Acta metall, mater. Vol. 43, No. 7, pp. 2773 2787, 1995
~ )
Pergamon
0956-7151(94)00464-1
Elsevier ScienceLtd
Copyright © 1995Acta MetallurgicaInc.
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0956-7151/95 $9.50+ 0.00
HIGH T E M P E R A T U R E D E F O R M A T I O N BEHAVIOR OF
PHYSICAL VAPOR DEPOSITED Ti-6A1-4V
J. WARREN,L. M. HSIUNG and H. N. G. WADLEY
Department of Materials Science and Engineering, University of Virginia, Charlottesville,
VA 22903, U.S.A.
(Received 6 October 1994)
Abstract--A detailed study has been conducted of the high temperature creep and microstructural
evolution accompanying the creep deformation of an initially nanocrystalline Ti~AIMV alloy. For test
temperatures of 600 and 680"~C the alloy transformed from an (c~ + ct') to a single phase e during creep
testing and exhibited exceptionally low creep resistance. During testing between 760 and 900°C, the alloy
transformed to a conventional (ct +/~) microstructure and exhibited up to ten times the creep rates of
conventional grain size (superplastic) Ti-6AI~4V. Creep models based on grain boundary sliding,
dislocation and diffusional creep were combined with relationships for phase evolution and grain growth
to predict stress-strain rate relationships at each test temperature. The analysis indicates that in the low
temperature region dislocation accommodated GBS, in conjunction with diffusional flow, are responsible
for creep whilst in the high temperature region diffusion accommodated GBS is the dominant mechanism.
1.
INTRODUCTION
Interest is growing in the use of physical vapor
deposition (PVD) methods for producing novel
structural, magnetic and ferroelectric materials [1],
for synthesizing coatings with improved thermal, wear
and corrosion protection [2] and for depositing metal
(or intermetallic) alloys on ceramic fibers during the
manufacture of metal matrix composites (M MCs) [3].
If deposition is conducted at low substrate homologous temperatures, add atom mobility is inhibited
and porous nanocrystalline (and sometimes even
amorphous) deposits are obtained [4]. Increasing the
substrate temperature to promote sufficient diffusion
to eliminate the porosity can still sometimes result in
PVD alloys containing nanocrystalline structures and
highly supersaturated and/or metastable phases that
may be impossible to produce by other methods [5].
The very fine grain size of these PVD alloys can
significantly affect their mechanical, electrical, and
magnetic properties and is an area of intense study [1].
One reason nanocrystalline materials have attracted
attention is because of their high strength at low
temperature [6]. For example, microhardness values
for nanocrystalline Pd and Cu are reported to be
three to four times greater than those of conventionally processed Pd and Cu [7]. However, this might be
expected to occur at the expense of a lessened resistance to creep at higher test temperatures T/> 0.4 T m
(where Tm is the absolute melting point) which
would have important beneficial consequences for the
consolidation of metal coated fiber preforms during
M M C manufacture [3].
The potential enhancement of the creep rate of
nanocrystalline alloys, and the mechanisms responsible for it, have not been widely studies in metals. In
nanocrystalline ceramics high creep rates at relatively
low stresses and homologous temperatures have been
reported [8] and were attributed to enhanced grain
boundary diffusion. In metals, creep can occur by
both the movement of dislocations and diffusive flow
(see Table 1 for a summary of creep rate-grain size
relations). In the metals case, it remains to be determined whether the creep rates change as much with
grain refinement into the submicron range or if the
changes can be explained by an extension (to small
grain size) of the large length scale creep mechanisms
or involve new physical processes associated with
small size [1].
Experimental studies of the creep behavior of PVD
materials are needed to resolve these issues. They
have been limited by the difficulty of sample preparation. It has proven difficult and time consuming to
prepare samples of sufficient quality and thickness
to allow conventional creep tests to be conducted by
direct deposition. Because of this, knowledge about
the creep behavior of technologically important alloys
(e.g. alloys based on AI, Ti, Ni, and Fe) with nanometer scale structure is presently unavailable inspite
of speculations that it may have potentially important
implications for the deformation processing of these
materials [1]. Of particular interest here is the possibility of enhancing the superplastic behavior of alloys
like Ti-6A1-4V which are used extensively for superplastic forming, and more recently for metal matrix
composites (MMCs) [3]. For this latter application,
2773
2774
WARREN et al.:
HIGH TEMPERATURE DEFORMATION OF Ti~fAI~4V
Table 1. The mechanismsresponsiblefor creep in alloysat T//-0.4 T~ and a t> 10-6#. Refer to text
for symboldefinitions
Creep mechanism
Constitutiverelationship
IOflod~ = k Td2 D~
Latticediffusion
(Nabarro Herringcreep[37])
150~a6
Grain boundarydiffusion
(Coblecreep [38])
~gb = ~
~/320-2
~gbs = ~ k T d D~
Dislocationaccommodatedgrainboundarysliding
(atter Langdon[30])
Diffusionaccommodatedgrainboundarysliding
(after Ashby Verrall[35])
Dislocationglide-plus-climb[27]
constitutive models for the creep behavior are
needed to better understand and model the consolidation process step used during the manufacture of
MMCs.
Conventionally fabricated, fine-grain size Ti-6AI4V exhibits superplastic behavior between 750 and
950°C [9-14]. In this range of temperatures grain
boundary sliding (GBS) is thought responsible for
the superplastic behavior [15]. The strain rate in this
regime increases inversely with grain size (see Table 1
for summary of creep constitutive relations) and so
maintaining a fine grain size is essential if short
processing times and low processing pressures are to
be achieved. Extensive thermomechanical deformation in the (~ +/3)-phase field by conventional
methods such as hot rolling, forging or extrusion
have been used to refine the coarse acicular microstructure carried over from ingot processing. The
practical limitation is the 3-7/xm range of today's
alloys [16]. In the superplastic temperature range of
Ti 6AI-4V, partitioning of the two substitutional
alloying elements between the ~- and /3-phase (A1
to a, V to /3) retards grain growth and extends
the superplastic temperature range up to 900-950°C
where the forming pressures are the lowest [14].
If the temperature is increased above 950°C the
equilibrium ~-phase volume fraction decreases allowing the fl-phase grains to coarsen, the GBS mechanism to become less significant, and the eventual loss
of a superplastic response. At temperatures below
750°C superplasticity is again not observed, but in
this case it is because both the (temperature dependent)
volume fraction of the (softer)/3-phase, and its diffusivity, are insufficient to significantly accommodate
the GBS mechanism responsible for superplastic
deformation [10, 11]. Below 750°C the deformation
behavior is thought to be dominated by dislocation
creep of the more creep resistant ~-phase and by
sliding of the lower diffusivity c~-~ grain boundaries
[11]. Consequently, superplasticity in Ti-6AI-4V
occurs only over a relatively narrow range of temperatures for which the z~- and /3-phases are present
in near equal volume fractions and the diffusivity
Dgb
%~=~-i
<" - - ~
#b
1+ ~ - )
/ a \"
of the fl-phase is sufficient to accommodate plastic
strain rates greater than 10 -4 1/s.
Efforts to enhance the superplastic phenomenon in
Ti alloys have included the use of alloy additions to
stabilize the/7-phase (e.g. Ni, Fe, Co) and increase its
diffusivity (they have diffusivities between 25 and 90
times higher than that of Ti in the fl-phase) [14]. This
has proven quite effective both in increasing the /3phase diffusivity and enhancing the/3-phase fraction
at lower process temperatures resulting in a significant
reduction in the minimum superplastic forming temperature and pressure in modified Ti-6AI-4V alloys.
Here, we have used a high rate sputtering technique
to produce thick nanocrystalline Ti-6AI-4V sheets
and systematically explored the stress and temperature
dependence of its creep behavior. Concurrent grain
growth and phase evolutions accompany the tests.
