Non-Monotonic Aging Temperature Dependence of Superelasticityof Ti72Nb15Zr10Al3 Quaternary Alloys

Hiroyuki Tada1,+, Tokujiro Yamamoto2, Xinmin Wang3 and Hidemi Kato3

1Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan2Department of Mechanical System Engineering, Utsunomiya University, Utsunomiya 321-8585, Japan3Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan

The influence of aging on the superelastic behavior of Ti72Nb15Zr10Al3 alloy (which is associated with the martensitic transformation from¢ to ¡″ martensite) was investigated. The precipitation of ½ phase during aging significantly affects the mechanical properties. A non-monotonicchange in the stress required for martensitic transformation was observed as the aging temperature changed from 453 to 603K. This variation instress may be attributed to two factors: change of chemical composition in the matrix and internal strain because of ½ phase formation. The likelyvariation in the stress for martensitic transformation associated with each of these effects was estimated. As the volume fraction of ½ phaseincreased, the change in the chemical composition produced a greater effect than the change in the internal strain.[doi:10.2320/matertrans.M2013120]

(Received March 26, 2013; Accepted May 28, 2013; Published July 5, 2013)

Keywords: titanium alloys, shape memory, superelastic alloy, aging, omega phase

1. Introduction

Ti­Ni shape memory and superelastic alloys have beensuccessfully applied in various fields. Unfortunately, the Nicontent of Ti­Ni alloys has led to concerns about nickelallergy; thus a number of investigations into various Ni free¢ type Ti alloys have been reported in recent years.1­4)

Especially, extensive research attention has been directedtowards improving the superelastic properties of Ti­Nb basedalloys. It has been reported that the shape memory andsuperelastic behavior in ¢ type Ti alloys are related to themartensitic transformation from the disordered ¢ phase(bcc) to the orthorhombic ¡″ martensite phase.2) It has alsobeen reported that mechanical properties can be improvedby the addition of 3rd or further elements to Ti­Nb binaryalloys.5­12) Moreover, additions of B, Si, O and N stabilizethe shape memory and superelastic behavior by increasingthe critical stress for slip.13­16) Another effective method toimprove superelastic properties is to induce precipitationhardening by aging treatment after solution treatment. It hasbeen reported that the formation of the isothermal ½ phase(½iso phase) is effective at increasing the superelastic recoverystrain in Ti­Nb alloys.17) Conversely, disappearance ofmicrostructural reversibility because of ½ phase formationwas observed in Ti­Nb­Sn alloys by Semboshi et al.18) ½iso

phase formation leads to regions of the matrix that arecompositionally depleted with respect to ¢-stabilizingelements. On subsequent isothermal aging, the ½iso phasegrows whilst ejecting the ¢-stabilizing elements into thesurrounding matrix.19) Extensive studies have been carriedout to see if the ½ phase can be used to improve themechanical properties of Ti alloys.20,21) It is obvious that themetastable ½iso phase is an important phase in ¢ type Ti alloysto control their mechanical and martensitic properties.

Some reports have pointed out that the critical stress formartensitic transformation does not change monotonically asa function of the aging temperature. Li et al. have reportedthat the critical stress for martensitic transformation remainsstable in TiNb24Zr2 alloy aged at 573K for 7.2, 10.8 and14.4 ks. They suggest that this aging behavior is related tosuppression of the extent of ¢-formation in the matrix, andthe large amount of ¢-stabilizing elements present in thealloy.22) Song et al. have reported that superelastic behaviordisappears after aging at 473, 523, 573, 773 and 823K in Ti­9.8Mo­3.9Nb­2V­3.1Al (mass%) alloy,23) even though thealloy shows superelastic behavior after aging at 373, 623, 673and 723K. They described the precipitation and coarseningof ¡ and ½ phase, and related them to this behavior. In ourprevious study, the stress required for martensitic trans-formation (·M) of Ti72Nb15Zr10Al3 alloy decreased withincreasing aging temperature from 453 to 553K.24) However,the details of this phenomenon and the mechanism ofthe non-monotonic aging temperature dependence are stillunclear. The present study focused on the aging propertiesof the quaternary Ti72Nb15Zr10Al3 alloy. To clarify themechanism of how aging affects superelasticity, the temper-ature dependences of the microstructures and superelasticproperties were investigated.

