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Deformation mechanisms in the O phase
Intermetallics 8 (2000) 1269±1282
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Deformation mechanisms in the O phase T.K. Nandy *, D. Banerjee Defence Metallurgical Research Laboratory, Hyderabad 500 058, India Received 1 October 1999; accepted 31 May 2000
Abstract The intermetallic Ti2AlNb has a ternary ordered, orthorhombic structure (which is a slightly distorted form of the hexagonal D019, Ti3Al phase) and is the major constituent of the `orthorhombic' alloys of the Ti±Al±Nb system. We explore in this paper the mechanical behaviour of this intermetallic over a wide range of strain rates and temperatures. Thermal activation analysis of the ¯ow behaviour indicates that at low temperatures the ¯ow behaviour is controlled by a strong thermally activated process with small activation volumes typical of a Peierls-type barrier. Dynamic recovery occurs at higher temperatures, but a speci®c ratecontrolling mechanism for ¯ow remains to be identi®ed. The creep of the intermetallic has also been examined in a temperature± strain-rate regime well removed from the DSA regime. Stress exponents decrease slowly from 7 to 5 with increasing temperature and the dislocation structure consists of a three dimensional network linked by attractive junctions. A network model of creep, as proposed for example by McLean, may be appropriate to describe the creep of this intermetallic. The eect of Nb content and a variety of quaternary additions on the mechanical behaviour of the intermetallic has also been evaluated. Nb is shown to strengthen the intermetallic through the thermal component of the ¯ow stress, while Si is found to have the strongest solid solution strengthening eect at low temperatures. Zr and oxygen additions enhance the dynamic strain ageing eect at intermediate temperatures. The Nb content does not aect the creep strength of the intermetallic. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Titanium aluminides, based on Ti3Al; B. Plastic deformation mechanisms; B. Solid-solution hardening; D. Defects: dislocation geometry and arrangement
1. Introduction The O phase based on the stoichiometry Ti2AlNb (orthorhombic structure with Cmcm symmetry) [1] is the major constituent of multiphase orthorhombic aluminides developed for high temperature applications [2,3]. The metallurgy of this intermetallic has been reviewed [4] and it is shown to exist in two ordered forms designated O1 and O2 (Fig. 1). A preliminary description of the mechanical behaviour of the low temperature, O2 phase is available [5±8]. An exhaustive study [9] has recently been completed of its deformation behaviour as a function of Nb content, and with several quaternary substitutional and interstitial (oxygen) additions over the domain of strain rate and temperature shown in Fig. 2. This work has been carried out on polycrystalline, single phase compositions. Additional work on the Ti±25Al±25Nb composition is reported by Popille et al. [10,11]. In this paper we summarise our * Corresponding author.
understanding of the rate- controlling mechanisms of ¯ow over the temperature±strain rate domain of Fig. 2, and the eect of substitutional and interstitial alloying, with a brief account of supporting data. More detailed descriptions of ¯ow behaviour in various strain rate temperature domains are under preparation and will be published elsewhere. 2. Experimental techniques All alloys were non-consumable vacuum arc-remelted several times to ensure chemical homogeneity. Since these alloys are dicult to process, a massive transformation from the high temperature b(bcc) phase of these compositions to the O2 phase [4] was utilized to realize equiaxed grains of the O2 phase through heat treatment of the cast alloys (without mechanical work). The heat treatment consisted of a high temperature solution treatment in the single phase b region followed by a transformation treatment at 900 C to induce the massive reaction. The resulting structure is shown for a
0966-9795/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0966-9795(00)00083-2
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typical composition in Fig. 3. The processing resulted in similar O2 grain sizes and interstitial contents for all compositions (Table 1), except in the cases where the oxygen content was deliberately varied to examine oxygen eects. Compression tests were carried out on cylindrical samples, 6 mm in diameter and 9 mm in length, using a screw-driven Instron machine or a computer-controlled Dartec servohydraulic machine (at higher tempertures) with the temperature maintained to 2 K. All strain rate change tests were carried out on the screw-driven machine. Lubricants such as graphite paste or glass (Deltaglaze) were used at low and high temperature respectively to minimize frictional eects, and a 20±30 min soak time was used to equilibriate temperature before commencing the tests. Creep tests were carried out in air under compression on cylindrical samples of 4 mm diameter and 8 mm length in a constant load machine with the temperature maintained to
1K. Two LVDTs were mounted on compression platens to measure displacement as a function of time. Deformation structures were examined in a Phillips 430T microscope in thin foils made from slices cut at 45 to the compression axis in both types of tests. This was done to maximize the probability of locating grains in which the slip plane would be parallel to the foil plane so as to observe the complete con®guration of dislocations gliding in the slip plane under the maximum resolved shear stress. Elastic modulii and lattice parameters have been measured for all compositions and are available in references [4,9,12]. Experimental details of techniques used in their measurement are provided in [9,12] respectively, and these data have been utilized in various analyses of the compression and creep data given in the subsequent sections of the paper. 3. Flow behaviour in the strain rate range 10ÿ2 to 10ÿ4 sÿ1 3.1. Flow stress, work hardening and strain rate sensitivity Flow stress versus temperature curves for a typical ternary and quaternary composition are shown in Fig. 4. Three distinct temperature regimes of behaviour are apparent. The ¯ow stress decreases quite rapidly with temperature in the low temperature regime, reaches a plateau or increases at intermediate temperatures, and decreases again at high temperatures. Fig. 5 shows typical stress±strain curves in each of these temperature regimes for the Ti±27Al±25Nb alloy. The work hardening rate is not aected by strain rate at low temperatures, but increases slightly with decreasing strain rate at intermediate temperatures, at high tem-
Fig. 1. (a) The crystal structure of the O2 phase in a [001] projection. The hexagonal unit cell of Ti3Al is outlined; (b) Burgers vectors in the O2 phase shown schematically in a hexagonal unit cell to facilitate comparison with Ti3Al.
Fig. 2. The temperature/strain-rate domain of mechanical behaviour investigated in this study.
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: V MkT 1n" MnkT 3 3 b b b3
Fig. 3. Microstructure of the Ti±27Al±25Nb alloy. This structure is typical of all alloy compositions evaluated in this study and shows equiaxed O2 grains formed by the massive transformation within original grains of the b phase.
peratures, on the other hand, the work hardening decreases signi®cantly with decreasing strain rate. The transients associated with strain rate jumps are described in Fig. 6. The strain rate sensitivity is positive at low temperatures. The total strain rate sensitivity is negative after an initial positive transient at intermediate temperatures, and is again positive at high temperatures while the transient peak remains. Serrations are observed in the stress±strain curves at intermediate temperatures (Fig. 7). The temperature dependence of the work hardening rate and total strain rate sensitivity is shown in Fig. 8 for a high-oxygen alloy. The three distinctive regimes of ¯ow stress behaviour as a function of temperature are re¯ected in the variation of work hardening and strain rate sensitivity as well. 3.2. Activation volumes The operational activation volume was determined in the three temperature regimes from strain rate jump tests from the expression.
1
that is, the stress dependence of the pre-exponential : term " 0 in the rate equation for thermally activated ¯ow, ÿ : : " "0 exp ÿG is neglected in comparison with the RT stress-dependence of G, the activation free enthalpy. As suggested by Kocks et al, [13], this is justi®ed when : ln " (n) is larger than 10. An the magnitude of the term dd ln average atomic volume (1.6910ÿ29 m3) has been used for the term b3, rather than the magnitude of the Burgers vector since the latter varies considerably depending on the slip system, and whether the activation event involves superpartials or perfect dislocations. A value of 5 has been used for the Taylor Factor (M) as in the case of Ti [14]. The activation volume is shown as a function of strain in Fig. 9 for the Ti±27Al±25Nb alloy at 228, 923 and 1073 K. Again, signi®cant dierences in the magnitude of the activation volume at each of these temperatures indicate that dierent rate-controlling mechanisms are operative. 3.3. Dislocation structures Three dierent slip systems are observed to be operative in the O2 phase at these strain rates. These are indicated in Fig. 1. The [100] and <110] dislocations, designated `a' and `a*', respectively, are analogus to <1120> dislocations in a-Ti, while [102] dislocations are analogus to <1123> dislocations. The <114] dislocation has not been observed in this study. Table 2 summarizes observations of the dislocation structure in the low and high temperature regimes. Dislocation structures formed on deformation at low temperatures (228 K, 10ÿ4 sÿ1 and 2% strain) are shown in Fig. 10 and 11. Fig. 10a shows `2c+a' dislocations in slip bands on pyramidal (221) planes in screw orientations, and
Table 1 Alloy compositions and grain sizea Alloy designation
Ti±27Al±18Nb Ti±27Al±20Nb Ti±27Al±22Nb Ti±27Al±25Nb Ti±27Al±20Nb±1Ta Ti±27Al±20Nb±1Mo Ti±27Al±20Nb±1V Ti±27Al±20Nb±1Zr Ti±27Al±20Nb±0.5Si GR1 GR2 a
Al
27.1 27.4 27.3 26.9 27.5 27.0 27.8 26.6 27.7 27.4 27.2
All compositions are in at.%
Nb
18.5 20.3 22.3 24.3 20.5 19.6 19.9 19.5 19.0 20.9 20.0
Quaternary elements
Interstitial content O
N
H
C
± ± ± ± 0.8Ta 0.8Mo 1.1V 0.9Zr 0.6Si ± ±
0.220 0.169 0.220 0.230 0.250 0.200 0.260 0.240 0.230 0.328 0.707
0.047 0.055 0.055 0.053 0.73 0.066 0.057 0.036 0.059 0.018 0.019
0.150 0.100 0.190 0.260 0.180 0.130 0.280 0.150 0.140 0.180 0.160
± 0.064 ± ± ± ± ± ± ± 0.047 0.044
Grain size (mm) 157 164 166 153 161 157 176 195 188 148 160
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Fig. 10b shows elongated screws of `2c+a' dislocations in (010) planes. `a' and `a*' dislocations in the basal plane are shown in Fig. 11a while `a*' dislocations gliding in the prismatic plane are shown in Fig. 11b. Detailed weak beam observations [9] are not included in this paper but their results are indicated in Table 2. It has not been possible to draw any conclusions regarding the relative CRSS of dierent slip systems. Pyramidal slip bands of `2c+a' dislocations are observed in almost all grains, as are random distributions of `a' and `a*' dislocations. An important feature of the overall dislocation structure is that no dislocation tangles or cell structures are present in samples deformed to about 2% true strain, but dipoles of `a*' dislocations and attractive junctions of all three types of dislocations are frequently observed. Low mobility orientations are found for all dislocations and are associated with classic features of dislocation dissociation in ordered alloys. The con®guration observed for `a*' dislocations gliding on (110) planes is identical to that for prismatic slip in a-Ti
Fig. 4. (a) Flow stress versus temperature curves for the Ti±27Al± 25Nb and Ti±27Al±20Nb±1Zr alloys; (b) modulus normalised ¯ow stress curves for the same alloys.
