microstructures and mechanical properties of nb–ti–c alloys

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Materials Science and Engineering A 485 (2008) 359–366 Microstructures and mechanical properties of Nb–Ti–C alloys Huisheng Jiao a , Ian P. Jones a,, Mark Aindow b a Department of Metallurgy and Materials, University of Birmingham, B15 2TT, UK b Department of Materials Science and Engineering, Institute of Materials Science, University of Connecticut, CT 06269-3136, USA Received 25 January 2007; received in revised form 29 July 2007; accepted 11 August 2007 Abstract The microstructures and mechanical properties of a series of ternary Nb–Ti–C alloys have been investigated. The microstructures were charac- terized using scanning electron microscopy, transmission electron microscopy and X-ray diffraction. The alloys contain only two phases: (Nb,Ti)C carbide and Nb solid solution. The solid solution is a ductile phase while the carbides strengthen the alloy. Compression tests were performed at room temperature and 1473 K. All of the alloys showed good ductility at room temperature, and the alloy with 20 at.% Ti and 20 at.% C showed a 0.2% offset yield stress of 197 MPa at 1473 K. The room-temperature and high-temperature strengths increased with increasing Ti and C content, but the room-temperature ductility decreased with increasing C content. The carbides deformed plastically, even at room temperature. Strategies for the future development of these alloys, aimed at balancing the high-temperature strength and room-temperature ductility, are discussed. © 2007 Elsevier B.V. All rights reserved. Keywords: Niobium alloys; Dispersion hardening; High-temperature properties 1. Introduction Niobium-based alloys have been investigated as next gener- ation high-temperature structure materials in place of Ni-based superalloys, which have a maximum operating temperature of about 1373K. Pure niobium has a relatively low density, a very high melting point (2741 K) and good room-temperature ductility. However, at temperatures above 1200K, the strength of Nb decreases substantially. In order to improve the high- temperature strength, various approaches have been utilised, including solid solution strengthening, precipitation strength- ening and composite strengthening. Solid solution strengthened Nb alloys with V, Ta, Mo and W have been reported [1], and also some two-phase in situ composites containing a bcc Nb solid solution (Nb ss ) and an intermetallic compound such as Nb 3 Al [2] or Nb 5 Si 3 [3]. The results showed that Nb–Mo–W alloys [4,5] had excellent strength even at temperatures above 1773K. However, those alloys exhibited very poor ductility and fracture toughness at room temperature, which is a major drawback in practical applications. Most of the Nb-based in situ composites also suffer from the same problem, although Corresponding author. Tel.: +44 121 4145184; fax: +44 121 414 5232. E-mail address: [email protected] (I.P. Jones). they show excellent high-temperature strength and creep resis- tance. In order to improve the low-temperature mechanical prop- erties of Nb-based alloys, various multi-element alloying approaches have been employed. One of the most promis- ing approaches is the introduction of carbides. For example, additions of HfC to Nb–5 at.%Mo–15 at.%W alloys gave con- current increases in both the high-temperature strength and the room-temperature fracture toughness [5]. Similarly, in multicomponent Nb–Al–Ti alloys [6–11] minor additions of TiC increased the high-temperature strength without impair- ing room-temperature ductility. Moreover, it has been shown that Nb–20Zr–C alloys exhibit both excellent high-temperature strength and good room-temperature toughness [12,13]. In research on Nb alloys, Ti is regarded as a toughen- ing element but no systematic studies of Nb–Ti–C alloys have been reported. As such, the purpose of this research is to examine the potential of the Nb–Ti–C system as new alloys for high-temperature applications. A series of three Nb-rich alloys was produced, and their microstructures were characterized using a combination of X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmis- sion electron microscopy (TEM). The mechanical behaviour of the alloys was assessed under ambient conditions and at elevated temperature, and the deformation microstructures 0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2007.08.035

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Page 1: Microstructures and mechanical properties of Nb–Ti–C alloys

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Materials Science and Engineering A 485 (2008) 359–366

Microstructures and mechanical properties of Nb–Ti–C alloys

Huisheng Jiao a, Ian P. Jones a,∗, Mark Aindow b

a Department of Metallurgy and Materials, University of Birmingham, B15 2TT, UKb Department of Materials Science and Engineering, Institute of Materials Science,