In order to be able to usefully use the information in
constitutive models, we have related the creep data
to the basic creep mechanisms and incorporated the
microstructural evolution. These observations and
their interpretation may interest those who manufacture composites via PVD routes, alloy developers
interested in extending the range of superplasticity in
metals and alloys, and the nanocrystalline materials
community in general.
2. E X P E R I M E N T A L P R O C E D U R E S
2.1. M a t e r i a l f a b r i c a t i o n a n d c o m p o s i t i o n
The material used for this study was 0.4 mm thick,
fully dense, argon plasma sputter deposited Ti-6A14V sheet material produced at the 3 M Metal Matrix
Composites Center (Mendota Heights, Minn.). It was
deposited on 100 x 150 × I mm fiat 303 series stainless steel plate, placed near conventional Ti-6A1-4V
alloy sputtering sources. The substrate was exposed
to the radiant heat of the argon plasma and rapidly
reached a steady temperature of 300°C during
deposition. Deposition was conducted in a high
vacuum chamber (10-6Torr background pressure)
at a deposition rate of ~ 0 . 8 / ~ m / m i n until a 0.4 mm
thick deposit had formed. At the conclusion of
WARREN et al.: HIGH TEMPERATURE DEFORMATION OF Ti~AI~,V
Table 2. Chemical composition o f T i 6AI 4V alloy sourcc and P V D
sheet
Element
Source (%wt)
PVD sheet (%wt)
AI
6.00
5.70
V
4.00
3.90
Ga~
0.20
0.19
Fe"
0.18
0.23
0:3
0.176/0.178
0.188/0.189
N2
0.0148/0.0163
0.0138/0.0139
Ti
balance
balance
~Weakc~-phasestabilizer,solid solutionstrengthener.
2//-phase stabilizer.
3Potent 7-phase stabilizer,0.2 maximumallowableconcentration.
deposition, the vacuum chamber was purged with
argon and allowed to cool. The thermal expansion
mismatch between the deposited Ti-alloy sheet and
the stainless steel plate conveniently caused the sheet
to debond from its substrate upon cooling. Chemical
analyses of the source sputter deposited materials
were performed (Table 2). They indicated little influence of the vapor deposition process on the sheet
composition.
2.2. Creep testing method
For tension tests, strips 10 mm wide and 150ram
long were cut from the PVD sheet using computer
controlled wire electronic discharge machining. To
facilitate gripping of the tensile specimens, the ends of
the strips were sandwiched between 65 × l0 × 1.5 mm
conventional Ti-6AI-4V tabs and spot-welded
together. This resulted in a specimen gauge length of
20 ram. Specimens in the as-deposited microstructural
state were then used to investigate the creep behavior.
Constant load, isothermal creep tests, were conducted
in a 99.97% purity flowing argon atmosphere at five
test temperatures of 600, 680, 760, 840 and 900~C.
The load for creep testing this material was applied
directly to the specimen by a load train mechanism
capable of applying small fixed loads (18-140 kN).
The creep test assembly was contained within a single
zone, programmable furnace housed in a ceramic
retort. The furnace had a 300 mm long constant
temperature hot zone. A low heating rate of 5°C/rain
to the test temperature was necessary to avoid thermal
shock of the ceramic retort assembly. During specimen testing the temperature was monitored by two
type K thermocouples mechanically attached to the
upper and lower ends of the specimens' effective
gauge length. A maximum temperature difference of
4°C was observed between the thermocouples at the
test temperatures. Because of the slow heating rate,
the specimen temperature stabilized within approx.
2 min of reaching the preprogrammed temperature
setting. The load was then applied 1 rain after temperature stabilization (thus each specimen was exposed
to a 3 rain soak at temperature prior to testing). To
obtain isothermal strain rate data over a range of
stresses, creep tests were conducted at progressively
higher fixed loads using a new specimen for each test.
Instantaneous gauge length extension was measured
using a molybdenum alloy extensometer outfitted with
2775
a linearly variable capacitive transducer (LVCT).
The transducer could repeatably resolve a 0.0005
engineering strain in the 20 mm specimen gauge length.
The high measurement accuracy of this transducer
enabled calculation of instantaneous gauge cross
section and therefore true flow stress from instantaneous gauge length extension (assuming volume
constancy). The true stress (a) and the point of
minimum true strain (~min) were then obtained for
each test together with the time to reach the minimum
strain rate. For these tests the true strain, at the onset
of the minimum true strain rate, was between 3 and
4%. Each creep test conducted at a fixed temperature
yielded a single data point on long a vs log Eminplot.
2.3. Microstructural characterization
Microstructural evolution accompanied each creep
test. To characterize it, samples were annealed at each
of the five creep test temperatures (600, 680, 760, 840,
900°C) for a range of times spanning those required
to reach the minimum strain rate during the creep
tests. The samples were enclosed in evacuated quartz
ampoules, heated at 5°C/rain to the annealing
temperature and water quenched to preserve the
microstructural features present at the annealing
temperature. The quenched specimens were then
mounted in epoxy, polished and etched (with Kroll's
reagent) and the average grain size for each test temperature measured using the Hilliard circle technique
[17]. Grain size information was obtained for the as
received state and after annealing at the two lowest
test temperatures using transmission electron microscopy (TEM) on specimen coupons annealed between
1 and 1.8 x 104min (310 h). For the higher test temperatures the grain size was sufficient to be reliably
resolved using SEM micrographs. X-ray diffraction
(XRD) patterns and selected area diffraction (SAD)
patterns were also taken to determine the phase(s)
present. In addition, specimens were analyzed in the
TEM after testing to determine the presence and
arrangement of dislocations in the gauge sections and
determine the effect of strain on the microstructure.
3. P V D M I C R O S T R U C T U R E S
XRD of the PVD material in the as-deposited
condition indicated it had a HCP crystal structure.
A TEM micrograph of this mierostructure is shown
in Fig. 1. TEM analysis indicated the presence of two
components of the microstructure; an (HCP) ~-phase
and a martensitic (HCP) ~'-phase. The presence of ~'
in the microstructure is not unreasonable considering that (1) vanadium supersaturated ~ transforms
martensitically to ~' during water quenching in
conventional Ti-6AI-4V [18]; and (2) deposition
from the vapor phase onto a relatively cold substrate
involves cooling rates many orders of magnitude
greater than liquid-quenching (vapor quenching is
estimated to have cooling rates of 10~3°K/s, liquidquenching has substantially lower rates of 104-10s
2776
WARREN
et al.:
HIGH TEMPERATURE DEFORMATION OF Ti--6AI4V
Fig. I. TEM micrograph of as-deposited Ti~6AI~4V
material. The arrows highlight the :~'-phase.
°K/s [19]). In the as-deposited condition the dislocation density was very high and grain boundaries
were not clearly defined making an accurate grain size
measurement difficult. We estimated the grain size to
be in the 30-100 nm range.
T E M micrographs and SAD patterns for samples
annealed at 600 and 6 8 0 C for 1 min and then water
quenched are shown in Fig. 2. Figure 2(A) is the
microstructure of the 6 0 0 C sample which consisted
of single phase :~ with a grain size of 150 nm. This
coarsened with time so that after 310 h the average
grain size was 810 nm. Both X R D and S A D analysis
indicated that it was still comprised of only the
-phase.
Fig. 2. TEM micrographs of specimens annealed for 1 min
at: (A) 600'C and (B) 680C.
A 1 min anneal at 680~C also resulted in a single
phase ~ microstructure but with a grain size of 260 nm
[Fig. 2(B)]. More rapid coarsening also occurred at
680°C. Annealing for 14 h at 6 8 0 C (the duration of
the longest creep test at this temperature) resulted
in a grain size of 730 nm. After annealing for 14 h at
680°C the microstructure was predominately c~-phase
with a small (~0.05) volume fraction of fl-phase at
grain boundary triple points.
