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Dislocation dynamics in carbon-doped titanium aluminide alloys
Materials Science and Engineering A239 – 240 (1997) 39 – 45
Dislocation dynamics in carbon-doped titanium aluminide alloys U. Christoph, F. Appel *, R. Wagner Institute for Materials Research, GKSS-Research Center, Max-Planck-Str., D-21502 Geesthacht, Germany
Abstract Different thermal treatments were conducted on carbon containing two-phase titanium aluminide alloys to obtain solid solution and precipitation hardening effects. The strengthening mechanisms were characterized by activation parameters of the glide processes and electron microscope observations. Carbon in solid solution was found to be less efficient than carbide precipitates for hardening the material. Fine dispersions of Ti3AlC perovskite precipitates form arrays of strong glide obstacles so that perfect and twinning partial dislocations were effectively pinned. This mechanism results in a high athermal contribution to the flow stress, which significantly improves the high temperature strength of the material. © 1997 Elsevier Science S.A. Keywords: Solid solution hardening; Precipitation hardening; Perovskite precipitates; Activation volume; Activation energy
1. Introduction Two-phase titanium aluminide alloys are being considered as light weight materials to replace nickel-based superalloys for some high temperature aero-engine applications. Thus, their mechanical properties have to be assessed against the high standards set by the superalloys. At an intended service temperature of 700°C the strength and creep resistance of the titanium aluminides are particularly inferior to those shown by superalloys. To overcome this through design would require relatively massive structural components and would reduce the weight saving offered by the titanium aluminides. In an attempt to overcome these problems several studies have been performed on titanium aluminides which have been subjected to solid solution and precipitation hardening treatments. Of the doping elements investigated, carbon seems to be the most promising as significant improvements in strength properties have been achieved [1–3]. Nevertheless, the details of the hardening mechanisms are still unknown. The intention of the present study was to examine more closely these strengthening processes in order to assess the potential of carbon doping for extending the service range of the titanium aluminides towards higher temperatures. Thus, particular emphasis has been placed on the interaction of perfect and twinning partial dislocations with
the carbon related defects over a wide temperature range in order to characterize the glide resistance provided by these defects and to see whether it degrades at the intended service temperature.
2. Experimental methods and analysis TiAl alloys with the baseline composition Ti– 48.5at.%Al were prepared by arc melting and systematically doped with carbon so that its content (c) varied between 0.02 and 0.4 at.%. After hot isostatic pressing at 1458 K and 1.4 kbar for 4 h the alloys were subjected to different thermal treatments. Annealing at 1523 K and quenching resulted in a carbon solid solution, whereas Ti3AlC precipitates of perovskite type were formed by subsequent aging at 1023 K. From the impurity related defects different types of glide resistance may arise. Solute atoms or small precipitates can be overcome with the aid of thermal activation. Thus, the glide resistance depends on temperature T and strain rate a˚. When the effects of T and a˚ are coupled by an Arrhenius type equation, the related stress component can be described as [4,5] t*= i
1 (DF*+ kT ln a˚ /a˚0) i Vi
with * 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 5 5 8 - 3
DF*= DGi + Vt*. i i
(1)
U. Christoph et al. / Materials Science and Engineering A239–240 (1997) 39–45
40
The activation parameters used refer to the impurity related defects and have the following meaning: Vi activation volume, DF*i free energy of activation, DGi Gibbs free energy of activation. k is the Boltzmann constant and a˚0 is considered to be constant. The possible variables in Vi are the diameter DRi and separation distance li of the impurity related defects. Thus, the reciprocal activation volume was used as a measure of the density of glide obstacles impeding the thermally activated dislocation motion. Overcoming of obstacles with long-range stress fields, such as large precipitates, cannot be supported by thermal activation. This leads to an athermal stress component tmi which is independent of a˚ and T, apart from the small variation of the shear modulus m with T. When both types of impurity defects are present, the most common approach is to add linearly the two stress components t =t*+t i mi.
(2)
t describes the total glide resistance to crystallographic shear, which can be converted into a stress s applied on the polycrystalline material by use of an appropriate Taylor factor of f =3.06 as s =f · t. Similarly, the macroscopic strain rate may be expressed as o; = a˚ /f. The activation parameters defined by Eqs. (1) and (2) can be related to the temperature and strain rate sensitivities [6,7] by Vi =fkT/(Ds/D ln o; )T, DGi =
Qe + Vi s(T/mf )((m/(T) , 1−(T/m)((m/(T)
Qe = − TVi (Ds/DT)o; /f.
(3) (4) (5)
The stress increments (Ds/DT)o; and (Ds/D ln o; )T were determined by temperature and strain rate cycling tests as described in [5,6]. The glide resistance of impurity related defects may therefore be characterized in terms of the activation parameters DGi, DF *, Vi and t *. It i i should be noted, however, that apart from the impurity related mechanisms several other thermal and athermal processes may contribute to the flow stress of titanium aluminides. The glide resistance of these processes has been investigated in [5,6]. At sufficiently high deformation temperatures and low strain rates, solute segregation into or near to the dislocation cores may occur. This produces another type of glide resistance known as dynamic strain aging and is characterized by a serrated stress strain curve. This mechanism was investigated by static strain aging experiments [7]. The mechanical tests were supplemented by transmission electron microscopy (TEM) examination of the deformation induced defect structure.
