- Email: [email protected]
Analysis of thermal and athermal deformation mechanisms during creep of γ-TiAl alloys
Materials Science and Engineering A239 – 240 (1997) 429 – 437
Analysis of thermal and athermal deformation mechanisms during creep of g-TiAl alloys M.A. Morris *, M. Leboeuf Institute of Structural Metallurgy, Uni6ersity of Neuchaˆtel, A6. Belle6aux 51, 2000 Neuchaˆtel, Switzerland
Abstract The creep deformation of a near-g titanium aluminide alloy with equiaxed and lamellar structures has been studied to understand its behaviour as a function of microstructural evolution during the early stages of creep. The lamellar alloy exhibits more pronounced hardening during the primary stage of creep leading to a much better creep resistance and a minimum creep rate two orders of magnitude lower than that of the equiaxed alloy. Transmission electron microscopy observations have confirmed that the active deformation mechanisms are the same for both microstructural states, namely extensive slip of single 1/2110 dislocations and mechanical twinning. Using the values of apparent activation energies and activation volumes measured for both microstructural states, it has been possible to describe the better creep resistance of the lamellar alloy to the presence of a higher density of interfaces at which dislocations remain immobile. © 1997 Elsevier Science S.A. Keywords: Titanium aluminides; Creep; Twinning; Electron microscopy
1. Introduction The creep resistance of two-phase titanium aluminide alloys has been demonstrated to depend on microstructural features such as lamellar volume fraction or grain size but also appears to be influenced by other parameters such as the morphology of each phase [1 –4]. The presence of lamellar interfaces leads to improved creep resistance and this has been interpreted as due to the fact that interfaces may inhibit dislocation glide [3,5–7]. On the other hand it has been suggested that the decreased creep resistance of the duplex microstructure compared to that of the equiaxed g microstructure is due to the better glide mobility of 1/2110 dislocations within the g matrix in the presence of a2 lamellae [8]. Although the alloys generally exhibit power law creep behaviour, the values of the stress exponent, n, appear to increase with increasing applied stress [6,9]. This has been interpreted as being due to a transition from diffusional creep at low stresses to dislocation glide creep at high stresses [4,10,11]. Little work has been carried out to understand the primary creep regime in these alloys and although it is
* Corresponding author. 0921-5093/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. PII S 0 9 2 1 - 5 0 9 3 ( 9 7 ) 0 0 6 1 3 - 8
clear that primary creep strains can be quite large, the understanding necessary to minimize it has not yet been obtained. For a complete understanding of the creep properties it is necessary to correlate microstructural analysis with the constitutive equations governing the possible creep mechanisms. While the existence of a minimum creep rate has been evaluated in many single and two-phase alloys, the fundamental parameters controlling the deformation process responsible for this decrease in strain rate are still poorly understood [6]. A recent creep study carried out on two TiAl alloys with the same grain size and respective duplex and lamellar structures has confirmed the better creep resistance of the latter [12,13]. In the duplex alloy, extensive twinning activity was observed within the g grains which were responsible for the subdivision of the g grains during the primary stage of creep leading to the decrease in strain rate. In the lamellar alloy the hardening mechanism responsible for the decrease in strain rate was attributed to the accumulation of dislocations at g/g or a2/g interfaces. However, the controlling mechanism responsible for the minimum creep rate was the same in the two alloys, i.e. dislocation propagation across the g matrix with subsequent accumulation and emission from twin interfaces in the duplex alloy or from g/g or a2/g interfaces in the lamellar alloy.
430
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
In the present study we have compared the creep properties and microstructural features of the same alloy in two microstructural states, i.e. equiaxed and lamellar, but having different grain sizes. The main aim was to examine the evolution of the deformed microstructure during the primary stage of creep responsible for the hardening and the onset of the minimum creep rate. The effect of the initial microstructure on the creep resistance of the alloy will be discussed in terms of the active deformation mechanisms analysed.
2. Experimental The alloy used in the present study had a composition Ti46.5Al2Cr3Nb0.1W (at.%) and was received in two conditions, as equiaxed and lamellar microstructures (the annealed alloys were kindly supplied by Dr Y.-W. Kim from UES Materials, Dayton, OH), produced by different annealing treatments carried out at 1275 and 1350°C, followed by air cooling. The creep tests were carried out in tension on cylindrical specimens machined to a diameter of 3 mm and with 28 mm gauge length using a creep machine equipped to maintain constant stress throughout the tests. The tests were performed at 700°C for stresses ranging between 220 and 380 MPa. The machine was equipped with a data acquisition unit which monitored the elongation of the specimens every second. Most tests were performed to about 4 – 5% strain with other tests interrupted at intermediate strains between 0.8 and 3% to analyse the evolution of the deformed microstructures. The specimens were rapidly cooled under load to avoid any dislocation rearrangement prior to observations by transmission electron microscopy (TEM). Some tests were performed to determine the activation energy of the creep process at constant structure by carrying out fast temperature jumps every 15°C between 670–720°C. Microstructural analysis of the undeformed and deformed specimens was performed by X-ray diffraction, TEM and scanning electron microscopy (SEM). The latter was carried out using crystallographic contrast from backscattered electrons to obtain information about any large scale substructure formation during the primary stage of creep. Quantitative measurements of the grain size, volume fraction of the a2 phase as well as other aspects of the deformed structures were carried out using an image analyser directly attached to the SEM which allowed accumulation of a large number of images. At least 300 grains were analysed for each measured condition. For all TEM and SEM observations discs were cut perpendicular to the tensile axis from the deformed samples and electropolished. Dislocation analyses were carried out from projected images obtained by tilting the specimens to different known orientations (zone
axes) from which different diffraction vectors were chosen to obtain invisibility under some contrast conditions. Weak beam images were taken using the g:3g condition.
