For the last decade, there has been
research aimed at engineering plastic
instability into the deformation behavior
of body centered cubic (b.c.c.) metals.
At dynamic strain rates, the adiabatic
shear band deformation mode
has been shown to improve the performance
of kinetic energy penetrator materials.
However, for some b.c.c. metals
the transition to localized plastic deformation
dominates at all strain rates.
This limits the traditional engineering
properties (e.g., ductility and toughness)
and feasibility of incorporation
into a long rod penetrator system.
Recently, we demonstrated that nanocrystalline
tantalum shows significant
promise as it deforms via adiabatic
shear bands in dynamic compression
but shows significant tensile elongation
in quasi-static deformation.
|HOW WOULD YOU...
...describe the overall significance
of this paper?
We show that when the grain
size of tantalum is reduced to the
nanocrystalline regime through
severe plastic deformation, it can
retain significant tensile elongation
and deform via adiabatic shear
bands at dynamic strain rates. This
combination of properties indicates
that this class of materials may be
well suited for some specific extreme
...describe this work to a
materials science and engineering
professional with no experience in
your technical specialty?
Focused ion beam based methods
have been widely applied to examine
the size-dependent response of
many materials. In contrast, we use
focused ion beam based tension and
compression experiments to examine
the “bulk” properties of ultrafine-
grained and nanocrystalline
body centered cubic metals. This,
combined with miniaturized high
strain rates experiments, allows us
to examine the effect of grain size on
the response of tantalum in multiple
stress states and across a wide
range of applied strain rates.
...describe this work to a
Nanocrystalline materials have
characteristic length scales smaller
than 100 nm (where a nanometer
is defined as 1-billionth of a
meter or 10–9 m). Some materials
processing approaches to produce
nanocrystalline materials result
in very limited physical volumes
of materials. Miniaturized
mechanical testing allows scientists
and engineers to scale down the
experiment to meet the limited
sample volumes. Using miniaturized
mechanical testing techniques, we
find that nanocrystalline tantalum
possesses exceptional mechanical
properties that are attractive for
Extreme service conditions have
posed great challenges for the design
and manufacturing of new materials.
Examples of such conditions include
nuclear radiation, high temperatures,
environmentally hostile conditions,
and high strain rate impact. Kinetic
energy (KE) penetrators truly push
materials to the extreme. Exceptional
engineering properties (e.g., yield
strength, ductility and toughness) are
required to survive launch and flight.
During penetration into a thick armor
plate, penetrator materials that deform
by adiabatic shear band (ASB) formation
show superior performance.1–2
For the last decade, top-down and
bottom-up processing approaches have
been examined as a means to induce
the ASB deformation mode at dynamic
strain rates in ultra-fine-grained
(UFG) and nanocrystalline (NC) body
centered cubic (b.c.c.) metals.3–14
UFG materials are defined here as having
characteristic grain sizes from 100 to
500 nm, while NC materials have grain
sizes smaller than 100 nm. Wright's
model for the susceptibility of viscoplastic
materials to ASB formation15
has been used to guide in the materials
design and processing. Details of
the model and the applicability to UFG
and NC b.c.c. metals will be discussed
in greater detail later.
In this research summary, we will
focus on UFG and NC tantalum (Ta)
processed by high pressure torsion
(HPT). The density of Ta is generally
considered too low for incorporation
into real penetrator systems, though it
is a model material for study as it is
generally considered to be more ductile
than tungsten (W). We will present our
approach to systematically examine the
effect of grain size on the mechanical
properties and deformation modes of
b.c.c. metals across a range of stress
states and applied strain rates. We will
show that NC Ta can be engineered to
retain the ability to plastically deform
under quasi-static tension and to strain
localize during dynamic compression.