SEM micrographs of samples annealed at temperatures of 760, 840 and 900~C (for 1 min) followed by
water quenching are shown in Fig. 3(A-C). Annealing at 760"C resulted in a predominantly a-phase
microstructure with a small (0.09) volume fraction
of polygonal fl-phase grains. A fi-phase "film" was
also present on some of the e grain facets, Fig. 3(A).
The amount of fl-phase present was insufficient to
completely " c o a t " each ~ grain and large areas of the
Fig. 3. Microstructures after a 1 min anneal followed by
an immediate water quench from: (A) 760; (B) 840; and
(C) 900 ~C.
WARREN et al.:
1.0
. . . . . . . .
I
. . . . . . . .
I
. . . . . . . .
~
HIGH TEMPERATURE DEFORMATION OF Ti~iAl~,V
. . . . . . . .
l
. . . . . . . .
(a) LOW temperature region
E•0.8
"N
l
. . . . . . .
600°C
0,6
.E
o~ 0.4
<
0.2
0.0 ........ I ........ I ........ I ........ I . . . . . . . . [ . . . . . .
101
102
103
104
105
106
107
Annealing time (s)
2.4
]
I
I
T
I
(b) H i g h t e m p e r a t u r e r e g i o n
~
2.0
~
1.6
c
"~
1.2
~0.8
~:
0.4
0.0
I
2000
40100
I
6000
I0
I
10000
80 0
t2000
2777
The reduced vanadium content in the //-phase at
900°C raises its martensitic start temperature (M~) to
approx. 700"C [18] and so prior ,8 grains transform to
a martensitic ~'-phase + retained fl microstructure
during quenching, This grain size is still significantly
less than conventionally processed alloys which,
after a similar anneal at 900~C, have an average grain
size of 4 p r o [9]. Figure 4(a and b) summarize the
measured grain sizes of samples annealed for varying
times in the low and high temperature regimes
respectively. The //-phase volume fraction agrees
reasonably well with the experimental data reported
by Meier et al. [10] for conventional alloys (see Fig. 5).
Not all the //-phase was present at the ~-grain
boundaries. For the specimens annealed for 1 rain
at 760, 840 and 900°C and water quenched small
white, intercrystalline precipitates were seen within the
-phase grains [Fig. 3(A-C)]. T E M microdiffraction
and selected area diffraction (SAD) analysis indicated
these to be//-phase precipitates. They were absent in
samples annealed for 2 h or more at 9 0 0 C . At 840~C
however, the diffusion kinetics are slower and the
precipitates are present in the microstructure even
after a 3 h annealing treatment.
Annealingtime (s)
Fig. 4. The results of grain growth experiments conducted
in: (a) low temperature, ~-phase region; and (b) high
temperature, (~ +/~)-phase region.
microstructure were comprised of ~ grain clusters
(~ c< grain boundaries). The average grain size after
1 rain at 760°C was 500 nm.
A 1 min anneal at 840~C resulted in equiaxed
~-grains and an intergranular ~-phase, Fig. 3(B),
similar in morphology to that seen in Fig. 3(A). The
volume fraction o f / / - p h a s e had increased to 0.21.
The average grain size at the start of the 840~C creep
test temperature was approx. 800 nm, still significantly
lower than the 3.0pro grain size of conventional
Ti 6Al-4V following a similar anneal [9].
A 1 rain 9 0 0 C anneal with a subsequent water
quench, Fig. 3(C), resulted in a microstructure
consisting of grains containing c~' laths + retained //
and c~-grains (the average grain size was 1.1 pro).
5O
i
i
i
PVD T i - ~
4. CREEP MEASUREMENTS
4.1.
L o w temperature creep region
The stress dependence of the minimum creep rate
at test temperatures of 600 and 6 8 0 C is shown in
103
(a)
cast Ti-6AI-4V, T= 650°C [20]
.°.o.o-°..o-o.--"
1o2
. . . ,o
J
P
lO ~
I0 °
10-5
PVD Ti-6AI-4V, T=600°C
v f
.....
i
........
10 7
i
........
10~
i
. . . .
10-5
10 4
Minimumstrain rate groin (1 /S)
102
.....
I
........
I
........
I
. . . .
p
,'"
E 40
n
g
~
~
6
8
0
°
C
_ / ~ ",d TiCO~A?,~'vO[111]
~ 20
o..
10
10 0
0
750
I
I
1 0 _7
........
I
10 ~
,
, ,,,,,d
10-5
,
, ,,,,,d
1 0 -4
,
......
10 ~
I
800
850
900
Temperature (°C)
950
Fig. 5. A comparison between the/~-phase volume fraction
of the conventional Ti 6Al~4V alloy and the PVD alloy.
Minimum strain rate Emin (1 /s)
Fig. 6. True stress vs minimum true strain rate for PVD
Ti-6AI~4V at: (a) 600; and (b) 680"C. The deformation
behavior of cast Ti 6Al~4V at 650C is also shown in (a).
2778
W A R R E N et al.: H I G H T E M P E R A T U R E D E F O R M A T I O N OF T i ~ A I M V
Table 3. Creep stress exponent n, strain rate sensitivity m, and
temperature dependent material parameter B results for the PVD
Ti 6Al~4V alloy
Temperature
("C)
Creepstress exponent n,
(m - 1/n)
600
680
760
840
900
3.40 (0.30)
3.00 (0.33)
1.70 (0.60)
1.34 (0.75)
1.70 (0.60)
B[1/(s MPa")]
3.6 x
1.2 x
1.6 x
1.9 x
1.2 x
10- H
10 9
10 6
10 5
10-5
4.2. High temperature creep region
Fig. 6(a a n d b). respectively. C r e e p d a t a for the
c o n v e n t i o n a l l y p r o c e s s e d alloy at 600°C o r for a n y
m i c r o s t r u c t u r e at 680uC w a s n o t available so, f o r
c o m p a r i s o n p u r p o s e s , the d e f o r m a t i o n b e h a v i o r o f
cast T i - 6 A I 4V is also s h o w n in Fig. 6(a) [20]. A least
s q u a r e s analysis o f the e x p e r i m e n t a l d a t a w a s used to
fit a s t r a i g h t line t h r o u g h the d a t a
points
o f a log a - l o g ~min plot. T h e slop m defines the strain
rate sensitivity
m -
0 log a
(1)
0 log g~,,"
T h e reciprocal o f m is the creep stress e x p o n e n t n in
the N o r t o n p o w e r law creep r e l a t i o n s h i p
Ban
gmin =
A list o f true stresses, a s s o c i a t e d m i n i m u m t r u e
strain rates a n d g r a i n sizes w h e n the m i n i m u m creep
rate w a s a t t a i n e d are given in T a b l e 4. T h e d u r a t i o n
o f the t r a n s i e n t creep stage (i.e. the time to reach the
m e a s u r e d m i n i m u m s t r a i n rate) is also given in the
table.
T a b l e 3 lists the m e a s u r e d s t r a i n rate sensitivity
values a n d T a b l e 4 s u m m a r i z e s the true s t r e s s - s t r a i n
rate values a n d g r a i n sizes f o r the creep tests perf o r m e d in the high t e m p e r a t u r e range. I n the 760 to
900°C t e m p e r a t u r e r a n g e the P V D alloy d e f o r m e d
superplastically. T o t a l engineering s t r a i n s in excess
o f t w o g a u g e lengths were r o u t i n e l y o b t a i n e d .
F i g u r e 7 ( a - c ) s h o w s the true s t r e s s - m i n i m u m t r u e
s t r a i n rate r e l a t i o n s h i p s for the three test t e m p e r a tures. F o r c o m p a r i s o n , the s u p e r p l a s t i c b e h a v i o r o f
c o n v e n t i o n a l l y p r o c e s s e d T i - 6 A 1 - 4 V is also i n c l u d e d
[9, 21]. F o r a given true stress, the P V D m a t e r i a l
exhibited u p to a ten-fold increase in s t r a i n rate at
760°C. A h i g h e r s t r a i n rate is also seen at the h i g h e r
test t e m p e r a t u r e s b u t the difference b e c o m e s less.
