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
THE EFFECTS OF SHEAR BANDING IN 6-4 TITANIUM ON ROUND
AND SQUARE TAYLOR IMPACTS
James U. Cazamias
LLNL, L-414, PO Box 808, Livermore, CA 94551
Abstract. The most common use of the Taylor impact test is not to measure the dynamic flow
stresses of materials, but to validate and/or calibrate constitutive models by comparing the shapes of
recovered cylinders with computer predictions. Importantly, the Taylor test provides a link between
the intermediate strain rates of the split-Hopkinson bar and the extremely high strain rates of the plate
impact test. While round specimens (essentially a 2D experiment) are commonly used, square samples
have the advantage of providing a true three dimensional experimental setting. In particular, the
interaction of release waves along the diagonals allows for the possibility of geometric strain
localization which suggests shear banding. We performed round and square Taylor impacts on 6-4
Titanium (a known shear banding material) to see if we could observe differences in behavior. We
observed that square specimens undergo significantly larger amounts of shear band deformation when
compared to round bars at a given velocity. As the velocity is increased, the round bars begin to
exhibit the behavior of lower velocity square bars.
INTRODUCTION
than the round. The three dimensional flow of the
Taylor sample provides a more robust test for
model predictions. It can also facilitate probing of
the 3rd stress invariant.
The utility of using square rods for model validation was first investigated in [6]. They performed
Taylor tests of 1020 steel rods with a length-towidth ratio of roughly 6.5 at nominally 240 m/s. It
was noted that square rods exhibit a distinctive,
three dimensional deformation pattern. They did
not examine round Taylor specimens. The
phenomenology of a Taylor impact test involving
rods with square and circular cross-sections was
examined in [7]. The deformed configuration in the
impact region varies markedly for the two
geometries, which was attributed to lateral wave
effects.
The interaction of release waves along the diagonals in square bars allows for the possibility of
strain localization. In simulations of experiment,
transient localization near the impact face was
observed [7]. Considering the simplicity of their
strength model (Johnson-Cook), that it nevertheless
The most common use of the Taylor test [1,2] is
not to measure dynamic flow stresses of materials
but to validate and/or calibrate constitutive models
by comparing the shapes of recovered cylinders with
computer predictions (for references, see [3]). There
has also been some effort to calibrate hardness maps
with code predictions (for example, see [4]). The
Taylor impact test provides a link between the
intermediate strain rates of the split-Hopkinson bar
(103 s"1) and extremely high strain rates of the plate
impact test (>106). The standard configuration of
circular rods is usually considered [5]. These
problems are easily modeled assuming conditions
of axisymmetry (2D) and can be modeled in three
dimensions when required (i.e., for textured/nonisotropic materials).
A potentially more useful test involves impacts
with square rods, where a true three-dimensional
setting is obtained. For 3D code validation
purposes, the ability to rectilinearly grid the square
rod makes the square Taylor test more diagnostic
587
TABLE 1. Experimental Parameters
predicted localization in the square bar is suggestive
that the square Taylor test could be used to study
adiabatic shear banding. Adiabatic shear bands (for
example, see [8]) are regions where plastic
deformation is highly concentrated due to an
instability that occurs when softening mechanisms
overcome hardening mechanisms.
Shear bands often play major roles in terminal
ballistics, affecting both targets and penetrators. For
example, titanium alloys are a common armor
material [9-12]. In light armor applications, shear
banding in titanium targets can result in plugging,
which is beneficial to the projectile. Complications
arise because titanium alloys that shear band under
normal impact may not shear band under oblique
impact and vice versa; also microstructural differences in compositionally identical materials result
in different shear banding behaviors under
oblique/normal impact [13]. In heavy armor
applications, shear banding is an issue for
penetrators. Depleted uranium (DU) projectiles flow
plastically at the penetrator/target interface via shear
banding (self-sharpening), resulting in smaller
diameter craters and enhanced penetration when
compared to tungsten heavy alloy (WHA)
projectiles which undergo "normal" plastic flow
(mushrooming) [14].
We performed square and round Taylor tests on a
relevant material known to exhibit shear banding,
the titanium alloy Ti-6Al-4V (see, for example,
[15]), in order to see if we could observe any differences in behavior.