KINETIC ENERGY PENETRATOR MATERIALS
In large caliber applications, KE
rounds consist of high aspect ratio long
rod penetrators of either depleted uranium
(DU) alloys or tungsten heavy
alloys (WHAs). Launch accelerations
are transferred between the grooved
interface of the sabot and the mating
surface on the penetrator. Muzzle velocities
often approach 1.7 km/s; the
associated accelerations and sabot discard
require exceptional engineering
properties (e.g., yield strength, ductility
Alekseevski16 and Tate17 independently derived one-dimensional KE
projectile penetration models. Their
models follow a general framework
incorporating the strength of the penetrator
material, Y, and the resistance
(strength) of the target material, R. Given
penetrator density, , target density,
, the relation between the striking velocity,
v, and the penetration velocity,
U, is given in Equation 1. From inspection
of this model, it follows that highdensity
and high-strength materials are
desirable for this application.
The Alekseevski–Tate equation
(Equation 1) would predict very similar
performance for DU and WHA,
given the similarities in density and
mechanical properties. However, DU
alloys are well-known to have superior
penetration performance to WHAs.1,2
One method to experimentally quantify
the performance of KE penetrators is to
measure their penetration into thick or
effectively-infinite targets. Figure 1a
(reproduced from Magness1) shows a
comparison of the depth of penetration
and traces of actual penetration tunnels
from DU alloy and 97 wt.% WHA rods
fired into a thick mild steel target. The penetrators were equal in density (18.6
g/cc), mass (65 g) and geometry (length
to diameter ratio equal to 10). Magness
reported the volume displaced for a
given impact energy is nearly identical
for equal density DU and WHA penetrators.
WHAs show stable deformation
and flow behavior during ballistic
impact while DU penetrators deform
via ASBs. This translates into narrower
and deeper penetration channels
for DU. Schematics of this deformation
process for non-shearing conventional
tungsten alloys and DU alloys
are shown in Figure 1b,c, respectively
(similarly reproduced from Magness1).
The basic concepts of ASBs have
been discussed in greater detail in a
number of references.15,18 In the ballistic
impact of DU alloys, thermal
softening from plastic work quickly
overwhelms the stabilizing influences
of strain hardening and strain rate
sensitivity.1,2 DU alloys have a lower
specific heat and melting temperature
than WHAs, which adds to the relative
tendency for ASB formation. WHAs
however, typically show higher strain
rate sensitivities than DU alloys. This
stabilizing influence tends to suppress
strain localizations. For an in-depth
discussion of the comparison of DU
and WHA, readers should refer to the
original works by Magness.
MOTIVATION FOR UFG AND NC METALS
UFG and NC metals have been
considered for KE penetrator applications.
Because of the Hall19–Petch20
effect, these materials typically show
increased yield strengths relative to
their coarse grained (CG) counterparts;
improvements in performance for these
high strength materials are implied by
Equation 1. Perhaps more importantly,
UFG and NC b.c.c. metals can show
localized plastic deformation during
dynamic compression.4,7–9,12 The most
significant accomplishment to date has
been demonstration of this deformation
mode in UFG and NC tungsten (W).9,12
There is limited evidence that a similar
transition in deformation mode resulted
in improved penetration performance
in a relatively low-density nanocrystalline
tungsten composite alloy.21
Wright's model for the susceptibility
of visco-plastic materials to ASB
formation can be used to describe the
motivation for fine grained metals.
Wright15 derived Equation 2 for
called the susceptibility to ASB, where a is the non-dimensional thermal softening
parameter defined by a = is the flow stress, T the temperature,
ρ the density, and c the specific
heat of the material), n the strain
hardening exponent, and m the strain
rate sensitivity (SRS).
Grain size reductions in b.c.c. metals
typically result in a significant increase
in their susceptibility to ASB formation
through associated changes in the
strength, strain hardening behavior
and SRS. NC metals are considerably
stronger than their CG counterparts.