3. Results Fig. 1 shows examples of the initial equiaxed and lamellar microstructures of the alloy. The former (seen in Fig. 1a and b) was constituted of equiaxed g grains of average size : 10 mm and : 7% volume fraction of a2 and B2 phases which was distributed along grain boundaries. Both these phases are seen as brighter regions using atomic number contrast in the SEM and could be distinguished only by electron diffraction in the TEM. The presence of the B2 phase was also confirmed by X-ray diffraction analysis. Some (about 1%) of the a2 regions became lamellar, as seen in Fig. 1b, but this fraction seems insufficient to consider the structure as duplex. The lamellar structure seen in Fig. 1c and d has an average grain size : 350 mm and the lamellar spacing was about 1.5 mm. For both microstructural states the X-ray spectra confirmed that there was no preferred orientation or specific texture in the material. In Fig. 2a we show curves of the variation of strain rate as a function of strain obtained from creep tests of the equiaxed alloy performed under stresses ranging between 228 and 340 MPa. In Fig. 2b we see the comparison of this variation between the two materials tested under identical applied stresses. We note that the lamellar alloy has a much higher creep resistance with values of the minimum creep rate about two orders of magnitude lower than those of the alloy with equiaxed structure. In both materials the initial strain rates ranged between 2–4× 10 − 4 s − 1 and decreased rapidly during the first 1% strain, but the hardening was more pronounced in the lamellar alloy. Generally the strain rate reached minimum values at about 2–2.5% strain, and in the equiaxed alloy these ranged between 2.2× 10 − 8 and 4.4× 10 − 7 s − 1for the lower and higher stresses used. In the lamellar alloy, even though the applied stresses used were 50–100 MPa higher, the minimum creep rates reached values ranging between 3.3×10 − 9 and 5.8 ×10 − 8 s − 1. The minimum creep rates remain rather constant during the secondary or steady state region of the creep curve. During this stage the data have been analysed by relating the strain rate dependence on applied stress through the general power law equation o; = s n exp (− Q/RT). The log–log plots of minimum strain rates versus applied stress are shown in Fig. 3 for both alloys. We note that the stress exponent is higher in the lamellar material, n: 13, than in the equiaxed alloy, n: 8.
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
431
Fig. 1. General microstructures of the as-received alloy observed by atomic number contrast in the SEM. (a) Distribution of a2 and B2 phases (seen as brighter) along boundaries between equiaxed g grains; (b) details from a small lamellar region in the equiaxed structure; (c) general distribution of grains in the lamellar structure; and (d) details from the lamellar spacing and the small recrystallised g grains initially present at boundaries between lamellar grains.
From temperature jumps carried out during the secondary stage of creep (between 2 – 4% strain) we have measured activation energies of 420 and 450 kJ mol − 1 in the equiaxed and lamellar alloys respectively. Also, additional tensile tests were performed at 700°C to carry out strain rate jumps at constant structure over a wide range of strain. From these tests we have determined the activation volumes characterising the controlling mechanism responsible for the constant creep rate using the equation V = mkT(Dlno; /Ds), where m= 3 is the Taylor factor, k the Boltzmann constant, T the absolute temperature, o; the strain rate and s the corresponding stress. The values obtained were V = 7.29 0.5 ×10 − 27 and 89 0.5 ×10 − 27 m3 for the equiaxed and lamellar alloys respectively and were strain independent up to about 4% strain. Such values correspond to about V=2859 25 b 3 and 3509 25 b 3 where b= 2.83x10 − 10 m is the Burgers vector of either a single 1/2110 or a dissociated 1/2101 superdislocation.
3.1. Deformed microstructures The major difference between the deformed microstructures of the two materials was the more pronounced twinning activity and the higher dislocation density observed within the g matrix of the equiaxed alloy. In the latter, twinning was observed from the initial stages of deformation even at the lower applied stress. Fig. 4 shows examples of twinned grains ob-
served by crystallographic contrast in the SEM from electropolished discs cut from the gauge length of specimens deformed under different creep conditions. This contrast occurs because the thin twinned regions are rotated by 180° with respect to the matrix and therefore a thin slab of twinned region appears as a line. In Table 1 we show the different fractions of grains that twinned determined from such micrographs. We note an increase in the number of grains that deform by mechanical twinning with increasing strain for all the applied stresses. The effect of increasing the applied stress on increasing twinning activity is weak and only evident at strains after the onset of the minimum creep rate (see Table 1). At lower strains the higher applied stress affects mainly the twinning intensity (i.e. the total number of twins and the thickness of the twinned layer) activated within a given grain. The twinning activity observed in the lamellar alloy was much less pronounced and although some twins were seen across the g lamellae in the SEM, their density was not sufficient to quantify them. TEM observations made from specimens deformed under the same creep conditions have confirmed the activity of mechanical twins in the equiaxed alloy. Fig. 5 shows twin transfer across adjacent grains observed from specimens crept to the same 1.5% strain under applied stresses of 255 MPa (Fig. 5a) and 340 MPa (Fig. 5b) and we see that in the latter there is a higher twin density. Fig. 6 shows another example of a grain
432
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
Fig. 2. (a) Plots of variation of strain rate with strain from the creep tests of the equiaxed alloy. (b) Comparison of this variation between the two materials tested under identical conditions.
deformed to 3% strain under a stress of 340 MPa where we note that during the secondary stage of creep in this alloy the microstructure shows a subdivision of the g grain due to the twin activity and a high dislocation density. Dislocation analyses carried out from several grains have confirmed that practically all are single dislocations with Burgers vectors 1/2110 as confirmed in the example shown in Fig. 7 where all the dislocations are invisible with g = 002. These dislocations appear pinned along their length as seen more clearly in Fig. 8. In this grain we have confirmed the presence of both 1/2 [11( 0] (only segments visible with g= 1( 11) and 1/2[110] Burgers vectors. The long segments that are pinned along their length have screw character, confirming that the short edge segments propagate by trailing the long screw segments behind. In all cases debris and small dislocation loops were also detected. Some of the 1/2 [11( 0] dislocations seen as large square configurations are characterised by two
Fig. 3. plots of minimum creep rate versus applied stress for both alloys. Note the higher stress exponent obtained in the lamellar material.
major line directions [11( 0] (screw orientation) and [110] (pure edge) and lie on the (001) plane. If climb processes were involved this should take place on the (11( 0) plane, perpendicular to the Burgers vector, and this would mean that there should be a pure edge segment trailing behind. Instead we observe that the loops are on (001) planes and that the trailing segments left behind have screw orientation. Such configurations were common features observed in all the grains even where the dislocation density was very high, confirming that the 1/2110 dislocations observed in this alloy propagate on (001) planes by glide only and climbing processes are not involved. Similar configurations have also been observed within the g matrix of the lamellar alloy but the dislocation density was never high. Although most of the dislocations also have Burgers vectors 1/2110, some superdislocations were observed, in most cases lying close to the a2 interface and sometimes reacting with the 1/2110 dislocations from the g matrix to produce small dislocation networks. Such an example is shown in Fig. 9 where the majority of dislocations seen within the g lamella have Burgers vector 1/2110 (visible with g= 1( 1( 1 and invisible with g= 002). In Fig. 9a we see two small dislocation networks close to the a2 lath (marked by arrows). One of these networks is shown in Fig. 9b by weak beam contrast taken under different diffraction conditions from which we confirm the presence of [1( 01] superdislocations. The image taken with g = 002 confirms the invisibility of single dislocations and also the extent of the superdislocation dissociations. This configuration indicates that superdislocations remain rather immobile near the a2/g interface from which they are presumably emitted. The most typical type of deformed microstructure observed in this material corresponds to that shown in Fig. 10.