3. Flow stresses and activation parameters The flow stresses and reciprocal activation volumes were measured at 293 and 973 K. Fig. 1 shows the dependencies of these values on the carbon concentration for the two series of materials investigated. For the quenched materials, relatively large values of 1/Vi were determined at room temperature, which increased slightly with c. It is therefore concluded that carbon atoms in solid solution (or in the form of tiny agglomerates) act as weak glide obstacles, which can apparently be easily overcome with the aid of thermal activation. These impurity related defects are therefore manifested in the activation volume but are rather ineffective for hardening the material. In contrast the room temperature values of 1/Vi of the aged material slightly decreased with c. This indicates that the density of thermal obstacles decreases with c. It should be mentioned that the activation volumes estimated on the aged materials are quite similar to those of conventional (undoped) two-phase titanium aluminides [5,6]. The Gibbs free energy at room temperature of aged materials is practically independent of c and amounts to DGi = 0.7 eV.
(6)
This value is again very similar to those estimated on conventional two-phase titanium aluminides [5,6]. The glide resistance determining the dislocation velocity in these materials has been attributed to lattice friction, localized pinning and jog dragging [5,6]. Because of the close agreement of the activation parameters these factors are also thought to control the dislocation mobility in the aged carbon doped material. This implies that the flow stress increase observed after aging is essentially athermal in nature and thus the related glide obstacles cannot be overcome with the aid of thermal activation. This is supported by the fact that the high flow stresses of the heavily doped materials were maintained up to 973 K. The materials were also tested after HIP’ing, where the carbon is probably present in the form of coarse precipitates of H-phase Ti2AlC and perovskite phase Ti3AlC [8]. It is interesting to note that in this condition the yield stress is almost independent of carbon concentration and exhibits the same values as after homogenisation and quenching (Fig. 1(a)). The related reciprocal activation volumes determined at 293 K decrease significantly with c. This clearly indicates that the precipitates are relatively large particles which act as athermal glide obstacles. However, the coarse dispersion of these precipitates seems to be less effective in strengthening the material. This observation agrees with the widely accepted view that both the size and dispersion of the particles are important for effective precipitation hardening.
U. Christoph et al. / Materials Science and Engineering A239–240 (1997) 39–45
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Fig. 1. Dependency of the flow stress s and the reciprocal activation volume 1/Vi on the carbon content, (a) homogenized and quenched with carbon atoms in solid solution or in the form of tiny agglomerates. The drawn lines refer to the room temperature values of the materials in the as HIP’ed condition where the carbon is present as a coarse dispersion of the H-phase Ti2AlC and the perovskite phase Ti3AlC. (b) quenched and aged materials which contain a fine dispersion of Ti3AlC perovskite type precipitates.
4. Static and dynamic strain aging The materials investigated exhibited discontinuous yielding and a negative strain rate sensitivity over the temperature range 450 – 650 K. These phenomena are usually associated with the Portevin – Le Chatelier effect which arises from the dynamic interaction of diffusing defects with the dislocations. The resulting glide resistance and strain aging phenomena were investigated using the classical yield-point return technique. Samples were deformed to different levels of prestrain, aged in situ on the load frame for certain aging periods ta, and then retested. This method ensures good specimen alignment and allows the stress level during aging to be kept constant. In most cases the samples were aged under a relaxing stress starting from the flow stress sa of the material at strain o. The experiments were performed at the aging temperatures T = 423, 523 and 623 K for aging time ta =3.5 −106 s. Fig. 2 shows the load elongation trace of a strain aging experiment and defines the aging parameters. The investigations were performed on the Ti – 48.5at.%Al – 0.37at.%C alloy, which had been subjected to the three different thermal treatments described previously. The results presented here
refer to the as HIP’ed condition but are similar for the other two conditions of the material. Fig. 3 demonstrates the early stages of strain aging kinetics determined for the three temperatures. Each aging condition was examined for strain o= 1.25% using separate samples to avoid any influence of the strain dependence of Ds. The strain age yield points apparently become saturated over the time scale of the experiments leading to the saturation values Dss. The parameters characterizing the kinetics of strain aging are compiled in Table 1. From the present data an activation energy can be determined if the times necessary to achieve a given degree of completeness of dislocation pinning and the related temperatures are combined in an Arrhenius plot. Fig. 4 demonstrates this plot for the saturation times ts(T) and the shorter times tr(T) which correspond to the stress increments Dsr = 0.8 · Dss. A mean activation energy of Qa = 0.77 eV was determined from the slopes of the lines corresponding to ts and tr. This energy is significantly smaller than the self diffusion energy for g(TiAl) of Qsd = 3.01 eV [9]. Thus, a classical vacancy diffusion mechanism can clearly be ruled out. This conclusion is supported by the experimental observation that excess vacancies produced by
42
U. Christoph et al. / Materials Science and Engineering A239–240 (1997) 39–45 Table 1 Parameters characterizing strain aging of a Ti – 48.5at.%Al– 0.37at.%C alloy T (K)
Dss (MPa)
ts (s)
Dsr (MPa)
tr (s)
423 523 623
32 30.2 12.7
286 797 4350 566
25.6 24.1 10.2
32 823 149 25.5
o =1.25%; o; =4.16 · 10−4 s−1; Dss, saturation value of the strain age yield points; Dsr =0.8 · Dss; ts, tr, related aging times.