[15] and Ti3Al [16] at this temperature. In both these materials, screw orientations become increasingly less mobile at lower temperatures. The low mobility of screw orientations of `a*' dislocations is apparent when `a*' dislocations glide in the basal plane (Fig. 11a). The screw segments in this case are APB dissociated on the prismatic cross-slip plane, but cannot bow out under the
Fig. 5. Stress±strain curves for the Ti±27Al±25Nb alloy at 228, 923 and 1173 K.
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Table 2 A summary of dislocation con®gurations in the O2 phase Slip system
Low temperature 228 K 10ÿ4Sÿ1
High temperature, 1073 K 10ÿ4Sÿ1
High temperature, 990 K 300 MPa, creep
Pyramidal (221) `2c+a'
Dislocations in slip bands Screw orientations immobile Slip plane disordering Four-fold dissociation Cross-slip of superpartials
Randomly distributed Screw orientations immobile No Slip plane discordering Edge segments pinned by climb and trail loops Four-fold dissociation Cross-slip of superpartials
Absent except as reaction product of `a*' and `c' dislocations
Prismatic, (010) `2c+a'
Randomly distributed Screw orientations immobile Two-fold APB dissociation
Absent
Absent
Prismatic (010) `c'
Absent
Absent
Edge segments immobile, but climb
Basal, (001) `a'
Randomly distributed Point pinning of screw orientations Curved segments drag SISF dissociated cusps two-fold APB dissociation
Randomly distributed Curved segments drag SISF dissociated cusps two-fold APB dissociation
Randomly distributed 2-fold APB dissociation
Prismatic, (110) and basal, (001) `a*'
Randomly distributed
Randomly distributed
Randomly distributed
Screw orientations less mobile two-fold APB dissociation
Screw orientations less mobile three-fold dissociation
Smoothly curved three-fold dissociation
General features
`a*' Dipoles Attractive junctions No tangles or cell structure
Attractive junctions No tangles or cell structures
Attractive junctions No subgrain structure
action of a relatively lower resolved shear stress. Even under the action of a high resolved shear stress on the (110) planes, the `a*' dislocations tend to elongate in screw directions (Fig. 11b). Attractive junctions are still observed at high temperatures (1073 K), and again, no subgrain structures or dislocation tangles are present. `2c+a' dislocations are now randomly distributed (Fig. 12). Two types of con®gurations are apparent in the ®gure: straight, paired segments in screw orientations and paired dislocations with a coiled appearance. These dislocations trail loops of the superpartials which are thought to be generated by climb processes. `a' Dislocations are observed as highly cusped loops on the basal plane (Fig. 13a). The cusps are associated with SISF faults. The barrier to the motion of their screw orientations no longer exists. The dissociation product of `a*' dislocations at high temperatures is dierent from that at low temperatures. They are triple dissociated into complex faults, rather than APB dissociated, and screw orientations are less mobile (Fig. 13b). 3.4. Alloying eects The concentration of Nb has been varied from 18 at.% to the stoichiometric value of 25 at.% in this study, and the eect of a variety of quaternary alloying additions to a base ternary composition containing 20 at.% Nb has been evaluated. No change in the basic character of ¯ow behaviour (as described in Section 3.1) has been observed for any of the compositions studied.
Edge segments climb dissociated and climb out of the slip plane
The ¯ow stress at low temperatures can be separated into a thermal component and a long-range fraction, and the mechanical threshold for glide obtained using the Kocks et al. [13], assuming a triangular obstacle pro®le (which appears to be valid for a-Ti [14,17]). The eect of Nb content and quaternary additions is shown in Fig. 14. No Fleischer-type analysis [18,19] has been attempted for the eect of niobium since such an analysis is unlikely to be valid in concentrated solid solutions. The eect of quaternary additions has been evaluated through Fleischer plots for the combined atomic size and modulus mismatch parameter for both edge and screw dislocations. While no correlations are observed between the thermal component of the ¯ow stress and the mismatch parameter in either case, a reasonable correlation does exist between the long-range component of the ¯ow stress and the mismatch parameter for edge dislocations and this is shown in Fig. 15. The atomic mismatch parameters are obtained from a speci®c atomic volume derived from lattice parameter data since quaternary additions aect the a, b and c parameters of the base O2 composition dierently. Thus, "a
1 da0 a0 dc
2
" 1 j" j2
3
and, "0
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Fig. 6. Transients associated with strain-rate jumps in the three temperature regimes and the determination of stress changes to obtain the strain-rate sensitivity.
p where a0 3 abc=16 and " 1 d dc and is the shear modulus. The data used are available in [4,9]. Since an anomalous strengthening has been observed at intermediate temperatures, the eect of Nb content and various quaternary additions is shown in Fig. 16 in terms of a modulus normalised dierence between the peak ¯ow stress (in the anomalous regime) and the longrange stress. Thus the plot evaluates the strength of the anomalous eect and shows that Zr strongly aects the ¯ow stress at intermediate temperatures (as does oxygen in Fig. 8). The eect of quaternary additions at high temperatures is shown in Fig. 17, in terms of a modulus normalised ¯ow stress at 1173 K. Mo is seen to be the most eective strengthening addition at high temperatures. 4. Creep 4.1. Stress exponents and activation parameters Creep of the O2 alloys was evaluated in the temperature range from 973 to 1023 K and stresses ranging from 250 to 500 MPa. Creep at all stresses showed
Fig. 7. Serrated yielding at 773 K in the Ti±27Al±25Nb alloy.
`normal' primary creep after stress jumps characteristic of class-II pure metal behaviour, while stress dips result in an apparent incubation period followed by a `normal' transient. A well-de®ned steady state is obtained at all stress levels. Fig. 18 shows conventional stress±steady state strain rate plots of the ternary alloys. Stress exponents decrease mildly from 7 at 973 K to 5 at 1023 K. The Nb concentration of the ternary alloys does not aect creep strength. The steady state creep behaviour of the quaternary alloys is shown in Fig. 19 at 973 K. Quaternary additions do not signi®cantly change the stress exponents. Since the changes in stress exponents with temperature are small, they have been ignored in obtaining activation energy values for ternary and quaternary alloys from Arrhenius plots (Table 3). The activation volume derived from the steady-state strain rate
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Table 3 Activation energy values in creep in comparison to data for diusion and creep in Ti3Al Alloy
Activation energy (kJ/mol)
Ref.
Ti±27Al±18Nb Ti±27Al±20Nb Ti±27Al±25Nb Ti±27Al±20Nb±1Ta
327 315 294 326
Ti±27Al±20Nb±1Mo Ti±27Al±20Nb±1V Ti±27Al±20Nb±1Zr Ti±27Al±20Nb±0.5Si
347 348 330 310
Interdiusion in Ti3Al
312
[40]
Creep of Ti3Al Ti±25Al Ti±27Al
206 260±400
[41] [42]
Current work
Fig. 9. Activation volume as a function of strain in the Ti±27Al±25Nb alloy: (a) 228 K, (b) 923 and 1073 K.
: ln " where n dd ln 4.2. Dislocation structure Fig. 8. Modulus normalised ¯ow stress, work hardening rate and strain-rate sensitivity in the Ti±27Al±20Nb alloy containing 0.7 at.% oxygen.
at dierent stress levels is: shown in Fig. 20. Since the ln " magnitude of the term dd ln in creep is of the order of 4± 7, the stress dependence of the prexponential term in the rate equation can no longer be ignored. The activation volume is therefore derived assuming a dislocation density which is a square function of the applied stress. On the assumption that creep may be climb controlled (as discussed in greater detail in the subsequent section), the Taylor factor, M, is not included in the calculation since the climb of dislocations occurs under normal stresses or osmotic forces. Then, the expression for activation volume is V
1 n ÿ 2kT b3
4
Fig. 21 shows dislocation structures in creep. `a' dislocations are present as loops which are APB dissociated. The SISF dissociated cusps, formed on deformation at higher strain rates, are absent. Edge segments of such loops climb out of their slip plane. `a*' dislocations are triple dissociated on prismatic (110) planes as at higher strain rates at these temperatures. However, the barrier to the motion of screw orientations is no longer present and the dislocations are smoothly curved. No evidence for the climb of these dislocations has been found. Perfect `c' dislocations (c[001]), rather than `2c+a' dislocations, are randomly distributed with a predominance of edge segments. It has been deduced that these glide on prismatic, (010), planes and that edge segments climb out of their slip plane. No subgrain structures are observed. Attractive junctions of `a', `c' and `a*' dislocations are commonly
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Fig. 10. Deformation at 228 K, `2c+a', [102], dislocations: (a) screw segments in slip bands lying in (221) planes, (b) elongated screw orientations in the (010) plane (from Ref. [5]).
present and `a*' dislocations are pinned in their glide plane by such attractive junctions as shown in Fig. 22. Thus, the dislocation structure consists of a threedimensional network of dislocations linked by attractive junctions.