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
433
Fig. 4. Examples of grains deformed by mechanical twinning in the equiaxed alloy observed by SEM after different creep conditions: (a) s= 255 MPa, o =0.8%; (b) s= 255 MPa, o = 1.5%; (c) s= 300 MPa, o = 4.2%; (d) s=340 MPa, o =0.8%. See text for details.
Here we see two adjacent g lamellae under two diffraction conditions deformed by 1/2[11( 0] dislocations (only two superdislocations are visible with g = 002) and by twins that propagate across the lamellae. Such mechanical twins were commonly seen across the lamellae but the twin layer thickness was too thin to represent any significant contribution to the total strain of the material. Fig. 10c shows details from Fig. 10b (marked by arrows) in which the emission of bowed single dislocations occurs at the intersections between the twins and the g/g or a2/g interfaces. This indicates that the dislocation sources are at the interfaces where stress concentrations are important. These interfaces are also sinks where dislocation accumulation occurs as illustrated in Table 1 Fraction, F, of twinned grains measured from the equiaxed alloy deformed by creep under different applied stresses oplastic (%)
F twinned grains (%)
oplastic (%)
s =225 MPa
s= 300 MPa
1.5 3.0
1.5 4.2
20 28
s =255 MPa
s = 340 MPa
0.8 1.5 3.0 4.2
0.8 1.5 3.0 5.1
11 25 30 45
F twinned grains (%)
22 44
12 26 45 54
Fig. 11 where we show dislocation networks at two different interfaces imaged under weak beam contrast conditions.
4. Discussion The different response of our alloys during the primary stage of creep and, in particular, the instantaneous strain measured on loading has been analysed in terms of the mean free path of mobile dislocations. The total shear strain can be expressed by g = rbl (r=density of mobile dislocations, b = Burgers vector, l= mean free path for dislocations). The total density of mobile dislocations producing the strain can be calculated if the size of the initial microstructure is known. Thus, in the equiaxed alloy the distance across which dislocations can initially propagate is given by the grain size (l: 10 mm) while in the lamellar alloy this distance is given by the lamellar spacing (l= 1.5 mm). The total instantaneous strain measured on loading at 320 MPa was oinst = 0.004 and 0.006 in the equiaxed and lamellar structures respectively (note that the macroscopic strain, oinst , is related to the shear strain by: oinst =ginst/ 3). Using these values (and after subtracting the elastic strain contribution from both alloys) we obtain a mobile dislocation density of 2× 1012 m − 2 for the equiaxed alloy (this value was confirmed from TEM micrographs) and 2.8× 1013 m − 2 for the lamellar one; i.e. the dislocation density responsible for the initial
434
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
Fig. 6. Example of a grain deformed to 3% strain under a stress of 340 MPa in the equiaxed alloy. Note the subdivision of the g grain by the twin interfaces and a high dislocation density during the secondary stage of creep.
the grains deform by mechanical twinning, much of the hardening responsible for the fast decrease of strain rate is produced by twins in some grains but must be produced by interactions of 1/2110 dislocations in Fig. 5. Examples of grains deformed by mechanical twinning in the equiaxed alloy observed by TEM after 1.5% creep strain under different applied stresses: (a) s= 255 MPa; (b) s= 340 MPa.
strain produced on loading is about ten times higher in the lamellar alloy. These results confirm previous conclusions [4] whereby the large primary creep observed in lamellar structures had been attributed to the abundance of a2/g interfaces acting as dislocation sources. On the other hand TEM observations made after 0.8% strain have confirmed that the equiaxed alloy contains a higher remnant dislocation density within the g matrix than the lamellar alloy indicating that in the latter the majority of dislocations produced on loading propagate across the g lamellae, accumulate at the a2/g interfaces and interact with pre-existing dislocation networks. Also, the hardening process is more pronounced in the lamellar alloy such that after 1% strain its creep rate is almost two orders of magnitude lower than that of the equiaxed alloy. This represents a far superior capacity of accumulating dislocations at the a2/g interfaces of the lamellar material thereby removing mobile dislocations and hindering further deformation. In the equiaxed alloy the twinning activity increases with increasing strain subdividing the initial grains and increasing the number of twin interfaces where more dislocation accumulation and emission become possible, leading to the decrease in strain rate. Since at the onset of the minimum creep rate only about 30 –40% of
Fig. 7. Details from an area analysed in Fig. 6 confirming that practically all dislocations have Burgers vectors 1/2110 as they are invisible with g =002.
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
435
from the early stages of the creep process is due to the macroscopic applied stress which favours mechanical twinning as a major slip system. This does not exclude the activation of twinning in other types of grain at a later stage in the deformation process when, due to hardening, local constraints across adjacent grains will create local shear stresses and control the deformation process. Also, in the same way as already shown in our previous studies [13,14], from the measurements of the twin layer thickness and of the twin spacing we have estimated the contribution that twinning dislocations make to the total strain of the equiaxed material and
Fig. 8. Dislocation configurations analysed in the equiaxed alloy after 1.5% creep strain under a stress of 340 MPa. Both 1/2[11( 0] and 1/2[110] dislocations are present and they are pinned along their screw direction. See text for details.
the rest of the grains. From X-ray diffraction as well as from TEM analysis we have confirmed that there is no specific texture or preferred grain orientations in our alloy and that the observed twinning activity in some grains only corresponds to those having slip systems with favourable Schmid factors. In particular, we have noted that grains with tensile orientation [110] exhibit a high twin density on the two systems with maximum Schmid factors (m =0.48). In the case of grains with tensile axis [011] in which the Schmid factor for twinning (m =0.28) is always lower than that for 1/ 2110(001) slip (m =0.36) the grains only deform by slip. Generally from our analyses in the present and previous studies [14] we have concluded that mechanical twinning is only favoured for those systems whose Schmid factors are higher than those to activate single dislocations and that the twinning activity observed
Fig. 9. (a) Example of the deformed microstructure in the g matrix of the lamellar alloy. Note the small networks seen near the a2 interface (marked by arrows). (b) And (c) details from one of the networks under different diffraction conditions confirming the presence of single 1/2[110] segments and dissociated superdislocations.