University of Connecticut, CT 06269-3136, USA

Received 25 January 2007; received in revised form 29 July 2007; accepted 11 August 2007

bstract

The microstructures and mechanical properties of a series of ternary Nb–Ti–C alloys have been investigated. The microstructures were charac-erized using scanning electron microscopy, transmission electron microscopy and X-ray diffraction. The alloys contain only two phases: (Nb,Ti)Carbide and Nb solid solution. The solid solution is a ductile phase while the carbides strengthen the alloy. Compression tests were performed atoom temperature and 1473 K. All of the alloys showed good ductility at room temperature, and the alloy with 20 at.% Ti and 20 at.% C showed a

.2% offset yield stress of 197 MPa at 1473 K. The room-temperature and high-temperature strengths increased with increasing Ti and C content,ut the room-temperature ductility decreased with increasing C content. The carbides deformed plastically, even at room temperature. Strategiesor the future development of these alloys, aimed at balancing the high-temperature strength and room-temperature ductility, are discussed. 2007 Elsevier B.V. All rights reserved.

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eywords: Niobium alloys; Dispersion hardening; High-temperature properties

. Introduction

Niobium-based alloys have been investigated as next gener-tion high-temperature structure materials in place of Ni-baseduperalloys, which have a maximum operating temperature ofbout 1373 K. Pure niobium has a relatively low density, aery high melting point (2741 K) and good room-temperatureuctility. However, at temperatures above 1200 K, the strengthf Nb decreases substantially. In order to improve the high-emperature strength, various approaches have been utilised,ncluding solid solution strengthening, precipitation strength-ning and composite strengthening. Solid solution strengthenedb alloys with V, Ta, Mo and W have been reported [1], and

lso some two-phase in situ composites containing a bcc Nbolid solution (Nbss) and an intermetallic compound such asb3Al [2] or Nb5Si3 [3]. The results showed that Nb–Mo–W

lloys [4,5] had excellent strength even at temperatures above773 K. However, those alloys exhibited very poor ductility

nd fracture toughness at room temperature, which is a majorrawback in practical applications. Most of the Nb-based initu composites also suffer from the same problem, although

∗ Corresponding author. Tel.: +44 121 4145184; fax: +44 121 414 5232.E-mail address: [email protected] (I.P. Jones).

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921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2007.08.035

hey show excellent high-temperature strength and creep resis-ance.

In order to improve the low-temperature mechanical prop-rties of Nb-based alloys, various multi-element alloyingpproaches have been employed. One of the most promis-ng approaches is the introduction of carbides. For example,dditions of HfC to Nb–5 at.%Mo–15 at.%W alloys gave con-urrent increases in both the high-temperature strength andhe room-temperature fracture toughness [5]. Similarly, in

ulticomponent Nb–Al–Ti alloys [6–11] minor additions ofiC increased the high-temperature strength without impair-

ng room-temperature ductility. Moreover, it has been shownhat Nb–20Zr–C alloys exhibit both excellent high-temperaturetrength and good room-temperature toughness [12,13].

In research on Nb alloys, Ti is regarded as a toughen-ng element but no systematic studies of Nb–Ti–C alloysave been reported. As such, the purpose of this researchs to examine the potential of the Nb–Ti–C system asew alloys for high-temperature applications. A series ofhree Nb-rich alloys was produced, and their microstructuresere characterized using a combination of X-ray diffraction

XRD), scanning electron microscopy (SEM) and transmis-ion electron microscopy (TEM). The mechanical behaviourf the alloys was assessed under ambient conditions andt elevated temperature, and the deformation microstructures

Page 2: Microstructures and mechanical properties of Nb–Ti–C alloys

360 H. Jiao et al. / Materials Science and Engineering A 485 (2008) 359–366

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Fig. 1. Isothermal section of the Nb–Ti–C phase diagram at 1873 K [15].

ere evaluated using TEM to reveal the deformation micro-echanisms.

. Experimental procedure

The nominal compositions of the alloys in this study areb–15Ti–5C, Nb–20Ti–5C, Nb–20Ti–10C and Nb–20Ti–20C

all in atomic %), which are indicated on an isothermal sectionf the Nb–Ti–C ternary phase diagram in Fig. 1. High purityb, Ti and TiC powders were used as the starting materials.he alloys were prepared by arc-melting and casting into but-

ons. The buttons were then heat-treated at 2000 K for 4 h inacuum, followed by argon gas quenching. The density of theb–20Ti–20C was measured to be 7.4 g/cm3. TEM specimensere prepared by twin-jet electropolishing to perforation usingsolution of 10 vol.% sulphuric acid in methanol at 243 K and5 V. TEM observations were performed using a Philips CM20perating at 200 kV.

