Creep behaviour and creep microstructures of a
high-temperature titanium alloy Ti–5.8Al–4.0Sn–3.5Zr–
0.7Nb–0.35Si–0.06C (Timetal 834)
Part I. Primary and steady-state creep
M. Es-Souni*
Materials Testing and Joining, University of Applied Sciences, Grenzstrasses 3, D-24 149 Kiel, Germany
Received 4 January 2001; received in revised form 19 February 2001; accepted 1 March 2001
Abstract
The tensile creep behaviour of the high-temperature near a-Ti alloy Ti–5.8Al–4.0Sn–3.5Zr–0.7Nb–0.35Si–
0.06C (Timetal 834) with a duplex microstructure has been extensively investigated in the temperature range from
500�C to 625�C and the stress range from 100 to 550 MPa. Both primary and secondary creep are being
considered. The results of the primary creep are analysed in terms of the dependencies of stress on strain (strain
hardening) and on strain rate (strain rate sensitivity). It is shown that the strain-hardening exponent depends on
temperature, and takes values between 0.5 for 500�C and 0.33 for higher temperatures; this would give a
dependence of the primary creep strain of s2 and s3. The strain rate exponents obtained in both primary and
secondary creep have been found to be similar; this is also the case for the activation energies. It is thought that, in
the stress and temperature range investigated, creep is controlled by bow-out and climb of dislocation segments
pinned at lath boundaries and second-phase particle. Analysis of the dislocation substructure is presented to give
some support for this mechanism. D 2001 Elsevier Science Inc. All rights reserved.
Keywords: Ti alloys; Primary creep; Stress-dip; Strain hardening; Strain recovery
1. Introduction
The search for alloys with improved high-tem-
perature specific strength and creep-resistance prop-
erties for aerospace applications has led in the last
decades to sustained research activities to develop
new alloys and/or improve existing ones. A sub-
stantial part of these activities has been devoted to
Ti alloys, due to their high strength-to-weight ratio
[1,2], and among these alloys, the intermetallics
based on Ti aluminides (g-TiAl, a2-Ti3Al-Nb) have
received a strong interest, with the aim to extend the
temperature range of utilisation of conventional Ti
alloys, which levels at 600�C [2]. However, due to
intrinsic brittleness, lower creep resistance than
conventional Ni base alloys, environmental sensitiv-
ity, and high processing cost, the Ti aluminides are
believed to be at best suited for high-temperature
components with low-toughness specifications [2].
In contrast, conventional Ti alloys enjoy an ever-
increasing market share in aerospace materials, and
a substantial data on controlling microstructure and
properties, machining, welding, corrosion, standards,
etc. are available [3].
1044-5803/01/$ – see front matter D 2001 Elsevier Science Inc. All rights reserved.
PII: S1044 -5803 (01 )00136 -X
* Tel.: +49-431-210-2660; fax: +49-431-210-62660.
E-mail address: [email protected] (M.
Es-Souni).
Materials Characterization 46 (2001) 365–379
Ti alloys offer, through control of processing
history and microstructure, a wide range of proper-
ties. Good high-temperature strength and creep-
resistance properties are usually obtained with near
a-Ti alloys containing Al, Zr, Sn, Mo, and Nb in
variable amounts as well as a small concentration of
Si in the range from 0.2 to 0.3 wt.% [3–5]. The
microstructure usually consists of coarse trans-
formed b grains containing interlocked a laths
separated with thin retained b films; avoiding grain
boundary a and/or primary a grains is generally
considered of benefit to the creep properties [4,5].
However, a good balance between creep, toughness,
and fatigue resistance properties are obtained with
microstructures containing approximately. Fifteen
percent of primary a interspersed with fully trans-
formed b grains [4,5].
Creep of metals and alloys is generally analysed
in terms of steady-state or secondary creep, where,
depending on stress and temperature, a number of
mechanisms have been advanced to account for the
accumulation of strain as a function of time (for an
overview, see Refs. [6,7]). However, in engineering
applications, the creep strain has to be kept so low
that in many alloy systems, the primary creep
regime is rarely exceeded. It is, therefore, surprising
that few work [8–12] has dealt with the under-
standing of the mechanisms of primary creep in
engineering alloys, and a detailed experimental work
is still lacking.
High-temperature Ti alloys, including a2-Ti3Al-
and g-TiAl-based intermetallic alloys, are generally
characterised by a pronounced primary creep regime
[12,13]; the rate-controlling mechanisms have been
discussed in terms of bow-out of pinned dislocation
segments at interfaces in the case of g-TiAl [12] and
in terms of the rate of annihilation of dislocations at
lath and grain boundaries in the case of a2-Ti3Al
[13]. In a recent work [14–16], it has been shown on
the conventional near a-Ti Alloy Ti6242Si that the
primary creep can be analysed in terms of strain
hardening and strain recovery, which is thought to
allow a better understanding of the primary creep
mechanisms. Furthermore, full unloading experi-
ments and corresponding investigations of the ane-
lastic creep recovery showed the similarities of the
kinetics of primary and anelastic creep. It was
inferred, with support of TEM investigations of
dislocation structures, that primary creep is, to some
extent, anelastic in nature and is dominated by climb-
controlled bow-out of pinned dislocation segments.
In order to contribute to further understanding of
creep mechanisms and how they are affected by
microstructure and alloying effects, the present work
has been conducted on the high-temperature near
a-Ti alloy Ti–5.8Al–4.0Sn–3.5Zr–0.7Nb–0.35Si–
0.06C (Timetal 834), which is supposed to be creep-
resistant up to 600�C. In addition to steady state, a
detailed investigation of the kinetics of primary creep
has been conducted. The tensile creep stresses and
strains were kept low, so as to insure practical rele-
vance of the experiments. The results are discussed in
terms of strain hardening and strain rate sensitivity
and their dependencies on stress and temperature. In
a forthcoming paper, the kinetics of anelastic recov-
ery and their dependencies on stress and temperature
will be presented.
2. Experimental
The alloy investigated was supplied by TIMET
UK as rectangular, rolled plates of 17-mm thickness.