Fig. 11. Deformation at 228 K: (a) `a' dislocations in the basal plane. Screw orientations parallel to the Burgers vector and curved `a' segments shown by the arrow marked C1. The second set of screw segments are `a*' dislocations; (b) `a*' dislocations in the (110) plane. The Burgers vector is almost parallel to the g-vector.
5. Discussion The results described in the previous sections indicate that four distinct rate-controlling mechanisms exist for ¯ow in the O2 phase over the temperature/strain rate domain that has been investigated (Fig. 2). These distinct ¯ow mechanisms are apparent in the variation of ¯ow stress, work hardening and strain rate sensitivity with temperature, as well as the magnitudes of the activation volumes associated with ¯ow in each of these domains, as seen in Figs. 4, 8 and 9. In this section, we discuss ¯ow behaviour in these domains and our hypotheses on speci®c rate-controlling mechanisms.
Fig. 12. Deformation at 1073 K. Randomly distributed `2c+a' dislocations are present as paired, screw oriented segments and pairs which appear to be coiled. Small loops are also visible.
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Fig. 14. Solid-solution strengthening in the O2 phase for the thermal and long-range components of stress.
Fig. 13. Deformation at 1073 K: (a) cusped `a' dislocations in the basal plane. The straight segments are `a*' dislocations. The absence of screw segments should be contrasted with Fig. 11a. (b) `a*' dislocations in the (110) plane. Two sets of `a*' dislocations and `2c+a' dislocations are present in the micrograph.
5.1. The low temperature domain (77±298 K) The temperature dependence of ¯ow stress in this range is much stronger than that of fcc metals such as Cu, not as strong as that of bcc metals such as Ta, and very similar to that of a-Ti [14]. The ¯ow behaviour of polycrystalline materials with several independent slip systems may be controlled by that slip system with the lowest CRSS, if a reasonable dierence in CRSS exists for the dierent slip systems. It is on this basis that Conrad [14] concludes that ¯ow in a-Ti is controlled by the rate-controlling mechanism for <1120> prismatic slip. The temperature dependence of ¯ow stress in the O2 phase is quite similar to that of <1120> prismatic glide in both a-Ti [14] and Ti3Al [20]. The magnitude of the activation volume, 50±200b3, is also very similar to that of polycrystalline a-Ti, and <1120> {1100} glide in a-Ti [15] and Ti3Al [16].
Fig. 15. The variation of the long-range component of ¯ow stress per atomic percent of quaternary addition plotted against a combined atomic size and modulus mismatch parameter for edge dislocations (after Refs. [18,19]).
The dislocation structures observed indicate that two broad rate-controlling mechanisms may be operative. First, since extensive dislocation interactions are possible, the rate-controlling mechanism may be de®ned by repulsive interactions between glide and forest dislocations as in fcc materials such as Cu. The temperature dependence of ¯ow stress (Fig. 4) and the magnitude and strain-dependence of activation volume (Fig. 9) immediately eliminate this possibility. Nevertheless, the presence of attractive junctions constitutes the source of a long-range stress [21] in the ¯ow stress versus temperature curve. Secondly, the rate-controlling mechanism can be de®ned by one or more of obstacles to
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Fig. 16. The modulus normalised dierence between the peak ¯ow stress and the long-range component of ¯ow stress as a function of Nb content. Data for quaternary alloys are plotted at the base Nb concentration.
Fig. 18. The steady-state strain ate plotted against applied stress in creep for ternary alloys (from Ref. [5]).
Fig. 17. The ¯ow stress at 1173 K for dierent quaternary alloys compared with the Ti±27Al±25Nb alloy.
dislocation motion derived from the intrinsic properties of the slip system. This is extremely likely since each of the operative slip systems contain such obstacles as summarised in Table 2. The speci®c rate-controlling mechanism amongst these possibilities is harder to identify. Since no single crystal data are available for the O2 phase, no quantitative estimates for CRSS exist. Further, in contrast to Ti3Al, [22] the frequency of occurrence of pyramidal `2c+a' glide, basal glide and prismatic glide is qualitatively similar in polycrystalline O2 phase, so that it has not been possible to draw any conclusions regarding the softest slip system. Therefore, only indirect evidence is utilised to speculate on the possible rate-controlling mechanisms for ¯ow in this temperature domain. Since (a) the temperature dependence of ¯ow stress, (b) the magnitude of activation volume, and (c) the dislocation con®guration
Fig. 19. The steady-state strain rate plotted against applied stress in creep for quaternary alloys at 973 K in comparison with the base ternary alloy, Ti±27Al±20Nb.
for `a*' (110) glide, are all similar to that of a-Ti and Ti3Al for [1120] prismatic glide, it is concluded that the rate-controlling mechanism is governed by the kinetics of glide in the `a*' (110) slip system. The magnitude of the activation volume (50±200b3) and other detailed analysis led Conrad [14] to conclude that prismatic glide in Ti is controlled by interstitials acting as obstacles to dislocation motion. More recently Farenc et al. [23] proposed (in a development of suggestions by Sob et al. [24] and Naka et al. [15,25]) that <1120> dislocations in Ti (and equivalent superpartials
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Fig. 20. The activation volume in creep as a function of applied stress for the Ti±27Al±25Nb alloy.
of ordered Ti3Al) have a non-planar core structure and their glide is controlled by the recombination of partials and nucleation of kink pairs. They derive appropriate activation volumes controlled by the jump distance of kinks perpendicular to the dislocation line before locking occurs in a Peierls energy well by dissociation into the non-planar structure. Similar considerations may apply to `a*' (110) glide in O2, given the similarity in dislocation con®gurations. No tests have been carried out in this study in the temperature range 300±500 K where a discontinuity in the temperature dependence of activation volume occurs in aTi [14,23]. Fig. 14 indicates that Nb strongly aects the thermal component of ¯ow stress in the low temperature regime and only mildly in¯uences the long-range stress component. Si is the strongest solid solution strengthening element and increases both the thermal and long-range stress components. The thermal component of the ¯ow stress could not be correlated with modulus or size mismatch factors for quaternary additions. If the mechanism discussed earlier for the glide of `a*' dislocations is valid, then Nb and various quaternary additions may be deduced to aect the recombination stress required to transform the hypothesised non-planar core structure of the `a*' superpartials. The long-range stress component correlates with the combined size and modulus mismatch factor for edge dislocations (Fig. 15), and is thus associated with conventional strengthening. In a polycrystalline material such as a-Ti, the Hall±Petch constant, k, has an athermal nature [14]. It is possible that the mild decrease of the long- range stress component with Nb may arise from an eect on this term. Grain size eects have not been evaluated in this study.
Fig. 21. Dislocation structures in creep: (a) [001], `c', dislocations showing the dominance of edge segments; (b) `a' dislocations in the basal plane; (c) `a*' dislocations in prismatic plane along with short segments of `c' dislocations (from Ref. [5]).
5.2. The intermediate temperature domain (500±1000 K) The intermediate temperature domain is initiated by the appearance of a plateau in the ¯ow stress versus temperature plots, or an anomalous increase in the ¯ow stress in the modulus normalised plots. Fig. 8 for the
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Fig. 22. `a*' Dislocations in the prismatic plane pinned by attractive junctions with `c' dislocations.
magnitude of the activation volume (obtained from the instantaneous strain rate sensitivity) and its strain dependence in this temperature domain (Fig. 9) suggest a forest intersection mechanism as may be expected in a weakly temperature-dependent regime. The negative strain rate sensitivity distinguishes dynamic strain aging behaviour from the eects rising from dislocation exhaustion processes in many intermetallics which also exhibit peaks in work hardening coupled with anomalous strengthening, but where the strain rate sensitivity can be zero or very slightly positive [31]. The activation energy of the dynamic strain aging process has not been determined in this study. Nevertheless, oxygen can be deduced to be the solute responsible for the dynamic strain aging eect. Fig. 23 shows the temperatures for the onset of serrations at two different strain rates in the Ti±27Al±25Nb alloy and compares this data to the eect in a-Ti where oxygen has been shown to be the main contributor to the dynamic strain-ageing eect in this temperature regime [14]. The peak ¯ow stress in this temperature domain is much higher for the Zr containing alloys than for other quaternary, substitutional additions (Fig. 16). This strong dynamic strain aging eect of Zr and Si may be related to their atomic radius (0.16 nm for Zr and 0.117 nm for Si) in relation to that of Ti (0.147 nm), Al (0.143 nm), Nb (0.147 nm) and Ta (0.147 nm). It is possible that other contributions to anomalous behaviour exist in this temperature regime. For example, the CRSS for pyramidal, `2c+a', glide in Ti3Al shows anomalous strengthening over the temperature range 400±1000 K [32]. `2c+a' glide in the O2 phase may show anomalous behaviour as well. 5.3. High temperatures (1000±1173 K) at strain rates 10ÿ4 to 10ÿ2 sÿ1
Fig. 23. A strain±rate temperature plot indicating the start of serrations in the stress±strain curves of Ti±27Al±25Nb, with data from a-Ti [14] superimposed.
