Primary, secondary and anelastic creep of a high temperature near a-ti alloy Ti6242Si

Transcription

1 Materials Characterization 45 (2000) 153± 164 Primary, secondary and anelastic creep of a high temperature near a-ti alloy Ti6242Si M. Es-Souni* Institute for Materials Technology, Fachhochschule Kiel, University of Applied Sciences, Grenzstrasse 3, D Kiel, Germany Received 9 February 2000; received in revised form 24 March 2000; accepted 25 March 2000 Abstract The creep behavior of the near a-ti alloy Ti6242Si is investigated at 500 C using constant stress tensile creep testing. Emphasis is put on primary and anelastic creep and their dependencies on processed microstructure and applied stress. The results of steady state creep are also reported. It is shown that the primary creep strain depends strongly on microstructure. Its dependence on stress is linear in the low stress regime, whereas a weak dependence is observed for high applied stresses. Unloading experiments lead to a time-dependent strain recovery that is also dependent on microstructure and prior stress. Unloading in the primary creep regime results in the recovery of almost all of the creep strain. However, a substantial strain recovery was also obtained upon unloading from steady state. It is shown that primary and anelastic creep strains are intimately related, and depend on microstructure and stress. The results are discussed with respect to existing dislocation creep models and the observed dislocation structures. D 2000 Elsevier Science Inc. All rights reserved. Keywords: Creep behavior; a-ti alloy; Anelastic creep; Applied stress 1. Introduction The creep behavior of metals and alloys is most commonly analyzed in terms of steady state creep, where the dependence of the steady state creep rate on stress and temperature is described using different analytical/empirical approaches (for a review see Nabarro and de Villers [1]). However, in many applications involving a stringent control of the creep strain, primary creep can have a large contribution to the creep strain, and it is surprising that only few investigations address this issue [2 ±8]. * Tel.: ; fax: address: mohammed.es-souni@fh-kiel.de (M. Es-Souni). Primary creep takes place at the very beginning of the creep test and is characterized first by a high strain rate, which then decelerates to a constant value denoting the beginning of secondary creep. The primary creep strain is time dependant and is usually described by empirical relations, such as the Andrade law [1], i.e., e = e 0 + bt m, where e 0 is the instantaneous strain on loading, b is a constant and m is a coefficient near 1/3, or Garofalo's equation [9] (Eq. (1)): e pr ˆ e 0 e T 1 exp mt Š 1 where e T is the limiting transient creep and m is a constant. In dislocation creep, the evolution of the primary creep rate has been described in terms of the motion of mobile dislocations under the applied stress and concomitant build-up of an internal /00/$ ± see front matter D 2000 Elsevier Science Inc. All rights reserved. PII: S (00)