Fig. 2. Sequence of static strain aging experiments performed under a relaxing stress. The stress increments Ds were measured as the difference in stress before aging and the peak level on reloading. Different time intervals ta between unloading and subsequently reloading are indicated.
eral phenomenon of the titanium aluminides. Unfortunately, little information can be deduced for dislocation pinning by the segregation of impurity atoms at the dislocation cores due to the lack of diffusion data for impurity atoms. However, it can be speculated that the aging phenomena arise from fast diffusing impurity elements. This being the case, iron or boron atoms should be considered as recent studies have revealed that these elements have high mobilities in a2(Ti3Al) (C.H. Herzig, Unpublished results). Most titanium aluminides of technical relevance contain significant levels of these elements, 100–300 ppm by weight.
5. Dislocation interactions with perovskite precipitates
homogenization of the samples at 1458 K and subsequent quenching apparently do not affect the aging phenomena. Furthermore, even enhanced self-diffusion along dislocation cores appears to have no effect, the activation energy expected for this process being about half that for bulk diffusion [10]. Similar strain aging characteristics have been observed on other two-phase alloys [7,11,12]. Thus, it is speculated that the dislocation locking mechanism behind the aging effects is not a consequence of the carbon doping but rather a gen-
In order to identify the hardening mechanism detailed electron microscope investigations were performed on the aged alloy Ti–48.5at.%Al–0.37at.%C, which exhibited the highest flow stress. Conventional and high resolution TEM examinations revealed needle-shaped Ti3AlC precipitates of perovskite type. These defects were elongated along their [001]-axis and exhibited the same structural characteristics as have been described in [8,13], namely
Fig. 3. Kinetics of strain aging under relaxing loads and the deformation parameters indicated.
Fig. 4. Arrhenius plot showing the variation of the aging times ts and tr with temperature.
U. Christoph et al. / Materials Science and Engineering A239–240 (1997) 39–45
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Fig. 5.
[001]p [001]m, 100]p 100]m.
(7)
p and m designate the precipitate and the matrix, respectively. The precipitates had an average length l = 22 nm and a width (along 100]) dp =3.3 nm. The deformation structure observed after 3% compression at room temperature consisted mainly of 1/2110] ordinary dislocations, 011] superdislocations and 1/6112( ] order twins. As demonstrated in Fig. 5, perfect and twinning partial dislocations were pinned by the perovskite precipitates, the obstacle spacing along the dislocations was typically lc =50 – 100 nm. The high glide resistance provided by the precipitates is manifested by the strong bowing-out of the dislocation
segments. The bowing process is particularly pronounced by the twinning partial dislocations because of their low line tension. It is interesting to note that the stressed configuration of the dislocations was apparently not relaxed during unloading and thin foil preparation. However, there are two factors which are thought to impede such relaxations. Between the TiAl matrix and the precipitates mismatch strains of 2–4% occur, depending on lattice direction. This results in significant coherency stresses, which are certainly present in the thin foils. Furthermore, the backward motion of the dislocations is certainly impeded by lattice friction forces due to the directional bonding of the material [5].
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U. Christoph et al. / Materials Science and Engineering A239–240 (1997) 39–45
Fig. 5. (Contd.) Deformation structure of an aged Ti–48.5at.%Al – 0.37at.%C alloy generated during room temperature compression to strain o= 3%. Pseudo-weak beam image recorded using g= (002)TiAl reflection from near the [020] pole in the g/3.1g condition, and high resolution image in 110]g projection. Note the high density of Ti3AlC-precipitates which are manifested by strain contrast. (a) Pinning of [011] superdislocations by the precipitates. The inset shows line tension configurations calculated for different stresses and projected into the image plane. For the segment analyzed, the length lc = 110 nm, the half axis q =80 nm and effective shear stress tc =299 MPa have been attributed. (b) Low magnification high resolution micrograph showing a deformation twin propagated through an array of needle shaped perovskite precipitates. (c) High resolution image showing the deflection of a deformation twin in the local region of a perovskite precipitate. Note the irregular shape of the twin/matrix interface (inset).