(2)
102
.......
w h e r e i ~ . is the m i n i m u m strain rate, a is the applied
true stress, B is a t e m p e r a t u r e d e p e n d e n t m a t e r i a l
p a r a m e t e r . T h e e x p e r i m e n t a l l y d e t e r m i n e d values o f
B, n a n d m for the low t e m p e r a t u r e r a n g e are given
in T a b l e 3. T h e low values o f m indicate t h a t u n d e r
these test c o n d i t i o n s s u p e r p l a s t i c b e h a v i o r did n o t
t
v
1
101
• conventional
T = 7 6 0 ° C [21]
o conventional
T= 750°C [9]
• PVD processed T= 760°C
i
i
J
i ....
I
,
,
,J
....
10 ~,
10 -5
I
. . . . .
ill
10-3
10-2
102
Table 4. Experimentally determined ~'mi.values and measured times
to reach i,,i. for the test temperatures and stresses used in the study.
The estimated grain size at the time ~mi.was measured are also shown
13_
T
CC)
True
stress
(MPa)
600
600
600
600
54.2
32.0
15.9
7.5
1.3 x
3.9 ×
4.0 z
2.0 x
10
10
10
10
5
6
7
~
50
117
1333
18,600
0.2
0.3
0.4
0.7
680
680
680
680
55.5
32.0
17.0
8.0
1.8 x
3.8 ×
1.0 x
5.0 x
10
10
10
10
4
5
5
7
3
23
117
833
0.3
0.4
0.5
0.7
760
760
760
760
760
46.2
31.2
21.0
12.0
6.5
9.5 ×
5.5 ×
3.0 x
1.0 x
3.7 x
10
10
10
10
10
4
4
4
4
5
0.5
1.3
1.7
2.8
9.6
0.6
0.6
0.7
0.7
0.8
840
840
840
840
50.2
30.7
10.1
6.5
2.5 x
1.8 x
4.0 ×
1.2x
10 ~
10 3
I0 4
10 4
0.2
0.3
1.0
1.3
0.8
0.8
0.9
0.9
900
900
900
900
30.7
20.2
10.9
5.8
4.2 x
1.6 x
6.6 x
2.6 x
10
10
10
10
0.1
0.3
0.7
1.3
1.1
1.1
1.2
1.2
3
~
4
a
.......
q)
(tl
100
~'i~
(I.s)
.... I
0..
Occur.
Duration
of transient
creep stage
(min)~
"-'~
Grain
size at
imin ( / i r a ) 2
~Each specimen held at test temperature for 3 min prior to the start
of the test.
-'The effect of strain enhanced grain growth is not included.
101
~0
~0
• conventional
T = 8 5 0 ° C [21]
. conventional
T = 8 5 0 ° C [9]
= PVD processed T = 840°C
I
........
I
.......
cO
10 °
10 -5
........
102
........
10 -4
I
10-3
........
I
10 . 2
. . . . . . .
(e)
•o
u)
o9
101
cr o
cO
10 °
10 -5
........
* conventional
• PVD processed
I
........
10 -4
T = 9 0 0 ° C [g]
T = 900°C
I
.......
10 .3
10 -2
Minimum strain rate era/n (1 / s)
Fig. 7. True stress vs minimum true strain rate for PVD
Ti~iAl-4V at: (a) 760; (b) 840; and (c) 900°C. The behavior
of conventionally processed (superplastic) alloy is also
shown.
WARREN
et al.:
HIGH TEMPERATURE DEFORMATION OF Ti~AIM-V
2779
5. DEFORMATION MICROSTRUCTURES
To obtain insight into the possible mechanisms
responsible for creep T E M analysis was performed
on specimens prepared from grip and strained gauge
sections. Figure 8(A and B) show the gauge section
of a PVD sample tested at 600°C and a stress of
7.2 MPa. The test conducted under these conditions
required 310 h to attain the measured minimum creep
rate at a total engineering strain of 0.045. Dislocations were present at the grain boundaries but
the majority of grain interiors were dislocation free as
shown in Fig. 8(B); providing evidence for a GBS
dislocation accommodation mechanism [22].
Figure 9(A and B) are T E M micrographs of
sections removed from the unstrained grip and the
deformed gauge regions of a PVD specimen creep
tested at 600°C and 55 MPa. The specimen had been
" q u e n c h e d " (at ~ 2 0 C / m i n ) with argon gas at
the tests' completion to preserve the deformation
structure. The total engineering strain when Emm was
reached (after 3.5 h of testing) was approx. 0.18. The
micrographs in Fig. 9 reveal the presence of a high
density of dislocations in the deformed gauge section
Fig. 9(B), while the microstructure of the grip region,
Fig. 9(A), is relatively dislocation free. Figure 10 is a
T E M micrograph of the grain boundaries in detail
and again shows that the dislocation density at the
grain boundary was significantly greater than in the
grain interior.
Fig. 9. TEM micrograph of."(A) grip section; and (B) gauge
section for a sample tested at 600°C and 55 MPa.
Fig. 10. Detail of grain boundaries in gauge secnon for
a sample tested at 600°C at a stress of 55 MPa. Arrows
highlight grain boundary dislocations.
Fig. 8. (A) TEM micrograph of gauge section from a creep
test conducted at 600°C and 7.2 MPa; and (B) detail of
dislocation arrangement at a grain boundary.
Fig. 11. TEM micrograph of a gauge section for a sample
tested at 840°C and 50 MPa. Arrows highlight the fl-phase.
2780
WARREN et al.: HIGH TEMPERATURE DEFORMATION OF Ti~AI~4V
Figure 11 is a TEM micrograph of a gauge section
removed from an argon quenched specimen tested at
840°C and a stress of 50 MPa. The total engineering
strain when g~,~,was reached (after 2 rain) was 0.45.
The strained microstructure consisted of a-grains,
of low dislocation density, and smaller intergranular
/?-grains. Even though the strain was large, only a
low density of dislocations were present in the
-phase.
6. MICROSTRUCTURAL EVOLUTION
RELATIONSHIPS
6.1. Grain growth
At similar stresses and temperatures the superplastic strain rates measured in this alloy are between
3-10 times higher than those of conventionally
processed material. In the PVD alloy the high temperature superplastic behavior was not observed at
test temperatures of 680°C or below but the strain
rates were still much greater than those expected for
a conventionally processed alloy. To explain these
phenomena we will explore the extension of conventional creep models to the phase distributions
and sub-micron grain sizes present in the PVD
material. However, to do this, the kinetics of grain
growth during the test must be established since grain
coarsening significantly effects some creep mechanisms particularly dislocation accommodated GBS
(oc 1/d), diffusion accommodated GBS (3c l/d 2) and
the lattice (so 1/d 2) and grain boundary (oc 1/d 3)
diffusional creep mechanism (Table 1).
The as-deposited specimens had a metastable
(:~ + ~'),
heavily
dislocated,
nanocrystalline
( ~ 100 nm) mierostructure. Heating the specimen to
creep test temperatures caused grain growth and,
at temperatures of 760°C and above, substantial
fl-phase formation. The measured isothermal strain
rate behavior is therefore not for a constant microstructure but for one which evolves with testing time.
In particular significant grain growth occurred during
the long primary creep stage when the applied stress
was low. This allowed for a substantial increase in
the grain size prior to attaining the minimum strain
rate. For example, at 600"C and an applied stress of
7.2 MPa, the minimum creep rate was attained in
310 h while testing at 54 MPa results in a 1 h test time
to reach the minimum strain rate (see Table 3). The
grain size differs by a factor of three between the two
test conditions (and similar trends are seen at other
temperatures).