2 154 M. Es-Souni / Materials Characterization 45 (2000) 153±164 stress (strain hardening) that results in a decaying strain rate [1]. The microstructural models underlying primary creep include the operation of dislocation sources under the applied stress and climb of edge segments [10], bowing of pinned network dislocations and escape (for stresses larger than the Orowan stress) [6], refinement and concurrent coarsening of network dislocations [11] or the formation and evolution of subcells, within which dislocation motion is impeded by a pattern of internal stresses [2]. Anelastic strain has been defined by Zener [12] as a time-dependent, recoverable component of strain; it has been shown [13,14] to depend on microstructure and on prior stress (applied stress before unloading). Anelastic creep strain is not only of technological interest, designers have to take it in to account [15], but also of fundamental concern because it may provide an improved understanding of the creep mechanisms [16,11]. Anelastic creep has been observed in pure metals [13,16 ± 18] and engineering alloys [6,14,15,19,20] for large stress reductions. Its extent, which depends on prior creep strain, may be a multiple or a fraction of the elastic contraction, depending on the system investigated. The dependence of anelastic strain, e a (Eq. (2)), on time is usually described in terms of an empirical relation of the type: e a ˆ klog 1 t 2 where k is a constant depending on stress and temperature, and t is the unloading time. The contribution of anelasticity to creep has been recognized by Zener [12] and extensively investigated by Lubahn [20] and Henderson and Sneddon [13,14], from a phenomenological and empirical point of view, particularly as to the intimate relationship between primary and anelastic creep [13,14]. As pointed out by Lloyd and McElroy [11], this contribution leads to the general relationship for creep suggested by Zener [12]: e ˆ e 0 e a e T e st; 3 where e s is the steady state creep rate. The implications of anelasticity on the overall creep process have been previously reported [11]. Discussions concerning the mechanisms of anelastic recovery have been documented [6,11,16]. Unbowing of pinned network dislocations first proposed by Lloyd and McElroy [11], is most frequently claimed to be responsible for anelastic recovery [6,15,19], and transmission electron microscope (TEM) observations of the dislocation structures showing bowed dislocations between precipitates have been presented to provide support for this mechanism [6,15]. This mechanism has been questioned, however, by Gibeling and Nix [16] and Pahutova et al. [17] as to its validity to account for the high anelastic strains observed upon unloading of pure Al, Cu, and Zr specimens. They proposed an alternative mechanism involving a contribution from subgrain migration and dissolution [17], as well as backward motion of free dislocations within subgrains [16]. In the present work, the effects of stress and processed microstructures on primary and anelastic creep are examined on the high temperature near a-ti alloy Ti6242 Si. The creep behavior of this alloy has been investigated in some detail by Bania and Hall [21], particularly as to the influence of primary a on primary and steady state creep. However, a comparative study is still lacking. Furthermore, the anelastic behavior has not been addressed at all. In this work, full unloading experiments were performed in order to determine the anelastic contribution to creep. The effects of the total strain reached in the primary and the secondary creep regimes on the amount of recoverable anelastic strain were also examined. The results are discussed with respect to the different models mentioned above. 2. Experimental details The alloy investigated is a near a-ti alloy Ti6242 Si of the following composition (in wt.%): Al 5.9, Si 0.1%, Zr 4.2%, Mo 2%, Sn 2.5% and balance titanium. It was provided by the Deutsche Titan Gesellschaft (DTG) in form of 40-mm diameter rods. The material has been forged in the a + b phase field. The b-transus temperature was estimated metallographically to be approximately 1000 C. Tensile specimens as shown in Fig. 1 were machined parallel to the rod axis, following the specifications of the German standard DIN They were ultrasonically cleaned in acetone and subsequently heat-treated in Ar-atmosphere following the Fig. 1. Specimen configuration for tensile creep testing; dimensions in mm.

3 M. Es-Souni / Materials Characterization 45 (2000) 153± Table 1 Heat treatment schemes and observed microstructures Heat treatment Microstructure As-received globular a interspersed with a + b areas; hot forming texture a + b heat-treated: 910 C/1 h/ac/643 C/7 h/ac globular a interspersed with a + b areas; volume fraction of a: about 60% b-5 C heat-treated: 995 C/1 h/ac/643 C/7 h/ac fully transformed b, ``basket-weave'' structure b heat-treated: 1004 C/1 h/ac/643 C/7 h/ac fully transformed b, primary b grains and a laths are coarser than in the preceding case schemes summarized in Table 1, in order to produce the desired microstructures. The creep testing system consists of a 50-kN capacity hydraulic machine with a load control of 0.1%. The strain was measured between two ridges at the extremities of the gauge length (Fig. 1) by employing a standard creep extensometer design [22]. The creep tests were performed in air in a three zone furnace allowing a temperature control of better than 0.5 C. The machine is computer controlled and allows a simultaneous record and graphical display of test parameters and data. The data sampling rate could be varied allowing for a maximum of 90 to 120 readings/min for unloading and loading experiments and a minimum of 1 reading/5 min for the steady state regime. Constant stress loading conditions were assured by a continuous load control, assuming constant volume of the specimen gauge. Single specimen as well as multiple specimen tests were performed. The dependence of anelastic strain on creep strain and stress were generally investigated using single specimen tests. However, the results obtained were also reproducible, in the range of experimental accuracy of the system, using multiple specimen tests. An example of a creep testing run and data analysis is shown in Fig. 2. Microstructures were investigated by means of light microscopy, scanning electron microscopy (SEM) and TEM. Thin foil specimens for TEM were prepared by twin jet electrolytic polishing of specimens cut parallel to the gauge section in a 5% perchloric acid in ethanol at 20 C. 3. Experimental results 3.1. Microstructural forms The microstructures investigated are described in Table 1, and shown in Fig. 3. The as-received and the a + b heat-treated conditions show a duplex micro- Fig. 2. Example of a creep testing run and data analysis (see below for details).