436
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
Fig. 10. (a) And (b) typical example (under two diffraction conditions) of adjacent g lamellae deformed by twins and single dislocations observed after 3% creep strain under 340 MPa. (c) Details from (b) where emission of bowed dislocations occurs at the intersections between the twin and the g/g interfaces.
this is about 10– 20%. This means that the importance of the twins is not so much that they are responsible for a significant amount of strain but that they lead to a subdivision of the microstructure during the primary stage of creep reducing the mean free path of the 1/2110 dislocations as they propagate between twins instead of propagating across the entire grain. As the dislocations are accumulated at twin interfaces this leads to a decrease of strain rate. However, in those grains that do not deform by mechanical twinning the same decrease in strain rate needs to occur to ensure a homogeneous deformation of the specimen and this can occur either by a decrease in the density of primary
1/2110 dislocations or by a decrease in their speed. In this way, the twinning activity determines (directly or indirectly) the hardening process observed during the primary stage of creep. During the secondary stage of creep (i.e.between 2–4% strain) the strain rate remains rather constant near its minimum value. During this stage our observations confirm that the deformation process is characterised by dislocation motion across twin interfaces or entire g grains in the equiaxed alloy and across g lamellae in the lamellar material. The dislocation configurations analysed and the emission of bowed 1/2110 segments (as those in Fig. 10b) are the same in both types of alloys. Although the deformation process appears to be the same in both materials the minimum creep rate is two orders of magnitude lower in the lamellar alloy. This has been examined in terms of the creep parameters measured from the two alloys. The stress exponents, n, describing the creep rate dependence on applied stress are high for the two alloys studied, n= 8 and 13, indicating that the controlling creep mechanism cannot be associated with dislocation climb or recovery processes for which we should expect a value of n: 4–5 [6]. When such high stress exponents are obtained it is possible to rationalise the creep behaviour assuming the existence of an athermal threshold stress, s0, and express the strain rate as:o; = A(s− s0)n% exp (− Q/RT). To obtain the value of the threshold stress, the stress exponent n% used should be that normally obtained for creep of the matrix in the absence of other obstacles. In the case of single phase TiAl alloys deformed at low stresses the value obtained is n% =4 [6]. Using this value we have plotted in Fig. 12 the applied stress, s, versus o; 1/4 and from the intercept of the lines on the ordinate we obtain the threshold stresses as s0 = 132 and 237 MPa for the equiaxed and the lamellar materials respectively. These values represent the stress concentrations that need to be overcome
Fig. 11. Examples, observed by weak beam contrast after 3% creep strain under 340 MPa, of dislocations accumulated at the a2/g interfaces of the lamellar alloy.
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
437
rates and the stress concentration required to initiate dislocation motion is the same in both alloys but that the higher stress exponent or the higher threshold stress measured in the lamellar alloy are a consequence of the higher density of interfaces where dislocations remain immobile.
5. Conclusions
Fig. 12. Plots of the applied stress, s, vs. o; 1/4 for the equiaxed and the lamellar materials.
to initiate dislocation motion in the g matrix and the higher value of threshold stress measured in the lamellar alloy reflects one of two possibilities: either a higher stress concentration is necessary to emit dislocations from the interfaces of this alloy or the higher density of interfaces producing this emission leads to a larger average value of the stress required. In our alloys we have measured activation energies, Q= 420 and 450 kJ mol − 1 in the equiaxed and lamellar alloys, which are higher than the value of 290 kJ mol − 1 reported for self diffusion of Ti in TiAl [15], indicating that the values measured represent apparent activation energies. This means that the controlling mechanism responsible for the creep rate of the alloys cannot take place under the thermal energy alone but requires the help of a local stress. In this case the creep rate can be expressed as [13,14]:o; = o; 0 exp − {(Q0 −Vtloc)/RT)}, where o; 0 represents a temperature independent parameter that will depend on the microstructure. The term inside the exponential corresponds to the apparent activation energy, Q =Q0 −Vtloc, which can be considered as the sum of two terms: the thermal energy, Q0, and a mechanically produced energy, Vtloc. The term V is the activation volume and tloc is the local shear stress acting on the dislocation segment helping the thermally activated event to occur. Introducing the values of the apparent activation energies and the experimentally measured activation volumes, V, in the above equation we have been able to deduce values of the local shear stresses, tloc. We have considered two possible cases, one in which a self-diffusion process is taking place (i.e. Q0 : 290 kJ mol − 1) and we deduce a local stress tloc : 30 MPa for both alloys. The second case assumes a thermally activated process controlled by pipe diffusion (i.e. Q0 :150 kJ mol − 1) and again we obtain the same value for both alloys, tloc :62 MPa. This means that the controlling mechanism responsible for the creep
The creep behaviour of a g-based TiAl alloy with equiaxed and lamellar microstructures has been analysed using detailed observations of the deformation process as a function of strain and applied stress. The lamellar alloy exhibits more pronounced hardening during the primary stage of creep leading to a much better creep resistance and a creep rate two orders of magnitude lower than that of the equiaxed alloy. TEM observations have confirmed that the active deformation mechanisms are the same for both microstructural states, namely extensive slip of single 1/2110 dislocations and mechanical twinning. Using the values of apparent activation energies and activation volumes measured for both microstructural states, it has been possible to describe the better creep resistance of the lamellar alloy as the result of a higher density of interfaces present where dislocations remain immobile.
References [1] S.W. Schwenker, Y.-W. Kim, in: Gamma Titanium Aluminides, Y.-W.Kim, R. Wagner, M. Yamaguchi (Eds.), TMS, Las Vegas, NV, 1995, p. 985. [2] T. Takahashi, H. Nagai, H. Oikawa, Mater. Trans. JIM 30 (1989) 1044. [3] R.W. Hayes, B. London, Acta Metall. Mater. 40 (1992) 2167. [4] M. Es-Souni, A. Bartels, R. Wagner, Acta Metall. Mater. 43 (1995) 153. [5] T. Takahashi, H. Nagai, H. Oikawa, Mater. Trans. JIM 30 (1989) 1044. [6] R.W. Hayes, P.A. McQuay, Scr. Metall. Mater. 30 (1994) 259. [7] J. Beddoes, W. Wallace, L. Zhao, Int. Mater. Rev. 40 (1995) 197. [8] B.D. Worth, J.W. Jones, J.E. Allison, Metall. Mater. Trans. A 26 (1995) 2947. [9] D.A. Wheeler, B. London, D.E. Larsen Jr., Scr. Metall. Mater. 26 (1995) 934. [10] R.W. Hayes, P.L. Martin, Acta Metall. Mater. 40 (1995) 2761. [11] J. Beddoes, L. Zhao, J. Triantafillou, P. Au, W. Wallace, in: Gamma Titanium Aluminides, Y.-W. Kim, R. Wagner, M. Yamaguchi (Eds.), TMS, Las Vegas, NV, 1995, p. 959. [12] M.A. Morris, T. Lipe, Intermetallics 5 (1997) 329. [13] M.A. Morris, M. Leboeuf, Intermetallics 5 (1997) 339. [14] M.A. Morris, M. Leboeuf, J. Mater. Res. (1998) in press. [15] S. Kroll, H. Mehrer, N. Stolwijk, C. Herzig, R. Rosenkranz, G.Z. Frommeyer, Metallkd 83 (1992) 591.