The cast analysis and the corresponding b-transus
Table 1
Cast analysis and b-transus temperature of the alloy under investigation
Analysis (wt.%) Al Sn Zr Nb Mo Si C Fe O N H
Top 5.77 4.05 3.53 0.69 0.53 0.30 0.07 0.006 0.110 0.0015 0.0020
Bottom 5.71 3.97 3.74 0.67 0.52 0.34 0.06 0.008 0.105 0.0025 0.0020
b-transus temperature top and bottom: 1050/1055�C
Top and bottom refer to the top and bottom of the rolled plate, respectively.
Table 2
Mechanical properties at room temperature and 600�C
Specimen Temperature (�C) Rp0.2 (MPa) Rm (MPa) A5 (%) Z (%)
Top RT 923 1038 13.0 26.0
Bottom RT 934 1055 11.5 25.0
Top 600 521 666 20.5 60.0
Bottom 600 509 670 16.0 57.0
Rp0.2 = proof stress at 0.2% plastic deformation; Rm= ultimate tensile strength (UTS); A5 = fracture strain (L0 = 5d0);
Z = reduction in area.
M. Es-Souni / Materials Characterization 46 (2001) 365–379366
Fig. 1. (a) Light micrograph of the as-received duplex microstructure. Primary a particles (bright contrast) and the fine
Widmannstatten structure of the transformed b grains are shown. (b) BSE micrograph of the as-received microstructure shows
coarsened b particle at the primary a boundaries and bright contrast contours (long arrows). Notice also the presence of small
dark dots indicating the presence of coarse silicide particles (short arrows). (c) BSE micrograph of the heat-treated condition.
Notice spheroidisation of the thin b films and the presence of bright contrast dots. (d) High-resolution BSE micrograph of the
same area as above. Notice dark dots indicating the coarsening of the silicide particles. (e) Starting dislocation substructure in an
a lath, notice the curved dislocations pinned at lath boundaries. g= h1010], B near h1213]. (f) Semi-coherent Ti5(Si,Zr)6 silicide
particles in an a lath.
M. Es-Souni / Materials Characterization 46 (2001) 365–379 367
temperature provided in the test report are given in
Table 1. The tensile properties of the as-received
condition (hot-rolled and heat-treated following the
scheme: 1022�C/2 h/oil quench + 700�C/2 h/air cool-
ing; this is an aerospace standard procedure that
provides approximately 15% primary a) are summar-
ised in Table 2.
The procedures for creep testing, apparatus, and
data handling are described in the Ref. [15] and
follow the recommendations of Evans and Wilshire
[7]. The specimens with a diameter of 8 mm and a
gage length of 50 mm, containing machined ridges
for extensometer grips, were machined from the as-
received bars, with the tensile axis being parallel to
the rolling direction. They were ultrasonically
cleaned in acetone and dried before testing or heat
treatment. The specimens were tested in the as-
received and heat-treated conditions. The heat treat-
ment was conducted in an argon atmosphere follow-
ing the scheme: 910�C/1 h/AC+ 643�C/24 h/AC.
This is not a standard recommended heat treatment
for this alloy. It has been conducted in order to help
understand the creep mechanism of the alloy, partic-
ularly as to the influence of silicide precipitates and
alloying elements in solid solution.
Constant stress tensile creep tests were conducted
in air under a stress range from 100 to 550 MPa and a
temperature range from 500�C to 625�C; the temper-
ature was controlled to ± 0.5�C in a three-zone
furnace using one set of three Pt/PtRh thermocouples
and PID controllers. The creep elongation was meas-
ured by means of one set of two linear variable
differential transformers, allowing a relative accuracy
of 0.1% over the whole elongation range. Both static
and stress dip tests were carried out; the tests were
usually run up to a plastic strain far below 1%. With
regard to the stress dip experiments, it should be
pointed out that partial unloading from the initial
stress was always conducted after a similar level of
prestrain has been achieved (usually 0.008), since the
degree of prior deformation determine the stress
response of the microstructure upon partial loading.
The data sampling rates were chosen as follows: 100
data sets per minute during loading and unloading
and 2 data sets per minute during the remaining
testing time.
Microstructures were investigated by means of
light microscopy on specimens etched with Klemm
reagent. Analytical scanning electron microscopy
(SEM, Philips XL30 +EDAX SUTW detector) was
conducted on polished, nonetched specimen surfaces
using the back-scattered electron (BSE) imaging
mode. Transmission electron microscopy (TEM, Phi-
lips CM 30) studies were performed on thin foil
specimens prepared using twin-jet electrolytic polish-
ing in a 5% perchloric acid solution at � 20�C.
3. Experimental results
3.1. Initial microstructures
The initial microstructure of the as-received con-
dition consists of fine transformed b grains with the
characteristic Widmannstatten structure and approx-
imately 17% of globular, primary a grains (Fig. 1a).
Investigations of longitudinal and cross-section speci-
mens revealed a quite regular microstructure with, as
far as can be revealed by light microscopy, no marked
texture. Thin grain boundary a grains/films can also
be seen decorating the primary b grains. The mean
grain size of prior b grains was determined by the
linear intercept method for two-phase microstructures
advised by Ref. [17] to be 70 ± 5 mm; a mean primary
a particle size of 8 ± 2 mm was also found using the
same method.
SEM investigations on polished, nonetched speci-
mens using the BSE imaging mode reveals that the alaths are separated by discontinuous b films (bright
contrast), which, in many areas, have undergone
Fig. 2. Examples of the creep curves for the two
microstructures at 500�C and different applied true stresses.
Fig. 3. Primary creep strain as a function of true stress. The
primary creep strain was determined by the intercept
method. AR= as-received; HT= heat-treated.
M. Es-Souni / Materials Characterization 46 (2001) 365–379368
spheroidisation (Fig. 1b). At the boundaries between
transformed b grains and globular primary a, coars-ened b particles can also be seen. An EDS semi-
quantitative analysis of these particles shows that
they are enriched with Mo and Nb, in comparison
to the matrix. Furthermore, close examination of the
globular a grains reveals a brighter contrast of the
areas immediately adjacent to the transformed b, viz.to the coarse b particles, which suggests that the
particle growth may be the result of diffusion flux
of the b-stabilising elements (Mo, Nb) from the bulk
of the a grains.