4 156 M. Es-Souni / Materials Characterization 45 (2000) 153±164 Fig. 3. (a) Light micrograph (LM) of the as-received condition showing globular a and a + b areas; (b) LM of the starting globular microstructure, a + b heat-treated condition (see Table 1); (c) back-scattered electron (BS) micrograph of the a + b heattreated condition showing primary a and fully transformed b areas; (d) LM of the ``basket weave'' microstructure obtained after heat treatment at 995 C (see Table 1); (e) BS micrograph of the lath structure showing a laths (dark) surrounded by b films (bright). Notice also dark dots which denote silicide precipitates. structure consisting of primary a and transformed b areas with a fine interlocked structure of a-platelets and b-films (Fig. 3a, b and c). A detailed examination of the as-received microstructure reveals that the primary a-grains are irregular in shape and extend over large areas (Fig. 3a). The b and near b heattreated conditions consist of a fully transformed b- structure demonstrating the characteristic ``basket weave'' morphology consisting of a laths surrounded by retained b films (Fig. 3d and e). Furthermore, tiny a-films decorating the primary b grain boundaries were observed in both fully transformed structures.

5 M. Es-Souni / Materials Characterization 45 (2000) 153± Fig. 4. Double logarithmic plots of primary creep strain vs. applied stress for the different heats investigated (see Table 1). Fig. 3e also reveals fine dark dots, which are believed to be silicide particles, Ti 5 Si Primary creep The primary creep strain, e pr, was determined from the intercept of the regression line to the steady state creep portion of the creep curve with the true strain axis, as illustrated in Fig. 2. The results of e pr vs. stress are shown for the different microstructural forms investigated as double logarithmic plots in Fig. 4. As can be seen, e pr increases for all heat treatments with increasing stress, first linearly and then slowly for higher stresses. Comparison of the primary creep strains measured from the different processed microstructures indicates higher values for the duplex microstructures, viz. asreceived and 910 C heat-treated conditions, with highest values being those of the as-received condition. In the case of the ``basket weave'' microstruc- Fig. 5. Ratio of the primary creep strain to the elastic strain as a function of the applied stress.

6 158 M. Es-Souni / Materials Characterization 45 (2000) 153±164 globular, duplex microstructures, where higher ratios, up to 4, were observed Steady state creep Fig. 6. Stress dependence of the steady state creep rate for the different conditions at 500 C. tures, the amount of primary creep strain appears to be sensitive to the grain/lath size and/or the amount of retained b. Heat treatment just below the b-transus temperature, which leads to a finer microstructure and lower amount of retained b, results in a slightly lower creep strain in the stress range investigated. The present results agree with those reported by Bania and Hall [21] for the b and near b heat-treated conditions of a similar alloy tested at 510 C. Fig. 5 shows the ratio of the elastic to the primary creep strain vs. stress for the different heats investigated. The primary creep strain is always a fraction of the elastic strain; the values obtained depend on microstructure and decrease with increasing stress, and range from a maximum of approximately 0.5 for the as-received condition to maximum of near 0.25 for the b heat-treated condition. These results differ from those observed by Mishra et al. [23] on an Nballoyed a 2 -Ti 3 Al base alloy with basket weave and For any given microstructural condition, the steady state creep rate (Eq. (4)) depends on stress and temperature, and is usually described by a power-law equation of the type [1,22]: e s ˆ A 0 s n exp Q ; 4 RT where Çe s is the steady state creep rate, A 0 is a constant depending on microstructure, s is the applied stress, n is the stress exponent, Q is the activation energy for creep, R is the gas constant and T is the absolute temperature. In this work, the steady state creep strain rates were determined as a function of the applied stress from stress reduction experiments and from experiments conducted with the applied stress being held constant throughout the creep test. The results obtained from both kinds of tests were, however, identical in the range of accuracy of the creep system used. Fig. 6 shows double logarithmic plots of the steady state strain rate dependency on stress at 500 C. The regression lines yield stress exponents of 3.9 for the as-received and of 4.7 to 4.8 for the heat-treated conditions. All heat-treated conditions, i.e., b and a + b heat-treated, have very similar stress exponents. These results are quite different from those published by Bania and Hall [21], who report stress exponents ranging from 2.95 to 5.24 in the temperature range from 455 C to 565 C. Temperature change experiments in the temperature range from 500 C to 600 C were conducted in the steady state creep regime, in order to obtain the apparent activation energy for creep. To investigate Fig. 7. Steady state creep rate vs. reciprocal of absolute temperature and regression lines to give the apparent activation energies. Fig. 8. Example of anelastic behavior after unloading from an applied stress of 241 MPa.

