Scripta Materialia, Vol. 34, No. 6, pp. 897-902, 1996
Elsevier Science Ltd
Copyright 0 1996 Acta Metallurgica Inc.
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THE TRANSIENT CREEP OF VAPOR
DEPOSITED Ti-6Al-4V
J. Warren
Philips Lighting Company
High Intensity Discharge Lamp Development Laboratory
7265 Route 54, Bath, NY 14810 USA
H.N.G. Wadley
Department of Materials Science and Engineering
University of Virginia, Charlottesville, VA 22903 USA
(Received September 13, 1995)
1. Introduction
Titanium matrix composites can be synthesized by the consolidation of ceramic fibers (for example,
alumina and sihcon carbide monofilaments) coated with titanium alloy deposited on the fiber by physical
vapor deposition (PVD). Consolidation involves deformation of the matrix coating by both transient and
steady-state creep. In a recent paper (1) the mechanisms responsible for steady-state creep in PVD Ti-6AI4V, between 600” and 9OO”C,were determined. Tensile specimens were fabricated from nanocrystalline
PVD sheet and, in the as-deposited condition, heated to test temperature and crept under constant load
conditions. In addition to temperature and stress, the constitutive behavior was found to also depend upon
time-dependent microstructural features namely the grain size and, at temperatures greater than 68O”C,
the nucleation and subsequent growth of a BCC p-phase within a vanadium supersaturated HCP a-phase
“matrix”. It was concluded that conventional models for grain boundary sliding, accommodated by grain
boundary dislocations at low temperatures and grain boundary diffusion at high temperatures, adequately
modeled the observed behavior when both the time-dependent grain size and p-phase volume were
incorporated. This was then used to develop a time and temperature dependent constitutive response that
could be used to model the consolidation process (2).
The analysis of the data first presented in (1) has been extended here to consider the transient creep
behavior of the material and identify an analogous constitutive law for use in simulating the transient creep
contribution to consolidation.
2. Experimental
Data
The experimental results of constant load creep tests conducted on PVD Ti-6Al-4V specimens between
600” and 9OO”C,obtained from (l), has been reproduced in Table 1. The results of two additional creep
experiments (not presented in the original work) conducted at 950°C using the same experimental set-up
as described in (1) are also included in the table.
897
898
TRANSIENT CREEP
Vol. 34, No. 6
TABLE I
Experimental Data Obtained from Ref. (1) and Used In This Analysis
900
10.9
6.6 10”
42
1.2
9,
900
5.8
2.6 lo-’
78
1.2
1,
950
23.6
3.4 10”
4
>1.1*
>0.50*
950
6.6
4.4 lo-+
42
I,
,I
*estimated values
For each isothermal creep test the true stress IJ, steady-state creep rate ‘e, transient creep stage duration
or relaxation time t, (3), average grain size d (at t, ), and p-phase volume fraction present in the
microstructure at the time the creep load was applied (t = 0) is shown in Table 1. The transition from
Vol. 34, No. 6
TRANSIENT CREEP
1E-l
--
T~------l---
r--
~-
A=0.02255
1E-2
_
w
I
899
lE-3
ZlE-4
v)
.w
1E-5
*
950°C
0
900°C
(3
A
840°C
lE-6
1E-7
+
680°C
+
lE+O
760°C
600°C
.__-_, _.__.__
__ [__. ___
lE+l
lE+2
_...-.____._ __ --.,---...--
lE+3
tr
lE+4
lE+5
i
1
lE+6
w
Figure 1. Relationship between steady-state creep and the relaxation time.
transient creep to steady-state creep occurred, for each test, at a true strain of approximately 0.04 (4%).
This strain vahre, referred to as the asymptotic strain (4) and denoted by er, will be considered constant.
3. Discussion
In Fig. 1 the log of the steady-state creep rate, &,,has been plotted against the log of the relaxation time,
t,. A straight line fit to the data points was found using a least squares analysis and the highest correlation
with the data was obtained with an expression of the form
where A is a dimensionless constant. The relationship is essentially invariant over a wide range of stresses,
test temperatures, grain sizes and p-phase tractions and strongly suggests that the rate-controlling process
responsible for transient creep in the PVD material obeys a first-order chemical kinetics model as proposed
by Webster et d(3). This model assumes that the velocity of individual dislocation segments depends
900
TRANSIENT
Steady-State
CREEP
Vol. 34. No. 6
TABLE 2
Creep Parameters for PVD Ti-6AL4V (I)
T(“C)
Creep stress exponent, n
B (I/(sec Mpa”))
600
3.30
3.6 lo-”
680
3.00
1.2 IO-9
760
1.70
1.6 10”
840
1.34
1.9 10-S
900
1.70
1.2 IO-5
950
1.57
2.3 IO-’
upon the diffusive flux of vacancies to and from sites on dislocations and this diffusive flux can be fully
described by a first-order chemical kinetics relationship.