Heat treatment following the scheme mentioned
above does not change the volume fraction of
globular a. However, a pronounced spheroidisation
of the b particles can be seen (Fig. 1c). Using the
high-resolution imaging mode at low acceleration
voltage (e.g., Fig. 1d), it can be seen that the density
of dark dots has considerably increased, denoting a
substantial precipitation and/or coarsening of silicide
particles during the heat treatment at 910�C.TEM of the starting substructure shows a high
density of curved dislocation segments, usually
pinned at lath boundaries, as illustrated in Fig. 1e.
These dislocations are of the type h1120] and were
also observed in the globular a grains. The presence
of semicoherent silicide particles in inner lath and at
their boundaries is illustrated in Fig. 1f. The semi-
coherent particles has been reported [18], based on
electron diffraction investigation in an alloy of similar
composition after solution and ageing treatments, to
be of the type TiZr6Si3.
3.2. Primary creep behaviour
Fig. 2 shows examples of the creep curves
obtained at 500�C under the different stresses indi-
cated. Due to the small strains involved and the high
data sampling rates, the data are badly scattered,
particularly at low temperatures and/or stresses.
The primary creep strain is usually determined
by the intercept method, i.e., the intercept of the
regression line to the steady-state portion of the
creep curve with the strain axis at t = 0. Though
this method can lead to erroneous results particularly
at low stresses, where steady state is difficult to
discern, Fig. 3 shows the primary creep strain vs.
stress obtained at the different temperatures indi-
cated. Apart from the values at low stresses, primary
creep is seen to generally increase with increasing
stress. Furthermore, at 500�C, the primary creep
strain seems to increase linearly with increasing
stress for both microstructures. As the temperature
increases, the primary creep strain saturates at lower
values. Considering the effect of microstructure on
the magnitude of primary creep strain, it can be seen
that the as-received condition is characterised by an
overall lower primary creep strain than the heat-
treated one. Fig. 3 shows also that the primary creep
strains obtained at 600�C by the intercept method
are lower than those at 500�C and 550�C, and
apparently have a weak dependence on stress. For
Fig. 4. Examples of the dependence of the primary creep
strain rate on the primary creep strain.
Fig. 5. (a) Double logarithmic plots of the primary creep strain vs. true stress at constant strain rate. (b) Double logarithmic plots
of true strain vs. stress at different constant strain rates.
M. Es-Souni / Materials Characterization 46 (2001) 365–379 369
this reason, it is believed that the intercept method
fails to give an appropriate description of the
dynamic nature of primary creep and its depend-
encies on stress and temperature. An appropriate
method is presented below.
Primary creep can be regarded as a regime of creep
where two phenomena are concurrent: strain harden-
ing due to long range dislocation interaction, which is
responsible for the gradual decrease of the creep strain
rate, and strain recovery due to thermal activation of
short range dislocation movement. To account for
these two phenomena, the primary creep strain, epr,can be expressed as a function of stress, s, at constantstrain rate, by an empirical relation of the form:
epr ¼ Cs1m ; ð1Þ
where m is the strain-hardening exponent and C is a
constant dependent on strain rate and temperature. A
similar empirical relation can be used to express the
dependency of the primary creep strain rate on stress
at constant creep strain:
_epr ¼ C0s1n ; ð2Þ
where C 0 is a constant dependent on the stain and
temperature.
For this analysis to be accomplished, the strain
rate vs. strain curves are to be plotted, which presup-
poses that the strain– time curves are to be differ-
entiated. Due to the low strain variations and the high
sampling rates involved, the raw curves could not be
exploited. Therefore, these were first smoothed either
by recalculating the curves using an appropriate
fitting function or by average smoothing and differ-
entiation using a commercial software.
Plotting the creep rate vs. creep strain in a double
logarithmic scale leads to the creep curves exempli-
fied in Fig. 4. It can be seen that in the primary creep
regime, the dependence of the creep rate on creep
strain is linear and tends to a minimum as steady state
is approached. In the linear portion, the primary creep
rate can be expressed as:
_e ¼ Ae�p; ð3Þ
where A and p are constants dependent on stress and
temperature. Until otherwise stated, it is the linear
portion of the creep curve that has been taken into
account for the analysis below.
Fig. 5a shows the dependency of the primary
creep strain on stress at different temperatures for
the as-received and heat-treated conditions. In all
cases, the double logarithmic plots give straight
lines and indicate that Eq. (1) is valid for the stress
dependence of the creep strain at constant strain
rate. The values of m are given in Table 3 at the
indicated constant creep strain rates. These values
Table 3
Strain-hardening exponent, m, for the different temperatures
and constant strain rates indicated (see also Fig. 4c)
Temperature
(�C)As-received
m/_e (s � 1)
Heat-treated
m/_e (s � 1)
500 0.48/1�10� 8 0.51/2� 10� 8
550 0.35/5� 10� 8 0.33/1.10� 7
600 0.38/5� 10� 7 0.39/4� 10� 7
Fig. 6. (a) Double logarithmic plots of the primary creep
strain rate vs. true stress at constant primary creep strain. (b)
Double logarithmic plots of the strain rate dependence on
the stress at 500�C showing the variation of the slope at
different constant strains. (c) Double logarithmic plots of the
strain rate dependence on the stress at 600�C.
M. Es-Souni / Materials Characterization 46 (2001) 365–379370
depend strongly, however, on the strain rate, as
exemplified by Fig. 5b: At high strain rates, that is
at the beginning of the creep curve, the strain-
hardening exponent is highest, that is the stress–
strain curve is steepest; as the strain rate decreases,
that is approaching the steady-state creep rate, m
decreases and the slopes of stress–strain curves
become weaker. Nevertheless, it can be stated that
at high strain rates and/or low temperatures, the
primary creep strain depends on the square of the
applied stress; as the strain rate decreases, a cubic
dependence is approached.
The stress dependence of the primary creep
strain rate at constant strain is shown in Fig. 6
for both conditions. The double logarithmic plots
can also be well approximated by regression lines
and Eq. (2) is valid for the dependence of the
primary creep rate on stress. The values of n are
listed in Table 4.
