UDK 669.295:621.77:539.37/.38
Original scientific article/Izvirni znanstveni članek
ISSN 1580-2949 MTAEC9, 44(6)357(2010)
DEFORMATION MECHANISMS IN Ti3Al-Nb ALLOY AT ELEVATED TEMPERATURES
MEHANIZEM DEFORMACIJE V ZLITINI Ti3Al-Nb PRI POVIŠANIH TEMPERATURAH
Srdjan Tadic1, Radica Prokic-Cvetkovic1, Igor Balac1, Radmila Heinemann-Jancic2, Katarina Bojic1, Aleksandar Sedmak1
1Innovation Centre, Faculty of Mechanical Engineering, University of Belgrade, Serbia 2 Faculty of Technology and Metallurgy, University of Belgrade, Serbia srdjantadic26@gmail.com
Prejem rokopisa - received: 2010-09-10; sprejem za objavo - accepted for publication: 2010-11-20
Ti3Al-11Nb-1V (x/%) was made in a vacuum arc furnace. Hot-rolling was conducted at 1050 °C in a two-phase field of the alloy. Strain-rate jump tests were performed at T = 800-1100 °C and strain rates of 10-6 to 10-3 s-1. Creep stress exponent (n) and activation energy for deformation (Q) were used to identify deformation mechanisms. Two sequential mechanisms are revealed: (i) viscous glide, typical of solid solution alloys and, (ii) power law breakdown at lower temperatures. Activation energy for deformation was found to be strongly stress-dependant.
Keywords: Titanium intermetallics, deformation, viscous glide, power law breakdown
Zlitina Ti3Al-11Nb-1V (x/%) je bila izdelana v vakuumski obločni peči. Vroče valjanje je bilo opravljeno pri 1050 °C v dvofaznem območju zlitine. Sunkoviti preizkusi hitrosti deformacije so bili narejeni pri T = 800-1100 °C in pri hitrosti deformacije 10-6 to 10-3 s-1. Eksponent napetosti lezenja (n) in aktivacijska energija deformacije (Q) sta bila uporabljena za identifikacijo mehanizma deformacije. Odkrita sta bila dva sekvenčna mehanizma: (i) viskozno drsenje, ki je značilno za zlitine iz trdnih raztopin in (ii) prelom potenčnega zakona pri nižji temperaturi. Ugotovljeno je bilo, da je aktivacijska energija deformacije zelo odvisna od napetosti.
Ključne besede: titanova intermetalna zlitina, deformacija, viskozno drsenje, potenčni zakon, prelom zakona
1 INTRODUCTION
High-temperature mechanical properties and low density make the titanium aluminides attractive candidates for engine and airframe applications. Considerable efforts in research have been devoted to this class of materials, particularly to Ti3Al-Nb alloy. This alloy consists typically of the ordered Ti3Al a2 phase (DO19 structure, similar to h. c. p) and the b. c. c. ß solid solution phase 1.
The main handicap of Ti3Al-Nb alloys at room temperatures is attributed to limited ductility. It is ascribed due to the inadequate number of crystallo-graphic slip systems 2. However, at a higher temperature the alloy exhibits good ductility through thermal activated softening 3. The high-temperature plasticity, thermomechanical processing and deformation mechanisms attracted the attention of a number of authors 4. Three distinct high-temperature regimes of the thermo-mechanical processing were reported 5: warm working (below 950 °C), hot working in the two phase field (980-1040 °C) and a hot working regime above the ß-transus. In a more complex Ti-25Al-10Nb-3V-1Mo alloy, dynamic recovery and dynamic recrystallization were identified in the two-phase (a2+ß) field 6. It was suggested that the activation barrier for DRX in the (a2+ß) field depends on the cross-slip in the 02 phase 7. Creep 8 and superplastic deformation 9 has also been well
examined, although a lot of uncertainties remained. The identification of the rate controlling deformation mechanisms is still not fully clear in two phase alloys. Particularly confusing is the large scatter of activation energies 10,11 associated with deformation processes. Creep, transition to low-temperature creep and power law breakdown behaviour is the emphasis of this work. Deformation mechanisms are identified in terms of the creep stress exponent and activation energy for deformation.