The effective shear stresses tc acting on the pinned dislocation segments were estimated by analyzing their curvature. Line tension configurations were calculated for different stresses according to the DeWitt –Koehler model [10,14], which considers the dependence of the line energy of a dislocation on its orientation. Elastic isotropy was assumed for the sake of simplicity. Within the framework of this model the dislocation loops are apparently elliptical with the major semi-axis q (in mm) parallel to the Burgers vector. Loops of this configuration are related to the shear stress tc by [10,14] tc(MPa)=
m.b 1 · ln(1.61c/b). 4p(1− n) q
(8)
b is the Burgers vector and n is Poisson’s ratio. Line tension loops were calculated for different stresses using the elastic constants measured by Schafrik [15] and were projected into the foil plane (Fig. 5(a)). By comparison with the observed shape of loops, a mean effective shear stress tc =300 MPa was obtained. This value can be related to a normal stress sc =f · tc = 900 MPa, which is close to the flow stress s =1000 MPa at strain o= 3%. This, together with the high density of pinning centers, leads to the conclusion that a significant portion of the total flow stress in the aged materials arises from the interaction of perfect and twinning partial dislocations with the precipitates. In their {111} slip planes the 011] superdislocations typically bow
out at the precipitates through angles c= 110°. This corresponds to interaction forces of fm = 1.5 · 10 − 8 N or fm/mb 2 = 0.57. It is therefore speculated that the precipitates are still shearable and can be overcome by the dislocations without Orowan looping. This view is supported by the TEM observations and the experimental finding that the work hardening coefficient ds/do of the aged materials does not depend on the carbon concentration. Due to the relatively large size of the precipitates it is speculated that their overcoming by the dislocations is essentially an athermal process as has been suggested by the concentration dependence of the activation volume (Fig. 1(b)). This view is supported by the observed structures of the dislocations and deformation twins. The dislocations apparently penetrate the obstacle array deeply along paths of easy movement and become immobilized at groups of unfavourably arranged particles leading to bundles of immobilized dislocations. Similarly twinning partial dislocations are often immobilized at the precipitates. Thus, in the local region of the precipitates the shape of the twin/matrix interfaces is much less regular and the twins are often deflected (Fig. 5(b) and (c)). Such processes often lead to fragmentation of the twins, i.e. islands of untwinned regions occur. As overcoming of the precipitates cannot be supported by thermal activation, the resulting glide resistance will be maintained under low creep rates. Hardening of two-phase titanium aluminides by fine
U. Christoph et al. / Materials Science and Engineering A239–240 (1997) 39–45
dispersions of Ti3AlC precipitates therefore seems to be a suitable metallurgical technique for improving the high temperature strength and creep resistance of the material. The high degree to which carbon additions improve the creep resistance has been demonstrated on a Ti – 48at.%Al – 4at.%V alloy containing 0.3at.%C [2]. However, in contrast to the analysis presented above, the enhanced glide resistance was attributed to a solute atmosphere drag mechanism.
6. Conclusions The effects of carbon additions on the mechanical properties of two-phase titanium aluminides have been investigated by mechanical testing and TEM observations. Fine dispersions of Ti3AlC precipitates of perovskite type form arrays of strong glide obstacles so that perfect and twinning partial dislocations are effectively pinned. The mechanism results in a high athermal contribution to the flow stress, which significantly improves the high temperature strength. In comparison, carbon in solid solution is less efficient for hardening the material. In the intermediate temperature interval 450 – 650 K strain aging phenomena occur. The observed fast kinetics and low activation energy of the aging process are not consistent with the mobility of defects in g(TiAl) obtained from the literature. The species causing the static and dynamic strain aging effects have not been identified due to the lack of diffusion data. It appears, however, that they are solute atoms and could be Fe or B, both of which are present in significant amounts in most technical alloys.
.
45
Acknowledgements The authors would like to thank U. Lorenz, J. Mu¨llauer, M. Oehring and J. Paul for helpful discussions and support. The financial support by the ‘Deutsche Forschungsgemeinschaft’ is gratefully acknowledged. References [1] W.H. Tian, M. Nemoto, in: Y.-W. Kim, R. Wagner, M. Yamaguchi (Eds.), Gamma Titanium Aluminides, TMS, Warrendale, PA, 1995, p. 689. [2] B.D. Worth, J.W. Jones, J.E. Allison, Metall. Trans. A 26A (1995) 2961. [3] F. Appel, H. Clemens, R. Wagner, in: W.O. Soboyejo, T.S. Srivatsan, H.L. Fraser (Eds.), Deformation and Fracture of Ordered Intermetallics III, TMS, Warrendale, PA, 1996, p. 123. [4] G. Scho¨ck, Phys. Stat. Sol. 8 (1965) 499. [5] F. Appel, U. Sparka, R. Wagner, in: J. Horton, J. Baker, S. Hanada, R.D. Noebe, D.S. Schwartz (Eds.), High-Temperature Ordered Intermetallic Alloys VI, MRS, Pittsburgh, PA, 1995, p. 623. [6] F. Appel, U. Lorenz, M. Oehring, U. Sparka, R. Wagner, Mater. Sci. Eng. A233 (1997) 1. [7] U. Christoph, F. Appel, R. Wagner, in: C.C. Koch, N.S. Stolloff, C.T. Liu, A. Wanner (Eds.), High Temperature Ordered Intermetallic Alloys VII, MRS, Pittsburgh, PA, 1997, p. 207. [8] S. Chen, P.A. Beaven, R. Wagner, Scr. Metall. Mater. 26 (1992) 1205. [9] S. Kroll, H. Mehrer, N. Stolwijk, Ch. Herzig, R. Rosenkranz, G. Frommeyer, Z. Metallkde. 83 (1992) 8. [10] J.P. Hirth, J. Lothe, Theory of Dislocations, 2nd ed., Krieger, Malabar, 1992, p. 506. [11] A. Barthels, C. Koeppe, T. Zhang, H. Mecking, in: Y.-W. Kim, R. Wagner, M. Yamaguchi (Eds.), Gamma Titanium Aluminides, TMS, Warrendale, PA, 1995, p. 655. [12] M.A. Morris, T. Lipe, D.G. Morris, Scr. Mater. 34 (1996) 1337. [13] W.H. Tian, T. Sano, M. Nemoto, Philos. Mag. A68 (1993) 965. [14] G. DeWitt, J.S. Koehler, Phys. Rev. 116 (1959) 1113. [15] R.E. Schafrik, Metall. Trans. A 8A (1977) 1003.