For the constant creep strains indicated, it can be
seen that the strain rate sensitivity coefficient varies
between 0.15 and 0.23; it is lowest for the as-received
condition at 500�C. However, as illustrated in Fig. 6b,the values of n depend on the creep strain. At low
creep strains, the strain sensitivity exponent first takes
low values and then increases with the primary creep
strain. Furthermore, it can be seen that n varies more
strongly with the creep strain at lower temperatures
(Fig. 6b and c), since at 600�C very similar values of
n are obtained at strains in the range from 2� 10� 4
to 9� 10� 4.
3.3. Steady-state creep
The steady-state creep rates have been determined
from specimens loaded to the given stresses. Partic-
ularly at the lower temperatures and/or stresses,
steady-state creep was difficult to identify; the speci-
mens were probably still in the primary creep regime
and this might explain the scatter in the data under
these particular testing conditions. The stress depend-
ence of the steady-state creep rate for both conditions
is illustrated in Fig. 7 in double logarithmic plots.
Each data set can be well fitted to a regression line
that indicate the validity of power law creep of the
form (Eq. (4)):
_ess ¼ As1nss ; ð4Þ
where _ess is the steady-state creep rate (in s� 1), A is a
constant, and nss is the strain rate exponent in the
secondary creep regime. The results also show that
the as-received condition is characterised by a higher
creep resistance. The strain rate exponents, nss,
obtained at the different temperatures are shown in
Table 5. They lie between 0.19 and 0.24, and
correspond to stress exponents, nss� 1, in the range
from 4.1 to 5.2 with the lowest value being obtained
for the heat-treated condition at 500�C.
3.4. Stress dip experiments
Stress dip experiments have been reported to
deliver useful information about the mechanisms of
transient creep through the constant structure creep
rate (CSCR), i.e., the forward creep rate established
immediately after a stress reduction from the initial
stress [19]. In this work, stress dip experiments were
performed for both conditions at 550�C and an initial
stress of 400 MPa.
The creep curves are shown in Fig. 8. For small
stress reductions, forward creep takes place immedi-
ately after partial unloading; however stress reduc-
tions to 300 MPa, and lower, result in anelastic
recovery, i.e., negative creep, which, before forward
Table 4
Values of the strain rate exponent, n, at the indicated
constant primary creep strain (in parentheses) according to
Eq. (2)
Temperature
(�C)As-received
n (e= cte)Heat-treated
n (e = cte)
500 0.15 (2� 10� 4) 0.23 (4� 10� 4)
550 0.20 (2� 10� 4) 0.17 (3� 10� 4)
600 0.20 (2� 10� 4 0.19 (3� 10� 4)
Fig. 7. Stress dependence of the steady-state creep rate for
the microstructures investigated at different temperatures.
Table 5
Strain rate exponents, nss, values for steady-state creep at
different temperatures
Temperature (�C) As-received nss Heat-treated nss
500 0.19 0.24
550 0.19 0.22
600 0.21 0.22
M. Es-Souni / Materials Characterization 46 (2001) 365–379 371
creep becomes again predominant, is followed by a
period of net zero creep rate. The duration of negative
creep was found to depend on the amount of stress
reduction, i.e., large stress reduction from the initial
stress resulted in a longer duration of negative creep.
The forward creep rate immediately following
stress reduction, which has been termed ‘‘constant
structure creep rate’’ because the dislocation structure
is believed to remain constant immediately following a
sudden stress reduction [19], is plotted as function of
stress in Fig. 9a and b for the as-received and heat-
treated conditions, respectively. In the case of the heat-
treated condition, a linear dependence is obtained in a
double logarithmic scale and a strain rate exponent of
0.21 is obtained. Compared to the steady-state creep
rate, obtained from the same stress reduction creep
curves at longer time, it can be seen the ‘‘CSCR’’ is
apparently lower than steady-state creep, particularly at
low stresses. However, the steady-state creep rates
obtained from single-load specimens practically super-
pose to the ‘‘CSCR,’’ as illustrated in Fig. 9b. The strain
rate exponents obtained from the three curves lie all in a
very close range (0.21, 0.22, 0.21). With regard to the
as-received condition, a similar behaviour is observed,
though the data were more scattered (Fig. 9a). The
strain rate exponents obtained are 0.23 and 0.22 for the
‘‘CSCR’’ and steady-state creep, respectively. How-
ever, given the natural scatter in the creep data, it is
concluded that there is no significant difference among
the different creep rates plotted in Fig. 9a and b.
3.5. Activation energy
The activation energies for primary and steady-
state creep were determined at constant stress assum-
ing an Arrhenius-like relationship between the creep
rate and temperature of the form (Eq. (5)):
_e ¼ ks1nexp � Q
RT
� �; ð5Þ
where k is a constant, Q is the apparent activation
energy for creep, R is the gas constant, and T is the
absolute temperature. At constant stress, Q is
obtained from Eq. (6):
@log_e@ 1
T
� � !
s
¼ � Q
R: ð6Þ
The apparent activation energy for steady-state creep
was determined by means of temperature change
experiments maintaining the applied stress constant
and/or from the creep curves obtained at different
temperatures at constant stress. Fig. 10a shows the
linear dependence of the natural logarithm of the
steady-state creep rate of the as-received condition
on the reciprocal of the absolute temperature. The
apparent activation energy obtained from the slope
was found to be 345 kJ/mol � 1. A lower value of
330 kJ/mol � 1 was found when the steady creep rate
values are taken from Fig. 7 at the same stress of
300 MPa (Fig. 10b). The heat-treated condition is
characterised by a lower activation energy, which
was found to apparently depend on stress; the values
are 304 kJ/mol� 1 at a stress of 350 MPa and 287
kJ/mol � 1 at 300 MPa (Fig. 10b). These apparently
Fig. 8. Strain vs. time for stress dip experiments. Notice
negative creep upon large unloading stresses.
Fig. 9. Stress dependence of the CSCR for the as-received
(a) and heat-treated (b) microstructures at 550�C. Compar-
ison with steady-state creep rate from single-load specimens
and from stress dip are also shown.
M. Es-Souni / Materials Characterization 46 (2001) 365–379372
different values are, however, believed to arise from
the insufficient number of data and their scatter,
since if there were a real dependence of the
activation energy on stress a lower value would
have been found at the higher stress. The activation
energy of creep corresponding to the heat-treated
condition is therefore thought to be in the range
between the values given above, but probably in the
vicinity of 304 kJ/mol � 1, since at the higher stress,
the onset of steady-state creep is more easily
identified, and the steady-state creep rates deter-
mined at 350 MPa are more likely to be very close
to the real ones. The values determined here all lie
below those reported by Anders et al. [4], who
found an activation energy in the range from 430 to
490 kJ mol� 1, though based on three experimental
data points.