2 EXPERIMENTAL
The alloy was prepared from a Ti-6Al-4V (with an extra low interstitials quality), high-purity aluminium and niobium flakes. It was smelted in a vacuum arc furnace under a low-pressure 'argon blanket'. Remelting was repeated several times in order to obtain a homogeneous, pore-free rod 20 mm in diameter. The nominal chemical composition of the alloy was as follows (by x/%): 24 % Al, 11 % Nb and 1 % V, Ti - the rest. After cleaning, the rod was hot-rolled on a laboratory two-high mill with ^-calibrated rolls, down to a diameter of 6 mm. Hot-rolling was conducted at 1050 °C in the two-phase field, well below the ß-transus temperature. The rolling direction was swapped between two successive passes to eliminate the temperature gradient.
Compression test specimens with 0 = 6 mm and 12 mm in height were machined from the previously chemically cleaned rod. The specimens were coated with fine molybdenum-sulfide powder to minimise barrelling. A series of strain-rate jump tests 12 were conducted on an "Instron" testing machine in a water-cooled vacuum chamber at temperatures ranging from 800 °C to 1100 °C. The temperature of the chamber was maintained within ±5 °C. The true strain rates were calculated 13 to be in the range from 10-6 to 10-3 s1. The tests were conducted down to 50 % of reduction of the specimen height. True stress was normalized with shear modulus ß = 5.1 X 103-9r 14.
Metallographic specimens were prepared by wet grinding and diamond-paste polishing down to 1/4 ^m. Keller's etchant was used to reveal the microstructure under the optical microscope.
3 RESULTS
The microstructure of the hot-rolled bar in a view normal to the rolling direction is shown in Figure 1. The microstructure consists of a homogeneously distributed «2 phase in the ß matrix. The average grain size of the «2 phase is 17 pm.
The results of strain-rate jump test are summarized in Figure 2. It appears that stress follows a rather strong dependency on temperature and strain rate. For iso-structural tests, (T = const.), the stress sensitivity parameter, n, can be calculated as
'd ln £
n =
d ln o
(1)
The acquired data suggests that, according to Eq.1, the overall results might be separated into two fields: a low-stress regime with n = 3 (3.0 < n <3.2) and an upper, high-stress regime, with n = 5 up to 9. Contrary to the low-stress field, where n is almost constant, in the high-stress region n gradually increases with temperature and stress. The boundary between low- and high-stress regions may be approximated using a straight line and
Figure 2: Strain-rates v^. normalized stress in the T = 1073-1373K range
Slika 2: Odvisnost hitrost deformacje - normalizirana napetost v območju T = 1073-1373 K
denotes, in fact, the transition between different deformation mechanisms.
The n = 3 value corresponds to alloy-type creep behaviour (Class A), the so-called viscous glide creep 15. In contrast to this, metal-type creep behaviour (Class M) is recognized with n = 5 and usually points to a dislocation climb mechanism 16. However, the stress- dependent gradual increase of n-values up to 9 suggests that power law breakdown (PLB) may be more probable 17.
The apparent activation energy for creep is given by, 'd ln
Öapp =-R
31/T
(2)
where R is the gas constant. For constant stress values in the range of o/^ = 4 x 10-4 - 2 x 10-3, the application of Eq. 2 is illustrated on Figure 3. Calculated activation
Figure 1: Microstructure of hot-rolled Ti3Al-Nb alloy; (OM, x200) Slika 1: Mikrostruktura vroče valjane zlitine Ti3Al-Nb (OM, povečava 200-kratna)
Figure 3: Activation energy for deformation. (Filled symbols - low stress regime in Figure 2 hollow - high stress regime.) Slika 3: Aktivacijska energija derformacije (polni znaki - režim majhne napetosti na sliki 2, prazni znaki - režim velike napetosti)
Figure 4: Semi-logarithmic stress- dependence of activation energies Slika 4: Semilogaritmicna odvisnost napetosti od aktivacijske energije
energies are shown in Figure 4. In the low-stress region, activation energies are within the range typical of lattice self-diffusion 10'11. In the high-stress regime, Q values are higher and might be related to PLB 5. Stress-dependent Q values require that, apart from the creep, dislocation glide mechanisms are operative. However, it is not yet clear which one is rate controlling.
Phenomenological relationship for power-law creep takes the well known form
ekT Dfib
= A
/ \n O

(3)
where A is a dimensionless constant, characteristic of that particular creep mechanism, D is the effective diffusion coefficient and all others have their usual meaning.