7 M. Es-Souni / Materials Characterization 45 (2000) 153± Fig. 9. Comparison of forward and anelastic strains for an applied stress of 241 MPa. Fig. 11. Ratio of the anelastic creep strain to the elastic strain as a function of the plastic creep strain. the dependency of the activation energy on stress, the experiments were performed at two different applied constant stresses of 241 and 338 MPa. Fig. 7 shows the results as the logarithm of the steady state creep rate vs. the reciprocal of the absolute temperature. The slopes obtained from the regression lines yield activation energies ranging from 304 to 316 kj/mol, and may be considered as very similar in the range of accuracy of the creep system used. This apparent activation energy for creep is substantially lower than the range of values (from 360 to 420 kj/mol) reported by Bania and Hall [21] for their so-called high activation energy regime (from 495 C to 565 C), and is higher than the activation energy for dislocation climb-controlled creep and for self-diffusion reported for pure a-ti [24,25]. The values obtained remain unaffected by the applied stress and processed microstructure, which indicates that the operating creep mechanism(s) is (are) independent of processed microstructure and, in the stress range investigated, of applied stress Anelastic creep behavior Fig. 8 shows an example of anelastic, recovery strain vs. unloading time. Following the instantaneous elastic contraction, strain recovery takes place, first at a high rate followed by a continuous decay. This behavior is similar to that reported for pure metals [13,16±18] and some engineering alloys [6,14,15,19]. The forward and the anelastic creep curves are compared in Fig. 9; they show that the kinetics of strain accumulation and strain recovery are very similar at high strain rates; the curves separate as strain rate decreases. Increasing the applied stress does not change the overall behavior. Fig. 10 shows the dependence of the anelastic strain on microstructure and creep strain achieved Fig. 10. Anelastic creep strain as a function of plastic creep strain. Fig. 12. Anelastic strain, e a, vs. primary creep strain, e pr, for the different heats and stresses investigated.

8 160 M. Es-Souni / Materials Characterization 45 (2000) 153±164 Fig. 13. Anelastic strain vs. stress upon unloading from steady state. before unloading for two different applied stresses. The following observations can be made. (a) The amount of anelastic strain first increases rapidly with increasing creep strain during primary creep, then slowly as steady state is approached. A similar behavior was also observed by Gibeling and Nix [16] on pure fcc metals. (b) For similar creep strains, the amount of anelastic strain increases with the applied stress. (c) As for primary creep strain, the amount of anelastic creep strain depends on processed microstructure. The b heat-treated specimens, which show lower primary creep strains, are also characterized by lower anelastic creep strains. (d) Unloading in the early stages of creep (during primary creep) results in the recovery of almost all of the creep strain. Fig. 11 shows the ratio of the anelastic to the elastic strain (e a /e e ) as a function of the creep strain for two different stress levels. As can be seen, e a /e e saturates for all heats investigated at a value which depends only slightly on microstructure and applied stress. This value is always a fraction of the elastic strain, with a maximum of about 0.7 for the asreceived condition (not shown). This is quite different from the results reported on pure fcc metals [16] and on an a 2 -Ti 3 Al±Nb base alloy [23], where e a /e e ratios higher than 1 were reported. That anelastic creep is intimately related to primary creep can be seen in Fig. 12, where e a increases almost linearly with increasing primary creep strain. Figs. 10 and 12 suggest that anelastic contributions to the primary creep strain may predominate, as already observed by Henderson and Sneddon [13,14]. They also show that anelastic creep continues into steady state, where it also contributes, though to a lesser extent than for primary creep, to the creep strain. The dependence of anelastic creep strain on stress is shown in Fig. 13 as a double logarithmic plot; the plotted values of e a are those obtained upon unloading from steady state. As ex- Fig. 14. TEMs showing the dislocation structures of crept specimens at 500 C and 241 MPa (total plastic creep strain 3%). (a) The dislocation structure in a globular grain, the beam direction B is h1216] and the operating diffraction vector g is h2201i. (b) The dislocation structure in a lath. Notice the strongly bowed out dislocations in both micrographs (arrows).