The activation energy of primary creep is
expected to be similar to that of steady-state creep
since the substructure is supposed to evolve during
primary creep to a stable one in steady-state creep,
and for this reason the mechanism(s) governing
recovery is(are) expected to be the same. Never-
theless, the activation energy for primary creep was
determined at different constant stresses and a
constant strain of 3� 10� 4 (Fig. 10c). The results
show that the as-received condition is characterised
by a higher activation energy of 361 kJ/mol � 1,
whereas the heat-treated condition shows a lower
value (257 kJ/mol� 1), than the activation energy of
steady-state creep. Whether these differences have a
physical significance or only arise from an insuffi-
cient number of data and/or experimental errors due
to the very low strains involved cannot be stated at
this stage.
Fig. 10. (a) Dependence of the natural logarithm of the
steady-state creep rate on the reciprocal of the absolute
temperature determined for the as-received condition from
temperature change experiments. (b) Similar to (a). The data
are from single-load specimens. (c) Determination of the
activation energy of primary creep at different stresses and
constant primary creep strain.
Fig. 11. High-resolution BSE micrographs showing the crept
microstructures of (a) as-received and (b) heat-treated
conditions. Notice the high-density silicide particles and
spheroidisation of the b particles. Creep conditions:
T= 600�C, s= 200 MPa.
M. Es-Souni / Materials Characterization 46 (2001) 365–379 373
3.6. Microstructures associated with creep
The microstructures of crept specimens prepared
from longitudinal sections were investigated by
means of SEM. The dislocation substructures of as-
received and crept specimens were investigated in the
TEM from thin foils prepared from slices cut parallel
to the tensile axis.
The SEM micrographs of the as-received con-
dition shown in Fig. 11 do not reveal any substan-
tial change in the microstructure when compared to
the noncrept one. Only some spheroidisation of the
b films could be seen and possibly some coarsen-
ing of the silicide particles; cracks or voids were
not observed even at the vicinity of the specimen
surface. The microstructure of the heat-treated
condition is basically not affected by the creep
testing, regardless from the coarsening of second-
phase particles.
The dislocation substructures corresponding to an
as-received specimen deformed at 200 MPa and
550�C to a strain of 10� 2 show the formation of
stable dislocation configuration in the primary agrains leading to cell formation (Fig. 12a). The
terrace-like aspect of the dislocation segments that
constitute the cell boundaries strongly suggest a net-
work rearrangement by climb of edge segment. In the
a laths, two main types of dislocation substructure
were observed: (1) curved and pinned dislocations at
the lath boundaries and (2) dislocation network in the
lath interior; the latter is composed of long disloca-
tions that seem to contain many super jogs as a result
of dislocation interactions and/or cross slip (e.g.,
arrows in Fig. 12b).
4. Discussion
4.1. Primary creep
The experimental results presented above show
that the primary creep behaviour of the microstruc-
tures investigated can be meaningfully described in
terms of strain hardening and strain sensitivity phe-
nomena. This allows a suitable analysis of primary
creep and how its mechanisms are affected by stress
and temperature to be made. The strain hardening and
strain sensitivity coefficients obtained at the different
temperatures and stresses were derived using Eqs.
(1)–(3). In Eq. (3), the coefficient p can be written as
(Eq. (7)) [20]:
p ¼ � @log_e@loge
� �s;T
: ð7Þ
Considering Andrade creep and its discussion by
Nabarro and de Villers [6] involving a model based
on work hardening by dislocation pile up and climb-
Fig. 12. TEM micrographs of the dislocation substructure of the as-received condition after creep showing subgrains in an a lath
(a) ( g= h2201], B near h1216]) and (b) bowed dislocations pinned at lath boundaries and jogged long screw dislocations (small
arrows) in the lath interior ( g= h0112], B near h0111]). Creep testing conditions: T= 550�C, s= 200 MPa, creep strain = 10� 2.
M. Es-Souni / Materials Characterization 46 (2001) 365–379374
controlled recovery, the exponent p should be equal
to 2. However, p has been found to vary with stress
and temperature, which suggests that the primary
creep behaviour of the microstructure under inves-
tigation does not follow Andrade law. Reconsidering
p, it can be rewritten as [20]:
p ¼ @logs@log_e
� ��1
e;T
@logs@log_e
� �_e;T¼ m
nð8Þ
where m is the strain hardening and n is the strain rate
sensitivity exponents. This equation presupposes,
however, that a unique relationship between stress,
strain, and creep strain rate, as formulated in the
mechanical equation of state [20], exists. Under
conditions of metallurgical stability, it has been
shown that Eq. (8) holds for certain materials,
particularly at low strains [21,22]. In the case where
m and n are both independent of strain and strain rate,
the deformation behaviour in constant strain rate
tensile tests may be expressed [20–22] by Eq. (9).
s ¼ Kem _en; ð9Þ
where s is the true stress and K is an empirical
constant. Although the results presented above show
that both n and m depend on the strain and strain rate,
Eq. (9) has been fitted to the results of s vs. primary
creep strain, using the values of n and m obtained
above. Fig. 13 shows for two temperatures that Eq.
(9) describes well the experimental results; the values
of the constant K were found to decrease with
decreasing strain rate, as shown in Table 6.
It is not the purpose of this work to discuss the
validity of the mechanical equation of state nor to
present a universal model of the creep deformation
behaviour of materials, particularly when these are
characterised by such complex microstructures as
those presented in this work. The observations of
metallurgical instabilities made on the crept speci-
mens also suggest that the deformation phenomena
are complex in nature and can be at best described by
empirical equations. Nevertheless, the analysis pre-
sented above can be considered in terms of its
opportunity to help understanding the deformation
phenomena particularly in the primary creep regime,
where the two concurrent phenomena of strain hard-
ening, as described by the strain hardening coeffi-
cient, m, and strain recovery, related to the strain
sensitivity coefficient, n, are operating.