Test
1
2
3
4
Specimen
Square
Round
Square
Round
V(m/s)
245
245
218
215
The nature of failure for the Ti bars was greatly
different than the failure of Al bars. All of the rods
exhibited fracture due to shear banding. We can use
the Wilkins-Guinan formula [16]
-^--0.12
27
(1)
0.88
to estimate the length of the rod if it had not fractured. Taking p0 = 4.46 gm/cm3, Y = 1.81 GPa
(see Test 4) and v(elocity) in km/s gives
-1.23V1
(2)
In Test 1 (Fig. 1), the entire face of the rod was
removed, leaving a 86.06 mm rod which is 9.18
mm shorter (roughly 1 diameter) than the predicted
value of 95.24 mm. On the impact plate, Ti alloy
residue is observed. In the impact indentation, the
amount of residue varies on either side of a diagonal
of the original square face. While difficult to observe
in the photograph, flow marks appear perpendicular
to 1 set of opposing faces. Looking at the recovered
fragments, we observe that fracture did not split the
bar along the diagonal, but rather parallel to 1 set of
opposing sides, perpendicular to the impact surface.
In Test 2 (Fig. 2), the entire face of the rod was
removed, leaving a 91 mm rod (the rod is bent ~ 70
mm from the rear surface, so this measurement is
approximate; regardless, examination of the impact
end of the rod showed no evidence of the original
impact face), and the rod is about 4 mm shorter
(roughly 1/3 diameter) than the predicted value of
95.24 mm. There is also a large piece (~ 5 mm)
missing at roughly 45 degrees which is the
preferential shear direction for ID stress. Looking at
the impact plate, we observe Ti alloy residue
flowing in one direction. It is not clear whether the
bend in the rod is a recovery effect or due to sliding
on the impact surface. Looking at the recovered
fragments, their size supports the ~ 4 mm estimate
RESULTS AND DISCUSSION
Four reverse Taylor impact tests were performed.
An over-sized 4340 steel plate (50.7 mm diameter,
9.53 mm thickness) hardened to 50 Rockwell C
impacted 101.6 mm long Ti-6Al-4V rods of
varying cross-sectional configurations. The crosssectional dimensions of the rods were varied so as
to nominally maintain a constant cross-sectional
area with the round bars having a diameter, D =
12.7 mm, and the square bars having a width, W =
11.2 mm. All rods were machined from the center
of the same 15.9 mm diameter bar to minimize
material variability. The rods were soft caught in
ceiling tiles. Impactor plates were also recovered,
from which one could observe a slight indentation
(< 0.025 mm) at the impact point. See Table 1.
588
at roughly 45 degrees which is the preferential shear
direction for ID stress. Looking at the impact plate,
we observe Ti alloy residue flow marks appear perpendicular to 1 set of opposing sides in one direction. Looking at the recovered fragments, there
appear to be two shear fracture zones. At the impact
surface, shear travels from one set of opposing faces
of the bar to the center at a depth of - 3 mm. On
one side of the bar, the fracture continues, resulting
in the missing piece. In the other, unfractured piece,
one can observe a nascent shear crack.
In Test 4 (Fig. 4), the rod is recovered relatively
intact (there is a small amount of shear fracture at
the edges of the impact face which flow away from
the center of the rod). This allows the calculation of
a flow stress of Y = 1.81 GPa [Eq. 1]. Looking at
the impact plate, we observe small amounts of Ti
alloy residue around the edges of the impact
indentation.
from the bar length measurement. The fracture
process consists of two parts. At the impact surface,
shear cracks travel from the circumference of the bar
to the center to a depth of ~ 4 mm. The fracture
resulting in the recovered piece appears to start at
this center point and travels outward.
FIGURE 1. Recovered elements of Test 1.
FIGURE 3. Recovered elements of Test 3.
FIGURE 2. Recovered elements of Test 2,
In Test 3 (Fig. 3), the entire face of the rod is
removed, leaving a 94.1 mm rod which is about
1.4 mm shorter than the predicted value of 96.5
mm. There is also a large piece (~ 3 mm) missing
FIGURE 4. Recovered elements of Test 4.
589
CONCLUSION
7.