high oxygen alloy contains all the classic signatures of a dynamic strain aging eect [26], that is a peak in the ¯ow stress and work hardening rate and a negative strain rate sensitivity, accompanied by serrations in the stress±strain curves. The instantaneous strain rate sensitivity (de®ned by i in Fig. 6) is always positive and is determined by the basic dislocation mechanism controlling ¯ow [27±30]. The
The ¯ow stress decreases more rapidly with temperature beyond 1000 K, and this decrease is more apparent at higher strains. The transformation from O2 to O1 at temperatures above 1200 K precluded a very detailed analysis at temperatures well beyond the dynamic strain-ageing regime at these strain rates. A distinctive ¯ow behaviour is, however, apparent from the very strong eect of strain rate on work hardening behaviour (Fig. 5) and the magnitude and strain dependence of activation volume (Fig. 9). A variety of mechanisms may account for the lack of work hardening at low strain rates. Recrystallisation or high-angle, grainboundary migration have been ruled out by optical metallography following the tests. Thus, dislocation mechanisms are required to explain the behaviour. It is clear that climb or cross-slip assisted recovery must occur to explain the lack of work hardening. However, ¯ow may be controlled by recovery, or the operation of high temperature thermally activated mechanisms such
T.K. Nandy, D. Banerjee / Intermetallics 8 (2000) 1269±1282
between the other possibilities. It is also dicult to determine precisely the eect of alloying additions to the ¯ow stress since (i) a possible strain-aging contribution continues to exist as yield points are still observed on strain rate jumps (Fig. 6), (ii) recovery rates may be determined by diusion of atomic species and (iii) the eect of alloying on the activation parameters of the rate-controlling obstacles to ¯ow is not known. Fig. 17 shows that Mo additions confer the highest strength at these temperatures.
Table 4 A summary of deformation mechanisms in the O2 phasea Temperature/ Activation strain-rate domain parameters
Possible rate-controlling mechanism
77±298 K 10ÿ4±10ÿ2 sÿ1
V=50±200 b3 Peierl's forces on Very mildly strain-dependent <100]{110) glide
500±1000 K 10ÿ4±10ÿ2 sÿ1
V=2000±2500 b3 Strain-dependent
Forest intersection mechanism with super-imposed dynamic strain aging
1000±1173 K 10ÿ4±10ÿ2 sÿ1
V=1000-1500 b3 Strain-independent
Mechanism not identi®ed, signi®cant dynamic recovery
973±1023 K 10ÿ9±10ÿ6 sÿ1 200±500 MPa
V=6±14 b3 n=4±7 Q=290±350 kJ/mol
Climb controlled network recovery
a
1281
5.4. Creep Stress exponents for steady state creep in ternary and quaternary alloys lie in the range 4±7, while activation energies lie between 295 and 350 kJ/mol (Table 3). No subgrain structure is formed in steady-state creep. Rather, the dislocation structure is typical of a threedimensional network of dislocations with three dierent Burgers vectors `a', `a*' and `c'. Evidence for a climb of `a' and `c' dislocations has been obtained, while `a*' dislocations are observed to only glide. The dislocation structure suggests that classical network theories of creep [35±39] should be applicable. In concept, these theories are remarkably simple. The network size is re®ned by the mechanical escape of dislocations from pinning points at the nodes of the network (at a critical link length de®ned by the applied stress) and their interaction to form attractive junctions. Coarsening of the network by glide and climb decreases the dislocation density. The balance between network recovery by coarsening and network re®nement de®nes the steady-state. A consideration of various processes involved in steady state creep within the framework of the network theory indicates that several processes must occur, each of which can de®ne the rate-controlling process. These are (1) the glide of free dislocations after escaping from the network (2) climb of the links (3) movement of the nodes of the network and (4) the escape of dislocations
V activation volume, Q activation energy, n stress exponent
as the motion of jogged screw dislocations [33] or the unzipping of attractive junctions [34], or any other dislocation mechanism. The dislocation structure (Table 2) suggests obstacles to the glide of dislocations in the form of attractive junctions, possible non-conservative motion of jogs in the screw orientation of `a*' dislocations, trailing of SISF dipoles of `a' dislocations in the basal plane, pinning of edge segments of `2c+a' dislocations by climb, and the immobilisation of their screw orientations by an unknown process. Since the activation volumes are strain-independent, thermal unzipping of attractive junctions should be ruled out as a possible rate-controlling mechanism. The activation volumes are also too large for dislocation climb to be the rate-controlling process. Current data are insucient to distinguish Table 5 A summary of alloying eects on the mechanical behaviour of the O2 phase Domain
Nb eects a
Substitutional additions
Oxygen eects
77±298 K 10ÿ4±10ÿ2 sÿ1
increases with Nb decreases midly with Nb
* for Si>Ta>Nb>Mo>Zr>V cfor V>Si>Mo>Ta>Zr>Nb
Inconclusive and not discussed in the paper
500±1000 K 10ÿ4±10ÿ2 sÿ1
peak ÿ =b decreases with Nb
1000±1173 K 10ÿ4±10ÿ2 sÿ1
Not evaluated in this work
peak ÿ = for Zr>Si>Mo>V>Ta at 1173 K Mo>V>Zr>Ta at 10ÿ4Sÿ1
peak ÿ = increases strongly with oxygen Not evaluated
Creep 973±1023 K 10ÿ9sÿ1±10ÿ6 sÿ1
Steady-state creep insensitive to Nb
Steady-state creep strength for Zr higher than other elements
Not evaluated
a b c
, thermal component of ¯ow stress at low temperature. , modulus. long-range component of ¯ow stress.
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from the attractive junctions by an athermal stress [21] or its thermal unzipping [34]. The values of stress exponents and activation energies (Table 3) suggest that climb of dislocations is the ratecontrolling step. While no diusivity data are available for the O2 phase, the activation energy values for creep lie in the range of the activation energy for interdiusion in Ti3Al. Further support for climb control emerges from the magnitude of the activation volume (Fig. 20) which ranges from 6b3 to 14b3. If the climb of superdislocations should occur in a coupled manner, the process would require the attachment of two vacancies, one to each superpartial, for simultaneous climb by one atomic plane. The activation volumes would then be halved since the normalisation factor would be 2(b)3. No change in creep mechanism occurs with either Nb concentration or with any of the substitutional quaternary additions. 6. Conclusion In summary, the mechanical behaviour of the O2 phase has been examined over temperatures ranging from 77 to 1173 K and strain rates from 10ÿ4 to 10ÿ2 sÿ1, and in creep at stress levels from 200 to 500 MPa at temperatures ranging from 973 to 1023 K. Four distinct domains of ¯ow behaviour have been identi®ed, each with its unique rate-controlling mechanism of ¯ow. These are summarized in Table 4. Alloying eects have been evaluated. These include the variation of the Nb content of the intermetallic and a variety of substitutional additions, as well as interstitial oxygen. The eect of alloying is summarised in Table 5. Acknowledgements The authors are grateful to the Defence Research and Development Organisation of India and the Indo-US grant No. N00014-95-0132 for ®nancial support. Grant Rowe of GE, CR&D melted alloys with dierent oxygen contents for us. Patrick Veyssiere spent many hours discussing the intricacies of weak-beam microscopy and analysing various dislocation structures and con®gurations in the O2 phase. Jean-Loup Strudel contributed to the analysis of results. We thank all of them.
