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
YIELD AND STRENGTH PROPERTIES OF THE Ti-6-22-228 ALLOY
OVER A WIDE STRAIN RATE AND TEMPERATURE RANGE
L. Kruger1, G. I. Kanel2, S. V. Razorenov2, L. Meyer3, and G. S. Bezrouchko2
l
Nordmetall, Research and Consulting, 09235 Burkhardtsdorf, Germany,
Institute of Problems of Chemical Physics, Chernogolovka, 142432 Russia,
^Technical University Chemnitz, Materials and Impact Engineering, 09107 Chemnitz, Germany.
2
Abstract. A mechanical behavior of the Ti-6-22-22S alloy was studied under uniaxial strain conditions
at shock-wave loading and under uniaxial compressive stress conditions over a strain rate range of
10~4 s"1 to 103 s"1. The test temperature was varied from -175 °C to 620 °C. The strain-rate and the
temperature dependencies of the yield stress obtained from the uniaxial stress tests and from the shockwave experiments are in a good agreement and demonstrate a significant decrease in the yield strength
as the temperature increases. This indicates the thermal activation mechanism of plastic deformation of
the alloy is maintained at strain rates up to 106 s"1. Variation of sample thickness from 2.24 to 10 mm
results in relatively small variations in the dynamic yield strength and the spall strength over the whole
temperature range.
in pure metals, experiments with stainless steel
demonstrated a decrease in both the dynamic yield
strength and the spall strength at the temperature of
980 K to half of their values measured at room
temperature [6].
INTRODUCTION
On the basis of experiments with titanium
alloys up to a strain rate of 300 s"1 [1-3] it was
concluded the thermally activated mechanism is
responsible for the strain rate sensitivity of the flow
stress. The examination of the deformed structures
revealed that plasticity is the result of interaction of
dislocation motion through the lattice and twinning.
The extent of twinning increases with increasing
strain rate or decreasing temperature. Since titanium
alloys are important engineering and armor
materials, it would be important to expand their
strain-rate and temperature dependencies to
ultimately high strain rates of impact loading.
A general trend of the mechanical behavior of
shock-wave loaded metals [4-6] is that, whereas the
yield strength of pure metals under these conditions
does not depend on the temperature or even
abnormally increases with the temperature, alloys
may exhibit normal behavior with decreasing yield
strength as the temperature grows. The resistance to
spall fracture of metals usually does not vary much
with the temperature up to 85-90% of the melting
temperature, Tm, and drops precipitously with the
following increase in temperature up to Tm. Unlike
THE MATERIAL
An a-p titanium alloy Ti-6-22-22S with the
chemical composition (inwt. %): Al (5.75),
Sn (1.6), Zr (1.99), Mo (2.15), Cr (2.10), Si (0.13),
Fe (0.04), O (0.082), N (0.006), C (0.009) was
prepared in a vacuum arc furnace. The ingot was
diffusion annealed at 1100°C for 20 hours. After
that, a swaging process at 900°C in the a + p region
was performed. Finally, the material was solution
annealed and aged. The p-transition temperature of
the alloy is 960°C. The final bimodal microstructure
contains globular a-phase between the lamella
arrangement of a + p phase. The material density is
4.53 g/cm3, the longitudinal sound speed is
c/ = 6.01±0.04 km/s, the bulk sound speed is
cb = 4.87 km/s, and the Poisson's ratio is v= 0.327.
All samples were cut out of one massive block of
the alloy.
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\2.24 mm, 600°C
500
500 -
400
'o
o
•
300
200
100
0
0.0
1.0
0.2
0.4
0.6
0.8
1.0
Time, jas
FIGURE 2. Free surface velocity histories of the titanium
alloy samples at temperatures of 600°C and 620°C.
FIGURE 1. Free surface velocity histories of the titanium
alloy samples at room temperature.
plastic waves is smaller at elevated temperature as a
result of the decrease in the longitudinal sound
speed. The shape of velocity histories after spall
fracture indicates relatively rapid development of
the fracture process. Variation of sample thickness
from 2.24 mm to 10 mm results in relatively small
variations in the dynamic yield strength and the
spall strength over the whole temperature range.