Conventional constant strain-rate deformation tests were per-ormed at a strain rate of about 10−4 s−1 at room temperature inn ESH frame with a 200 kN capacity. Specimens for these testsith dimensions 4.5 mm × 4.5 mm × 9.0 mm were cut using an

lectro-discharge machine (EDM). High-temperature compres-ion was performed in a 1 kN Instron 8501 frame. The limitedoad capacity of the machine required smaller specimens withimensions of 2 mm × 2 mm × 4 mm. High-temperature con-tant strain-rate testing was carried out under vacuum.

. Results and analysis

.1. Microstructure

.1.1. Phase identificationXRD spectra obtained from as-cast samples of each of the

lloys are shown in Fig. 2. It was found that, in each case,

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Fig. 2. XRD spectra from as-cast samples of each of the alloys.

he alloys contained only two different phases: bcc Nbss andNb,Ti)C with the fcc NaCl-type structure. The peaks aris-ng from these phases are indicated in Fig. 2 by circles andquares, respectively. We note that it was not possible to mea-ure the volume fractions of the phases from such spectraecause of the effects of solidification texture upon the rela-ive intensities of the peaks. The values of the lattice parametersalculated from the XRD data were 0.3296 and 0.4377 nmor the Nbss and carbide phases, respectively. The latter valueies between those of NbC (0.440 nm) and TiC (0.433 nm), asxpected.

.1.2. SEM observationsExamples of SEM micrographs showing the microstructures

xhibited by the alloys are shown in Fig. 3. As expected fromhe XRD data, a two-phase microstructure consisting of Nbssnd carbide phases was observed in each case. Fig. 3a and bere obtained from the Nb–15Ti–5C alloy in the as-cast andeat-treated states, respectively. In the as-cast structure, thebss adopts a coarse dendritic morphology indicating that thishase solidifies first, and that a eutectic mixture of carbide andbss phases forms from the interdendritic liquid (Fig. 3c). Weote, however, that there are also finer needle-like carbides,p to 15 �m long and 1 �m wide, within the Nbss dendrites.hese presumably precipitate on cooling from the solidifica-

ion temperature due to supersaturation of C in the primarybss phase. After annealing at 2000 K for 24 h, more exten-

ive precipitation of the carbide phase was observed withinhe Nbss dendrites. Similar structures were observed in thether three alloys (Fig. 3e–g) with the volume fraction ofarbide increasing with carbon content, as expected. Imagenalysis showed that the volume fraction of (Nb,Ti)C is about0 and 40% in the Nb–20Ti–10C and Nb–20Ti–20C alloys,espectively.

.1.3. TEM observationsFig. 4a is a low magnification bright-field image of (Nb,Ti)C

recipitates in the Nbss matrix of the Nb–15Ti–5C alloy aftereat treatment. The carbides appear rod-like: 100–200 nm wide

Page 3: Microstructures and mechanical properties of Nb–Ti–C alloys

H. Jiao et al. / Materials Science and Engineering A 485 (2008) 359–366 361

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ig. 3. SEM images showing the overall microstructures of the alloys: Nb–15Tagnification images of (a) and (b), respectively. (e)–(g) as-cast Nb–20Ti–5C,

nd 1–8 �m long. Higher magnification images, such as Fig. 4b,evealed a high density of tangled dislocations in the Nbss matrix,

ith very few defects in the carbides. We note, however, thatccasional stacking faults and dislocation nets were observedn the eutectic carbides. Although the interfaces between thearbides and the Nbss were abrupt and flat, it was not possi-

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in the as-cast state (a) and after annealing at 2000 K (b). (c) and (d) are higher0Ti–10C, and Nb–20Ti–20C, respectively.

le to analyse their defect structure due to the high densitiesf dislocations in the Nbss. Selected area diffraction patterns