Dislocation dynamics in carbon-doped titanium aluminide alloys U. Christoph, F. Appel *, R. Wagner Institute for Materials Research, GKSS-Research Center, Max-Planck-Str., D-21502 Geesthacht, Germany
Abstract Different thermal treatments were conducted on carbon containing two-phase titanium aluminide alloys to obtain solid solution and precipitation hardening effects. The strengthening mechanisms were characterized by activation parameters of the glide processes and electron microscope observations. Carbon in solid solution was found to be less efficient than carbide precipitates for hardening the material. Fine dispersions of Ti3AlC perovskite precipitates form arrays of strong glide obstacles so that perfect and twinning partial dislocations were effectively pinned. This mechanism results in a high athermal contribution to the flow stress, which significantly improves the high temperature strength of the material. © 1997 Elsevier Science S.A. Keywords: Solid solution hardening; Precipitation hardening; Perovskite precipitates; Activation volume; Activation energy
1. Introduction Two-phase titanium aluminide alloys are being considered as light weight materials to replace nickel-based superalloys for some high temperature aero-engine applications. Thus, their mechanical properties have to be assessed against the high standards set by the superalloys. At an intended service temperature of 700°C the strength and creep resistance of the titanium aluminides are particularly inferior to those shown by superalloys. To overcome this through design would require relatively massive structural components and would reduce the weight saving offered by the titanium aluminides. In an attempt to overcome these problems several studies have been performed on titanium aluminides which have been subjected to solid solution and precipitation hardening treatments. Of the doping elements investigated, carbon seems to be the most promising as significant improvements in strength properties have been achieved [1–3]. Nevertheless, the details of the hardening mechanisms are still unknown. The intention of the present study was to examine more closely these strengthening processes in order to assess the potential of carbon doping for extending the service range of the titanium aluminides towards higher temperatures. Thus, particular emphasis has been placed on the interaction of perfect and twinning partial dislocations with
the carbon related defects over a wide temperature range in order to characterize the glide resistance provided by these defects and to see whether it degrades at the intended service temperature.
2. Experimental methods and analysis TiAl alloys with the baseline composition Ti– 48.5at.%Al were prepared by arc melting and systematically doped with carbon so that its content (c) varied between 0.02 and 0.4 at.%. After hot isostatic pressing at 1458 K and 1.4 kbar for 4 h the alloys were subjected to different thermal treatments. Annealing at 1523 K and quenching resulted in a carbon solid solution, whereas Ti3AlC precipitates of perovskite type were formed by subsequent aging at 1023 K. From the impurity related defects different types of glide resistance may arise. Solute atoms or small precipitates can be overcome with the aid of thermal activation. Thus, the glide resistance depends on temperature T and strain rate a˚. When the effects of T and a˚ are coupled by an Arrhenius type equation, the related stress component can be described as [4,5] t*= i
1 (DF*+ kT ln a˚ /a˚0) i Vi
with * 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 5 5 8 - 3
DF*= DGi + Vt*. i i
(1)
U. Christoph et al. / Materials Science and Engineering A239–240 (1997) 39–45
40
The activation parameters used refer to the impurity related defects and have the following meaning: Vi activation volume, DF*i free energy of activation, DGi Gibbs free energy of activation. k is the Boltzmann constant and a˚0 is considered to be constant. The possible variables in Vi are the diameter DRi and separation distance li of the impurity related defects. Thus, the reciprocal activation volume was used as a measure of the density of glide obstacles impeding the thermally activated dislocation motion. Overcoming of obstacles with long-range stress fields, such as large precipitates, cannot be supported by thermal activation. This leads to an athermal stress component tmi which is independent of a˚ and T, apart from the small variation of the shear modulus m with T. When both types of impurity defects are present, the most common approach is to add linearly the two stress components t =t*+t i mi.
(2)
t describes the total glide resistance to crystallographic shear, which can be converted into a stress s applied on the polycrystalline material by use of an appropriate Taylor factor of f =3.06 as s =f · t. Similarly, the macroscopic strain rate may be expressed as o; = a˚ /f. The activation parameters defined by Eqs. (1) and (2) can be related to the temperature and strain rate sensitivities [6,7] by Vi =fkT/(Ds/D ln o; )T, DGi =
Qe + Vi s(T/mf )((m/(T) , 1−(T/m)((m/(T)
Qe = − TVi (Ds/DT)o; /f.
(3) (4) (5)
The stress increments (Ds/DT)o; and (Ds/D ln o; )T were determined by temperature and strain rate cycling tests as described in [5,6]. The glide resistance of impurity related defects may therefore be characterized in terms of the activation parameters DGi, DF *, Vi and t *. It i i should be noted, however, that apart from the impurity related mechanisms several other thermal and athermal processes may contribute to the flow stress of titanium aluminides. The glide resistance of these processes has been investigated in [5,6]. At sufficiently high deformation temperatures and low strain rates, solute segregation into or near to the dislocation cores may occur. This produces another type of glide resistance known as dynamic strain aging and is characterized by a serrated stress strain curve. This mechanism was investigated by static strain aging experiments [7]. The mechanical tests were supplemented by transmission electron microscopy (TEM) examination of the deformation induced defect structure.