4.1.1. Strain hardening during primary creep
The results presented above suggest that strain
hardening during primary creep is dependent on the
test temperature and the strain rate. Considering only
the linear portion of the log _e vs. log e curves, the
strain-hardening exponent is highest at 500�C and
practically takes a value of 0.5 for both heats. At
550�C and 600�C, the values obtained all lie near
0.33. This suggests that the response of the alloy to
creep deformation is different as the temperature
increases, and that 500�C constitutes a critical tem-
perature above which the resistance to creep defor-
mation by strain hardening becomes weaker.
Furthermore, the heat-treated condition is generally
characterised by higher primary creep strains that,
taking into account the microstructures involved,
point to the important role played by pinning centres
like second-phase particles and solute atoms.
In order to understand the dependence of the strain
hardening coefficient on temperature, it is necessary
to take into account the particular microstructure
involved during creep deformation. The starting dis-
location substructures have been shown above to be
mainly composed of a three-dimensional network of
Table 6
Values of K, m, and n for Eq. (9) fitted to the results of the
heat-treated condition
Temperature (�C)/_e (s� 1) K� 103 m n
500/2� 10� 8 799 0.47 0.23
550/1�10� 7 97 0.32 0.21
550/3.7� 10 � 8 68 0.26 0.21
Fig. 13. (a and b) Eq. (9) fitted to the experimental data of stress vs. primary creep strain.
M. Es-Souni / Materials Characterization 46 (2001) 365–379 375
dislocations pinned at lath boundaries and second-
phase particles. Under the conditions of low temper-
ature and relatively low applied stress, these disloca-
tions are expected to bow-out (e.g., Fig. 12b), giving
rise to long-range back stresses and therefore to an
apparently high work hardening rate, and this is
particularly true at ‘‘high’’ strain rates (e.g., Fig. 5b).
The strain hardening behaviour of a-Ti has been
investigated in previous work [23] in tensile, dynamic,
testing at different temperatures and strain rates. It has
been shown that the true stress varied as e0.5 for
stresses higher than the flow stress, in the temperature
range from 77 to 750 K. Although apparently similar
work hardening exponents were obtained in the
present work at 500�C, the mechanisms leading to
work hardening are expected to be different from
those obtained in dynamic tensile testing, since the
strains involved are by far different, viz. the strains in
tensile testing were approximately three orders of
magnitude higher than those in the present creep
testing. While in tensile testing the strain hardening
is controlled by dislocation glide and dislocation
interaction with forest dislocations and obstacles like
grain boundaries, the work hardening in creep testing,
where stress is kept below the yield stress and the
strains are very low, might either occur as a result of
the movement of short dislocation segments and their
pinning at lath boundaries or network dislocations,
and/or as a result of bow-out of pinned network
dislocations (e.g., Fig. 12). The latter should result
in a high contribution of anelasticity to creep strain,
which should be possible to deduce from unloading
experiments. Such unloading experiments were con-
ducted, and it has been observed that most of the creep
strain of specimens loaded in the primary creep
regime could be recovered anelastically [15]. The
applied stress before unloading has been found to
depend on the square root of the anelastic strain at
500�C, which in fact point seriously to the primary
creep strain being highly anelastic in nature at 500�C.As the temperature is increased, the strain-hardening
exponent decreases, which suggests that hardening is
reduced via concurrent recovery phenomena, which
are expected to become more important at higher
temperatures. The contribution of anelasticity to pri-
mary creep is, however, believed to remain consid-
erable, since the unloading experiments mentioned
above lead to increasing anelastic strains with increas-
ing temperature, though the proportion of primary
creep strain recovered upon unloading was lower than
that at 500�C. From the point of view of the disloca-
tion mechanisms, it is thought that the decrease in the
strain hardening rate at higher temperatures might
result to some extent from the climb controlled edge
segments of the curved dislocations pinned at lath
boundaries and second-phase particles.
4.1.2. Strain rate sensitivity during primary creep
The results presented above show that the strain
rate exponent in the primary creep regime depends
strongly on the creep strain and temperature. At
500�C and 550�C, the strain rate exponents decrease
with increasing creep strain, while they remain almost
constant at 600�C, and lie in the range of the strain
rate exponents found in the steady-state creep regime.
It follows that, at least for the lower temperatures, the
strain rate exponent is not constant during primary
creep, and that it tends towards a minimum at low
creep strains, i.e., at the beginning of the creep curve.
This suggests that, as the creep curve inflects (at
maximum curvature) towards steady state, the strain
rate sensitivity exponent becomes low, which indi-
cates that recovery phenomena are not as effective in
controlling the creep rate in this region of primary
creep as in the other portions of the creep curve. It is
thought that in this portion of the primary creep curve
long-range dislocation interactions reach a maximum,
presumably due to maximum (for the corresponding
stress) network refinement.
At constant stress and strain, the dependence of
the logarithm of the primary creep rate on the
reciprocal of the temperature leads to an activation
energy, which for the heat-treated condition appa-
rently depends on stress; the values increase from 227
kJ/mol � 1 for 200 MPa to 257 kJ/mol� 1 for 350
MPa. In fact, if there were any stress dependence of
the activation energy of creep, a decrease is rather
expected with increasing stress, following Eq. (10):
Qa ¼ Q0 � sv ð10Þ
where Q0 is the activation energy under very low
stress and v is the activation volume [6]. This can
only be explained if we assume that the activation
volume decreases with increasing stress, which is
physically not correct. Therefore, it is believed that
the insufficient number of data points is the reason for
the discrepancy between the values obtained at
different stresses, and that the activation energy of
primary creep takes values between 230 and 260 kJ/
mol � 1 for the heat-treated condition. For the as-
received condition, data could only be exploited for
the applied stress of 300 MPa; the activation energy
of 365 kJ/mol� 1 obtained is fairly high and might be
overestimated because of the small number of data
points. For both microstructures, the activation energy
obtained for primary creep differs from that obtained
for steady-state creep. However, taking into account
that primary creep constitutes a transient stadium,
where the substructure is believed to evolve towards a
more stable one that, when established, denotes the
beginning of secondary creep, the activation energies
for primary and secondary creep are expected to be of
M. Es-Souni / Materials Characterization 46 (2001) 365–379376
the same order of magnitude. The discrepancy
between the values obtained for primary and secon-
dary creep, although not high when considering the
well known scatter of creep data, are thought to arise
from the insufficient number of data points.
