Creep behaviour and creep microstructures of a high-temperature

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.


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.


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.


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


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.


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.


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.


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.


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


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


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.

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