3. Flow stresses and activation parameters The flow stresses and reciprocal activation volumes were measured at 293 and 973 K. Fig. 1 shows the dependencies of these values on the carbon concentration for the two series of materials investigated. For the quenched materials, relatively large values of 1/Vi were determined at room temperature, which increased slightly with c. It is therefore concluded that carbon atoms in solid solution (or in the form of tiny agglomerates) act as weak glide obstacles, which can apparently be easily overcome with the aid of thermal activation. These impurity related defects are therefore manifested in the activation volume but are rather ineffective for hardening the material. In contrast the room temperature values of 1/Vi of the aged material slightly decreased with c. This indicates that the density of thermal obstacles decreases with c. It should be mentioned that the activation volumes estimated on the aged materials are quite similar to those of conventional (undoped) two-phase titanium aluminides [5,6]. The Gibbs free energy at room temperature of aged materials is practically independent of c and amounts to DGi = 0.7 eV.
(6)
This value is again very similar to those estimated on conventional two-phase titanium aluminides [5,6]. The glide resistance determining the dislocation velocity in these materials has been attributed to lattice friction, localized pinning and jog dragging [5,6]. Because of the close agreement of the activation parameters these factors are also thought to control the dislocation mobility in the aged carbon doped material. This implies that the flow stress increase observed after aging is essentially athermal in nature and thus the related glide obstacles cannot be overcome with the aid of thermal activation. This is supported by the fact that the high flow stresses of the heavily doped materials were maintained up to 973 K. The materials were also tested after HIP’ing, where the carbon is probably present in the form of coarse precipitates of H-phase Ti2AlC and perovskite phase Ti3AlC [8]. It is interesting to note that in this condition the yield stress is almost independent of carbon concentration and exhibits the same values as after homogenisation and quenching (Fig. 1(a)). The related reciprocal activation volumes determined at 293 K decrease significantly with c. This clearly indicates that the precipitates are relatively large particles which act as athermal glide obstacles. However, the coarse dispersion of these precipitates seems to be less effective in strengthening the material. This observation agrees with the widely accepted view that both the size and dispersion of the particles are important for effective precipitation hardening.
U. Christoph et al. / Materials Science and Engineering A239–240 (1997) 39–45
41
Fig. 1. Dependency of the flow stress s and the reciprocal activation volume 1/Vi on the carbon content, (a) homogenized and quenched with carbon atoms in solid solution or in the form of tiny agglomerates. The drawn lines refer to the room temperature values of the materials in the as HIP’ed condition where the carbon is present as a coarse dispersion of the H-phase Ti2AlC and the perovskite phase Ti3AlC. (b) quenched and aged materials which contain a fine dispersion of Ti3AlC perovskite type precipitates.
4. Static and dynamic strain aging The materials investigated exhibited discontinuous yielding and a negative strain rate sensitivity over the temperature range 450 – 650 K. These phenomena are usually associated with the Portevin – Le Chatelier effect which arises from the dynamic interaction of diffusing defects with the dislocations. The resulting glide resistance and strain aging phenomena were investigated using the classical yield-point return technique. Samples were deformed to different levels of prestrain, aged in situ on the load frame for certain aging periods ta, and then retested. This method ensures good specimen alignment and allows the stress level during aging to be kept constant. In most cases the samples were aged under a relaxing stress starting from the flow stress sa of the material at strain o. The experiments were performed at the aging temperatures T = 423, 523 and 623 K for aging time ta =3.5 −106 s. Fig. 2 shows the load elongation trace of a strain aging experiment and defines the aging parameters. The investigations were performed on the Ti – 48.5at.%Al – 0.37at.%C alloy, which had been subjected to the three different thermal treatments described previously. The results presented here
refer to the as HIP’ed condition but are similar for the other two conditions of the material. Fig. 3 demonstrates the early stages of strain aging kinetics determined for the three temperatures. Each aging condition was examined for strain o= 1.25% using separate samples to avoid any influence of the strain dependence of Ds. The strain age yield points apparently become saturated over the time scale of the experiments leading to the saturation values Dss. The parameters characterizing the kinetics of strain aging are compiled in Table 1. From the present data an activation energy can be determined if the times necessary to achieve a given degree of completeness of dislocation pinning and the related temperatures are combined in an Arrhenius plot. Fig. 4 demonstrates this plot for the saturation times ts(T) and the shorter times tr(T) which correspond to the stress increments Dsr = 0.8 · Dss. A mean activation energy of Qa = 0.77 eV was determined from the slopes of the lines corresponding to ts and tr. This energy is significantly smaller than the self diffusion energy for g(TiAl) of Qsd = 3.01 eV [9]. Thus, a classical vacancy diffusion mechanism can clearly be ruled out. This conclusion is supported by the experimental observation that excess vacancies produced by
42
U. Christoph et al. / Materials Science and Engineering A239–240 (1997) 39–45 Table 1 Parameters characterizing strain aging of a Ti – 48.5at.%Al– 0.37at.%C alloy T (K)
Dss (MPa)
ts (s)
Dsr (MPa)
tr (s)
423 523 623
32 30.2 12.7
286 797 4350 566
25.6 24.1 10.2
32 823 149 25.5
o =1.25%; o; =4.16 · 10−4 s−1; Dss, saturation value of the strain age yield points; Dsr =0.8 · Dss; ts, tr, related aging times.