UFG and NC b.c.c. metals show little
strain hardening and are often assumed
to behave as a perfectly plastic material
(no strain hardening).8,10–12,14 The
SRS of b.c.c. metals typically decreases
with the characteristic grain size,7
though Ta does not appear to follow
this dependence in the lower bound
of the nanocrystalline regime.14 For
perfectly plastic materials, the susceptibility
reduces to Equation 3 where
is the thermal
softening parameter evaluated under
isothermal conditions is a normalizing
stress), and σO is the yield
strength. Application of this model to
UFG and NC shows that these materials
exhibit a significant increase in susceptibility
to adiabatic shear band formation
than their CG counterparts.8,10–12,14
Recent numerical simulations on the
effects of microstructure suggest that
UFG/NC b.c.c. metals are more prone
to form ASB.22
In some b.c.c. systems, localized
plastic deformation has been found to
dominate the response under quasistatic
and dynamic deformation.4,7
There is concern that localized plastic
deformation at low to moderate strain
rates will inherently limit the engineering
properties of these materials and
their eventual applicability in KE penetrator
systems. As mentioned earlier,
the launch forces experienced by KE
penetrators require exceptional engineering
properties at low to moderate
strain rates. Other than a few isolated
studies23 the tensile properties of UFG
and NC b.c.c. metals are largely unknown.
The tensile properties of these
materials will be studied along with
their propensity to deform via ASBs at
higher strain rates.
STRATEGY AND METHODOLOGY
In this research summary, we will
focus the discussion on tantalum. Similar
studies on W and other b.c.c. metals
from groups V and VI on the Periodic
Table are underway. Severe plastic deformation
(SPD) was used to refine the
grain size of CG Ta into the UFG and
NC regime. Specifically, commercial
purity tantalum disks were processed
by high pressure torsion (HPT) by Valiev.
24 In HPT processing, samples are
confined at high pressures between
two opposing Bridgeman anvils and
the disks are deformed in torsion. The
local shear strains vary as a function
of radial position (distance from the
center of the disk, r), and the number
of turns, N, as shown in Equation 4.25
The material presented here was confined
at a pressure of ~5 GPa, and was
deformed at room temperature in torsion
to maximum strains approaching
The site-specific indentation behavior
was examined using microhardness
testing and nanoindentation.
Microstructures were characterized
in a transmission electron microscope
(TEM)14 and with synchrotron based
x-ray diffraction.26 The dynamic compressive
response was investigated using
a desktop Kolsky bar apparatus.27
Readers should refer to Wei and coworkers
for a more detailed discussion
on the dynamic compression tests.5,14
The HPT processed samples yield very
small volumes of material. As mentioned
previously the total volume is
a thin disk that is roughly 10 mm in
diameter. Even the largest specimens
are too small to test in a conventional
Kolsky bar, and are difficult to fabricate
and handle for conventional quasistatic
uniaxial testing. Instead, focused
ion beam (FIB) based micromechanical
testing methods were employed to
investigate the quasi-static properties.
Microcompression specimens were
fabricated and tested using the methodologies
discussed in detail by Uchic
and Dimiduk.28 Micro- and nano-compression
experiments have been used
extensively in the literature to examine
the size-dependent mechanical properties
of materials.29–32 However, here we
have used this technique to probe the
site-specific "bulk" properties of UFG
and NC Ta. Assuming a grain size of 50
nm, a pillar with a 5 mm diameter would
possess nearly ~1.6 million grains. For
comparison, a CG bulk sample that is
several millimeters in diameter would
have a similar number of crystallites.
One could argue these measurements
of micro-specimens could represent
bulk response, though this is not considered
in depth in this summary.
"Dog-bone" microtension specimens
are fabricated using micro-electro
discharge machining followed by
final machining with the FIB. In-situ
scanning electron microscope (SEM)
tension tests were performed in a custom
test stage.33 The stage is similar
in principle to another presented elsewhere.