SADPs) taken from the Nbss and carbide phases (e.g. Fig. 4cnd d, respectively) are consistent with the XRD data. Compos-te SADPs such as Fig. 4e obtained from needle-like carbidesnd the surrounding Nbss revealed that the precipitates adopt a
Page 4: Microstructures and mechanical properties of Nb–Ti–C alloys

362 H. Jiao et al. / Materials Science and Engineering A 485 (2008) 359–366

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slabide, the atomic ratio of M/C ≈ 1, and the M atom positionsare occupied nearly equally by Ti and Nb atoms. In the Nbssmatrix, the data show 7 at.% C, which is not consistent with

Table 1EDXS data obtained from an annealed sample of the Nb15Ti5C alloy

ig. 4. (Nb,Ti)C precipitates in the Nbss of Nb–15Ti–5C. (a) Low-magnificatihe Nbss and an abrupt interface between this and the (Nb,Ti)C particle. (c) [0 0rom the interface region showing the N–W OR.

ell-defined orientation relationship (OR):

1 1 1}carbide//{1 1 0}Nb, {1 1̄ 0}carbide//{0 0 1}Nb

his is the Nishiyama–Wassermann (N–W) OR, which is onef the more common ORs between fcc and bcc structures. Nonique OR was observed for the eutectic carbides.

The character of the dislocations in the Nbss was investigatedsing diffraction contrast imaging and a partial analysis is shownn Fig. 5. In each case it was found that the Burgers vectors of

hese dislocations were (1/2)〈1 1 1〉 type.

The compositions of the carbide and the matrix were analysedy energy-dispersive X-ray spectrometry (EDXS) and examplesf the data obtained are shown in Fig. 6. In Fig. 6a, typical

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ght-field TEM image, (b) higher magnification image showing dislocations inDP from Nbss, (d) [0 1 1] SADP from (Nb,Ti)C particle. (e) Composite SADP

pectra obtained from the carbides and Nbss are shown over-apped. The results of the compositional analyses for one of thelloys (Nb–15Ti–5C) are summarised in Table 1. In the car-

Nb (at.%) Ti (at.%) C (at.%)

Nb,Ti)C 21.3 ± 0.7 24.3 ± 0.5 54.4 ± 0.7bss 80.1 ± 0.5 13.0 ± 0.2 7.0 ± 0.5

Page 5: Microstructures and mechanical properties of Nb–Ti–C alloys

H. Jiao et al. / Materials Science and E

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ig. 5. Bright-field TEM micrographs of dislocations in an annealed sample ofhe Nb–15Ti–5C alloy.

he overall composition. The error in the C content was proba-ly the result of contamination in the TEM during collection ofhe spectra. Fig. 6b is a linescan performed across one carbidearticle showing the concentration profiles for Nb, Ti and C.

.2. Room-temperature mechanical tests

No apparent change in hardness was detected between thes-cast and annealed specimens of each alloy. The values ofickers hardness for these alloys in the annealed state are listed

n Table 2.The compression stress–strain curves obtained from each

lloy at room temperature are shown in Fig. 7. It is evident thathese alloys exhibited excellent compressive ductility. The com-ression tests were interrupted when the strain reached 30%,xcept for Nb–20Ti–20C, which failed when the strain wasround 15%. Cracking was observed on the surface of this speci-en after the compression test, although Nb–20Ti–20C showedhigher compressive strength at room temperature than the other

lloys. The alloys with low carbon concentrations all exhibitedery low yield strength values of around 400 MPa. The values forhe Nb–15Ti–5C and Nb–20Ti–5C alloys are very similar andhus increasing the Ti concentration has no obvious beneficial

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ngineering A 485 (2008) 359–366 363

ffect on the strength. However, a significant increase in strengths obtained by increasing the carbon content from 5 to 20 at.%.he 0.2% offset strength of Nb–20Ti–20C is about 800 MPa at

oom temperature.

.3. High-temperature compression test

The yield strengths for the four alloys at 1473 K were obtainedy constant strain-rate compression under vacuum. The resultsre shown in Table 2. With increasing testing temperature, the.2% offset flow stress decreases dramatically. Similarly to theesults at room temperature, on increasing the carbide contentn the alloy, the yield stress increases. The 0.2% flow stress ofb–20Ti–20C is 197 MPa at 1473 K compared with 70 MPa forure Nb.