The solid lines that pass through the data sets in
Fig. 4 are the best fits to an empirical grain growth
relationship
d = do + kt a
(3)
where d is the instantaneous grain size, do the initial
grain size, t the time (s), a is the grain growth
exponent and k is a constant. The best fit constants
are given in Table 5. For the range of test tempera-
Table 5. Constants used in the empirical grain growth relationship
T(C)
do(/lm)
a
k(,um/s ~)
900
840
760
680
600
0.50
0.20
0.11
0.07
0.03
0.20
0.20
0.24
0.20
0.20
0.23
0.23
0.14
0.07
0.04
tures studied here the grain growth exponents were
~0.2.
For extended creep tests at 680'~C and all creep test
temperatures above 760c'C the fl-phase (whose formation and growth is controlled by the segregation
of A1 and V) retards grain growth. The grain
growth exponents experimentally determined for the
PVD alloy are typical of alloys that exhibit solute
segregation to grain boundaries or contain particles
(or phases) that inhibit grain growth (i.e. Zener grain
boundary pinning) [23].
To determine the grain size at ~m~,for a given stress
and strain rate (Table 4) we have assumed that the
empirical relationship for grain growth given in equation (3) approximate the grain coarsening kinetics of
the specimen during the transient creep stage of the
test. The effect of strain enhanced grain growth has
been shown to increase the grain size by approx.
25% in gauge sections strained to 200% [9]. We have
neglected this effect because of the small strains
required to reach {,n~, in this PVD alloy.
6.2. fl-Phase formation
The fl-phase volume fraction has strong effects
both on grain coarsening and the creep mechanisms
in Ti-6A1-4V alloys. At 900°C, 47% of the alloy
consisted of the fl-phase and decreased with decreasing test temperature. In addition to inhibiting grain
growth the b.c.c, fl-phase has more slip systems and
a diffusivity two orders of magnitude higher than the
c~-phase (see Table 6). Thus the deformation behavior
of an (c~ + fl) "composite" microstructure might be
expected to differ considerably from that of the
predominately single phase c~microstructure found in
the low test temperature region.
An empirical expression for the /?-phase volume
fraction present in the PVD alloy, as a function of test
temperature was determined from the experimental
data and is equal to
V/dT(°C)] = 11.870 - 3.088
x 10 2T+2.024 × 10-ST 2 (4)
where V, is the /?-phase fraction and T is the
temperature in degrees centigrade.
7. C R E E P
MECHANISMS
7.1. Activation energies for creep
Creep tests have been conducted over a broad
range of temperatures and the deformation behavior
coarsely partitioned into mechanistically different
WARREN et al.: HIGH TEMPERATURE DEFORMATION OF T i ~ A I ~ V
Temperature
-2
900
T
840
760
I
I
150 kJ / tool
(°C)
680
r
~
ii
600
I
(c~)
-8
• ~oE
g
-10
-12
-18
-20
0.0008
240 kJ / mol
I
0,0009
0.0010
1/T
[
0.0011
7 MP
0.0012
(l/K)
Fig. 12. The relationship between minimum strain rate and
I/T for the stress range covered in this work.
regions based on the measured values of activation
energy. Figure 12 shows the relationship between
In ~mm and 1/T for the entire range of test temperatures and stresses studied. It is evident that a distinct
transition in the deformation behavior exists between
680 and 760:C. This coincides with the formation of
the (high diffusivity) fl-phase in the microstructure,
Fig. 5. Thus, the "low temperature region" involves
creep of predominately a-phase microstructures
whilst the "high temperature region", exhibits superplastic behavior of a two phase (~ + fl) structure. The
average value of the activation energy for all stresses
in the low temperature region was 240 kJ/mol. This
is almost identical to the activation energy for dislocation creep in elemental ~-Ti (242 k J/tool) [24].
In the high temperature region the average value of
the activation energy was 150 k J/tool, similar to the
activation energy for volume diffusion in elemental
/~-Ti (131 kJ/mol) [25]. Thus, different creep mechanisms are rate limiting in the two regions.
7.2. Low temperature creep mechanisms
The creep resistance of the PVD alloy in the low
temperature range is significantly less than that observed in conventionally processed, two phase Ti
6AI-4V alloys. For example, at stresses of 50 MPa
and above, the steady state creep strain rates observed
in the PVD processed alloy at 6 8 0 C [Fig. 6(b)] are
equal to or surpasses the strain rates observed in conventionally processed, superplastic T i - 6 A I - 4 V alloys
even when these are tested at 7 6 0 C [Fig. 7(a)] [21].
Substantially higher strain rates than the conventional alloys are also seen at 600 C. For example, the
creep rate behavior of as-cast (coarse grain) Ti 6AI
4V alloy tested at 650°C [20] is significantly less than
that of the PVD alloy tested at 6 0 0 C , Fig. 6(a). Thus,
the steady state creep strain rates of the PVD alloy
appear to be up to two orders of magnitude greater
than those of their cast, coarse grain counterparts.
Although the creep rate for the PVD material is
2781
increased, the creep stress exponent of the PVD alloy
(n = 3.4) is similar to that of the cast material
(n = 3.8) suggesting that similar creep mechanisms
may be operative even though the grain sizes are very
different.
Micromechanical creep models based on a dislocation glide-climb mechanism predict creep exponents
of 3 [24]. This value arises from the assumption that
the steady state strain rate (~) is proportional to the
mobile dislocation density (p) and the average glide
velocity of the mobile dislocations (v), i.e. e" ~ pv.
If it is further assumed that p oc ff-~ and v 3c a then
e oc a 3 and n --- 3 [24]. The measured creep stress
exponents at 600 and 6 8 0 C were 3.4 and 3.0 respectively (see Table 2) and are consistent with a dislocation creep mechanism. The 240 kJ/mol activation
energy in this region is identical to that reported for
dislocation creep in ~-Ti [24]. Thus, it would appear
that the low temperature mechanism of creep in the
PVD alloy is dominated by a dislocation mechanism
similar to many pure metals and solid solution alloys
when tested at around 0.5 Tm [26].
Further insight can be gained by examining the
general form of the phenomenological rate equation
for the deformation of metals and alloys tested at
about 0.5 Tm (the Dorn relationship) [27].
-Q,
ff ,
where A is a dimensionless constant (the Dorn
constant), n is the creep stress exponent, # the temperature compensated shear modulus, b the Burgers
vector, ~ is the applied stress, Do,. is the pre-exponential
constant for lattice diffusion, Q~ is the activation
energy for lattice diffusion and k and T are the
Boltzmann's constant and absolute temperature
respectively.
If the same mechanism operates at 600 and 680"C,
the values of A and n in equation (5) can be determined from the experimental creep data taken at the
two temperatures. First the steady state creep rates
and stresses in equation (5) were normalized
(minkT
(~)"
O~#b = A
(6)
and the normalized data were then plotted on a
log-log plot to obtain values for A and n. Our best
estimates for the material constants used in equation
(6) are given in Table 6. Because of the bulk selfdiffusivity of the metastable ~-phase alloy was not
available, we have used the self-diffusion coefficients
lbr elemental a-Ti. The data for both of the temperatures in the low temperature range are seen to fall
on a single straight line, Fig. 13, with a slope of
n = 3.2 again supporting the view that dislocation
creep is the d o m i n a n t deformation mechanism at
both temperatures in this temperature range.
However, equation (6) gives no insight into why
the strain rates are approximately two orders of
magnitude higher in the PVD processed alloy; it has
2782
WARREN et al.: HIGH TEMPERATURE DEFORMATION OF Ti~iA1MV
Table 6. Material parameters used to model the creep behavior o f the P V D Ti 6 A I M V alloy
Material parameter
:~
Burgers vector, b (m)
R o o m temperature shear modulus, ,u0 (MPa)*
Atomic volume, f~(m 3)
Grain boundary energy, V (J/m-')
Pre-exponential lattice diffusion, Do, (m~/s)f
Pre-exponential boundary diffusion, D~,g, (m2/s)+
Power law creep exponent, n
Power law creep (Dorn) constant, A (a in MPa)
Activation energy lattice diffusion. Q, (k J/tool)
Activation energy boundary diffusion, Qgb (kJ/mol)
G r a i n boundary width, 3 (m)
fl
Reference
3.0 x 10 ,o
2.05 × l04
1.7 x 10 29
0.35
4.5 x 10 ~
1.3 x 10 7
3.782
1.2 × 10~'
131
77
6.0 × 10 w3
3.0 × 10 ~c~
4.35 x 104
1.7 × 10 29
0.35
6.6 x 10 ~
1.3 × 10 ~
4.85 j
3.6 x 1091
169
101
6.0 × 10 103
[24]
[24]
[24]
[24]
[25]
[16]
[16]
[16]
[25]
[ 16]
[16]
*~=(T) = #[)(1 1.21~(T- 300),1933)); gt~(T) = #0(I - 0.5((T
300)/1933)).