References [1] Banerjee D, Gogia AK, Nandy TK, Joshi VA. Acta Metall 1988;36:871. [2] Rowe RG. US patent 5032357;1991. [3] Gogia AK, Nandy TK, Banerjee D, Carisey T, Strudel JL, Franchet JM. Intermetallics 1998;6:741. [4] Banerjee D. Prog Mater Sci 1997;42:135. [5] Nandy TK, Banerjee D. In: Nathal MV et al., editors. Structural intermetallics 1997; Warrendale (PA): TMS, 1997. p. 777. [6] Banerjee D, Hall EL, Rowe RG. In: Johnson LA et al., editors. High temperature ordered intermetallic alloys-IV: Pittsburgh: MRS, 1991. p. 285. [7] Banerjee D, Rowe RG. In: Froes FH, Caplan I, editors. Titanium-92, science and technology; Warrendale (PA): TMS 1993. p. 1147. [8] Banerjee D. Philos Mag 1995;72:1559. [9] Nandy TK. PhD thesis, Banaras Hindu Universtiy and Defence Metallurgical Research Laboratory, India 1999. [10] Popille F. PhD thesis, Universite de Paris Sud, France 1996. [11] Popille F, Douin J. Philos Mag A 1996;73:1401. [12] Chu F, Mitchell TE, Mazumdar B, Miracle D, Nandy TK, Banerjee D. Intermetallics 1997;5:147. [13] Kocks UF, Argon AS, Ashby MF. Prog Mater Sci 1975;19:1. [14] Conrad H. ProgMaterSci 1981;26:123. [15] Naka S, Lasalmonie A, Costa P, Kubin LP. Philos Mag A 1988;57:717. [16] Inui H, Toda Y, Yamaguchi M. Philos Mag A 1993;67:1315. [17] Follansbee PS, Gray III GT. Metall Trans 1989;20A:863. [18] Fleischer RL. Acta Metall 1961;9:996. [19] Fleischer RL. Acta Metall 1963;11:203. [20] Minonishi Y. Philos Mag A 1991;63:1035. [21] Saada G. Acta Metall 1960;8:841. [22] Court SA, Lofvander JPA, Loretto MH, Fraser HL. Philos Mag A 1989;59:379. [23] Farenc S, Caillard D, Couret A. Acta Metall Mater 1995;43:3669. [24] Sob M, Kratochvil J, Kroupa F. Czech J Phys 1975;B25:872. [25] Naka S, Kubin LP, Perrier C. Philos Mag A 1991;63:1035. [26] Rodriguez P. Bull Mater Sci 1984;6:653. [27] Van Den Beukel A, Kocks UF. 1982; 30:1027. [28] McCormick PG. Acta Metall 1988;12:3061. [29] Kubin LP, Estrin Y. Acta Metall Mater 1990;38:697. [30] Hahner P. Acta Materiala 1997;45:3695. [31] Louchet F. Philos Mag A 1995;72:905. [32] Minonishi Y. Mater Sci Engg A 1995;192/193:830. [33] Sherby OD, Burke PM. Prog Mater Sci 1968;13:328. [34] Sastry DH, Tangri K. Philos Mag A 1975;35:513. [35] McLean D. Trans AIME 1968;242:18. [36] Lagneborg R. Met Sci J 1972;6:127. [37] Burton B. Philos Mag A 1982;45:657. [38] Ardell A, Przystupa MA. Mech Mater 1984;3:319. [39] Ajaja O. Scripta Metall 1990;24:1435. [40] Rusing J, Herzig Ch. Intermetallics 1996;4:647. [41] Mendiratta MG, Lipsitt HA. J Mater Sci 1980;15:2985. [42] Nagae Y, Maruyama K, Oikawa H. Mater Sci Engg 1996;213: 32.
www.elsevier.com/locate/intermet
Deformation mechanisms in the O phase T.K. Nandy *, D. Banerjee Defence Metallurgical Research Laboratory, Hyderabad 500 058, India Received 1 October 1999; accepted 31 May 2000
Abstract The intermetallic Ti2AlNb has a ternary ordered, orthorhombic structure (which is a slightly distorted form of the hexagonal D019, Ti3Al phase) and is the major constituent of the `orthorhombic' alloys of the Ti±Al±Nb system. We explore in this paper the mechanical behaviour of this intermetallic over a wide range of strain rates and temperatures. Thermal activation analysis of the ¯ow behaviour indicates that at low temperatures the ¯ow behaviour is controlled by a strong thermally activated process with small activation volumes typical of a Peierls-type barrier. Dynamic recovery occurs at higher temperatures, but a speci®c ratecontrolling mechanism for ¯ow remains to be identi®ed. The creep of the intermetallic has also been examined in a temperature± strain-rate regime well removed from the DSA regime. Stress exponents decrease slowly from 7 to 5 with increasing temperature and the dislocation structure consists of a three dimensional network linked by attractive junctions. A network model of creep, as proposed for example by McLean, may be appropriate to describe the creep of this intermetallic. The eect of Nb content and a variety of quaternary additions on the mechanical behaviour of the intermetallic has also been evaluated. Nb is shown to strengthen the intermetallic through the thermal component of the ¯ow stress, while Si is found to have the strongest solid solution strengthening eect at low temperatures. Zr and oxygen additions enhance the dynamic strain ageing eect at intermediate temperatures. The Nb content does not aect the creep strength of the intermetallic. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Titanium aluminides, based on Ti3Al; B. Plastic deformation mechanisms; B. Solid-solution hardening; D. Defects: dislocation geometry and arrangement
1. Introduction The O phase based on the stoichiometry Ti2AlNb (orthorhombic structure with Cmcm symmetry) [1] is the major constituent of multiphase orthorhombic aluminides developed for high temperature applications [2,3]. The metallurgy of this intermetallic has been reviewed [4] and it is shown to exist in two ordered forms designated O1 and O2 (Fig. 1). A preliminary description of the mechanical behaviour of the low temperature, O2 phase is available [5±8]. An exhaustive study [9] has recently been completed of its deformation behaviour as a function of Nb content, and with several quaternary substitutional and interstitial (oxygen) additions over the domain of strain rate and temperature shown in Fig. 2. This work has been carried out on polycrystalline, single phase compositions. Additional work on the Ti±25Al±25Nb composition is reported by Popille et al. [10,11]. In this paper we summarise our * Corresponding author.
understanding of the rate- controlling mechanisms of ¯ow over the temperature±strain rate domain of Fig. 2, and the eect of substitutional and interstitial alloying, with a brief account of supporting data. More detailed descriptions of ¯ow behaviour in various strain rate temperature domains are under preparation and will be published elsewhere. 2. Experimental techniques All alloys were non-consumable vacuum arc-remelted several times to ensure chemical homogeneity. Since these alloys are dicult to process, a massive transformation from the high temperature b(bcc) phase of these compositions to the O2 phase [4] was utilized to realize equiaxed grains of the O2 phase through heat treatment of the cast alloys (without mechanical work). The heat treatment consisted of a high temperature solution treatment in the single phase b region followed by a transformation treatment at 900 C to induce the massive reaction. The resulting structure is shown for a
0966-9795/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0966-9795(00)00083-2
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typical composition in Fig. 3. The processing resulted in similar O2 grain sizes and interstitial contents for all compositions (Table 1), except in the cases where the oxygen content was deliberately varied to examine oxygen eects. Compression tests were carried out on cylindrical samples, 6 mm in diameter and 9 mm in length, using a screw-driven Instron machine or a computer-controlled Dartec servohydraulic machine (at higher tempertures) with the temperature maintained to 2 K. All strain rate change tests were carried out on the screw-driven machine. Lubricants such as graphite paste or glass (Deltaglaze) were used at low and high temperature respectively to minimize frictional eects, and a 20±30 min soak time was used to equilibriate temperature before commencing the tests. Creep tests were carried out in air under compression on cylindrical samples of 4 mm diameter and 8 mm length in a constant load machine with the temperature maintained to
1K. Two LVDTs were mounted on compression platens to measure displacement as a function of time. Deformation structures were examined in a Phillips 430T microscope in thin foils made from slices cut at 45 to the compression axis in both types of tests. This was done to maximize the probability of locating grains in which the slip plane would be parallel to the foil plane so as to observe the complete con®guration of dislocations gliding in the slip plane under the maximum resolved shear stress. Elastic modulii and lattice parameters have been measured for all compositions and are available in references [4,9,12]. Experimental details of techniques used in their measurement are provided in [9,12] respectively, and these data have been utilized in various analyses of the compression and creep data given in the subsequent sections of the paper. 3. Flow behaviour in the strain rate range 10ÿ2 to 10ÿ4 sÿ1 3.1. Flow stress, work hardening and strain rate sensitivity Flow stress versus temperature curves for a typical ternary and quaternary composition are shown in Fig. 4. Three distinct temperature regimes of behaviour are apparent. The ¯ow stress decreases quite rapidly with temperature in the low temperature regime, reaches a plateau or increases at intermediate temperatures, and decreases again at high temperatures. Fig. 5 shows typical stress±strain curves in each of these temperature regimes for the Ti±27Al±25Nb alloy. The work hardening rate is not aected by strain rate at low temperatures, but increases slightly with decreasing strain rate at intermediate temperatures, at high tem-
Fig. 1. (a) The crystal structure of the O2 phase in a [001] projection. The hexagonal unit cell of Ti3Al is outlined; (b) Burgers vectors in the O2 phase shown schematically in a hexagonal unit cell to facilitate comparison with Ti3Al.
Fig. 2. The temperature/strain-rate domain of mechanical behaviour investigated in this study.
T.K. Nandy, D. Banerjee / Intermetallics 8 (2000) 1269±1282
1271
: V MkT 1n" MnkT 3 3 b b b3
Fig. 3. Microstructure of the Ti±27Al±25Nb alloy. This structure is typical of all alloy compositions evaluated in this study and shows equiaxed O2 grains formed by the massive transformation within original grains of the b phase.
peratures, on the other hand, the work hardening decreases signi®cantly with decreasing strain rate. The transients associated with strain rate jumps are described in Fig. 6. The strain rate sensitivity is positive at low temperatures. The total strain rate sensitivity is negative after an initial positive transient at intermediate temperatures, and is again positive at high temperatures while the transient peak remains. Serrations are observed in the stress±strain curves at intermediate temperatures (Fig. 7). The temperature dependence of the work hardening rate and total strain rate sensitivity is shown in Fig. 8 for a high-oxygen alloy. The three distinctive regimes of ¯ow stress behaviour as a function of temperature are re¯ected in the variation of work hardening and strain rate sensitivity as well. 3.2. Activation volumes The operational activation volume was determined in the three temperature regimes from strain rate jump tests from the expression.