.4. Deformation microstructure

The Nb–Ti–C alloys exhibited substantial room-temperatureuctility in compression. After testing, the deformationicrostructures were examined using TEM. A high density

f dislocations could still be seen in the Nbss matrix, whichnderwent large-scale plastic deformation. Using the g·b = 0nvisibility criterion, the Burgers vector of the dislocationsas determined to be (1/2)〈1 1 1〉. It is difficult to define theifference in dislocation density between the deformed andndeformed alloys because the density in the undeformed speci-en is already rather high, but undoubtedly the density does rise.o deformation twins were detected in the bcc Nbss matrix. The

arbides in these alloys also experienced considerable defor-ation in compression. Fig. 8 shows an image of a deformed

Nb,Ti)C carbide; the SADP is shown in the inset. A high densityf linear features is observed inside the carbide. In the diffrac-ion pattern, there are pronounced streaks perpendicular to theseeatures, implying that they correspond to stacking faults and/oricrotwins.After deformation at high temperature, an even higher den-

ity of dislocations was present in the Nbss as shown in Fig. 9.ere again, these dislocations have (1/2)〈1 1 1〉-type Burgersectors. Dislocations and a high density of stacking faults wereresent in the eutectic (Nb,Ti)C particles (Fig. 10). Diffractionontrast analyses revealed that the Burgers vectors of the dis-ocations are (1/2)〈1 1 0〉, and that these lay on {1 1 1} planes.he stacking faults are shear-type, lie parallel to the glide planes

or the dislocations, and presumably arise through a dissociationrocess:

12 〈1 1 0〉 → 1

6 〈1 1 2〉 + SF + 16 〈1 1 2〉

n the smaller needle-shaped (Nb,Ti)C precipitates, very feweformation defects were observed. As such, it appears thathe defects in the larger eutectic carbides accommodate the

eformation of the surrounding Nbss, but the needle-like car-ide precipitates act as obstacles to block the motion ofhe dislocations in the Nbss phase, thus strengthening theatrix.
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364 H. Jiao et al. / Materials Science and Engineering A 485 (2008) 359–366

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ig. 6. EDXS data obtained from the Nbss and the carbide precipitates in an annb, Ti and C concentrations and (b)–(e) linescans across a precipitate showing

. Discussion

In developing new superalloys, several major aspects such asow-temperature fracture toughness, high-temperature strength,reep resistance and oxidation resistance should be consid-red. Clearly, these properties are controlled by the compositionnd microstructure of the alloy. At room temperature, theompression tests demonstrated pronounced ductility for theb–Ti–C alloys examined in this research. With the exceptionf Nb–20Ti–20C, which showed limited plastic deformationefore failure, all of the other alloys were very ductile. In these

lloys, Nbss is the ductile phase and (Nb,Ti)C strengthens andmbrittles the alloy. With increasing (Nb,Ti)C content the alloyecomes more brittle. However, from the compression tests, itan also be seen that with increasing (Nb,Ti)C content the yield

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able 2ummary of room-temperature hardness and 0.2% offset yield stress data

Nb–15Ti–5C Nb–20Ti–

ardness (HV) 196 19093 K (MPa) 380 360473 K (MPa) 87 80

sample of the Nb–15Ti–5C alloy. (a) Point analyses showing the difference inriation in Nb, C and Ti content.

trength increases, which confirms that (Nb,Ti)C is an effec-ive strengthening phase for Nbss. Comparing Nb–20Ti–5C withb–15Ti–5C, there is no noticeable difference in yield strength,hich suggests that Ti is not an effective solid solution strength-

ning element for Nb. From the EDXS analysis, there is only5 at.% Ti in (Nb,Ti)C and about 13 at.% Ti in Nbss. In most Nb-ased alloys, such as in Nb–silicide and Nb–Cr alloys, Ti actss an effective ductilising and toughening element [3]. The frac-ure toughness of Nb–Ti–Cr solid solution alloys increases withi content. In Nb–Ti–C alloys, the solubility of C in Nb is verymall, about 0.02 at.% at room temperature [14,15]. Therefore,

he effect of C additions to Nb alloys is to form dispersive car-ides, which strengthen the Nb matrix. In Nbss/Nb3Al alloys,t is found that Ti can increase the strength until 1273 K butecreases the strength above 1573 K [16]. The yield strengths of

5C Nb–20Ti–10C Nb–20Ti–20C

204 275405 803140 197

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H. Jiao et al. / Materials Science and Engineering A 485 (2008) 359–366 365

Fig. 7. Stress–strain curves for compression tests performed at room temperatureon annealed samples of each of the alloys.