4.2. Steady-state creep
The steady-state creep data obtained from single-
load specimens can be described by power law
creep, and the stress exponents (nss� 1) obtained
lie in the range from 5.2 to 4.1, which is usually
interpreted in terms of the creep rate being con-
trolled by climb of edge dislocation segments [6,7].
These values are very close to those reported on a
similar alloy [4]. The results also show that the as-
received condition is characterised by higher stress
exponents than the heat-treated one. Particularly at
low stresses and temperatures, the creep rates are
lower in the as-received condition, and become
equal to those of the heat-treated condition at higher
stresses and/or higher temperatures. The microstruc-
ture of the as-received condition, which consists
mainly of a solid solution with fine silicide precip-
itates and discontinuous b films, has a higher creep
resistance at low stresses and/or low temperatures
than the heat-treated one. Both extensive spheroid-
isation of the b films and precipitation and coarsen-
ing of intermetallic particles (TiZr6Si3 or TiZr5Si3)
are thought to confer a lower creep resistance to the
heat-treated condition. Furthermore, the depletion of
the matrix of alloying elements, to form the inter-
metallic particles mentioned above, might also
decrease the resistance to creep at lower stresses
and temperatures. As the temperature and/or stress
increase, the strain rate seems to be only marginally
influenced by the initial microstructure.
The activation energies of steady-state creep
determined above are 345 and 303 kJ/mol � 1 for
the as-received and heat-treated conditions, respec-
tively. The values reported by Anders et al. [4] (490
and 430 kJ/mol � 1 for water-quenched and air-
cooled specimens, respectively) are much higher than
those reported in the present work, and seem to
depend on the processing route, which might be an
indication that internal stresses contribute substan-
tially to their deformation kinetics. Unfortunately, a
consistent discussion of the creep mechanisms is
missing in their paper.
The activation energy of self-diffusion usually
reported for a-Ti lies in the range of 240 kJ/mol� 1
[24]. However, in a recent paper, Koppers et al. [25]
review and evaluate critically the values reported.
They show that the amount and nature of impurities,
particularly the fast diffusing impurities Fe, Ni, and
Co have a dramatic effect on Ti self-diffusion and
solute diffusion. In high-purity a-Ti, activation ener-
gies of 303 and 329 kJ/mol� 1 were found, respec-
tively, for Ti self-diffusion and Al solute diffusion.
The apparent activation energies for creep determined
in the present work fall within the range of the values
determined by Koppers et al. [25], although the as-
received condition shows a somewhat higher value.
The fact that the heat-treated condition is character-
ised by a lower value of 303 kJ/mol � 1 suggests that
diffusion is affected by the amount of alloying ele-
ments in solid solution, particularly Si and Zr since
these are expected to form silicides during the ‘‘age-
ing’’ treatment at 910�C. However, taking into con-
sideration the complex chemical composition under
consideration, it is quite difficult to state whether the
activation energies determined correspond to self or
solute diffusion. In both cases, alloying effects due the
interaction between the substrate and alloying ele-
ments are expected to affect the diffusion processes.
The steady-state creep rates determined from
single-load specimens at 550�C were found to be
very close, or even equal, to the CSCRs determined
from stress dip experiments. Other high-temperature
a-Ti-based alloys have been also shown to exhibit
similar behaviour [26]. According to Yaney et al.
[27], stress dip experiments can be used to distinguish
between alloy (A) and metal (M) creep behaviour. In
the case of A-type behaviour, a higher _ecs is expectedbecause the density of mobile dislocations established
at the initially higher stress is higher than it should be
upon stress reduction. In this case, stress exponents of
2 and 3 for constant structure and steady-state creep
rates, respectively, are expected (with regard to their
results, stress exponents of 2.8 and 3.3 were
obtained). However, it should be pointed out that
their CSCR results practically superpose to those of
the steady-state curve in the high stress regime (small
stress reductions). In the case of M-type behaviour,
lower strain rates are expected upon stress reduction
since the substructure initially formed is stronger, and
a finite amount of recovery has to be achieved before
steady state corresponding to the new stress level is
reached. The stress exponents obtained in this case
for high-purity Al are 4.7 and 8. Based on these
observations, the practical superposition of _ecs and _essobserved for the present microstructures is quite
difficult to explain. However, taking into account
anelastic transients, which in fact would lead to
apparently lower _ecs (Fig. 8 shows that this assump-
tion is quite legitimate), this superposition would
suggest a creep mechanism of A-type. Comparison
of the activation energies of creep with the activation
energy of Al solute diffusion might be regarded to be
an additional support for this mechanism. However,
the stress dependence of the creep strain rate is not
consistent with the model, and the activation energies
M. Es-Souni / Materials Characterization 46 (2001) 365–379 377
obtained can equally be attributed to self-diffusion.
Furthermore, microstructural observations point to
the formation of subgrains and suggest a climb
controlled creep mechanism (M-type).
It therefore seems that the stress dip experiments
are not conclusive as to the type of the operating
creep mechanism in the present microstructures.
Nevertheless, the microstructural observations, the
steady-state creep results, and the activation energies
obtained all taken together suggest a creep mecha-
nism based on climb of pinned dislocation segments.
The activation energies determined for the as-
received and heat-treated conditions constitute sup-
port for this mechanism if we suppose that the Ti self-
diffusion in the a phase is impeded by the presence of
alloying elements; an indication for the validity of
this supposition may lie in the lower activation
energy determined for the heat-treated condition,
where the precipitation of the intermetallic silicide
phases TiZr6Si3 lead to alloying elements depletion of
the a phase.
5. Conclusions
The creep behaviour of the high-temperature near
a-Ti alloy Timetal 834 with a duplex microstructure
has been investigated in constant stress tensile creep.
Both primary and secondary creep and their depend-
encies on microstructure, temperature, and applied
stress were considered. The following conclusions
can be inferred:� Heat treatment of the as-received duplex micro-
structure at 910�C for 1 h and subsequent
ageing at 650�C does not change the volume
fraction of primary a, but leads instead to
extensive spheroidisation of the b films and
precipitation plus coarsening of Ti5Si3 and Zr-
rich silicides, probably TiZr6Ti3. In both starting
microstructures, a high density of dislocation
segments pinned at lath boundaries and second-
phase particles were observed.� The dependence of primary creep on temper-
ature and stress is shown to be best described by
a model involving strain hardening and strain
recovery. The strain hardening and strain rate
exponents are found to depend on temperature.