A treatment of high-temperature data has been
done accounting for temperature derivatives of the
shear modulus according to Ref. [8] where the
measured temperature derivative of shear modulus
r\C*
— = -27MPa/K is presented as well as a pre-
EXPERIMENTAL PROCEDURES
Two series of shock-wave experiments with the
samples of 10 mm and 2.24 mm in thickness have
been carried out with aluminum flyer plates of
2.0 mm and 0.85 mm in thickness at the impact
velocity of 630 + 20 m/s and 680 + 20 m/s,
respectively. Samples were heated with resistive
heaters placed on the back surface [5] or cooled by
the liquid nitrogen. The power of the resistive
heater was 1 kW, which was sufficient to heat the
samples to 600°C within 10 to 15 minutes. The
temperature of the sample surface was controlled
locally at a distance of 7 to 8 mm from the central
axis of the sample using a thermocouple of 40 jam
in thickness. The free-surface velocity profiles were
recorded with the VISAR laser Doppler
velocimeter.
The study of material behavior over a range of
strain rates of 10"4 s"1 to 103 s"1 was performed using
a combination of servohydraulic testing machine,
drop-weight tower [7], compression Hopkinson bar
and rotating wheel. Tests at high temperatures were
conducted by using an induction heating device.
estimated value of -23 MPa/K. The temperature
derivative for bulk modulus was estimated using the
relationship
di
where
_
£iL=4.37, the
dp
(dp
_
Grueneisen coefficient
r=1.23, and the bulk coefficient of thermal
expansion a = (2.9±0.4)xlO~5 1/K.
The elastic-plastic waveforms contain
information on the incident yield strength and the
following strain hardening. In order to get this
information the stress-strain diagrams have been
recovered from the compressive parts of free
surface velocity histories. The estimations have
been done within a simple wave approach. The
compression wave was considered as a simple
centered wave, which is described by a fan of
characteristics immediately behind the front of the
RESULTS OF MEASUREMENTS
Figures 1 and 2 present examples of the free
surface velocity histories measured at room
temperature and at maximum tests temperatures of
600°C to 620°C. In all cases there are disperse
transitions between elastic precursor waves and
plastic shock waves that is considered as an
evidence of strain hardening behavior of the
material. The time interval between the elastic and
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elastic precursor wave. For simple waves, the
longitudinal stress increments da, the strain
increments dSx = -dV/V^ the resolved shear stress
T, and the pressure p are related by the equations
^
f s . T = -(a-p]
(1)
f!
4\
flow stresses at 0.2% plastic strain evaluated from
the measured free surface velocity histories are
presented in Fig. 4.
Figure 5 summarizes the room-temperature
yield strength data evaluated from the shock-wave
tests under uniaxial strain conditions and from the
uniaxial stress tests at lower strain rates. The yield
stresses at 0.2% plastic deformations are plotted
because it is difficult to determine precisely the
incident yield strength values from the Hopkinson
bar tests. The strain rates at shock compression have
been estimated as average compression rates in
middle sections of the samples.
The tensile stress value just before spalling, a*,
is determined from an analysis invoking the method
of characteristics. From the acoustic approach, the
following linear approximation [10]
where aa is the propagation velocity of part of the
compression wave at the longitudinal stress a in
Lagrangian coordinates [9]; the stresses are
assumed to be positive under compression. For a
centered simple wave the propagation velocity aa is
h
,
where h is the distance at which the stress history
a(f) of a compression wave is analyzed, and t is the
time interval after the elastic precursor front. When
a free surface velocity history Ufs(t) is analyzed
instead of a stress history o(0> an approach of
ufs(f) = 2up(f) and do(t) = paa-dup(f)
may be used. A more detailed analysis accounting
for an interaction between the incident compression
wave and the reflected unloading wave gives
(4)
is used, where c0 is the sound velocity, pQ is the
initial density, and AH/& is the velocity pullback.
However, in the elastic-plastic material the spall
pulse front should propagate at the longitudinal
elastic wave velocity, Ciy whereas the incident
rarefaction plastic wave ahead of it propagates at
bulk sound velocity c^. It was concluded by
Stepanov [11], that the relationship to calculate the
fracture stress a* is
Figure 3 shows examples of recovered stress
and strain histories at 20°C. The plastic strain /was
calculated according to the relationship
1
(5)
A more detailed analysis [12] confirmed
validity of the relationship (5) for the case of a
The initial dynamic yield strength values and the
8
&
15
2.0
*
o
I
ol
S 1.0 ~
^.,
Y
z\
-
A
2
'"
0.0
0.1
0.2
0.0
-2()0
0.3
Time, p.s
Sample thickness:
2.24mm (solid points)
10mm (open points)
-
0
200
400
^
"
"
600
Temperature, °C
FIGURE 3. Examples of recovered stress and strain histories
at 20°C.