¢D = D, exp ( Q,,kT): Ogb = Dt,.b exp( • Q~b/kT).
'Values are for 100% ~-phase Ti 6)~1.
~'Values are for 100%/)'-phase Ti 6AI 4V (2300 ppm H , charged alloy).
~Grain boundary width assumed to be equal to 2b.
no explicit grain size dependence. In other materials
tested near 0.5 Tm grain refinement also enhances
creep rates [28]. Here, not only is there a difference in
grain size between PVD and conventional Ti 6A1 4V,
but a large grain size evolution accompanies each creep
test so that the contribution of (grain size dependent)
mechanisms will be different for tests conducted at
each stress because of the different times required
to reach im~.. In nanocrystalline ceramics, grain size
variations during testing have been shown to complicate ascribing a mechanistic significance to the
experimentally determined creep exponent [29]. To
address this, the analysis has been extended to include
the effect of grain size and its growth on the creep
stress exponent (n).
In other small grain size materials the enhanced
creep rates (compared to their coarse grain counterparts) at similar test temperatures has been attributed
to GBS [28, 30]. Expressions for the strain rate due
to this (and other mechanisms) are summarized in
Table 1. According to Langdon [30] the contribution
10-I
. . . . . . .
]
. . . . . .
to the strain rate of the GBS mechanism can be added
to those of other mechanisms and thus the total creep
rate can, in principle, be expressed by a summation
of four independent mechanisms
z ~d -~ ~gbs -}- iv -J- ~gb
(7)
where id is due to dislocation creep [equation (5)],
igb~ is dislocation accommodated GBS, 4 is lattice
diffusional creep (Nabarro-Herring creep) and igb is
grain boundary creep (Coble creep). Each mechanism
has a different grain size dependence (see Table 1) and
the relative contribution of the four creep mechanisms will change as grains grow during a creep test
because of their different dependencies on grain size.
The value of n obtained from a Dorn analysis must
therefore be more carefully considered before definitive conclusions can be made as to the probable
mechanism(s) responsible for deformation, and the
creep rate dependence on microstructure.
Substituting expressions for ~d, igb~, iv, and i g b
from Table 1 into equation (7) and including the
effect of dislocation core diffusion (because at test
temperatures near 0.5 Tm dislocation core diffusion
dominates the effective diffusivity [24]) yields an
expression for the total strain rate
#b
['a ~"
0.96b2a 2
10 2
10fla
150fie6
+~
De. + ~
Dgb
..Q
:::L
(8)
10 ~
where ~ is the atomic volume, 6 is the grain boundary
width, d is the grain size at the minimum strain rate
achieved at a fixed value of a and T, Dgb is the grain
boundary diffusivity and De~ is the effective diffusion
coefficient due to dislocation core diffusion
I-o
.tO
v
A = 1.6 x 10 7
3.2
10 ~
(,0.oc(;;)
o 680°C
•
10 ~
10 -4
i
i
i
i
De.=D~ 1 + ~ - ~ .
600°C
(9)
L ILLI
10~3
. . . . . . .
10 ~
(o / ~)
Fig. [3. The dimensionless relationship between the normalized strain rate and true stress in the low temperature
c~-phase region.
where a~ is the cross-sectional area of the dislocation
core (~262). D~, is the diffusion coefficient for lattice
diffusion and D~ is the diffusion coefficient along the
dislocation core (assumed equal to the grain boundary
diffusion coefficient) [24].
WARREN
et al.:
HIGH TEMPERATURE DEFORMATION OF Ti~AI~4V
For conventional Ti 6A1-4V alloys the creep
resistant a-phase is generally thought to dominate the
deformation in the low temperature region (in fact it
is thought to dominate the deformation up to 825°C
because of the relatively low fraction of the fl-phase
present at this temperature, Fig. 5) [10]. For each of
the tests conducted here at 600°C, the microstructure
during the test consisted entirely of this more creep
resistant c~-phase, fl-phase formation was only observed in the sample subjected to the longest testing
time of 14 h at 680°C and even then resulted in only
a 5% fl-phase fraction. Hence, in the low temperature
region, it seems reasonable to treat the PVD alloy as
a single c~-phase system.
To solve equation (8), the temperature dependent
(either 600 or 680°C) material parameters for the
~-phase given in Table 6 were first substituted into
each mechanism in equation (8). A stress was then
selected and thus a time at test temperature to reach
~=, specified (from Table 4). The corresponding grain
size was obtained using equation (3) and substituted
into each mechanism in equation (8). The steady state
strain rate corresponding to the selected value of
stress, temperature and grain size was then calculated
and this process repeated for each of the stresses
used during testing. The resulting model predicted
strain rates were then plotted against stress and are
compared to the experimentally determined data in
Fig. 14(a and b).
10 2 -- ' . . . . . . .
I
........
I
........
I ~
..... I
.......
!
(a) 600°C
~
xperirnent
In = 3.4)
13I"
------
kd + kgbs (n = 2.6)
............
10 0
10 4
. . . . . . . .
I
. . . . . . . .
10 -7
/" /
~d (r} = 4.8)
.....
.....
i
10 4
f-
~d + ~g~ + ~v (n = 2.2)
~:d + Egbs + £v + ~gb (n = 3.5)
........
I
. . . . . . . .
I
~
,
10 -5
10`4
, L~
10 -3
Minimum strain rate ~m~n (1 / s)
2783
At low applied stress (i.e. longest testing time with
the most grain growth) the dislocation + dislocation
accommodated GBS creep (Q + igb~) model best fits
the data. GBS is the dominant contributor to the
strain rate: for both test temperatures and all test
stresses the strain rate contribution due to dislocation
creep is seen to be low, Fig. 14 (a and b). Given the
significant uncertainty in the diffusivity data of Table 6
the agreement between the magnitude of the predicted and the experimentally determined strain rates
appears fairly reasonable. Because grain growth is
lessened by increasing the stress (reducing the time
to reach imp,) the model predicted creep exponent
changes from the values predicted for constant grain
size material (Table 1). When concomitant grain
growth is introduced, the (Q+~g~) mechanisms
model predicts a creep stress exponent ofn = 2.6 even
though the stress dependence of GBS (with no grain
growth) predicts n = 2.
We see that the experimental creep rates at higher
applied stress (finer grain size) were higher than
those predicted by the (Q + g g b s ) model suggesting
an additional diffusive contribution to the overall
creep rate (especially at the 680°C test temperature).
Figure 14 shows the calculated stress-strain rate
relationship when the contribution due to lattice
diffusion, iv, is also included. The additional creep
due to lattice diffusion improves the agreement between model and experiment but reduces the value of
n to 2.2. Adding the contribution from grain boundary diffusion, ggb, results in predicted creep exponent
of 3.5 but the rates are seen to be two to three orders
of magnitude greater than the experimental values.
Langdon has also observed that the predicted grain
boundary diffusional creep rates are often greater
than experimental observations [30]. He attributed
the discrepancy to inhibition of diffusional creep by an
interface-reaction [31]. If grain boundary diffusional
flow is accomplished by dislocation climb in the plane
of the boundary and the boundary dislocations are
free to move, Fig. 15(a), the kinetics of diffusional
flow arc accurately predicted by the expressions in
Table 1. If however, the grain boundary dislocations
interact with solutes residing in the boundary plane,
Fig. 15(b), then the diffusional creep rate can be
10 2
(b) 680°C
O_
~
101
y
v
i/
---
10 0
10 -7
(n = 3.0)
..-"
_ ,
/"
i
,
~k__
4-
~ (n = 4 6 )
......
