Creep behaviour and creep microstructures of a high-temperature titanium alloy Ti-5.8Al-4.0Sn-3.5Zr
Creep behaviour and creep microstructures of a high-temperature titanium alloy Ti-5.8Al-4.0Sn-3.5Zr
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 500C to 625C 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 500C 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 600C .
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 . 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 .
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: firstname.lastname@example.org (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  and in terms of the rate of annihilation of dislocations at lath and grain boundaries in the case of a2-Ti3Al . 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 600C.
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: 1050/1055C Top and bottom refer to the top and bottom of the rolled plate, respectively. Table 2 Mechanical properties at room temperature and 600C 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.
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Fig. 1. (a) Light micrograph of the as-received duplex microstructure. Primary a particles (bright contrast) and the fine Widmannstätten 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 = h1̄010], B near h12̄13̄]. (f) Semi-coherent Ti5(Si,Zr)6 silicide particles in an a lath.
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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: 1022C/2 h/oil quench + 700C/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.  and follow the recommendations of Evans and Wilshire . 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: 910C/1 h/AC + 643C/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 500C to 625C; the temper- ature was controlled to ± 0.5C 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 20C. 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 Widmannstätten 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.  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 a laths 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 500C 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) 365–379 368
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 910C. 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 , 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 500C 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 500C, 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 600C by the intercept method are lower than those at 500C and 550C, 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.
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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 constant strain rate, by an empirical relation of the form: epr ¼ Cs 1 m ; 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 C0 s 1 n ; ð2Þ where C0 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 Aep ; 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 500C showing the variation of the slope at different constant strains. (c) Double logarithmic plots of the strain rate dependence on the stress at 600C. M. Es-Souni / Materials Characterization 46 (2001) 365–379 370
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 500C. 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 600C 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 As 1 nss ; 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 500C. 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 .
In this work, stress dip experiments were performed for both conditions at 550C 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 , 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. Thestrain 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 ks 1 n exp 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 550C. Compar- ison with steady-state creep rate from single-load specimens and from stress dip are also shown.
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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. , 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 = 600C, s = 200 MPa.
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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 550C to a strain of 10 2 show the formation of stable dislocation configuration in the primary a grains 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.
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)) : p ¼ @log_ e @loge s;T : ð7Þ Considering Andrade creep and its discussion by Nabarro and de Villers  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 = h22̄01], B near h1̄21̄6]) and (b) bowed dislocations pinned at lath boundaries and jogged long screw dislocations (small arrows) in the lath interior ( g = h01̄12], B near h011̄1]). Creep testing conditions: T = 550C, s = 200 MPa, creep strain = 10 2 .
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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 : p ¼ @logs @log_ e 1 e;T @logs @log_ e _ e;T ¼ m n ð8Þ 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 , 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 500C and practically takes a value of 0.5 for both heats. At 550C and 600C, 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 500C 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  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 500C, 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 . The applied stress before unloading has been found to depend on the square root of the anelastic strain at 500C, which in fact point seriously to the primary creep strain being highly anelastic in nature at 500C. 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 500C. 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 500C and 550C, the strain rate exponents decrease with increasing creep strain, while they remain almost constant at 600C, 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 . 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) 365–379 376
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 .
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.  (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 . However, in a recent paper, Köppers et al.  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 Köppers et al.
, 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 910C. 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 550C 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 . According to Yaney et al. , 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 expected because 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 _ ess observed 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 910C for 1 h and subsequent ageing at 650C 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 500C, 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  Boyer RR. An overview on the use of titanium in the aerospace industry. Mater Sci Eng, A 1996;213: 103–14.  Froes FH, Suryanarayana C, Eliezer D. Synthesis, properties and applications of titanium aluminides. J Mater Sci 1992;27:5113–40.  Maththew JD. Titanium, a technical guide. Metals Park (OH): ASM International, 1988.
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