FIGURE 4. Dynamic yield data as a function of temperature
for different impact conditions.
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;
OJ
°-
.•
:
^
1.0
O 3
£
. B
Uniaxial stress
CO
n n
10'
10
A
Sample thickness:
2.24mm (upper points)
10mm (lower points)
c*
0
1C'4
Spall strength
°
_
I1
io- D
^
A
4 A
1-D strain
(Shock)
[Q D
0
Q
1.5
(J)
2
5
10Z
-1
10"
-200
10
Strain Rate, s"
^
Yield strength
^n
•y^
0
P-.
V
i i i i i i i i
200
~
i
t
i
I
400
^7 i
i
i
1
i
600
Temperature, °C
FIGURE 6. Spall strength of Ti-6-22-22S alloy as a function of
temperature at two load durations in comparison with the yield
strength data.
FIGURE 5. Yield strength at 0.2% plastic strain of Ti-6-22-22S
alloy as a function of the strain rate.
triangular shape of the incident compression pulse.
In the case of trapezoidal shape of the waveform the
spall strength may be calculated using relationships
over the strain rate range of 10~4 s"1 to 106 s"1. This
indicates the thermal activation mechanism of
plastic deformation of the alloy is maintained. Note
that for pure metals a transition from a logarithmic
to linear dependence is often observed in a vicinity
of 104 s"1 strain rate [13]. This explains, why the
adiabatic shear bands are relative easily formed in
titanium alloys and are not formed in pure metals.
(6)
Here u} is the free surface velocity derivative ahead
of the spall pulse, CF < cl is the propagation
REFERENCES
1. Meyer, L.W. and Chiem, C.Y. In: Titanium, Science
velocity of the spall pulse front, 0"x+ and crx are
the stress time derivatives just ahead of the spall
pulse front and behind it, respectively, and hsp is the
spall plate thickness. The stress derivatives are
&x+ ~ P^b^i /2, ax_ - pCfU212 near the spall plane
and drx+ « 0 near the rear free surface of the sample
plate. Here u2 is the free surface velocity gradient
in the spall pulse front.
Figure 6 summarizes the spall strength data
over the temperature range from -170°C to 620°C
and the yield strength data. Whereas the yield
strength varies monotonously with the temperature,
the spall data exhibit a maximum tensile strength
near the room temperature.
and Technology, edited by G. Ltitjering et al., 1985,
pp. 1907-1914.
Meyer, L.W. Ibid, pp. 1851-1859.
Chichili, D.R., Ramesh, K.T., and Hemker, K.J. Ada
mater., pp. 1025-1043 (1998).
Rohde, R.W. Ada Metallurgica, 17, 353-363 (1969).
Kanel, G.I., Razorenov, S.V. Bogatch, AA., et al. J.
AppLPhys., 79(11), 8310-8317 (1996).
Zhuowei Gu and Xiaogang Jin, In: Shock
compression of condensed matter— 1997, ed. by S.C.
Schmidt et al., AIPCP 429, New York, 1998,467-470
7. Meyer, L.W and Kriiger, L. In: Mechanical Testing
and Evaluation, ASM Handbook, 8, 452-454 (2000).
Guinan, M. W. and Steinberg, D. J. J. Phys. Chem.
Solids, 35, 1501-1512(1974).
Fowles R. and Williams R.F. J. Appl Phys., 41(1),
360-363(1970).
10 Novikov, S.A., Divnov, I.I., and Ivanov, A.G. Phys.
of Metals and Metallography, 21(4), 608-615 (1966).
11. Stepanov, GV. Problems of Strength (USSR), No 8,
66-70(1976).
12. Kanel, G.I. Journ. of Applied Mech.s and Technical
Physics, 42(2) 358-362 (2001)
13. Sakino, K. J. Phys. IVFrance, Colloque Pr9, 10, 5762 (2000).
DISCUSSION
The strain-rate and the temperature
dependencies of the yield stress obtained from the
uniaxial stress tests and from the shock-wave
experiments are in a good agreement and
demonstrate, in general, a logarithmic dependence
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