~d + Egbs (n = 2.6)
...........
~'d + ~:gbs + cv (n = 2.2)
,,,,
-,',~i,-- ~o + ~gbs + ~v + Cgb (n = 2.4)
. . . . . . . . . . . . . . . .
I
, , , ,,,,
10 -s
10 -5
10 `4
10 -3
Minimum strain rate ~mJo (1 / S)
Fig. 14. Predicted true stress vs minimum strain rates for
PVD Ti~AI~4V at: (a) 600; and (b) 680~C.
.--
"-~--
~
----[ .....
J Di~e~ioo
of ehmb
(b)
Fig. 15. (a) Dislocation climb in the grain boundary plane
(Burger's vector is normal to plane); and (b) the climb step
inhibited by solutes located in the grain boundary.
2784
WARREN et al.: HIGH TEMPERATURE DEFORMATION OF Ti-6Al~4V
reduced since the boundary dislocations must either
by-pass the obstacles or drag them along [31]. In the
low temperature region the ~-phase is supersaturated
with the//-stabilizing element vanadium and its segregation to the grain boundaries (where it eventually
forms the intergranular /%phase seen at higher
temperatures) may act to obstruct the climb of
grain boundary dislocations as is depicted in
Fig. 15(b).
It appears to us that deformation in the low
temperature region is dominated by dislocation
accommodated GBS with additional contributions
from lattice and mobility limited grain boundary
diffusional creep (at the highest stresses). The
relatively high creep stress exponent results from
concurrent grain growth during creep testing, and
not from dislocation creep. In cases where a large
microstructural evolution accompanies testing, it
has been demonstrated that mechanistic significance
cannot be ascribed to the value of the creep stress
exponent without first accounting for grain growth.
7.3. High temperature creep mechanisms
Inspection of Table 3 indicates that the apparent
n value was less than two for test temperatures
>~760C. This, in addition to observed creep strains
greater than about two gauge lengths, is normally
indicative of a superplastic behavior. It has been well
established that GBS (accommodated by dislocations
or diffusion) is the primary mechanism responsible
for superplastic deformation of Ti 6AI-4V in the
3-7/~m grain size range [15, 21, 26]. Various workers
have reported that the optimum superplastic forming
temperatures (where the maximum value of m is
measured) are between 870 and 9 4 0 C [9-11, 32, 33]
with variations resulting from alloy compositional
differences.
The phenomenological rate equation for a single
phase, superplastically deforming material is a
modified Dorn relationship
"
where p in the grain size exponent (experimentally
in the 1.5-3.0 range) and D is a diffusion coefficient
(equal to D,. for lattice diffusion accommodated GBS
o r Og b for grain boundary diffusion accommodated
GBS) [27].
Inspection of the modified Dorn relationship for a
single phase alloy shows that reducing the grain size,
d, increases the attainable strain rate during superplastic forming. Equation (10), however, does not
consider the complexities inherent in the superplastic
flow behavior of the two phase alloys encountered in
Ti 6AI-4V above 760C. Experimentally, it has been
found that in order to achieve superplasticity in the
Ti 6AI-4V alloy system both a fine grain size and a
substantial volume fraction of the (less creep resistant)
/j-phase are necessary. In both the conventional and
PVD alloys tested at 760'>C the/j-phase exists at triple
point grain boundary junctions and does not form a
fully interconnected structure. Deformation at 760°C
must therefore involve either ~-~ GBS or plastic
deformation of the ~ grains. The ~-phase is therefore
expected to dominate the deformation behavior although the/J-phase could facilitate a limited amount
of sliding [11].
At 760°C the accommodation mechanism for GBS
could be either dislocation motion or grain boundary
diffusion [34]. Ignoring any microstructural evolution
effects it has been found that in equation 10, n = 2
(m =0.5) for GBS accommodated solely by
dislocation motion and n = 1 (m = 1) for sliding
accommodated solely by grain boundary diffusion.
The experimentally measured creep stress exponent
was determined to be n = 1.7 at 760°C, suggesting a
dislocation accommodated mechanism, however, this
analysis fails to take account of the effects of grain
coarsening on the creep stress exponent. At 840°C, we
note that the "apparent" n value of the experiments
was 1.3, a value more indicative of diffusion accommodated GBS. Further support of this can be found
in the relatively low density of dislocations adjacent
to the a-grain boundary in the specimen tested at
840C, Fig. 11.
To more carefully evaluate which mechanisms are
active, the flow stress strain rate behavior for both
phases in the alloy were assumed to be represented
by the additive contributions of the four independent
mechanisms previously defined in equation (7)
~ c,r /7 = [~d q- ggbs -~- ~v q- ~gbL or #
(11)
where ~ and ~# are the strain rates in the ~- and #phases respectively. The dislocation accommodated
GBS mechanism previously used in the low temperature region results in predicted creep rates at 760°C
that are about 15 times lower than the experimentally
measured values and has therefore been ignored in
the analysis. Hence an alternative mechanism must be
assumed responsible for GBS.
Hamilton et al. [16] have successfully used the
Ashby-Verrall (A-V) [35] mechanism for diffusion
accommodated GBS to model the superplastic
behavior of a conventional Ti-6A1-4V alloy and
obtained agreement with experimentally determined
strain rates to within a factor of about 3 (at a test
temperature of 870°C). We have therefore assumed
that ~gbs, in the high temperature region, can be
represented by the A - V relationship
•
%bs--
,00o v 0
kTd 2
+
~
/t (123
where 6 is the grain boundary width, F is the grain
boundary energy and the remaining parameters were
the same as previously defined.
To model the deformation behavior of a twophase, conventionally processed Ti-6AI 4V alloy,
Hamilton et al. [16] proposed and experimentally
verified that each phase in the alloy experiences
the same strain rate (an iso-strain rate assumption).
WARREN et al.:
HIGH TEMPERATURE DEFORMATION OF Ti~iAI~V
same strain rate (an iso-strain rate assumption). Thus
= i~ = ~r~.
(13)
The applied stress, or, can also be assumed to partition
according to a rule of mixtures
(14)
= V~a~ + Vt~a/~
where V~ and V~ are the volume fractions of the
c~- and/%phases [obtained from equation (4)] at the
creep test temperature, and a~, cr~ are the true stresses
in each phase.
A predicted strain rate was calculated, by solving
equations (11), (13) and (14) simultaneously, for
each experimental creep stress test, temperature,
/~-phase fraction [from equation (4)] and grain size
[from equation (3)]. The predicted g points were
then plotted on a log-log plot, fitted with a straight
line (using a least squares analysis) and compared
to experiment. Figure 16(a-c) compares the experimental results and the model predictions for the test
temperatures of 760, 840 and 900°C, respectively. In
contrast to the low temperature region, we discover
the, at first, surprising result that for all of the test
conditions modeled in the high temperature region
102
. . . .
''"1
......
"1
......
(a) z 6 o o c
,ol
....
O3
experiment (n = 1 7) o
(,t")
Ev + E1~bs -I- I~d (n = l.S) - - 100
10 - 5
E:v + E9bs + Ed + ~:gb (n = 1.5) .....
I
........
I
......
10 - 4
10 - 3
10 - 2
........
10 2
. . . . . . . .
1
.........
.~ ..
(b) 840°C
~15e9
2; t . 101
~
"~':'~ ....
o
experiment (n = 13) o
..i-,
oO
~v + ~ b s +. b.~ (n = 1.1) - - -
10 0
Ev+
........
10-4
10 2
Egbs + Ed + Egb (n = 1.1) ......
I
i
.
.
.
.
.
.
10 - 3
. . . . . . . .