At 500�C, the primary creep strain varies as
s2, at higher temperatures as s3. The
primary creep rate is found to vary with stress
as s4 – 6, depending on temperature and
microstructure. The results can be fitted to an
empirical relation of the type s =Kem_en.� In steady-state creep, the strain rate is found to
vary as s4–5. The CSCRs obtained via stress
dip experiments are shown to be very close to
steady-state creep rates obtained from single-
load specimens and those subjected to stress
dip. This is interpreted in terms of anelastic
strain being superposed to forward creep and
not in terms of the creep mechanism being
controlled by viscous glide (A-type). The acti-
vation energies of creep as determined for the
as-received and heat-treated microstructures
are 350 and 300 kJ/mol, respectively. These
values lie in the range of the activation energy
of self-diffusion of Ti in a-Ti. They are,
however, thought be influenced by alloying
effects. These results point to the creep mech-
anism being controlled by bow-out and climb
of dislocation segments pinned at lath bounda-
ries and second-phase particles.� The strain hardening in primary creep is thought
to be controlled by long-range stresses due to
bow-out of pinned dislocation segments. In
support, examples of the dislocation substruc-
tures have been presented.
References
[1] Boyer RR. An overview on the use of titanium in
the aerospace industry. Mater Sci Eng, A 1996;213:
103–14.
[2] Froes FH, Suryanarayana C, Eliezer D. Synthesis,
properties and applications of titanium aluminides.
J Mater Sci 1992;27:5113–40.
[3] Maththew JD. Titanium, a technical guide. Metals Park
(OH): ASM International, 1988.
[4] Anders C, Albrecht G, Luetjering G. Correlation be-
tween microstructure and creep behavior of the high
temperature Ti alloy IMI 834. Z Metallkd 1997;88:
197–203.
[5] Potozky P, Maier HJ, Christ H-J. Thermomechanical
fatigue behavior of the high temperature titanium alloy
IMI 834. Metall Mater Trans 1998;29A:2995–3004.
[6] Nabarro FRN, de Villers HL. The physics of creep.
London: Taylor & Francis, 1995. pp. 15–78.
[7] Evans RW, Wilshire B. Creep of metals and alloys.
London: Institute of Metals, 1985.
[8] Derby B, Ashby MF. A microstructural model for pri-
mary creep. Acta Metall 1987;35:1349–53.
[9] Li JC. A dislocation mechanism of transient creep.
Acta Metall 1963;11:1269–70.
[10] Beere W, Grossland IG. Primary and recoverable creep
in 20/25 stainless steel. Acta Metall 1987;30:1891–9.
[11] Ahmadieh A, Mukherjee K. Stress– temperature– time
correlation for high temperature creep curves. Mater
Sci Eng 1975;21:115–24.
[12] Es-Souni M, Bartel A, Wagner R. Creep behaviour of a
fully transformed near g-TiAl Alloy Ti –48Al –2Cr.
Acta Metall Mater 1995;43:153–61.
[13] Mishra RS, Banerjee D, Mukherjee AK. Primary creep
in a Ti – 25Al – 11Nb alloy. Mater Sci Eng 1995;
A192/193:756–62.
M. Es-Souni / Materials Characterization 46 (2001) 365–379378
[14] Es-Souni M. Primary and anelastic creep in a high
temperature near a-Ti alloy: effects of microstructure
and stress. In: Sarton LAJL, Zeedijk HB, editors. Pro-
ceedings of the 5th European Conference on Advanced
Materials and Processes and Applications. Zwijn-
drecht: Netherlands Society for Materials Science,
1997. pp. 233–6.
[15] Es-Souni M. Primary, secondary and anelastic creep of
a high temperature near a-Ti alloy Ti6242Si. Mater
Charact 2000;45:153–64.
[16] Es-Souni M. Primary and anelastic creep of a near a-Tialloy and their dependencies on stress and temperature.
Mech Time-Depend Mater 1999;2:211–28.
[17] In: Boyer HE, Gall TL, editors. Metals handbook. Met-
als Park (OH): ASM International, 1985. pp. 35.18–9.
[18] Ramachandra C, Singh AK, Sarma GMK. Micro-
structural characterisation of near-a titanium alloy
Ti – 6Al – 4Sn– 4Zr – 0.70Nb–0.5Mo–0.4Si. Metall
Trans 1993;24A:1273–80.
[19] Nakayama GS, Gibeling JC. Constant substructure
creep of aluminum following stress reductions. Acta
Metall Mater 1990;38:2023–30.
[20] Lubahn DJ. Deformation phenomena. In: Dorn JE,
editor. Mechanical behaviour at elevated temperature.
New York: McGraw-Hill, 1961. pp. 319–92.
[21] Yokobori T. The strength, fracture and fatigue of ma-
terials. Groningen: P. Noordhoff, 1964. pp. 94–9.
[22] Stuewe H-P. Superplastizitat. Z Metallkd 1970;61:
704–10.
[23] Orava RN, Stone G, Conrad H. The effects of temper-
ature and strain rate on the yield and flow stress of
a-titanium. Trans ASM 1966;59:171–84.
[24] Malakondaiah G, Rama Rao P. Creep of alpha-titanium
at low stresses. Acta Metall 1995;29:1263–75.
[25] Koppers M, Herzog CHR, Friesel M, Mishin Y. Intrin-
sic self-diffusion and substitutional Al diffusion in
a-Ti. Acta Mater 1997;45:4181–91.
[26] Es-Souni M. Creep deformation behaviour of three
high temperature near a-Ti alloys: IMI 834, IMI 829
and IMI 685. Metall Mater Trans, 2001;32A:285–93.
[27] Yaney DL, Gibeling JC, Nix WD. A new strain rate
change technique for distinguishing between pure met-
al and alloy type creep behavior. Acta Metall 1987;35:
1391–400.
M. Es-Souni / Materials Characterization 46 (2001) 365–379 379