1
that is, the stress dependence of the pre-exponential : term " 0 in the rate equation for thermally activated ¯ow, ÿ : : " "0 exp ÿG is neglected in comparison with the RT stress-dependence of G, the activation free enthalpy. As suggested by Kocks et al, [13], this is justi®ed when : ln " (n) is larger than 10. An the magnitude of the term dd ln average atomic volume (1.6910ÿ29 m3) has been used for the term b3, rather than the magnitude of the Burgers vector since the latter varies considerably depending on the slip system, and whether the activation event involves superpartials or perfect dislocations. A value of 5 has been used for the Taylor Factor (M) as in the case of Ti [14]. The activation volume is shown as a function of strain in Fig. 9 for the Ti±27Al±25Nb alloy at 228, 923 and 1073 K. Again, signi®cant dierences in the magnitude of the activation volume at each of these temperatures indicate that dierent rate-controlling mechanisms are operative. 3.3. Dislocation structures Three dierent slip systems are observed to be operative in the O2 phase at these strain rates. These are indicated in Fig. 1. The [100] and <110] dislocations, designated `a' and `a*', respectively, are analogus to <1120> dislocations in a-Ti, while [102] dislocations are analogus to <1123> dislocations. The <114] dislocation has not been observed in this study. Table 2 summarizes observations of the dislocation structure in the low and high temperature regimes. Dislocation structures formed on deformation at low temperatures (228 K, 10ÿ4 sÿ1 and 2% strain) are shown in Fig. 10 and 11. Fig. 10a shows `2c+a' dislocations in slip bands on pyramidal (221) planes in screw orientations, and
Table 1 Alloy compositions and grain sizea Alloy designation
Ti±27Al±18Nb Ti±27Al±20Nb Ti±27Al±22Nb Ti±27Al±25Nb Ti±27Al±20Nb±1Ta Ti±27Al±20Nb±1Mo Ti±27Al±20Nb±1V Ti±27Al±20Nb±1Zr Ti±27Al±20Nb±0.5Si GR1 GR2 a
Al
27.1 27.4 27.3 26.9 27.5 27.0 27.8 26.6 27.7 27.4 27.2
All compositions are in at.%
Nb
18.5 20.3 22.3 24.3 20.5 19.6 19.9 19.5 19.0 20.9 20.0
Quaternary elements
Interstitial content O
N
H
C
± ± ± ± 0.8Ta 0.8Mo 1.1V 0.9Zr 0.6Si ± ±
0.220 0.169 0.220 0.230 0.250 0.200 0.260 0.240 0.230 0.328 0.707
0.047 0.055 0.055 0.053 0.73 0.066 0.057 0.036 0.059 0.018 0.019
0.150 0.100 0.190 0.260 0.180 0.130 0.280 0.150 0.140 0.180 0.160
± 0.064 ± ± ± ± ± ± ± 0.047 0.044
Grain size (mm) 157 164 166 153 161 157 176 195 188 148 160
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Fig. 10b shows elongated screws of `2c+a' dislocations in (010) planes. `a' and `a*' dislocations in the basal plane are shown in Fig. 11a while `a*' dislocations gliding in the prismatic plane are shown in Fig. 11b. Detailed weak beam observations [9] are not included in this paper but their results are indicated in Table 2. It has not been possible to draw any conclusions regarding the relative CRSS of dierent slip systems. Pyramidal slip bands of `2c+a' dislocations are observed in almost all grains, as are random distributions of `a' and `a*' dislocations. An important feature of the overall dislocation structure is that no dislocation tangles or cell structures are present in samples deformed to about 2% true strain, but dipoles of `a*' dislocations and attractive junctions of all three types of dislocations are frequently observed. Low mobility orientations are found for all dislocations and are associated with classic features of dislocation dissociation in ordered alloys. The con®guration observed for `a*' dislocations gliding on (110) planes is identical to that for prismatic slip in a-Ti
Fig. 4. (a) Flow stress versus temperature curves for the Ti±27Al± 25Nb and Ti±27Al±20Nb±1Zr alloys; (b) modulus normalised ¯ow stress curves for the same alloys.
[15] and Ti3Al [16] at this temperature. In both these materials, screw orientations become increasingly less mobile at lower temperatures. The low mobility of screw orientations of `a*' dislocations is apparent when `a*' dislocations glide in the basal plane (Fig. 11a). The screw segments in this case are APB dissociated on the prismatic cross-slip plane, but cannot bow out under the
Fig. 5. Stress±strain curves for the Ti±27Al±25Nb alloy at 228, 923 and 1173 K.
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Table 2 A summary of dislocation con®gurations in the O2 phase Slip system
Low temperature 228 K 10ÿ4Sÿ1
High temperature, 1073 K 10ÿ4Sÿ1
High temperature, 990 K 300 MPa, creep
Pyramidal (221) `2c+a'
Dislocations in slip bands Screw orientations immobile Slip plane disordering Four-fold dissociation Cross-slip of superpartials
Randomly distributed Screw orientations immobile No Slip plane discordering Edge segments pinned by climb and trail loops Four-fold dissociation Cross-slip of superpartials
Absent except as reaction product of `a*' and `c' dislocations
Prismatic, (010) `2c+a'
Randomly distributed Screw orientations immobile Two-fold APB dissociation
Absent
Absent
Prismatic (010) `c'
Absent
Absent
Edge segments immobile, but climb
Basal, (001) `a'
Randomly distributed Point pinning of screw orientations Curved segments drag SISF dissociated cusps two-fold APB dissociation
Randomly distributed Curved segments drag SISF dissociated cusps two-fold APB dissociation
Randomly distributed 2-fold APB dissociation
Prismatic, (110) and basal, (001) `a*'
Randomly distributed
Randomly distributed
Randomly distributed
Screw orientations less mobile two-fold APB dissociation
Screw orientations less mobile three-fold dissociation
Smoothly curved three-fold dissociation
General features
`a*' Dipoles Attractive junctions No tangles or cell structure
Attractive junctions No tangles or cell structures
Attractive junctions No subgrain structure
action of a relatively lower resolved shear stress. Even under the action of a high resolved shear stress on the (110) planes, the `a*' dislocations tend to elongate in screw directions (Fig. 11b). Attractive junctions are still observed at high temperatures (1073 K), and again, no subgrain structures or dislocation tangles are present. `2c+a' dislocations are now randomly distributed (Fig. 12). Two types of con®gurations are apparent in the ®gure: straight, paired segments in screw orientations and paired dislocations with a coiled appearance. These dislocations trail loops of the superpartials which are thought to be generated by climb processes. `a' Dislocations are observed as highly cusped loops on the basal plane (Fig. 13a). The cusps are associated with SISF faults. The barrier to the motion of their screw orientations no longer exists. The dissociation product of `a*' dislocations at high temperatures is dierent from that at low temperatures. They are triple dissociated into complex faults, rather than APB dissociated, and screw orientations are less mobile (Fig. 13b). 3.4. Alloying eects The concentration of Nb has been varied from 18 at.% to the stoichiometric value of 25 at.% in this study, and the eect of a variety of quaternary alloying additions to a base ternary composition containing 20 at.% Nb has been evaluated. No change in the basic character of ¯ow behaviour (as described in Section 3.1) has been observed for any of the compositions studied.
Edge segments climb dissociated and climb out of the slip plane
The ¯ow stress at low temperatures can be separated into a thermal component and a long-range fraction, and the mechanical threshold for glide obtained using the Kocks et al. [13], assuming a triangular obstacle pro®le (which appears to be valid for a-Ti [14,17]). The eect of Nb content and quaternary additions is shown in Fig. 14. No Fleischer-type analysis [18,19] has been attempted for the eect of niobium since such an analysis is unlikely to be valid in concentrated solid solutions. The eect of quaternary additions has been evaluated through Fleischer plots for the combined atomic size and modulus mismatch parameter for both edge and screw dislocations. While no correlations are observed between the thermal component of the ¯ow stress and the mismatch parameter in either case, a reasonable correlation does exist between the long-range component of the ¯ow stress and the mismatch parameter for edge dislocations and this is shown in Fig. 15. The atomic mismatch parameters are obtained from a speci®c atomic volume derived from lattice parameter data since quaternary additions aect the a, b and c parameters of the base O2 composition dierently. Thus, "a
1 da0 a0 dc
2
" 1 j" j2
3
and, "0
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Fig. 6. Transients associated with strain-rate jumps in the three temperature regimes and the determination of stress changes to obtain the strain-rate sensitivity.
p where a0 3 abc=16 and " 1 d dc and is the shear modulus. The data used are available in [4,9]. Since an anomalous strengthening has been observed at intermediate temperatures, the eect of Nb content and various quaternary additions is shown in Fig. 16 in terms of a modulus normalised dierence between the peak ¯ow stress (in the anomalous regime) and the longrange stress. Thus the plot evaluates the strength of the anomalous eect and shows that Zr strongly aects the ¯ow stress at intermediate temperatures (as does oxygen in Fig. 8). The eect of quaternary additions at high temperatures is shown in Fig. 17, in terms of a modulus normalised ¯ow stress at 1173 K. Mo is seen to be the most eective strengthening addition at high temperatures. 4. Creep 4.1. Stress exponents and activation parameters Creep of the O2 alloys was evaluated in the temperature range from 973 to 1023 K and stresses ranging from 250 to 500 MPa. Creep at all stresses showed
Fig. 7. Serrated yielding at 773 K in the Ti±27Al±25Nb alloy.
`normal' primary creep after stress jumps characteristic of class-II pure metal behaviour, while stress dips result in an apparent incubation period followed by a `normal' transient. A well-de®ned steady state is obtained at all stress levels. Fig. 18 shows conventional stress±steady state strain rate plots of the ternary alloys. Stress exponents decrease mildly from 7 at 973 K to 5 at 1023 K. The Nb concentration of the ternary alloys does not aect creep strength. The steady state creep behaviour of the quaternary alloys is shown in Fig. 19 at 973 K. Quaternary additions do not signi®cantly change the stress exponents. Since the changes in stress exponents with temperature are small, they have been ignored in obtaining activation energy values for ternary and quaternary alloys from Arrhenius plots (Table 3). The activation volume derived from the steady-state strain rate
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Table 3 Activation energy values in creep in comparison to data for diusion and creep in Ti3Al Alloy
Activation energy (kJ/mol)
Ref.