(c) 900°C
i
10 - 2
. . . . . . . .
:.:~":.>. .:.>:';':':"~"
7) o
,~
Ed ( n = 4 7 )
--
i v + E~lbs + E d (n = 1.3) - - 10 0
10-4
,
,
Ev + Egbs + Ed + £gb (n = 13) ......
, , , ,,,I
i
i i i L ii
10 - 3
10 -2
M i n i m u m strain rate
~rnin
(1 / s )
Fig. 16. Predicted true stress vs minimum strain rates for
PVD Ti-6A1-4V at: (a) 760: (b) 840C; and (c) 900':C
A M 43~7
S
2785
the strain rate contribution due to Nabarro-Herring
creep, i~. was very small (between 30 and 90 times
lower than the dominant deformation mechanism)
and could be discounted as a significant mechanism.
This occurs because of the large increase in d (recall
~,. oC l / d 2 ) .
At 760~'C, Fig. 16(a), the dominant mechanism was
the A - V GBS mechanism whose contribution was
nearly 3 orders of magnitude greater than the dislocation creep contribution even at the highest
test stress of 46.2 MPa. Grain growth had the largest
effect on the creep test strain rates conducted at
760"C because a relatively large time difference was
required to reach imm ( ~ 10 min) for the highest and
lowest test stresses (Table 4). Equation (3) predicts
that this results in a 140% increase in grain size.
The effect of concurrent grain growth is to increase
the predicted creep exponent to n = 1.5, Fig. 16(a),
which is in good agreement with the experimental
value of n = 1.7. Thus when concurrent grain growth
is included in the analysis the predicted creep stress
exponent is shifted towards a value of 2; a value more
usually associated with a dislocation accommodated
GBS mechanism, and again emphasizes the need for
careful incorporation of coarsening when seeking to
ascribe a mechanistic significance to creep data.
The (i,. + ~gb~+ ~d) model simulation can be seen to
overestimate the strain rates by factors of about 2 at
the highest stress and about 3 at the lowest stress. By
including the strain rate contribution due to Coble
creep, (~, the simulation for 760°C was even further
from the experimental data again suggesting that the
Coble mechanism overestimates the diffusional contribution to the overall creep r a t e - - b u t to a lesser
extent than in the low temperature region.
The ((~ + ~gb~+ ~d + igb) model predictions for a test
temperature of 840°C are also in good agreement
with experimental data, Fig. 16(b). At 840~C the
model predicted a creep exponent of n = 1.1, which
was quite close to the experimentally determined value
of n = 1.3. The A V strain rate was the dominant
deformation mechanism at all stresses: it was nearly
80 times greater than the dislocation creep strain rate
contribution at the highest test stress (50.2 MPa).
Neglecting the Coble creep contribution resulted in
a modest reduction in the predicted strain rates,
Fig. 16(b) and gave slightly better agreement with the
data. The/~-phase volume fraction at 840'C increased
from 0.09 to 760°C to 0.21 and this may have been
responsible for the decrease in the value of n for two
reasons: (1) the minimum fl-phase volume fraction
required to "break up" the skeletal network of
grains and achieve fully accommodated superplastic
flow is approx. 0.26 [36]; and/or (2) the /~-phase
volume fraction more effectively inhibited concurrent
grain growth during the creep tests.
At 900'C, Fig. 16(c), the experimentally determined
value of n had increased to 1.7. The (g~.+igb~+gd)
model simulation, which incorporated the effect of
grain growth, also predicted an increase although
2786
WARREN et al.: HIGH TEMPERATURE DEFORMATION OF Ti~AI-4V
somewhat lower in value (n = 1.3). Based on the
material properties given in Table 6 the modeling
results predicted that the A-V mechanism was again
the dominant creep mechanism at all test stresses (the
strain rate contribution due to the A-V mechanism at
the highest stress of 30.7 MPa was about 18 times
greater than the dislocation creep contribution). The
simulation also predicted that the dislocation creep
rate behavior of the two phase alloy, which was now
of increasing significance, was dominated by the
dislocation creep parameters of the ~-phase.
Finally we note that at 900°C, the model somewhat
underestimates the measured strain rate at the highest
stress. This could be due to the choice of material
parameters in the analysis. The power law creep
constant, A, is a material sensitive parameter and the
value used in Table 6 is for a 10/tin grain size Ti-6AI
alloy. A "best fit" between the experimental data and
the simulation was obtained by modestly increasing
the e-phase power law creep constant by a factor
of 10, Fig. 17. A creep stress exponent of n = 1.4
was then obtained from the three data points in the
"diffusion accommodated GBS region" of Fig. 17
which was quite close to the value predicted by the
simulation (n = 1.3) over the same region.
To sum up, the GBS mechanism appears to play
a significant role in the deformation behavior of
this PVD alloy in the low temperature region and
a dominant role in the high temperature region. The
accommodation mechanism is either dislocation (at
low temperature) or diffusional (at high temperature):
the transition occurs at between 680 and 760cC due
to the more rapid diffusional kinetics and the formation of the high diffusivity /3-phase. Grain growth
during testing has resulted in subtle, but important,
changes in the relative contribution of the various
creep mechanisms. An example of this is the relatively
significant contribution of volume diffusion at 600C
and high stress because of the reduced amount of
coarsening. With the exception of the Coble creep
mechanism listed in Table 1 and introducing time and
temperature dependent microstructural parameters
provides a reasonable approach for the constitutive
10 2
modeling of materials whose microstructure evolves
during deformation processing.
8. CONCLUSIONS
1. A physical vapor deposition process has been
used to produce a Ti 6AI-4V alloy sheet which, in
the as-deposited condition, had a metastable, fully
dense, nanocrystalline (30-100nm) microstrueture
with a chemical composition practically identical to
the source material. When the as-deposited alloy was
heated to between 600 and 680°C a predominately
single phase (~) microstructure, with a sub-micron
grain size, formed. Between 760 and 900°C a
two-phase (~ +/~) microstructure was formed whose
fl-phase volume fraction increased rapidly above
approx. 850"~C. The PVD deposited alloy exhibited
sluggish grain growth kinetics (as evidenced by grain
growth exponents of about 0.2) between 600 and
900C.
2. Creep tests performed on the PVD material
between 600 and 680°C exhibited exceptionally high
creep rates (compared to conventionally processed
Ti-6A1 4V) with creep stress exponents greater than
3. Langdon's model of dislocation accommodated
GBS in conjunction with the added contribution of
mobility limited diffusional flow has been used to
explain the observed behavior. By incorporating the
effects of concurrent grain growth in this analysis,
creep stress exponents approaching 3 were predicted
(consistent with experimental observations) even
though the stress dependence for GBS, with no grain
growth, predicts n = 2.
3. Enhanced superplastic behavior was observed
when the PVD alloy was creep tested between 760
and 900°C. The dominant creep mechanism was
shown to be diffusion accommodated GBS. The
transition in the deformation mechanism occurred
concurrently with the appearance of the (more deformable) fl-phase. The Ashby-Verrall model, solved
by considering the flow stress strain rate behavior
of each phase simultaneously, the phase fractions
present at test temperature and the effect of concurrent grain growth has predicted, with reasonable
accuracy, the superplastic behavior of the two-phase,
PVD alloy.
o e~
- - A
---
Acknowledgements--We are grateful to J. Storer (3M) for
supplying the material used in this study and to J. A. Wert
for many helpful discussions about superplasticity in
Ti 6AI-4V.This work has been supported by the Advanced
Research Projects Agency (W. Barker, Program Manager)
and the National Aeronautics and Space Administration
(R. Hayduk, Program Monitor) through grant NAGW-1692
and through the ARPA/ONR funded URI program at
UCSB.
IV
rl
T = 90~
10 0
10 4
10 ~3
10 _2
Minimum strain rate ~nvin (1 / s)
Fig. 17. Stress-strain rate prediction based on a modified
e-phase power law creep constant.
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