Fig. 2. Sequence of static strain aging experiments performed under a relaxing stress. The stress increments Ds were measured as the difference in stress before aging and the peak level on reloading. Different time intervals ta between unloading and subsequently reloading are indicated.
eral phenomenon of the titanium aluminides. Unfortunately, little information can be deduced for dislocation pinning by the segregation of impurity atoms at the dislocation cores due to the lack of diffusion data for impurity atoms. However, it can be speculated that the aging phenomena arise from fast diffusing impurity elements. This being the case, iron or boron atoms should be considered as recent studies have revealed that these elements have high mobilities in a2(Ti3Al) (C.H. Herzig, Unpublished results). Most titanium aluminides of technical relevance contain significant levels of these elements, 100–300 ppm by weight.
5. Dislocation interactions with perovskite precipitates
homogenization of the samples at 1458 K and subsequent quenching apparently do not affect the aging phenomena. Furthermore, even enhanced self-diffusion along dislocation cores appears to have no effect, the activation energy expected for this process being about half that for bulk diffusion [10]. Similar strain aging characteristics have been observed on other two-phase alloys [7,11,12]. Thus, it is speculated that the dislocation locking mechanism behind the aging effects is not a consequence of the carbon doping but rather a gen-
In order to identify the hardening mechanism detailed electron microscope investigations were performed on the aged alloy Ti–48.5at.%Al–0.37at.%C, which exhibited the highest flow stress. Conventional and high resolution TEM examinations revealed needle-shaped Ti3AlC precipitates of perovskite type. These defects were elongated along their [001]-axis and exhibited the same structural characteristics as have been described in [8,13], namely
Fig. 3. Kinetics of strain aging under relaxing loads and the deformation parameters indicated.
Fig. 4. Arrhenius plot showing the variation of the aging times ts and tr with temperature.
U. Christoph et al. / Materials Science and Engineering A239–240 (1997) 39–45
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Fig. 5.
[001]p [001]m, 100]p 100]m.
(7)
p and m designate the precipitate and the matrix, respectively. The precipitates had an average length l = 22 nm and a width (along 100]) dp =3.3 nm. The deformation structure observed after 3% compression at room temperature consisted mainly of 1/2110] ordinary dislocations, 011] superdislocations and 1/6112( ] order twins. As demonstrated in Fig. 5, perfect and twinning partial dislocations were pinned by the perovskite precipitates, the obstacle spacing along the dislocations was typically lc =50 – 100 nm. The high glide resistance provided by the precipitates is manifested by the strong bowing-out of the dislocation
segments. The bowing process is particularly pronounced by the twinning partial dislocations because of their low line tension. It is interesting to note that the stressed configuration of the dislocations was apparently not relaxed during unloading and thin foil preparation. However, there are two factors which are thought to impede such relaxations. Between the TiAl matrix and the precipitates mismatch strains of 2–4% occur, depending on lattice direction. This results in significant coherency stresses, which are certainly present in the thin foils. Furthermore, the backward motion of the dislocations is certainly impeded by lattice friction forces due to the directional bonding of the material [5].
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U. Christoph et al. / Materials Science and Engineering A239–240 (1997) 39–45
Fig. 5. (Contd.) Deformation structure of an aged Ti–48.5at.%Al – 0.37at.%C alloy generated during room temperature compression to strain o= 3%. Pseudo-weak beam image recorded using g= (002)TiAl reflection from near the [020] pole in the g/3.1g condition, and high resolution image in 110]g projection. Note the high density of Ti3AlC-precipitates which are manifested by strain contrast. (a) Pinning of [011] superdislocations by the precipitates. The inset shows line tension configurations calculated for different stresses and projected into the image plane. For the segment analyzed, the length lc = 110 nm, the half axis q =80 nm and effective shear stress tc =299 MPa have been attributed. (b) Low magnification high resolution micrograph showing a deformation twin propagated through an array of needle shaped perovskite precipitates. (c) High resolution image showing the deflection of a deformation twin in the local region of a perovskite precipitate. Note the irregular shape of the twin/matrix interface (inset).
