discontinuity, density is p,
particle velocity is up, and P is the normal stress
perpendicular to the x direction (positive in compression). The initial velocity in the flier is Vb, and
quantities that differ from those in the target are
denote by a prime: p'0, u'p, and U's.
REFERENCES
1. Reinhart, W. D., Chhabildas, L. C., Carroll,
D. E., Thornhill, T. G., and Winfree, N. A.,
International Journal of Impact Engineering
(2001 (to appear)).
77
TABLE 2.
Results of analyses.
Symmetric analysis
P
up
p
GPa km/s g/cm3
Shot
HVLTi7-P
HVLTi7-P
HVLTi8-P
HVLTi8-P
Pins
Needles
Pins
Needles
229.1
228.0
252.3
254.4
4.885
4.885
5.200
5.200
Analysis that accounts for density change of flier
T
a (5)
p'Q
P
Up
p
K
mm/mm/K g/cm3
GPa km/s
g/cm3
644
644
770
770
8.181
8.212
8.383
8.336
9.8e-6
9.8e-6
10.1e-6
10.1e-6
4.373
4.373
4.355
4.355
228.3
227.2
251.1
253.2
4.868
4.868
5.175
5.175
8.160
8.194
8.355
8.294
250
200
11
4 *
10
fSf 150
x
X
X*
7 ;
X
0
v^
X
X
6
X
.X
.
.
.
.
.
0
1
2
3
4
5
FIGURE 4. Shock velocity versus particle velocity in the target, "x" =previous data (6, 7,
8). "o"=present work assuming symmetric impact.
"-)-" =present work compensated for thermal expansion of flier. Results using both pins and needles are
plotted.
200
^150
O
aTio°
0
0.8
4
5
MIL-HDBK-5H-98.
6. Morris, C. E., Letter to Lalit Chhabildas (1989).
7. Andriot, P., Lalle, P., and Dejean, J. P., Elastic
behaviour of pure titanium and tia6v4 titanium
alloy at high pressure (1994).
8. Hixson, R., Private communication with Lalit
Chhabildas (1999).
<**,
0.7
PQ/P
2
3
Up (km/s)
2. Brannon, R. M., and Chhabildas, L. C.,
International Journal of Impact Engineering, 17,
109-120 (1995).
3. Chhabildas, L. C., Kmetyk, L. N., Reinhart,
W. D., and Hall, C. A., International Journal of
Impact Engineering, 17, 183-194 (1995).
4. Carroll, D. E., Chhabildas, L. C., Reinhart,
W. D., Winfree, N. A., and Kerley, G. L,
"Computational characterization of three-stage
gun flyer plate launch", in these proceedings,
2001.
5. United States Department of Defense, Military
standardization handbook: Metallic materials and
elements for aerospace vehicle structures (1998),
250
0.6
1
FIGURE 6. Stress versiis particle velocity. Symbols as in Fie. 4.
up (km/s)
50
X
X
0
X
x
<**
50
X
5
X
cT °
xx
8
xx
2, io
X
9
X
0.9
FIGURE 5. Shock velocity versus specific volume
ratio V/VQ = po/p. Symbols as in Fig. 4.
78