Since the dislocation structure changes during
transient creep (4) it is further assumed that the rate of change itself, which depends upon dislocation
velocity, also obeys the first-order chemical kinetics relationship.
The relaxation time, t,, is a measure, albeit indirect, of the rate-controlling
processes responsible for
the hardening observed during transient creep and measures, directly, the time required to form the
invariant substructure responsible for steady-state creep. According to Webster ef al (3) this process is
the same one which controls steady-state creep. Hence, the two parameters are related and must differ
only by a constant of proportionality as has been experimentally verified here (Eq. 1). The mechanism
responsible for steady-state creep in the PVD alloy was grain boundary sliding accommodated by grain
boundary dislocations at low temperatures and grain boundary diffusion at high temperatures (1). Figure
1 shows that the proportionality
between both the relaxation time and the steady-state creep rate is
maintained even though a change in the accommodation mechanism has occurred. This result suggests
1) that a proportionality
between the steady-state strain rate and the relaxation time will be observed
provided each is governed by the same rate-controlling process regardless of the actual mechanism and
2) that grain boundary sliding must also be responsible for transient and steady-state creep deformation
in the PVD alloy.
Based on first-order chemical kinetics theory (3), the transient and steady-state creep strain of PVD
Ti-6Al-4V can then be expressed as
where t is the instantaneous
creep time.
E
The steady-state
=
q
Substituting
-
Eq. 1 into Eq. 2 results in
@(- !ft))+
ist
(3)
creep rate, ‘e,,can be expressed as a simple power law relationship
k, = Bo”
(4)
TRANSIENT
Vol. 34, No. 6
0.25
I’_
1
OM
.
LL-
.’
l.
030
0.02
,
,
,
,
,
,
-4
experiment
T..T.--T7._-_I__-T--
1
50
40
,
0
,
,
,
10
,
,
,
,
,
0.10
,
-
r-----l--7-y
I
,
,
,
20
,
experiment
,
30
,
,
,
40
50
,
I
,
,
,
,
60
,
70
0
80
-
Mb&r
--+-
experiment
, -_.-r--._
0.00 :.
, -
et al (2)
eo
20
00
timZ (s)
1 -T-T7--‘-
0.08
,
680°C
‘lo- 17.0 MPa
,.*’
008-
w
I
0.02 -
Webster et al (2)
time (s)
0.12
200
760°C
o.w_ 31.2 MPa
-+
.
loo
-I---
0
40
rrne 67
840°C
0.00,
\Mebateret al (2)
-
(sg
,
-I
900°C
vr---T--
10
,
T
WE- 5.8 MPa
experimental
-r-7--
f%le
_~._~_.~‘_~_~~~~~~
Webster et al (2)
-+
0
0.10
-I
950°C
0:~)
901
CREEP
0.04
0.06-
W
0.02
-
Wabater et al (2)~-
- -+ -
experiment
0.00
0
laoo2OoO3xm4Oalxm6Om7Ow
result, taken from each test temperature,
-
--r--r---r----7_
0
2mOo4Oom6aaOaOOOo
time (s)
Figure 2. An experimental
VUBbateretal(2)
time (s)
and compared
to the strain response predicted by Eq. 5.
where B is a temperature dependent constant and n is a temperature dependent creep stress exponent (see
Table 2). Substituting both Eq. 4 and the values for A and eI into Eq. 3 results in a constitutive
relationship which describes the transient and steady-state creep of this alloy between 600” and’950”C
TRANSIENTCREEP
902
E = 0.04 (1
-
Exp
(-44.35 Ba”t)) + Bo”t
Vol. 34. No. 6
(5)
Fig. 2 shows the experimental creep strain response of one sample, selected from each set of test
temperatures, compared to the predicted response based on Eq. 5. The figure shows that the accuracy of
the strain response predicted by Eq. 5 varies somewhat over the temperature range of the tests (note
especially the discrepancy at 760°C). Small adjustments (compared to the experimental uncertainty) in
the creep stress exponent, n, in Eq. 5 can force exact fits to the data.
The form of the transient creep model (5) is well suited for consolidation modeling where conditions
are usually isothermal so that values of B and n can be selected from Table 2.
Acknowledgments
This work was conducted with financial support provided by the Advanced Research Projects Agency (W.
Barker, Program Manager) and the National Aeronautics and Space Administration (D. Brewer, Program
Monitor) through grant NAG W- 1692.
References
1.
2.
3.
4.
J. Warren, L.M. Hsuing and H.N.G. Wadley, Acta metall. mater., vol. 43, no. 7, pp. 2773-2787 (1995).
J. Warren, D.M. Elzey and H.N.G. Wadley, Acta metall. mater., vol. 43, no 10, pp. 3605-3619 (1995).
G.A. Webster, A.P.D. Cox and J.E. Dorn,MetulSci,
J., vol. 3, pp. 221-225 (1969).
S. Takeuchi and A.S. Argon, .I. Mat. Sci., vol 11,pp. 1542-I 566 (1976).