The effective shear stresses tc acting on the pinned dislocation segments were estimated by analyzing their curvature. Line tension configurations were calculated for different stresses according to the DeWitt –Koehler model [10,14], which considers the dependence of the line energy of a dislocation on its orientation. Elastic isotropy was assumed for the sake of simplicity. Within the framework of this model the dislocation loops are apparently elliptical with the major semi-axis q (in mm) parallel to the Burgers vector. Loops of this configuration are related to the shear stress tc by [10,14] tc(MPa)=
m.b 1 · ln(1.61c/b). 4p(1− n) q
(8)
b is the Burgers vector and n is Poisson’s ratio. Line tension loops were calculated for different stresses using the elastic constants measured by Schafrik [15] and were projected into the foil plane (Fig. 5(a)). By comparison with the observed shape of loops, a mean effective shear stress tc =300 MPa was obtained. This value can be related to a normal stress sc =f · tc = 900 MPa, which is close to the flow stress s =1000 MPa at strain o= 3%. This, together with the high density of pinning centers, leads to the conclusion that a significant portion of the total flow stress in the aged materials arises from the interaction of perfect and twinning partial dislocations with the precipitates. In their {111} slip planes the 011] superdislocations typically bow
out at the precipitates through angles c= 110°. This corresponds to interaction forces of fm = 1.5 · 10 − 8 N or fm/mb 2 = 0.57. It is therefore speculated that the precipitates are still shearable and can be overcome by the dislocations without Orowan looping. This view is supported by the TEM observations and the experimental finding that the work hardening coefficient ds/do of the aged materials does not depend on the carbon concentration. Due to the relatively large size of the precipitates it is speculated that their overcoming by the dislocations is essentially an athermal process as has been suggested by the concentration dependence of the activation volume (Fig. 1(b)). This view is supported by the observed structures of the dislocations and deformation twins. The dislocations apparently penetrate the obstacle array deeply along paths of easy movement and become immobilized at groups of unfavourably arranged particles leading to bundles of immobilized dislocations. Similarly twinning partial dislocations are often immobilized at the precipitates. Thus, in the local region of the precipitates the shape of the twin/matrix interfaces is much less regular and the twins are often deflected (Fig. 5(b) and (c)). Such processes often lead to fragmentation of the twins, i.e. islands of untwinned regions occur. As overcoming of the precipitates cannot be supported by thermal activation, the resulting glide resistance will be maintained under low creep rates. Hardening of two-phase titanium aluminides by fine
U. Christoph et al. / Materials Science and Engineering A239–240 (1997) 39–45
dispersions of Ti3AlC precipitates therefore seems to be a suitable metallurgical technique for improving the high temperature strength and creep resistance of the material. The high degree to which carbon additions improve the creep resistance has been demonstrated on a Ti – 48at.%Al – 4at.%V alloy containing 0.3at.%C [2]. However, in contrast to the analysis presented above, the enhanced glide resistance was attributed to a solute atmosphere drag mechanism.
6. Conclusions The effects of carbon additions on the mechanical properties of two-phase titanium aluminides have been investigated by mechanical testing and TEM observations. Fine dispersions of Ti3AlC precipitates of perovskite type form arrays of strong glide obstacles so that perfect and twinning partial dislocations are effectively pinned. The mechanism results in a high athermal contribution to the flow stress, which significantly improves the high temperature strength. In comparison, carbon in solid solution is less efficient for hardening the material. In the intermediate temperature interval 450 – 650 K strain aging phenomena occur. The observed fast kinetics and low activation energy of the aging process are not consistent with the mobility of defects in g(TiAl) obtained from the literature. The species causing the static and dynamic strain aging effects have not been identified due to the lack of diffusion data. It appears, however, that they are solute atoms and could be Fe or B, both of which are present in significant amounts in most technical alloys.
.
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Acknowledgements The authors would like to thank U. Lorenz, J. Mu¨llauer, M. Oehring and J. Paul for helpful discussions and support. The financial support by the ‘Deutsche Forschungsgemeinschaft’ is gratefully acknowledged. References [1] W.H. Tian, M. Nemoto, in: Y.-W. Kim, R. Wagner, M. Yamaguchi (Eds.), Gamma Titanium Aluminides, TMS, Warrendale, PA, 1995, p. 689. [2] B.D. Worth, J.W. Jones, J.E. Allison, Metall. Trans. A 26A (1995) 2961. [3] F. Appel, H. Clemens, R. Wagner, in: W.O. Soboyejo, T.S. Srivatsan, H.L. Fraser (Eds.), Deformation and Fracture of Ordered Intermetallics III, TMS, Warrendale, PA, 1996, p. 123. [4] G. Scho¨ck, Phys. Stat. Sol. 8 (1965) 499. [5] F. Appel, U. Sparka, R. Wagner, in: J. Horton, J. Baker, S. Hanada, R.D. Noebe, D.S. Schwartz (Eds.), High-Temperature Ordered Intermetallic Alloys VI, MRS, Pittsburgh, PA, 1995, p. 623. [6] F. Appel, U. Lorenz, M. Oehring, U. Sparka, R. Wagner, Mater. Sci. Eng. A233 (1997) 1. [7] U. Christoph, F. Appel, R. Wagner, in: C.C. Koch, N.S. Stolloff, C.T. Liu, A. Wanner (Eds.), High Temperature Ordered Intermetallic Alloys VII, MRS, Pittsburgh, PA, 1997, p. 207. [8] S. Chen, P.A. Beaven, R. Wagner, Scr. Metall. Mater. 26 (1992) 1205. [9] S. Kroll, H. Mehrer, N. Stolwijk, Ch. Herzig, R. Rosenkranz, G. Frommeyer, Z. Metallkde. 83 (1992) 8. [10] J.P. Hirth, J. Lothe, Theory of Dislocations, 2nd ed., Krieger, Malabar, 1992, p. 506. [11] A. Barthels, C. Koeppe, T. Zhang, H. Mecking, in: Y.-W. Kim, R. Wagner, M. Yamaguchi (Eds.), Gamma Titanium Aluminides, TMS, Warrendale, PA, 1995, p. 655. [12] M.A. Morris, T. Lipe, D.G. Morris, Scr. Mater. 34 (1996) 1337. [13] W.H. Tian, T. Sano, M. Nemoto, Philos. Mag. A68 (1993) 965. [14] G. DeWitt, J.S. Koehler, Phys. Rev. 116 (1959) 1113. [15] R.E. Schafrik, Metall. Trans. A 8A (1977) 1003.