Analysis of thermal and athermal deformation mechanisms during creep of g-TiAl alloys M.A. Morris *, M. Leboeuf Institute of Structural Metallurgy, Uni6ersity of Neuchaˆtel, A6. Belle6aux 51, 2000 Neuchaˆtel, Switzerland
Abstract The creep deformation of a near-g titanium aluminide alloy with equiaxed and lamellar structures has been studied to understand its behaviour as a function of microstructural evolution during the early stages of creep. The lamellar alloy exhibits more pronounced hardening during the primary stage of creep leading to a much better creep resistance and a minimum creep rate two orders of magnitude lower than that of the equiaxed alloy. Transmission electron microscopy observations have confirmed that the active deformation mechanisms are the same for both microstructural states, namely extensive slip of single 1/2110 dislocations and mechanical twinning. Using the values of apparent activation energies and activation volumes measured for both microstructural states, it has been possible to describe the better creep resistance of the lamellar alloy to the presence of a higher density of interfaces at which dislocations remain immobile. © 1997 Elsevier Science S.A. Keywords: Titanium aluminides; Creep; Twinning; Electron microscopy
1. Introduction The creep resistance of two-phase titanium aluminide alloys has been demonstrated to depend on microstructural features such as lamellar volume fraction or grain size but also appears to be influenced by other parameters such as the morphology of each phase [1 –4]. The presence of lamellar interfaces leads to improved creep resistance and this has been interpreted as due to the fact that interfaces may inhibit dislocation glide [3,5–7]. On the other hand it has been suggested that the decreased creep resistance of the duplex microstructure compared to that of the equiaxed g microstructure is due to the better glide mobility of 1/2110 dislocations within the g matrix in the presence of a2 lamellae [8]. Although the alloys generally exhibit power law creep behaviour, the values of the stress exponent, n, appear to increase with increasing applied stress [6,9]. This has been interpreted as being due to a transition from diffusional creep at low stresses to dislocation glide creep at high stresses [4,10,11]. Little work has been carried out to understand the primary creep regime in these alloys and although it is
* Corresponding author. 0921-5093/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. PII S 0 9 2 1 - 5 0 9 3 ( 9 7 ) 0 0 6 1 3 - 8
clear that primary creep strains can be quite large, the understanding necessary to minimize it has not yet been obtained. For a complete understanding of the creep properties it is necessary to correlate microstructural analysis with the constitutive equations governing the possible creep mechanisms. While the existence of a minimum creep rate has been evaluated in many single and two-phase alloys, the fundamental parameters controlling the deformation process responsible for this decrease in strain rate are still poorly understood [6]. A recent creep study carried out on two TiAl alloys with the same grain size and respective duplex and lamellar structures has confirmed the better creep resistance of the latter [12,13]. In the duplex alloy, extensive twinning activity was observed within the g grains which were responsible for the subdivision of the g grains during the primary stage of creep leading to the decrease in strain rate. In the lamellar alloy the hardening mechanism responsible for the decrease in strain rate was attributed to the accumulation of dislocations at g/g or a2/g interfaces. However, the controlling mechanism responsible for the minimum creep rate was the same in the two alloys, i.e. dislocation propagation across the g matrix with subsequent accumulation and emission from twin interfaces in the duplex alloy or from g/g or a2/g interfaces in the lamellar alloy.
430
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
In the present study we have compared the creep properties and microstructural features of the same alloy in two microstructural states, i.e. equiaxed and lamellar, but having different grain sizes. The main aim was to examine the evolution of the deformed microstructure during the primary stage of creep responsible for the hardening and the onset of the minimum creep rate. The effect of the initial microstructure on the creep resistance of the alloy will be discussed in terms of the active deformation mechanisms analysed.
2. Experimental The alloy used in the present study had a composition Ti46.5Al2Cr3Nb0.1W (at.%) and was received in two conditions, as equiaxed and lamellar microstructures (the annealed alloys were kindly supplied by Dr Y.-W. Kim from UES Materials, Dayton, OH), produced by different annealing treatments carried out at 1275 and 1350°C, followed by air cooling. The creep tests were carried out in tension on cylindrical specimens machined to a diameter of 3 mm and with 28 mm gauge length using a creep machine equipped to maintain constant stress throughout the tests. The tests were performed at 700°C for stresses ranging between 220 and 380 MPa. The machine was equipped with a data acquisition unit which monitored the elongation of the specimens every second. Most tests were performed to about 4 – 5% strain with other tests interrupted at intermediate strains between 0.8 and 3% to analyse the evolution of the deformed microstructures. The specimens were rapidly cooled under load to avoid any dislocation rearrangement prior to observations by transmission electron microscopy (TEM). Some tests were performed to determine the activation energy of the creep process at constant structure by carrying out fast temperature jumps every 15°C between 670–720°C. Microstructural analysis of the undeformed and deformed specimens was performed by X-ray diffraction, TEM and scanning electron microscopy (SEM). The latter was carried out using crystallographic contrast from backscattered electrons to obtain information about any large scale substructure formation during the primary stage of creep. Quantitative measurements of the grain size, volume fraction of the a2 phase as well as other aspects of the deformed structures were carried out using an image analyser directly attached to the SEM which allowed accumulation of a large number of images. At least 300 grains were analysed for each measured condition. For all TEM and SEM observations discs were cut perpendicular to the tensile axis from the deformed samples and electropolished. Dislocation analyses were carried out from projected images obtained by tilting the specimens to different known orientations (zone
axes) from which different diffraction vectors were chosen to obtain invisibility under some contrast conditions. Weak beam images were taken using the g:3g condition.
3. Results Fig. 1 shows examples of the initial equiaxed and lamellar microstructures of the alloy. The former (seen in Fig. 1a and b) was constituted of equiaxed g grains of average size : 10 mm and : 7% volume fraction of a2 and B2 phases which was distributed along grain boundaries. Both these phases are seen as brighter regions using atomic number contrast in the SEM and could be distinguished only by electron diffraction in the TEM. The presence of the B2 phase was also confirmed by X-ray diffraction analysis. Some (about 1%) of the a2 regions became lamellar, as seen in Fig. 1b, but this fraction seems insufficient to consider the structure as duplex. The lamellar structure seen in Fig. 1c and d has an average grain size : 350 mm and the lamellar spacing was about 1.5 mm. For both microstructural states the X-ray spectra confirmed that there was no preferred orientation or specific texture in the material. In Fig. 2a we show curves of the variation of strain rate as a function of strain obtained from creep tests of the equiaxed alloy performed under stresses ranging between 228 and 340 MPa. In Fig. 2b we see the comparison of this variation between the two materials tested under identical applied stresses. We note that the lamellar alloy has a much higher creep resistance with values of the minimum creep rate about two orders of magnitude lower than those of the alloy with equiaxed structure. In both materials the initial strain rates ranged between 2–4× 10 − 4 s − 1 and decreased rapidly during the first 1% strain, but the hardening was more pronounced in the lamellar alloy. Generally the strain rate reached minimum values at about 2–2.5% strain, and in the equiaxed alloy these ranged between 2.2× 10 − 8 and 4.4× 10 − 7 s − 1for the lower and higher stresses used. In the lamellar alloy, even though the applied stresses used were 50–100 MPa higher, the minimum creep rates reached values ranging between 3.3×10 − 9 and 5.8 ×10 − 8 s − 1. The minimum creep rates remain rather constant during the secondary or steady state region of the creep curve. During this stage the data have been analysed by relating the strain rate dependence on applied stress through the general power law equation o; = s n exp (− Q/RT). The log–log plots of minimum strain rates versus applied stress are shown in Fig. 3 for both alloys. We note that the stress exponent is higher in the lamellar material, n: 13, than in the equiaxed alloy, n: 8.