9 M. Es-Souni / Materials Characterization 45 (2000) 153± Fig. 15. (a) LM of creep damage in a fully transformed microstructure. Arrows show cavities. (b) LM of cavities at a triple point. Notice also the strong deformation of the laths at the vicinity of the grain boundary. pected, an almost linear dependence is obtained. This agrees with the observations of Henderson and Sneddon obtained on an Al alloy [13] and pure Cu [14] Creep microstructures The dislocation structures observed on specimens, which have been cooled under load after a creep strain of about 3%, are shown in Fig. 14 both for globular and lath morphologies of the a phase. The micrographs show strongly bowed dislocations in the grain interior and at the lath boundaries. It can also be seen that many bowed dislocations have a pinned morphology. Fig. 14 also shows dislocation rings, which suggest intersection of dislocations gliding on different slip planes. These observations are similar to those made by Beere and Grossland [6] on a stainless steel, and Lupinc and Gabrielli [15] on a precipitation hardened Ni-base superalloy, where in both cases dislocation bowing between particles was reported. Evidence of recovery microstructures such as subgrains could not be unambiguously identified, though subgrains were observed in isolated a laths and grains, it is, however, not possible to state whether they arise from the creep process or from processing Creep damage Light microscopy observations of microstructures obtained after creep testing revealed creep damage in the b heat-treated condition tested to a creep strain of approximately 5%. This can be seen in Fig. 15a and b as cavities along prior b grain boundaries and at triple points. In both cases, the grain boundaries are nearly perpendicular to the stress axis. The formation of these cavities can be regarded to arise as a result of stress concentration in the soft grain boundary a and/ or as a result of strain incompatibilities between the coarse transformed b-grains, which are, in this case, thought to deform collectively. Evidence for extensive deformations near the vicinity of grain boundaries is demonstrated in Fig. 15b, where the bending of a-laths can be seen. In contrast such damage was not observed in the duplex microstructures up to a creep strain of 20%. 4. Discussion 4.1. Primary creep The amount of primary creep strain is sensitive to the volume fraction of primary a, and to some extent to the grain/lath size and/or the volume fraction of retained b (compare the results of the 1004 C and 995 C heat-treated specimens, where a slightly higher primary creep strain was observed for the former). The fact that the fully transformed structures show lower creep rates than the duplex ones suggests that strain hardening or dislocation pinning effects are stronger in the former. Nevertheless, all processed microstructures show similar behavior as to the dependence of primary creep strain on stress, i.e., the primary creep strain increases first linearly with the applied stress for low stress levels and then slowly, before it peaks for stress values which are microstructure-dependent. Based on models involving the density of mobile dislocations, i.e., strain hardening and recovery (whether due to climb of leading dislocations in a pile up [1], dislocation motion in subcells under the effects of internal stress [2] or the motion of network dislocations) the dependence of primary creep strain on stress has been shown to be parabolic (Eq. (5)): e pr ˆ as m A 5