The effective diffusion coefficient is calculated using Eq. 4:
D = Doexp(-Q / kT )	(4)
where Q represents the mean calculated activation energy and Do is the so-called frequency factor. For the ai phase, Do = 2.24 x 10-5 m^/s and for ß,, Do = 3.53 x 10-4 m2/s 18. The effective diffusion coefficient is calculated to be within the range of 1.5 x 10-20 - 5 x 10-17 m2/s which is in good agreement with 18. It should be pointed out that these values correspond to volume self-diffusion. For the viscous drag regime, appropriate diffusion would be Darken's chemical inter-diffusion and, for lower temperatures, pipe (core) diffusion is more likely to be operative 19. Anyway, due to the lack of consistent published data, volume self-diffusion is used in further calculations. By applying Eqs. 3 and 4 to the experimental results, the plot of Figure 5 is revealed. Two segments are clearly distinguishable: (i) a linear one, with n = 3 and A = 1 up to the normalized stress in the vicinity of o/^ = 10-3 and, beyond this stress, (ii) an exponential upward curve with continuous slope n = 5-9. Stress o/^ = JQ-3 at the departure of linearity is
Figure 5: Diffusion-compensated strain rate as a function of normalized applied stress. Theoretical predictions of Eq. 3 are included.
Slika 5: Hitrost deformacije kompenzirana z difuzijo v odvisnosti od normalizirane delujoče napetosti. Vključene so teoretične napovedi iz enačbe. 3.
widely accepted as a characteristic for PLB. Figure 5 also includes theoretical calculations for viscous-glide 20 and climb-controlled creep 21. Reasonable accord is more than clear, regardless of the diffusion approximations mentioned above.
It should be noted in Figure 5 that n = 5 is only a small segment of the experimental data regarding higher stresses. This fact supports some confirmations that the behavior of n = 5 might be suppressed between viscous glide and power-law-breakdown 22,23. In other words, with increasing stress (or lowering temperature), deformation advances sequentially: viscous-drag controlled glide ^ climb + glide controlled flow.
It is obvious that Eq. 3, due to PLB, cannot describe the overall deformation behaviour of the investigated alloy. For this reason, a more flexible, hyperbolic sine function is used:
Figure 6: Hyperbolic sine fit (Eq. 5) of the data Slika 6: Sinushiperbolični prikaz podatkov (enačbe 5)
ekT r —— = A sinh Dßb
o a — .. ^)
(5)
Eq. 5 gives a good description of the creep and hot-working data, Figure 6. However, it is not the best possible linear fit. It has been searched for reasonable linear fit, yet parameters A, a and n reflect the physical meaning of deformation. In Figure 6, stress exponent n ~ 3 reflects viscous drag at low stresses; a = 103 is the inverse of normalized stress for PLB, i.e. sinh(ao/^) = 1 and, A ~ 10-9 points to diffusion-normalized strain-rate for PLB. To repeat, some other values of A, a and n might yield better linearity of Eq. 5. However, it would be more valuable in technological modelling of hot-working), than from the academic merit of identification of deformation mechanisms.
4 DISCUSSION
Viscous glide has been reported to occur in a large number of solid solution alloys. In particular, aluminium alloys have been examined well Also, this phenomenon is observed commonly in a lot of intermetallics 28-31. Two mutually competitive mechanisms are operative in this stress regime, dislocation glide and climb. Within the certain combination of materials' and technological parameters glide is the slower one and thus becomes the rate controlling mechanism of deformation.
Several possible viscous drag mechanisms were proposed. Cottrell and Jaswon 32 proposed that the dragging results from segregation of solute atmospheres to moving dislocations. The dislocation speed is limited by the rate of the solute atmosphere movement. Also, segregation to stacking faults is proposed 33. Further, stress induced local ordering might be an obstacle to dislocation movement 34. Finally, in long-range ordered alloys, as it is in the a2 phase, dislocations are impeded due to anti-phase boundaries 35. If only solute atmosphere dragging is considered, Mohamed and Langdon 24 proposed the relationship for creep in viscous glide:
£ = -
^(1-v) kTD
6e2 cb5 ß
{ ß
(6)
example, from the quasi-binary phase diagram Ti3Al-Nb 36, it can be calculated that Vfß at T = 1373 K is 90 %, at T = 1273 K Vfß = 65 % while at T = 1073 K ß is only 30 %. This suggests strongly that the aluminium-rich ß-phase is predominantly in charge of viscous glide.