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
431
Fig. 1. General microstructures of the as-received alloy observed by atomic number contrast in the SEM. (a) Distribution of a2 and B2 phases (seen as brighter) along boundaries between equiaxed g grains; (b) details from a small lamellar region in the equiaxed structure; (c) general distribution of grains in the lamellar structure; and (d) details from the lamellar spacing and the small recrystallised g grains initially present at boundaries between lamellar grains.
From temperature jumps carried out during the secondary stage of creep (between 2 – 4% strain) we have measured activation energies of 420 and 450 kJ mol − 1 in the equiaxed and lamellar alloys respectively. Also, additional tensile tests were performed at 700°C to carry out strain rate jumps at constant structure over a wide range of strain. From these tests we have determined the activation volumes characterising the controlling mechanism responsible for the constant creep rate using the equation V = mkT(Dlno; /Ds), where m= 3 is the Taylor factor, k the Boltzmann constant, T the absolute temperature, o; the strain rate and s the corresponding stress. The values obtained were V = 7.29 0.5 ×10 − 27 and 89 0.5 ×10 − 27 m3 for the equiaxed and lamellar alloys respectively and were strain independent up to about 4% strain. Such values correspond to about V=2859 25 b 3 and 3509 25 b 3 where b= 2.83x10 − 10 m is the Burgers vector of either a single 1/2110 or a dissociated 1/2101 superdislocation.
3.1. Deformed microstructures The major difference between the deformed microstructures of the two materials was the more pronounced twinning activity and the higher dislocation density observed within the g matrix of the equiaxed alloy. In the latter, twinning was observed from the initial stages of deformation even at the lower applied stress. Fig. 4 shows examples of twinned grains ob-
served by crystallographic contrast in the SEM from electropolished discs cut from the gauge length of specimens deformed under different creep conditions. This contrast occurs because the thin twinned regions are rotated by 180° with respect to the matrix and therefore a thin slab of twinned region appears as a line. In Table 1 we show the different fractions of grains that twinned determined from such micrographs. We note an increase in the number of grains that deform by mechanical twinning with increasing strain for all the applied stresses. The effect of increasing the applied stress on increasing twinning activity is weak and only evident at strains after the onset of the minimum creep rate (see Table 1). At lower strains the higher applied stress affects mainly the twinning intensity (i.e. the total number of twins and the thickness of the twinned layer) activated within a given grain. The twinning activity observed in the lamellar alloy was much less pronounced and although some twins were seen across the g lamellae in the SEM, their density was not sufficient to quantify them. TEM observations made from specimens deformed under the same creep conditions have confirmed the activity of mechanical twins in the equiaxed alloy. Fig. 5 shows twin transfer across adjacent grains observed from specimens crept to the same 1.5% strain under applied stresses of 255 MPa (Fig. 5a) and 340 MPa (Fig. 5b) and we see that in the latter there is a higher twin density. Fig. 6 shows another example of a grain
432
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
Fig. 2. (a) Plots of variation of strain rate with strain from the creep tests of the equiaxed alloy. (b) Comparison of this variation between the two materials tested under identical conditions.
deformed to 3% strain under a stress of 340 MPa where we note that during the secondary stage of creep in this alloy the microstructure shows a subdivision of the g grain due to the twin activity and a high dislocation density. Dislocation analyses carried out from several grains have confirmed that practically all are single dislocations with Burgers vectors 1/2110 as confirmed in the example shown in Fig. 7 where all the dislocations are invisible with g = 002. These dislocations appear pinned along their length as seen more clearly in Fig. 8. In this grain we have confirmed the presence of both 1/2 [11( 0] (only segments visible with g= 1( 11) and 1/2[110] Burgers vectors. The long segments that are pinned along their length have screw character, confirming that the short edge segments propagate by trailing the long screw segments behind. In all cases debris and small dislocation loops were also detected. Some of the 1/2 [11( 0] dislocations seen as large square configurations are characterised by two
Fig. 3. plots of minimum creep rate versus applied stress for both alloys. Note the higher stress exponent obtained in the lamellar material.
major line directions [11( 0] (screw orientation) and [110] (pure edge) and lie on the (001) plane. If climb processes were involved this should take place on the (11( 0) plane, perpendicular to the Burgers vector, and this would mean that there should be a pure edge segment trailing behind. Instead we observe that the loops are on (001) planes and that the trailing segments left behind have screw orientation. Such configurations were common features observed in all the grains even where the dislocation density was very high, confirming that the 1/2110 dislocations observed in this alloy propagate on (001) planes by glide only and climbing processes are not involved. Similar configurations have also been observed within the g matrix of the lamellar alloy but the dislocation density was never high. Although most of the dislocations also have Burgers vectors 1/2110, some superdislocations were observed, in most cases lying close to the a2 interface and sometimes reacting with the 1/2110 dislocations from the g matrix to produce small dislocation networks. Such an example is shown in Fig. 9 where the majority of dislocations seen within the g lamella have Burgers vector 1/2110 (visible with g= 1( 1( 1 and invisible with g= 002). In Fig. 9a we see two small dislocation networks close to the a2 lath (marked by arrows). One of these networks is shown in Fig. 9b by weak beam contrast taken under different diffraction conditions from which we confirm the presence of [1( 01] superdislocations. The image taken with g = 002 confirms the invisibility of single dislocations and also the extent of the superdislocation dissociations. This configuration indicates that superdislocations remain rather immobile near the a2/g interface from which they are presumably emitted. The most typical type of deformed microstructure observed in this material corresponds to that shown in Fig. 10.