10 162 M. Es-Souni / Materials Characterization 45 (2000) 153±164 where a is a constant, s A is the applied stress and m = 2 ± 3. However, it has been shown by Henderson and Sneddon [13,14] that during creep of an Al alloy and pure Cu the stress dependence of strain follows a relationship given by: e ˆ Ks Cs n t m 6 where K and C are constants depending on temperature, t is the time and n and m are constants. The unit stress dependence of creep strain was shown to predominate at low stresses, where creep recovery on unloading was high. The linear dependence of primary creep strain on the applied stress observed at low stresses in this work suggests that primary creep might be controlled by climb-controlled bowing of pinned dislocations: for stresses lower than the Orowan stress, i.e., s = Gb/l, where G is the shear modulus, b is the Burgers vector and l is the mean distance between pinning points, the theoretical treatment by Beere and Grossland [6] gives the maximum transient creep strain as (Eq. (7)): e 1 cs 8G ln l 1 7 l 0 where l is the dislocation links length and l 0 is a lower cut off radius. Eq. (6) gives a linear dependence of the transient strain on stress, assuming that l is independent on stress, for stresses far below the yield stress. Furthermore, the fact that a large fraction of the creep strain, and particularly almost the whole primary creep strain (Figs. 9 and 10), is recovered after unloading might be a serious indication of the primary creep strain being anelastic in nature, that is recoverable, below a certain stress level. Evidence of the anelastic nature of primary creep was also obtained by Henderson and Sneddon [13,14]. At high stresses, the dependence of primary creep strain on stress is no longer linear and decreases slightly with higher applied stress. Evidence of a parabolic dependence of creep strain on stress, as reported by Henderson and Sneddon [13,14], could not be observed for the present alloy, in the stress range investigated. Bania and Hall [21] investigated the primary creep behavior of a Ti6242Si as a function of microstructure and stress at 510 C. Analysis of their results in terms of double logarithmic plots of strain vs. stress yield, for the low stress regime, stress exponents in the range from 1.20 to 3.9, depending on microstructure. Furthermore, the reported results show both parabolic increase and saturation of primary creep strain with increasing stress, with no clear evidence for a microstructure influence on this behavior. At present it is not possible to give a satisfactory explanation for the deviation from the predicted parabolic behavior observed at high stresses in this work. However, as stress increases, it is expected that on loading more dislocation segments will break away from their pinning points, thus leading to strain hardening and subsequently to a rapid deceleration of the creep strain rate towards steady state. That the ratio of recovered strain to the plastic strain decreases as strain and/or stress increase (Fig. 11), particularly for the b heat-treated condition, may confirm the above assumption. However, more work is needed in order to understand primary creep, particularly as to the kinetics of the phenomenon and their dependencies on stress and temperatures Steady state creep The stress dependence of steady state creep rate follows power-law creep as given by Eq. (3). The stress exponents experimentally determined in this work at 500 C are 3.9 for the as-received condition and about 4.8 for the heat-treated conditions. In the case of the as-received condition, the steady state creep behavior is thought to be affected by texture since the a + b heat-treated condition, which exhibits a similar microstructure, i.e., a similar volume fraction of primary a, is characterized by a stress exponent of 4.9. These results are quite different from those of Bania and Hall [21], where stress exponents in the range from 2.95 to 5.24 were reported, and where a peculiar dependence of the stress exponent on temperature may be noticed (n = 3.30 at 495 C, n = 5.24 at 540 C, n = 2.95 at 565 C). At the present time, and in the absence of detailed information relevant to their creep testing conditions, it is not possible to explain the discrepancies to their work. The stress exponents determined in the present work suggest a dislocation climb-controlled creep mechanism, as discussed by Nabarro and de Villers [1]. In this case, the activation energy is expected to be equal to the activation energy for self-diffusion. The apparent activation energy determined in this work lies between 303 and 316 kj/mol in the temperature range from 500 C to 600 C, and is independent of stress over the range investigated. This value is higher than the activation energy for self-diffusion, which is of the order of 242 kj/mol [24]; it is also higher than the activation energy for diffusion of solute atoms in a-ti [25]. Allowing for correction of temperature effects on the elastic modulus, E, according to [1] (Eq. (8)): Q c ˆ Q nkt 2 de 8 E dt where n is the stress exponent, and de/dt is the slope of E vs. T taken from Ref. [26], a value of 286 kj/mol is obtained which is still higher than the activation energy for self-diffusion. However,