Ti±27Al±18Nb Ti±27Al±20Nb Ti±27Al±25Nb Ti±27Al±20Nb±1Ta
327 315 294 326
Ti±27Al±20Nb±1Mo Ti±27Al±20Nb±1V Ti±27Al±20Nb±1Zr Ti±27Al±20Nb±0.5Si
347 348 330 310
Interdiusion in Ti3Al
312
[40]
Creep of Ti3Al Ti±25Al Ti±27Al
206 260±400
[41] [42]
Current work
Fig. 9. Activation volume as a function of strain in the Ti±27Al±25Nb alloy: (a) 228 K, (b) 923 and 1073 K.
: ln " where n dd ln 4.2. Dislocation structure Fig. 8. Modulus normalised ¯ow stress, work hardening rate and strain-rate sensitivity in the Ti±27Al±20Nb alloy containing 0.7 at.% oxygen.
at dierent stress levels is: shown in Fig. 20. Since the ln " magnitude of the term dd ln in creep is of the order of 4± 7, the stress dependence of the prexponential term in the rate equation can no longer be ignored. The activation volume is therefore derived assuming a dislocation density which is a square function of the applied stress. On the assumption that creep may be climb controlled (as discussed in greater detail in the subsequent section), the Taylor factor, M, is not included in the calculation since the climb of dislocations occurs under normal stresses or osmotic forces. Then, the expression for activation volume is V
1 n ÿ 2kT b3
4
Fig. 21 shows dislocation structures in creep. `a' dislocations are present as loops which are APB dissociated. The SISF dissociated cusps, formed on deformation at higher strain rates, are absent. Edge segments of such loops climb out of their slip plane. `a*' dislocations are triple dissociated on prismatic (110) planes as at higher strain rates at these temperatures. However, the barrier to the motion of screw orientations is no longer present and the dislocations are smoothly curved. No evidence for the climb of these dislocations has been found. Perfect `c' dislocations (c[001]), rather than `2c+a' dislocations, are randomly distributed with a predominance of edge segments. It has been deduced that these glide on prismatic, (010), planes and that edge segments climb out of their slip plane. No subgrain structures are observed. Attractive junctions of `a', `c' and `a*' dislocations are commonly
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Fig. 10. Deformation at 228 K, `2c+a', [102], dislocations: (a) screw segments in slip bands lying in (221) planes, (b) elongated screw orientations in the (010) plane (from Ref. [5]).
present and `a*' dislocations are pinned in their glide plane by such attractive junctions as shown in Fig. 22. Thus, the dislocation structure consists of a threedimensional network of dislocations linked by attractive junctions.
Fig. 11. Deformation at 228 K: (a) `a' dislocations in the basal plane. Screw orientations parallel to the Burgers vector and curved `a' segments shown by the arrow marked C1. The second set of screw segments are `a*' dislocations; (b) `a*' dislocations in the (110) plane. The Burgers vector is almost parallel to the g-vector.
5. Discussion The results described in the previous sections indicate that four distinct rate-controlling mechanisms exist for ¯ow in the O2 phase over the temperature/strain rate domain that has been investigated (Fig. 2). These distinct ¯ow mechanisms are apparent in the variation of ¯ow stress, work hardening and strain rate sensitivity with temperature, as well as the magnitudes of the activation volumes associated with ¯ow in each of these domains, as seen in Figs. 4, 8 and 9. In this section, we discuss ¯ow behaviour in these domains and our hypotheses on speci®c rate-controlling mechanisms.
Fig. 12. Deformation at 1073 K. Randomly distributed `2c+a' dislocations are present as paired, screw oriented segments and pairs which appear to be coiled. Small loops are also visible.
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Fig. 14. Solid-solution strengthening in the O2 phase for the thermal and long-range components of stress.
Fig. 13. Deformation at 1073 K: (a) cusped `a' dislocations in the basal plane. The straight segments are `a*' dislocations. The absence of screw segments should be contrasted with Fig. 11a. (b) `a*' dislocations in the (110) plane. Two sets of `a*' dislocations and `2c+a' dislocations are present in the micrograph.
5.1. The low temperature domain (77±298 K) The temperature dependence of ¯ow stress in this range is much stronger than that of fcc metals such as Cu, not as strong as that of bcc metals such as Ta, and very similar to that of a-Ti [14]. The ¯ow behaviour of polycrystalline materials with several independent slip systems may be controlled by that slip system with the lowest CRSS, if a reasonable dierence in CRSS exists for the dierent slip systems. It is on this basis that Conrad [14] concludes that ¯ow in a-Ti is controlled by the rate-controlling mechanism for <1120> prismatic slip. The temperature dependence of ¯ow stress in the O2 phase is quite similar to that of <1120> prismatic glide in both a-Ti [14] and Ti3Al [20]. The magnitude of the activation volume, 50±200b3, is also very similar to that of polycrystalline a-Ti, and <1120> {1100} glide in a-Ti [15] and Ti3Al [16].
Fig. 15. The variation of the long-range component of ¯ow stress per atomic percent of quaternary addition plotted against a combined atomic size and modulus mismatch parameter for edge dislocations (after Refs. [18,19]).
The dislocation structures observed indicate that two broad rate-controlling mechanisms may be operative. First, since extensive dislocation interactions are possible, the rate-controlling mechanism may be de®ned by repulsive interactions between glide and forest dislocations as in fcc materials such as Cu. The temperature dependence of ¯ow stress (Fig. 4) and the magnitude and strain-dependence of activation volume (Fig. 9) immediately eliminate this possibility. Nevertheless, the presence of attractive junctions constitutes the source of a long-range stress [21] in the ¯ow stress versus temperature curve. Secondly, the rate-controlling mechanism can be de®ned by one or more of obstacles to
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Fig. 16. The modulus normalised dierence between the peak ¯ow stress and the long-range component of ¯ow stress as a function of Nb content. Data for quaternary alloys are plotted at the base Nb concentration.
Fig. 18. The steady-state strain ate plotted against applied stress in creep for ternary alloys (from Ref. [5]).
Fig. 17. The ¯ow stress at 1173 K for dierent quaternary alloys compared with the Ti±27Al±25Nb alloy.
dislocation motion derived from the intrinsic properties of the slip system. This is extremely likely since each of the operative slip systems contain such obstacles as summarised in Table 2. The speci®c rate-controlling mechanism amongst these possibilities is harder to identify. Since no single crystal data are available for the O2 phase, no quantitative estimates for CRSS exist. Further, in contrast to Ti3Al, [22] the frequency of occurrence of pyramidal `2c+a' glide, basal glide and prismatic glide is qualitatively similar in polycrystalline O2 phase, so that it has not been possible to draw any conclusions regarding the softest slip system. Therefore, only indirect evidence is utilised to speculate on the possible rate-controlling mechanisms for ¯ow in this temperature domain. Since (a) the temperature dependence of ¯ow stress, (b) the magnitude of activation volume, and (c) the dislocation con®guration
Fig. 19. The steady-state strain rate plotted against applied stress in creep for quaternary alloys at 973 K in comparison with the base ternary alloy, Ti±27Al±20Nb.
for `a*' (110) glide, are all similar to that of a-Ti and Ti3Al for [1120] prismatic glide, it is concluded that the rate-controlling mechanism is governed by the kinetics of glide in the `a*' (110) slip system. The magnitude of the activation volume (50±200b3) and other detailed analysis led Conrad [14] to conclude that prismatic glide in Ti is controlled by interstitials acting as obstacles to dislocation motion. More recently Farenc et al. [23] proposed (in a development of suggestions by Sob et al. [24] and Naka et al. [15,25]) that <1120> dislocations in Ti (and equivalent superpartials
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Fig. 20. The activation volume in creep as a function of applied stress for the Ti±27Al±25Nb alloy.
of ordered Ti3Al) have a non-planar core structure and their glide is controlled by the recombination of partials and nucleation of kink pairs. They derive appropriate activation volumes controlled by the jump distance of kinks perpendicular to the dislocation line before locking occurs in a Peierls energy well by dissociation into the non-planar structure. Similar considerations may apply to `a*' (110) glide in O2, given the similarity in dislocation con®gurations. No tests have been carried out in this study in the temperature range 300±500 K where a discontinuity in the temperature dependence of activation volume occurs in aTi [14,23]. Fig. 14 indicates that Nb strongly aects the thermal component of ¯ow stress in the low temperature regime and only mildly in¯uences the long-range stress component. Si is the strongest solid solution strengthening element and increases both the thermal and long-range stress components. The thermal component of the ¯ow stress could not be correlated with modulus or size mismatch factors for quaternary additions. If the mechanism discussed earlier for the glide of `a*' dislocations is valid, then Nb and various quaternary additions may be deduced to aect the recombination stress required to transform the hypothesised non-planar core structure of the `a*' superpartials. The long-range stress component correlates with the combined size and modulus mismatch factor for edge dislocations (Fig. 15), and is thus associated with conventional strengthening. In a polycrystalline material such as a-Ti, the Hall±Petch constant, k, has an athermal nature [14]. It is possible that the mild decrease of the long- range stress component with Nb may arise from an eect on this term. Grain size eects have not been evaluated in this study.
Fig. 21. Dislocation structures in creep: (a) [001], `c', dislocations showing the dominance of edge segments; (b) `a' dislocations in the basal plane; (c) `a*' dislocations in prismatic plane along with short segments of `c' dislocations (from Ref. [5]).