36,35 Tensile specimens were positioned
in a grip (milled from a high
aspect ratio tungsten needle) using a
3-axis piezoelectric stage. Loads were
applied using a linear actuator with a
reported resolution of ~1 nm and were
measured using a data acquisition program
from a strain gage based S-beam
load cell (capacity of 100 g and resolution
of ~0.01 g). Strains were calculated
from successive SEM micrographs
taken during testing using the open
source digital image correlation script
developed by Eberl and coworkers.36
RESULTS AND DISCUSSION
Given the variation in strain as a
function of radial position (Equation
4), it follows that the microstructures
and extent of grain refinement vary
as a function of position on the bulk
HPT specimens. Microhardness measurements
illustrate the variation in
strength as a function of radial position
as shown in Figure 2. The hardness
quickly climbs from ~2.5 GPa at r~0.5
mm to over 4 GPa at r~2.5 mm. The
hardness remains comparatively constant
for r > 2.5 mm.
The grain size, d (in nanometers),
for each radial position was estimated
from the hardness, H (in GPa), using
the Hall–Petch relation for Ta37 given
in Equation 5. Grain sizes were also
estimated from synchrotron x-ray
peak broadening.26 Both estimates for
grain size as a function of radial position
are plotted in Figure 2. Grain size
estimates from x-ray peak broadening
and hardness are comparable. The estimates
indicate the grains are UFG near
the center and the threshold for transition
into the truly NC occurs around
r~1 mm. Figure 3 shows a TEM micrograph
and the associated grain size
distribution for a specimen cut near r~2
mm which confirms the characteristic
NC grain size. Mainly equiaxed grains
with an average grain size of 43 nm
Figure 4 shows the compressive response
of pure Ta over a wide range of
grain sizes and applied strain rates. CG
Ta showed a comparatively low compressive
yield strength and showed significant
strain hardening.5 UFG compression
samples were cut near the center
of the HPT disk and are significantly
stronger than CG Ta; yield stresses
exceeding 1 GPa were typical.14,26 This
and other UFG samples deformed in
microcompression showed little to no
strain hardening though plastic buckling
may complicate analysis of the
true strain hardening response.14 The
UFG specimen tested in dynamic compression
showed some strain softening.
UFG specimens showed at most
evidence of fairly diffuse strain localization.
In contrast, localized plastic
deformation was found in quasi-static
and dynamic compression of NC Ta as
shown in Figure 4b and c. In microcompression
tests, shear bands were found
for specimens near the extreme edge of
the specimens (r>5 mm).26 It is unlikely
that the shear bands were adiabatic in
nature; however there is a clear change
in deformation mode. Adiabatic shear
bands were found in dynamic compression
of the NC Ta.14 The NC sample
shown in Figure 4a had a yield strength
exceeding 2 GPa followed by a sharp
stress collapse after yielding. The yield
strengths of dynamically deformed NC
Ta samples were significantly higher
than the quasi-static compression specimens
though this is not necessarily
due to strain rate sensitivity. The UFG
and NC Ta show little strain hardening
and deform in a manner that is effectively
elastic-perfectly plastic. The microcompression
specimens had an aspect
ratio (ratio to length to diameter)
of ~2 and were therefore more prone to
structural instability which can affect
the measured response.
Investigations of the tensile properties
of UFG and NC Ta are still in the
early stages,26 but a demonstration of
the approach is presented in Figure 5.
Figure 5a shows an SEM micrograph
of a typical microtension specimen
loaded in the grip. The stress-strain response
for a tension sample cut at position
r~3.9 mm is presented in Figure
5b. Figure 2 would suggest the grain
size of this specimen is roughly 40 to
60 nm. The minimum cross-section of
the sample was roughly 9 in width
and thickness and the overall length
was ~65 . In quasi-static tension,
significant plastic strain of 3 to 4% was
found prior to necking and fracture.
The specimen eventually fractured in
the gage length as shown in Figure 5b.