11 M. Es-Souni / Materials Characterization 45 (2000) 153± the relatively high concentration of substitutional solute atoms in the alloy under investigation is expected to affect the self-diffusion of Ti, and may account for the high activation energy obtained. Furthermore, the fact that the activation energy is independent of stress indicates that the creep mechanism is governed by the diffusion of vacancies, i.e., by dislocation climb [1]. Recovery creep theories are based on substructure evolution from the primary creep to the steady state creep stage, where a dynamic equilibrium between dislocation emission and annihilation is established. However, since strain recovery was observed beyond the primary creep regime, as illustrated in Fig. 10, and since strain recovery is dependent on primary creep [15,16], it is thought that primary creep is prolonged into secondary creep. The contribution of anelastic deformation to creep would thus lead, particularly for low applied stresses, to an apparently higher creep strain rate than would be expected if only dynamic equilibrium of mobile dislocation density were operating. Based on these results, the model discussed by Beere and Grossland [6] and Lloyd and McElroy [11] involving a dislocation density with a distribution of dislocation link lengths, and therefore a distribution of flow stresses, is thought to be more appropriate to describe the results obtained in this work. In this model the dislocation links with flow stresses higher than the applied stress are immobile and contribute only to the anelastic strain, whereas permanent strain is achieved by the movement of dislocations with flow stresses lower than the applied stress. Steady state is established when the rates of network refinement (work hardening) and coarsening (recovery) are in dynamic equilibrium. The model would also account for the observed anelastic recovery beyond the primary creep stage, assuming that the unbowing of pinned dislocations control the anelastic recovery. This might be supported by the dislocation structures presented above. The network model, however, predicts a stress exponent of 4 [11] instead of 4.7± 4.9 obtained, although Lloyd and McElroy claim that with a Gaussian distribution of dislocation link lengths higher stress exponents might be expected Anelastic creep The experimental results described above show that anelastic recovery is intimately related to primary creep. Furthermore, the anelastic strains have been shown to be always a constant fraction of the elastic strain, with a maximum of 0.7 for the as-received and 0.45 for the heat-treated conditions. An almost linear dependence of anelastic strain on stress has also been obtained. As discussed above, a mechanism involving the unbowing of pinned dislocation segments is more appropriate to describe the results obtained in the present work. Following the analysis of Gibeling and Nix [16], this mechanism would provide a recovery strain approximately equal to 1/3 of the elastic strain, which agrees well with the results of the heat-treated conditions of Fig. 12. Gibeling and Nix [16] argue that the mechanism of unbowing of pinned dislocations in the glide plane should occur at rates which are much too fast to account for the existence of the two kinetics of backflow observed, e.g., Fig. 8. However, if unbowing is assumed to be climb-controlled, the existence of these kinetics may be explained in terms of vacancies being exhausted during climb of edge segments under the effects of internal stress, where, according to Ref. [27], two kinetics corresponding to a transient and a steady state stage are expected. A detailed analysis of these kinetics and their dependencies on stress and temperature will be published in a forthcoming paper. 5. Conclusions The creep behavior of an near a-ti alloy Ti6242Si has been investigated at 500 C using constant stress tensile creep testing. Emphasis was placed on the primary and anelastic, recoverable creep. The following concluding remarks may be inferred from the observations and discussion presented above: For low stresses the primary creep strain shows a linear dependence on stress for all processed microstructures investigated. Primary creep is thought to contain a substantial amount of anelasticity. Unloading in the primary creep regime leads to a substantial creep recovery. For low stresses, primary creep is thought to be controlled by bowing of pinned dislocations. Anelastic, recoverable strain is intimately related to primary creep. Higher primary creep strains lead to higher recoverable strains. Like forward creep, it also shows a transient and a steady state regime. Anelastic strain continues into the steady state creep regime. It is thought that a mechanism based on dynamic equilibrium of strain hardening and recovery may not be sufficient to describe steady state creep in the alloy microstructures investigated.

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