Fig. 8. Bright-field TEM micrographs obtained from a sample of theNb–15Ti–5C alloy deformed at room temperature. The Nbss matrix containsa high density of dislocations and there is complex contrast from defects in the(Nb,Ti)C precipitate. The additional reflections and streaking in the SADP indi-cate that this contrast arises from microtwins and stacking faults on {1 1 1} inthe carbide.

Fig. 9. Bright-field TEM image obtained using g = 110 from Nb–15Ti–5C aftercompression at 1473 K. A high density of dislocations is evident.

Fig. 10. Bright-field TEM images obtained from samples of the Nb–15Ti–5Calloy deformed at 1473 K showing (a) a high density of stacking faults in sec-oe

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ndary (Nb,Ti)C precipitates, and (b) dislocations and stacking faults in largerutectic (Nb,Ti)C particles.

he current alloys at 1473 K show that the Nb15Ti5C is nearlys soft as pure Nb, with a strength of 87 MPa. This suggests thatt 1473 K the solid solution strengthening effect of Ti in Nbss ismall. However, the Nb–20Ti–20C exhibits a strength of around00 MPa, which is promising for further development.

At room temperature, dispersion hardening is not the mainource of strength for the Nb–Ti–C alloys, while as the temper-ture increases, second-phase particle hardening may make aore significant contribution to the overall strength of the alloy.ore recently, studies of carbide strengthened Nb alloys, such asb–Zr–C [12] and Nb–Ti [6,8] alloys, have been published. Forrecipitate hardening Nb-carbide alloys, the ideal microstruc-ure is a finely dispersed carbide in a Nbss matrix. However, ins-cast Nb–Ti–C alloys, many (Nb,Ti)C particles are oversizedthe ideal size is less than 100 nm) which is not suitable forrowan strengthening (dislocation looping). Therefore, in order

o improve the strength of the alloy, solid solution hardening by

l, V, Mo, Hf and W, is one choice, the other approach being toecrease the size of the (Nb,Ti)C particles by using cold and/orot working. From our results, it is confirmed that the (Nb,Ti)C
Page 8: Microstructures and mechanical properties of Nb–Ti–C alloys

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s a promising reinforcing phase for Nbss. However, the strengthf Nb–20Ti–20C still needs to be increased further for applica-ions around 1473 K. In order to balance the room-temperatureoughness and elevated temperature strength by further alloying,aution must be employed to maintain the appropriate room-emperature toughness. Of all the alloying elements, Mo andf appear to be the most promising [1,16] for solid solution

trengthening and further investigation is underway.

. Conclusions

Based upon mechanical tests and microstructural analyses ofb–(15–20)Ti–(5–20)C alloys, the following conclusions cane drawn:

1) In the as-cast state, the alloys consist of Nb solid solutionand (Nb,Ti)C carbide. Two types of (Nb,Ti)C have beenobserved, large irregularly shaped eutectic carbides and finerneedle-shaped secondary precipitates. After annealing at1700 ◦C, more secondary carbides precipitated in the Nbssmatrix. With increasing C content in the alloys, the volumefraction of carbide increases.

2) The alloys exhibited excellent ductility in compression atroom temperature. The 0.2% flow stress increased withincreasing volume fraction of carbide in the alloys. Dueto the difference in thermal expansion coefficient betweencarbide and Nbss, a high density of dislocations was intro-duced into the Nbss during casting. After deformation, aneven higher density of dislocations with Burgers vector of

(1/2)〈1 1 1〉 was observed in Nbss with a high density ofstacking faults and microtwins in the carbides.

3) The (Nb,Ti)C particles effectively strengthen the Nbssphase, but further alloying is needed to increase the high-

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gineering A 485 (2008) 359–366

temperature strength of Nb–20Ti–20C. Alloying with Moand Hf appears to be a promising approach.

cknowledgements

The authors would like to thank EPSRC (GR/R23350/01(P)),olls-Royce plc and DSTL for financial support. In particular,e are grateful to Dr. Bob Broomfield (R-R plc) and Dr. Mikeinstone (DSTL) for their help and advice.

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