There is some apparent evidence of
strain hardening, though this observation
requires additional analysis and
The mechanical properties of this
NC Ta are an encouraging sign that
UFG and NC b.c.c. metals may one day
be viable alternatives for KE applications;
NC Ta shows some tensile elongation
at quasi-static strain rates and
ASB formation during dynamic compression.
indicate a critical grain size for
transition in quasi-static deformation
mode may occur around ~50 nm.26 In
practice, transition to this deformation
mode in penetrator materials should be
largely avoided in order to retain materials
that can be launched in actual long
rod KE penetrators.
While some of the basic concepts of
shear band formation in UFG and NC
b.c.c. metals have been examined in
uniaxial mechanical testing, there are
no known accompanying ballistic demonstrations
of this concept. Top-down
and bottom-up processing routes will
need to be developed to manufacture
sizable samples of fully dense materials
for ballistic tests. For example, HPT
processing commonly yields a thin
sample that is roughly ~10 to 12 mm
in diameter. By comparison, the 65 g
sub-scale penetrator rods fired by Magness1
were nearly ~8 mm in diameter
and ~80 mm long. Equal channel angular
extrusion has been investigated as
an alternative processing route, though
this process alone has not been suffi -
cient to induce ASBs in Ta5 or W.9,10
However, the collection of work to
date and the exceptional combination
of properties of NC Ta show that this
class of materials may one day offer an
alternative to DU alloys.
The mechanical properties of UFG
and NC Ta were investigated by using
site-specifi c microstructural analysis
and mechanical testing of samples
processed by HPT. A single HPT processed
sample shows gradient in microstructures
and mechanical properties,
with grain sizes ranging from the
truly nanocrystalline to several hundred
nanometers in diameter. Consistent
with Wright?s model for susceptibility
to ASB formation, NC Ta shows
a transition in deformation mode owing
to its enhanced strength and reduced
strain hardening relative to CG
Ta. An early demonstration shows that
NC Ta retains the ability to plastically
deform in quasi-static tension testing.
This work indicates that UFG and NC
metals may have promise in KE penetrator
The authors are grateful to L.S.
Magness, W.N. Sharpe, B.G. Butler,
X.L. Wu, and L.J. Kecskes; and would
like to thank Professor R.Z. Valiev for
providing the HPT Ta. Q. Wei would
like to acknowledge the support from
U.S. Army Research Laboratory under
Contract No. W911QX-06-C-0124 and
1. L.S. Magness and T.G. Farrand, "Deformation Behavior
and its Relation to the Penetration Performance
of High-Density KE Penetrator Materials," Proceedings
of the Army Science Conference (Durham, NC:
Defense Technical Information Center, 1990), pp.
2. L.S. Magness, Mech. Mater., 17 (1994), pp. 147-154.
3. Q. Wei, D. Jia, K.T. Ramesh, and E. Ma, Appl. Phys.
Lett., 81 (2002), pp. 1240-1242.
4. D. Jia, K.T. Ramesh, and E. Ma, Acta Mater., 51
(2003), pp. 3495-3509.