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
433
Fig. 4. Examples of grains deformed by mechanical twinning in the equiaxed alloy observed by SEM after different creep conditions: (a) s= 255 MPa, o =0.8%; (b) s= 255 MPa, o = 1.5%; (c) s= 300 MPa, o = 4.2%; (d) s=340 MPa, o =0.8%. See text for details.
Here we see two adjacent g lamellae under two diffraction conditions deformed by 1/2[11( 0] dislocations (only two superdislocations are visible with g = 002) and by twins that propagate across the lamellae. Such mechanical twins were commonly seen across the lamellae but the twin layer thickness was too thin to represent any significant contribution to the total strain of the material. Fig. 10c shows details from Fig. 10b (marked by arrows) in which the emission of bowed single dislocations occurs at the intersections between the twins and the g/g or a2/g interfaces. This indicates that the dislocation sources are at the interfaces where stress concentrations are important. These interfaces are also sinks where dislocation accumulation occurs as illustrated in Table 1 Fraction, F, of twinned grains measured from the equiaxed alloy deformed by creep under different applied stresses oplastic (%)
F twinned grains (%)
oplastic (%)
s =225 MPa
s= 300 MPa
1.5 3.0
1.5 4.2
20 28
s =255 MPa
s = 340 MPa
0.8 1.5 3.0 4.2
0.8 1.5 3.0 5.1
11 25 30 45
F twinned grains (%)
22 44
12 26 45 54
Fig. 11 where we show dislocation networks at two different interfaces imaged under weak beam contrast conditions.
4. Discussion The different response of our alloys during the primary stage of creep and, in particular, the instantaneous strain measured on loading has been analysed in terms of the mean free path of mobile dislocations. The total shear strain can be expressed by g = rbl (r=density of mobile dislocations, b = Burgers vector, l= mean free path for dislocations). The total density of mobile dislocations producing the strain can be calculated if the size of the initial microstructure is known. Thus, in the equiaxed alloy the distance across which dislocations can initially propagate is given by the grain size (l: 10 mm) while in the lamellar alloy this distance is given by the lamellar spacing (l= 1.5 mm). The total instantaneous strain measured on loading at 320 MPa was oinst = 0.004 and 0.006 in the equiaxed and lamellar structures respectively (note that the macroscopic strain, oinst , is related to the shear strain by: oinst =ginst/ 3). Using these values (and after subtracting the elastic strain contribution from both alloys) we obtain a mobile dislocation density of 2× 1012 m − 2 for the equiaxed alloy (this value was confirmed from TEM micrographs) and 2.8× 1013 m − 2 for the lamellar one; i.e. the dislocation density responsible for the initial
434
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
Fig. 6. Example of a grain deformed to 3% strain under a stress of 340 MPa in the equiaxed alloy. Note the subdivision of the g grain by the twin interfaces and a high dislocation density during the secondary stage of creep.
the grains deform by mechanical twinning, much of the hardening responsible for the fast decrease of strain rate is produced by twins in some grains but must be produced by interactions of 1/2110 dislocations in Fig. 5. Examples of grains deformed by mechanical twinning in the equiaxed alloy observed by TEM after 1.5% creep strain under different applied stresses: (a) s= 255 MPa; (b) s= 340 MPa.
strain produced on loading is about ten times higher in the lamellar alloy. These results confirm previous conclusions [4] whereby the large primary creep observed in lamellar structures had been attributed to the abundance of a2/g interfaces acting as dislocation sources. On the other hand TEM observations made after 0.8% strain have confirmed that the equiaxed alloy contains a higher remnant dislocation density within the g matrix than the lamellar alloy indicating that in the latter the majority of dislocations produced on loading propagate across the g lamellae, accumulate at the a2/g interfaces and interact with pre-existing dislocation networks. Also, the hardening process is more pronounced in the lamellar alloy such that after 1% strain its creep rate is almost two orders of magnitude lower than that of the equiaxed alloy. This represents a far superior capacity of accumulating dislocations at the a2/g interfaces of the lamellar material thereby removing mobile dislocations and hindering further deformation. In the equiaxed alloy the twinning activity increases with increasing strain subdividing the initial grains and increasing the number of twin interfaces where more dislocation accumulation and emission become possible, leading to the decrease in strain rate. Since at the onset of the minimum creep rate only about 30 –40% of
Fig. 7. Details from an area analysed in Fig. 6 confirming that practically all dislocations have Burgers vectors 1/2110 as they are invisible with g =002.
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
435
from the early stages of the creep process is due to the macroscopic applied stress which favours mechanical twinning as a major slip system. This does not exclude the activation of twinning in other types of grain at a later stage in the deformation process when, due to hardening, local constraints across adjacent grains will create local shear stresses and control the deformation process. Also, in the same way as already shown in our previous studies [13,14], from the measurements of the twin layer thickness and of the twin spacing we have estimated the contribution that twinning dislocations make to the total strain of the equiaxed material and
Fig. 8. Dislocation configurations analysed in the equiaxed alloy after 1.5% creep strain under a stress of 340 MPa. Both 1/2[11( 0] and 1/2[110] dislocations are present and they are pinned along their screw direction. See text for details.
the rest of the grains. From X-ray diffraction as well as from TEM analysis we have confirmed that there is no specific texture or preferred grain orientations in our alloy and that the observed twinning activity in some grains only corresponds to those having slip systems with favourable Schmid factors. In particular, we have noted that grains with tensile orientation [110] exhibit a high twin density on the two systems with maximum Schmid factors (m =0.48). In the case of grains with tensile axis [011] in which the Schmid factor for twinning (m =0.28) is always lower than that for 1/ 2110(001) slip (m =0.36) the grains only deform by slip. Generally from our analyses in the present and previous studies [14] we have concluded that mechanical twinning is only favoured for those systems whose Schmid factors are higher than those to activate single dislocations and that the twinning activity observed
Fig. 9. (a) Example of the deformed microstructure in the g matrix of the lamellar alloy. Note the small networks seen near the a2 interface (marked by arrows). (b) And (c) details from one of the networks under different diffraction conditions confirming the presence of single 1/2[110] segments and dissociated superdislocations.