The transition from viscous glide to climb controlled creep has been the subject of numerous investigations 37-41. There is a general agreement that the transition is due to the breakaway of dislocations from solute atmospheres. Under some critical stress the glide becomes faster than the climb and the latter starts to be the rate controlling mechanism. The break-away stress is propo-sed42:
o=

kTb3
(7)
Wm is the maximum interaction energy between a, solute atoms and dislocations, c is the solute concentration and ß is the factor which depends on the nature of the impurity clouds. Interaction energy Wm is
1	(1+v ^			
W =-—	I1-v )	ß	AV,	(8)
where e is the solute-solvent size difference, c is the concentration of solute atoms and D is the chemical diffusion coefficient for the solute atoms. Eq. 6 serves as an explanation that viscous glide occurs preferably in materials with a relatively large atom size mismatch (e) and higher solute concentrations (c). InTi3Al-Nb alloy, both aluminium and niobium atoms act as solutes in the ß-phase solid solution. In the a2 phase niobium may substitute both Ti and Al atoms. The atomic volumes of Ti and Nb are almost identical. However, the atomic diameter of an Al atom is much lower than that of a titanium atom 19. Also, viscous glide seems to be particularly strong at high temperatures where the volume fraction of the ß-phase (Vfß) dominates over a2. For
Where v is Poisson's ratio (v = 0.24), ß is shear modulus (Eq.1) and AVa is volume difference between solute and solvent atoms. From 19, Vai = 1.66 x 10-29 m3 and VTi = 1.81 x 10-29 m3, and AVa = 0.15 x 10-29 m3. With b = 2.83 x 1010 m, and the atomic concentration of aluminium Cai = 0.25, Eqs. 8 and 7 give good agreement within the order of magnitude with the experimentally determined o/ß ~ 10 3. However, there is no doubt that interstitial impurities sustain break-away stress strongly.
While the viscous glide regime is clearly distinguishable, the distinction between five-power-law and PLB isn't so obvious. Close inspection of Figure 2, 5, and 6 suggests strongly that the n = 5, regime is not particularly a defined creep regime of this alloy, but presents only the very beginning of PLB. Suppression of five-power-law between viscous glide and PLB is also found in some Al-Mg 43 and Al-Zn alloys 44.
Typically, within PLB, as n increases activation energy decreases. However, in this work, a conflicting result was found - activation energy is somewhat higher as n increases. The behaviour of the Q values in Figure 4 excludes inaccurate scatter of data. Such a result might be rationalized trough the fact that the ductile ß-phase and more rigid a2-phase may behave quite differently during deformation. Eq. 2, used to calculate activation energy, is derived from
( Q
£ = Ao" exp
RT
(9)
If multiple deformation processes occurs through sequential serial steps, (as glide and climb are), activation energy corresponds to the slowest one. However, if parallel, simultaneous mechanisms are operative, activation energy corresponds to the fastest one. Assum-
1
n
3
ing that applied stress is equally distributed on both phases, the so-called iso-stress model45 results in:
>£ = ^^ + (10)
o = 0 = o.
meaning that the strain-rates of phases might depend strongly on volume fractions (V). Combining Eqs 9, 10 yields
^ ß« 2 ^ „ ( Q s ^
£ = A«o V^ exp
RT
+ AsOVs exp
RT
(11)
A similar result can be obtained from a so-called iso-strain-rate model 46 (£ = £^ = £s). The main conclusion from Eq.11 (and similar two-phase deformation models 47-50), is that simultaneous mechanisms may be operative in the «2 and S phases during deformation. In that case, apparent activation energy might be reflected by the 'faster' phase. The same issue might be seen in Figure 5, where experimental results follow the faster of the two theoretical mechanisms.
5	CONCLUSIONS
Strain-rate-jump tests were performed on two-phase TisAl-Nb alloy in a wide range of temperatures (1073-1373 K) and strain rates from (lO-6 to lO-3 s1). Deformation mechanisms were identified in terms of stress-exponent (n), activation energy (Q) and fitting with known theoretical equations.
1.	Viscous glide (n = 3 and Q close to lattice self diffusion) was identified at a high temperature, low-stress regime.
2.	The five power law is suppressed between the viscous glide and power law breakdown.
3.	Power law breakdown begins at o/ß ~ 10-3, very common in most metals and alloys, and features a continuous, stress dependent, increase of n and Q.
4.	Deformation behaviour of the alloy can be well described with hyperbolic sine function.
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