5. Q. Wei et al., Mater. Sci. Eng. A, 358 (2003), pp. 266-272.
6. Q. Wei, S. Cheng, K.T. Ramesh, and E. Ma, Mater. Sci. Eng. A, 381 (2004), pp. 71-79; doi:10.1016/j.
7. Q. Wei, T. Jiao, K.T. Ramesh, and E. Ma, Scr. Mater., 50 (2004), pp. 359-364.
8. Q. Wei et al., Acta Mater., 52 (2004), pp. 1859-1869.
9. Q. Wei et al., Appl. Phys. Lett., 86 (2005); doi: 10.1063/1.1875754.
10. Q. Wei et al., Acta Mater., 54 (2006), pp. 77-87,
11. Q. Wei, K.T. Ramesh, B.E. Schuster, L.J. Kecskes, and R.J. Dowding, JOM, 58 (9) (2006), pp. 40-44.
12. Q. Wei et al., Acta Mater., 54 (2006), pp. 4079-4089, doi:10.1016/j.actamat.2006.05.005.
13. Q. Wei et al., Mater. Sci. Eng. A, 493 (2008), pp. 58-64; doi:10.1016/j.msea.2007.05.126.
14. Q. Wei et al., Acta Mater., 59 (2011), pp. 2423-2436.
15. T.W. Wright, The Physics and Mathematics of Adiabatic Shear Bands (Cambridge, U.K.: Cambridge
16. V.P. Alekseevskii, Fizika Goreniya i Vzryva (Combustion, Explosion, and Shock Waves), 2 (1966), pp.
17. A.A. Tate, J. Mech. Phys. Solids, 15 (1967), pp. 387-399.
18. Y. Bai and B. Dodd, Adiabatic Shear Localization: Occurrence, Theories and Applications (London: Pergamon
19. E.O. Hall, Proc. Phys. Soc. B, 64 (1951), pp. 747-752.
20. N.J. Petch, J. Iron and Steel Institute, 174 (1953), pp. 25-28.
21. L.S. Magness et al., Proc. SPIE–Int. Soc. Opt. Eng., 4608 (2002), pp. 216-224; doi:10.1117/12.465225.
22. Y.Z. Guo, Y.L. Li, Z. Pan, F.H. Zhou, and Q. Wei, Mechanics of Materials, 42 (2010), pp. 1020-1029;
23. S. Cheng, W.W. Milligan, X.-L. Wang, H. Choo, and P.K. Liaw, Mater. Sci. Eng. A, 493 (2008), pp. 226-231.
24. R.Z. Valiev, R.K. Islamgaliev, and I.V. Alexandrov, Prog. Mater. Sci., 45 (2000), pp. 103-189.
25. A.P. Zhilyaev and T.G. Langdon, Prog. Mater. Sci., 53 (2008), pp. 893-979.
26. J.P. Ligda, B.E. Schuster, and Q. Wei, unpublished work (2011).
27. D. Jia and K.T. Ramesh, Exp. Mech., 44 (2004), pp. 445-454; doi:10.1177/0014485104047608.
28. M.D. Uchic and D.M. Dimiduk, Mater. Sci. Eng. A, 400-401 (2005), pp. 268-278.
29. M.D. Uchic, P.A. Shade, and D.M. Dimiduk, Annual Review of Materials Research, 39 (2009), pp. 361-386;
30. J.R. Greer, W.C. Oliver, and W.D. Nix, Acta Mater., 53 (2005), pp. 1821-1830.
31. M.B. Lowry et al., Acta Mater., 58 (2010), pp. 5160-5167.
32. D. Kaufmann, R. Monig, C.A. Volkert, and O. Kraft, Int. J. Plasticity, 27 (2011), pp. 470-478.
33. B.E. Schuster, W.N. Sharpe, J.P. Ligda, and Q. Wei, unpublished results.
34. M.D. Uchic, D.M. Dimiduk, R. Wheeler, P.A. Shade, and H.L. Fraser, Scr. Mater., 54 (2006), pp. 759-764;
35. P.A. Shade et al., Acta Mater., 57 (2009), pp. 4580-4587; doi:10.1016/j.actamat.2009.06.029.
36. C. Eberl, D.S. Gianola, and S. Bundschuh, Mathworks (Natick, MA: The Mathworks, Inc., 2006), File
37. K.T. Hartwig, S.N. Mathaudhu, H.J. Maier, and I. Karaman, in Ultrafine Grained Materials II, ed. Y. T. Zhu
et al. (Warrendale, PA: TMS, 2002), pp. 151-160.
B.E. Schuster is with the Weapons and Materials
Research Directorate, U.S. Army Research Laboratory,
Aberdeen Proving Ground, MD 21005, USA;
firstname.lastname@example.org; J.P. Ligda, Z.L. Pan,
and Q. Wei are with the University of North Carolina
at Charlotte, 9201 University City Blvd., Charlotte,