For shear banding materials, 3D effects can
dramatically modify the material response. Square
Taylor specimens appear to undergo significantly
larger amounts of shear band deformation when
compared to round bars. It appears that round bars
exhibit "square bar failure" at higher impact velocities. Combining these results with stress wave measurements might give temporal data on shear band
formation which would be a useful parameter for
understanding penetration resistance. Unlike other
shear band tests (e.g. torsional SHE, which is
simple shear), this is a compression test, which is a
much more important geometry.
The square Taylor test provides a better defined
geometry and enhances shear band effects, resulting
in a higher quality experiment than a round Taylor
test. Consequently, the square Taylor impact test
provides a simple way to study plastic
flow/localization effects under compression-shear
loading.
8.
9.
10.
11.
12.
13.
ACKNOWLEDGEMENTS
This work was performed at the Institute for
Advanced Technology (IAT) at the University of
Texas at Austin and supported by the U.S. Army
Research Lab (ARL) under contract DAAA21-93-C0101. Thanks to G.C. Bessette and S.J. Bless.
14.
REFERENCES
1.
2.
3.
4.
5.
6.
15.
Taylor, G, Proc. R. Soc. A 194, 289-299 (1948).
Whiffen, A. C, Proc. R. Soc. A 194, 300-322
(1948).
Field, J. E., Walley, S. M, Bourne, N. K., and
Huntley, J. M., "Review of Experimental
Techniques for High Rate Deformation Studies,"
in Proc. Acoustics and Vibration Asia 98, 1998,
pp. 9-38.
Armstrong, R. W., and Zerilli, F. J., "Dislocation
Aspects of Shock-Wave and High-Strain-Rate
Phenomena,"
in Fundamental Issues and
Applications of Shock-Wave and High-StrainRate Phenomena, 2001, pp. 115-124.
Lichtenberger, A., Dormeval, R, and Chartagnac,
P., Test de Taylor, DYMAT RE/003/88 (1989).
Luttwak, G., Rosenberg, Z., and Falcovitz, J.,
"Experimental and Computational Study of
Taylor Impact with Square Rods," in Proceedings
16.
590
of the 15th International Symposium
on
Ballistics, 1995, pp. 291-298.
Bessette, G. C., and Cazamias, J. U., "An
Examination of the Taylor Impact Problem for
Experiments Involving Square and Circular
Rods," in Fundamental Issues and Applications
of
Shock-Wave
and
High-Strain-Rate
Phenomena, 415-420 (2001).
Meyers, M. A., Dynamic Behavior of Materials,
1994.
Gooch, W., Burkins, M. S., Ernst, H.-J., and Wolf,
T., "Ballistic Penetration of Titanium Against
Laboratory Penetrators with Aspect-Ratios of 10
or Greater," in 15th International Symposium on
Ballistics, 1995.
Gooch, W., Burkins, M. S., Ernst, H.-J., and Wolf,
T., "Ballistic Penetration of Titanium Alloy Ti6A1-4V," in Lightweight Armor
Systems
Symposium '95, 1996a.
Gooch, W., Burkins, M. S., and Frank, K.,
"Ballistic Penetration of Titanium Against
Laboratory Penetrators," in 1st Australian
Congress on Applied Mechanics, 1996b.
Bless, S. J., Gooch, W., Satapathy, S., Campos, J.,
and Lee, M., Int. J. Imp. Engng. 20, 121-129
(1997).
Weerasooriya, T., Magness, L., and Burkins, M.,
"High Strain-Rate Behavior of Two Ti-6Al-4V
Alloys with Different Microstructures," in
Fundamental Issues and Applications of ShockWave and High-Strain-Rate Phenomena, 2001,
pp. 33-36.
Magness, L. S., and Farrand, T. G., "Deformation
Behavior and Its Relationship to the Penetration
Performance of High-Density KE Penetrator
Materials," in Proc. 1990 Army Science
Conference, 1993.
Mazeau, C., Beylat, L., Longere, P., and Louvigne,
P. F., in J. Phys. IV Colloq. C3 7, 429-434 (1997).
Wilkins, M. L., and Guinan, M. W., J. Appl. Phys.,
44, 1200-1206 (1973).