5.2. The intermediate temperature domain (500±1000 K) The intermediate temperature domain is initiated by the appearance of a plateau in the ¯ow stress versus temperature plots, or an anomalous increase in the ¯ow stress in the modulus normalised plots. Fig. 8 for the
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Fig. 22. `a*' Dislocations in the prismatic plane pinned by attractive junctions with `c' dislocations.
magnitude of the activation volume (obtained from the instantaneous strain rate sensitivity) and its strain dependence in this temperature domain (Fig. 9) suggest a forest intersection mechanism as may be expected in a weakly temperature-dependent regime. The negative strain rate sensitivity distinguishes dynamic strain aging behaviour from the eects rising from dislocation exhaustion processes in many intermetallics which also exhibit peaks in work hardening coupled with anomalous strengthening, but where the strain rate sensitivity can be zero or very slightly positive [31]. The activation energy of the dynamic strain aging process has not been determined in this study. Nevertheless, oxygen can be deduced to be the solute responsible for the dynamic strain aging eect. Fig. 23 shows the temperatures for the onset of serrations at two different strain rates in the Ti±27Al±25Nb alloy and compares this data to the eect in a-Ti where oxygen has been shown to be the main contributor to the dynamic strain-ageing eect in this temperature regime [14]. The peak ¯ow stress in this temperature domain is much higher for the Zr containing alloys than for other quaternary, substitutional additions (Fig. 16). This strong dynamic strain aging eect of Zr and Si may be related to their atomic radius (0.16 nm for Zr and 0.117 nm for Si) in relation to that of Ti (0.147 nm), Al (0.143 nm), Nb (0.147 nm) and Ta (0.147 nm). It is possible that other contributions to anomalous behaviour exist in this temperature regime. For example, the CRSS for pyramidal, `2c+a', glide in Ti3Al shows anomalous strengthening over the temperature range 400±1000 K [32]. `2c+a' glide in the O2 phase may show anomalous behaviour as well. 5.3. High temperatures (1000±1173 K) at strain rates 10ÿ4 to 10ÿ2 sÿ1
Fig. 23. A strain±rate temperature plot indicating the start of serrations in the stress±strain curves of Ti±27Al±25Nb, with data from a-Ti [14] superimposed.
high oxygen alloy contains all the classic signatures of a dynamic strain aging eect [26], that is a peak in the ¯ow stress and work hardening rate and a negative strain rate sensitivity, accompanied by serrations in the stress±strain curves. The instantaneous strain rate sensitivity (de®ned by i in Fig. 6) is always positive and is determined by the basic dislocation mechanism controlling ¯ow [27±30]. The
The ¯ow stress decreases more rapidly with temperature beyond 1000 K, and this decrease is more apparent at higher strains. The transformation from O2 to O1 at temperatures above 1200 K precluded a very detailed analysis at temperatures well beyond the dynamic strain-ageing regime at these strain rates. A distinctive ¯ow behaviour is, however, apparent from the very strong eect of strain rate on work hardening behaviour (Fig. 5) and the magnitude and strain dependence of activation volume (Fig. 9). A variety of mechanisms may account for the lack of work hardening at low strain rates. Recrystallisation or high-angle, grainboundary migration have been ruled out by optical metallography following the tests. Thus, dislocation mechanisms are required to explain the behaviour. It is clear that climb or cross-slip assisted recovery must occur to explain the lack of work hardening. However, ¯ow may be controlled by recovery, or the operation of high temperature thermally activated mechanisms such
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between the other possibilities. It is also dicult to determine precisely the eect of alloying additions to the ¯ow stress since (i) a possible strain-aging contribution continues to exist as yield points are still observed on strain rate jumps (Fig. 6), (ii) recovery rates may be determined by diusion of atomic species and (iii) the eect of alloying on the activation parameters of the rate-controlling obstacles to ¯ow is not known. Fig. 17 shows that Mo additions confer the highest strength at these temperatures.
Table 4 A summary of deformation mechanisms in the O2 phasea Temperature/ Activation strain-rate domain parameters
Possible rate-controlling mechanism
77±298 K 10ÿ4±10ÿ2 sÿ1
V=50±200 b3 Peierl's forces on Very mildly strain-dependent <100]{110) glide
500±1000 K 10ÿ4±10ÿ2 sÿ1
V=2000±2500 b3 Strain-dependent
Forest intersection mechanism with super-imposed dynamic strain aging
1000±1173 K 10ÿ4±10ÿ2 sÿ1
V=1000-1500 b3 Strain-independent
Mechanism not identi®ed, signi®cant dynamic recovery
973±1023 K 10ÿ9±10ÿ6 sÿ1 200±500 MPa
V=6±14 b3 n=4±7 Q=290±350 kJ/mol
Climb controlled network recovery
a
1281
5.4. Creep Stress exponents for steady state creep in ternary and quaternary alloys lie in the range 4±7, while activation energies lie between 295 and 350 kJ/mol (Table 3). No subgrain structure is formed in steady-state creep. Rather, the dislocation structure is typical of a threedimensional network of dislocations with three dierent Burgers vectors `a', `a*' and `c'. Evidence for a climb of `a' and `c' dislocations has been obtained, while `a*' dislocations are observed to only glide. The dislocation structure suggests that classical network theories of creep [35±39] should be applicable. In concept, these theories are remarkably simple. The network size is re®ned by the mechanical escape of dislocations from pinning points at the nodes of the network (at a critical link length de®ned by the applied stress) and their interaction to form attractive junctions. Coarsening of the network by glide and climb decreases the dislocation density. The balance between network recovery by coarsening and network re®nement de®nes the steady-state. A consideration of various processes involved in steady state creep within the framework of the network theory indicates that several processes must occur, each of which can de®ne the rate-controlling process. These are (1) the glide of free dislocations after escaping from the network (2) climb of the links (3) movement of the nodes of the network and (4) the escape of dislocations
V activation volume, Q activation energy, n stress exponent
as the motion of jogged screw dislocations [33] or the unzipping of attractive junctions [34], or any other dislocation mechanism. The dislocation structure (Table 2) suggests obstacles to the glide of dislocations in the form of attractive junctions, possible non-conservative motion of jogs in the screw orientation of `a*' dislocations, trailing of SISF dipoles of `a' dislocations in the basal plane, pinning of edge segments of `2c+a' dislocations by climb, and the immobilisation of their screw orientations by an unknown process. Since the activation volumes are strain-independent, thermal unzipping of attractive junctions should be ruled out as a possible rate-controlling mechanism. The activation volumes are also too large for dislocation climb to be the rate-controlling process. Current data are insucient to distinguish Table 5 A summary of alloying eects on the mechanical behaviour of the O2 phase Domain
Nb eects a
Substitutional additions
Oxygen eects
77±298 K 10ÿ4±10ÿ2 sÿ1
increases with Nb decreases midly with Nb
* for Si>Ta>Nb>Mo>Zr>V cfor V>Si>Mo>Ta>Zr>Nb
Inconclusive and not discussed in the paper
500±1000 K 10ÿ4±10ÿ2 sÿ1
peak ÿ =b decreases with Nb
1000±1173 K 10ÿ4±10ÿ2 sÿ1
Not evaluated in this work
peak ÿ = for Zr>Si>Mo>V>Ta at 1173 K Mo>V>Zr>Ta at 10ÿ4Sÿ1
peak ÿ = increases strongly with oxygen Not evaluated
Creep 973±1023 K 10ÿ9sÿ1±10ÿ6 sÿ1
Steady-state creep insensitive to Nb
Steady-state creep strength for Zr higher than other elements
Not evaluated
a b c
, thermal component of ¯ow stress at low temperature. , modulus. long-range component of ¯ow stress.
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from the attractive junctions by an athermal stress [21] or its thermal unzipping [34]. The values of stress exponents and activation energies (Table 3) suggest that climb of dislocations is the ratecontrolling step. While no diusivity data are available for the O2 phase, the activation energy values for creep lie in the range of the activation energy for interdiusion in Ti3Al. Further support for climb control emerges from the magnitude of the activation volume (Fig. 20) which ranges from 6b3 to 14b3. If the climb of superdislocations should occur in a coupled manner, the process would require the attachment of two vacancies, one to each superpartial, for simultaneous climb by one atomic plane. The activation volumes would then be halved since the normalisation factor would be 2(b)3. No change in creep mechanism occurs with either Nb concentration or with any of the substitutional quaternary additions. 6. Conclusion In summary, the mechanical behaviour of the O2 phase has been examined over temperatures ranging from 77 to 1173 K and strain rates from 10ÿ4 to 10ÿ2 sÿ1, and in creep at stress levels from 200 to 500 MPa at temperatures ranging from 973 to 1023 K. Four distinct domains of ¯ow behaviour have been identi®ed, each with its unique rate-controlling mechanism of ¯ow. These are summarized in Table 4. Alloying eects have been evaluated. These include the variation of the Nb content of the intermetallic and a variety of substitutional additions, as well as interstitial oxygen. The eect of alloying is summarised in Table 5. Acknowledgements The authors are grateful to the Defence Research and Development Organisation of India and the Indo-US grant No. N00014-95-0132 for ®nancial support. Grant Rowe of GE, CR&D melted alloys with dierent oxygen contents for us. Patrick Veyssiere spent many hours discussing the intricacies of weak-beam microscopy and analysing various dislocation structures and con®gurations in the O2 phase. Jean-Loup Strudel contributed to the analysis of results. We thank all of them.
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