436
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
Fig. 10. (a) And (b) typical example (under two diffraction conditions) of adjacent g lamellae deformed by twins and single dislocations observed after 3% creep strain under 340 MPa. (c) Details from (b) where emission of bowed dislocations occurs at the intersections between the twin and the g/g interfaces.
this is about 10– 20%. This means that the importance of the twins is not so much that they are responsible for a significant amount of strain but that they lead to a subdivision of the microstructure during the primary stage of creep reducing the mean free path of the 1/2110 dislocations as they propagate between twins instead of propagating across the entire grain. As the dislocations are accumulated at twin interfaces this leads to a decrease of strain rate. However, in those grains that do not deform by mechanical twinning the same decrease in strain rate needs to occur to ensure a homogeneous deformation of the specimen and this can occur either by a decrease in the density of primary
1/2110 dislocations or by a decrease in their speed. In this way, the twinning activity determines (directly or indirectly) the hardening process observed during the primary stage of creep. During the secondary stage of creep (i.e.between 2–4% strain) the strain rate remains rather constant near its minimum value. During this stage our observations confirm that the deformation process is characterised by dislocation motion across twin interfaces or entire g grains in the equiaxed alloy and across g lamellae in the lamellar material. The dislocation configurations analysed and the emission of bowed 1/2110 segments (as those in Fig. 10b) are the same in both types of alloys. Although the deformation process appears to be the same in both materials the minimum creep rate is two orders of magnitude lower in the lamellar alloy. This has been examined in terms of the creep parameters measured from the two alloys. The stress exponents, n, describing the creep rate dependence on applied stress are high for the two alloys studied, n= 8 and 13, indicating that the controlling creep mechanism cannot be associated with dislocation climb or recovery processes for which we should expect a value of n: 4–5 [6]. When such high stress exponents are obtained it is possible to rationalise the creep behaviour assuming the existence of an athermal threshold stress, s0, and express the strain rate as:o; = A(s− s0)n% exp (− Q/RT). To obtain the value of the threshold stress, the stress exponent n% used should be that normally obtained for creep of the matrix in the absence of other obstacles. In the case of single phase TiAl alloys deformed at low stresses the value obtained is n% =4 [6]. Using this value we have plotted in Fig. 12 the applied stress, s, versus o; 1/4 and from the intercept of the lines on the ordinate we obtain the threshold stresses as s0 = 132 and 237 MPa for the equiaxed and the lamellar materials respectively. These values represent the stress concentrations that need to be overcome
Fig. 11. Examples, observed by weak beam contrast after 3% creep strain under 340 MPa, of dislocations accumulated at the a2/g interfaces of the lamellar alloy.
M.A. Morris, M. Leboeuf / Materials Science and Engineering A239–240 (1997) 429–437
437
rates and the stress concentration required to initiate dislocation motion is the same in both alloys but that the higher stress exponent or the higher threshold stress measured in the lamellar alloy are a consequence of the higher density of interfaces where dislocations remain immobile.
5. Conclusions
Fig. 12. Plots of the applied stress, s, vs. o; 1/4 for the equiaxed and the lamellar materials.
to initiate dislocation motion in the g matrix and the higher value of threshold stress measured in the lamellar alloy reflects one of two possibilities: either a higher stress concentration is necessary to emit dislocations from the interfaces of this alloy or the higher density of interfaces producing this emission leads to a larger average value of the stress required. In our alloys we have measured activation energies, Q= 420 and 450 kJ mol − 1 in the equiaxed and lamellar alloys, which are higher than the value of 290 kJ mol − 1 reported for self diffusion of Ti in TiAl [15], indicating that the values measured represent apparent activation energies. This means that the controlling mechanism responsible for the creep rate of the alloys cannot take place under the thermal energy alone but requires the help of a local stress. In this case the creep rate can be expressed as [13,14]:o; = o; 0 exp − {(Q0 −Vtloc)/RT)}, where o; 0 represents a temperature independent parameter that will depend on the microstructure. The term inside the exponential corresponds to the apparent activation energy, Q =Q0 −Vtloc, which can be considered as the sum of two terms: the thermal energy, Q0, and a mechanically produced energy, Vtloc. The term V is the activation volume and tloc is the local shear stress acting on the dislocation segment helping the thermally activated event to occur. Introducing the values of the apparent activation energies and the experimentally measured activation volumes, V, in the above equation we have been able to deduce values of the local shear stresses, tloc. We have considered two possible cases, one in which a self-diffusion process is taking place (i.e. Q0 : 290 kJ mol − 1) and we deduce a local stress tloc : 30 MPa for both alloys. The second case assumes a thermally activated process controlled by pipe diffusion (i.e. Q0 :150 kJ mol − 1) and again we obtain the same value for both alloys, tloc :62 MPa. This means that the controlling mechanism responsible for the creep
The creep behaviour of a g-based TiAl alloy with equiaxed and lamellar microstructures has been analysed using detailed observations of the deformation process as a function of strain and applied stress. The lamellar alloy exhibits more pronounced hardening during the primary stage of creep leading to a much better creep resistance and a creep rate two orders of magnitude lower than that of the equiaxed alloy. TEM observations have confirmed that the active deformation mechanisms are the same for both microstructural states, namely extensive slip of single 1/2110 dislocations and mechanical twinning. Using the values of apparent activation energies and activation volumes measured for both microstructural states, it has been possible to describe the better creep resistance of the lamellar alloy as the result of a higher density of interfaces present where dislocations remain immobile.
References [1] S.W. Schwenker, Y.-W. Kim, in: Gamma Titanium Aluminides, Y.-W.Kim, R. Wagner, M. Yamaguchi (Eds.), TMS, Las Vegas, NV, 1995, p. 985. [2] T. Takahashi, H. Nagai, H. Oikawa, Mater. Trans. JIM 30 (1989) 1044. [3] R.W. Hayes, B. London, Acta Metall. Mater. 40 (1992) 2167. [4] M. Es-Souni, A. Bartels, R. Wagner, Acta Metall. Mater. 43 (1995) 153. [5] T. Takahashi, H. Nagai, H. Oikawa, Mater. Trans. JIM 30 (1989) 1044. [6] R.W. Hayes, P.A. McQuay, Scr. Metall. Mater. 30 (1994) 259. [7] J. Beddoes, W. Wallace, L. Zhao, Int. Mater. Rev. 40 (1995) 197. [8] B.D. Worth, J.W. Jones, J.E. Allison, Metall. Mater. Trans. A 26 (1995) 2947. [9] D.A. Wheeler, B. London, D.E. Larsen Jr., Scr. Metall. Mater. 26 (1995) 934. [10] R.W. Hayes, P.L. Martin, Acta Metall. Mater. 40 (1995) 2761. [11] J. Beddoes, L. Zhao, J. Triantafillou, P. Au, W. Wallace, in: Gamma Titanium Aluminides, Y.-W. Kim, R. Wagner, M. Yamaguchi (Eds.), TMS, Las Vegas, NV, 1995, p. 959. [12] M.A. Morris, T. Lipe, Intermetallics 5 (1997) 329. [13] M.A. Morris, M. Leboeuf, Intermetallics 5 (1997) 339. [14] M.A. Morris, M. Leboeuf, J. Mater. Res. (1998) in press. [15] S. Kroll, H. Mehrer, N. Stolwijk, C. Herzig, R. Rosenkranz, G.Z. Frommeyer, Metallkd 83 (1992) 591.