2. Materials and Methods

2.1 Sample materialsA quaternary Ti­Nb­Zr­Al alloy with a nominal atomic

composition of Ti72Nb15Zr10Al3 was prepared by arc-meltingin an Ar atmosphere. Each ingot was melted 8 times to ensurethorough mixing of components. The mass loss after meltingwas less than 0.1% for all ingots and was thereforeconsidered negligible. The arc-melted ingots were thensealed in an evacuated quartz tube for homogenization at1373K for 3.6 ks, followed by quenching in water. Theingots were then cold-rolled by up to 80% reduction until thethickness of the rolled plates was reduced to 1mm. The

+Corresponding author, E-mail: h.tada@charmant.co.jp. Graduate Student,Tohoku University. Present address: Charmant Inc., Sabae 916-0088,Japan

Materials Transactions, Vol. 54, No. 8 (2013) pp. 1502 to 1509©2013 The Japan Institute of Metals and Materials

specimens for tensile and bend tests were punched out fromthe cold-rolled plates. The punched out specimens werethen solution-treated at 973K for 0.6 ks in evacuated quartztubes, followed by quenching in water. Finally, the specimenswere aged at various temperatures (between 353 and 1323K)for 3.6 ks. After heat treatment, the oxidized surface ofthe specimens was removed by chemical etching andmechanical polishing at room temperature. The solutionused for chemical etching was H2O, HNO3 and HF (5 : 4 : 1by volume).

2.2 Microstructural characterizationTransformation temperatures were measured by differ-

ential scanning calorimetry (DSC, Perkin Elmer DSC8500) ata controlled heating and cooling rate of 20Kmin¹1.

X-ray diffraction (XRD, Bruker D8 Advance) patterns,obtained with a Cu K¡ radiation source, were used to identifythe phases of the parent alloy and precipitates. The specimensfor XRD were mechanically polished using SiC waterproofemery papers (up to 2000 grit) and finally polished with0.03 µm colloidal silica suspension.

Microstructures were observed with transmission electronmicroscopy (TEM, JEM-2010), using an accelerating voltageof 200 kV. Specimens were prepared for TEM by twin-jetpolishing at 223K using an electrolyte solution of 6 vol%perchloric acid and 94 vol% methanol.

2.3 Mechanical evaluationThe Vickers hardness of each aged specimen was

measured with a load of 196N and holding time of 15 s.Simple tensile tests were carried out at room temperature

(298K) at a strain rate of 5 © 10¹4 s¹1 for aged specimens tomeasure the ultimate tensile strength (·max), stress for slip(·y) and fracture strain (¾br).

Bend tests were performed at room temperature to evaluatethe shape memory effect (SME). The elongation (�l) of theouter edge of the bent specimen was calculated from:

�l ¼ 2³ðRþ tÞ � 2³ Rþ t

2

� �; ð1Þ

where R is the bending radius and t is the specimen thickness.As schematically shown in Fig. 1, the applied bendingstrain was calculated from the bending radius of thespecimen:

¾bend ¼t

ð2Rþ tÞ ; ð2Þ

where ¾bend is the conventional strain. The specimens bentaround a rod were photographed and then heated at 573Kfor 0.3 ks to allow shape recovery. After recovery heating,the residual strain (¾r) remaining because of incompleterecovery was calculated using eq. (2). The total amount ofrecovery strain ¾tot was determined as ¾tot = ¾bend ¹ ¾r. Theaged specimens were also subjected to loading-unloadingtensile tests with a strain gauge extensometer at roomtemperature at a strain rate of 5 © 10¹4 s¹1, to observesuperelastic behavior. The cross section of the gage wasabout 1 © 2mm, and the gage length was 10mm. Tensilestress was applied until the strain reached 4.0%, and then thestress was removed.

3. Results

3.1 Influence of aging temperature on microstructureThe martensitic transformation temperature of the

Ti72Nb15Zr10Al3 alloy was investigated by DSC measure-ment, as shown in Fig. 2. There is small peak from 360 to430K on heating and from 240 to 330K on cooling, which isrelated to martensitic transformation.

Figure 3 shows the X-ray diffraction patterns taken atroom temperature for the Ti72Nb15Zr10Al3 solution treatedspecimens before and after aging for 3.6 ks at temperaturesbetween 453 and 753K. The specimen before agingconsisted of ¢ phase and ¡″ phase. After aging at 453K,no significant change was observed. Only ¢ phase was foundfor specimens aged at 503 and 553K, while diffraction peaksfrom ¢ phase, ½ phase and ¡ phase were observed in thespecimen aged at 603 and 653K. In the specimens aged at703 and 753K, diffraction peaks from the ¢ phase wereobserved, along with peaks from ¡ phase.

The TEM micrographs of the solution treated specimen,and the specimens aged at 453, 503 or 553K for 3.6 ks areshown in Fig. 4. The selected area diffraction (SAD) patternstaken along the [110]¢ zone axis are shown in the insets ofeach micrograph. Diffraction spots corresponding to ¢ phasewas observed in the solution treated specimen and thespecimen aged at 453K.25,26) The specimens aged at 503 and553K, gave diffraction spots from ¢ and ½ phases. The

Bend residual recovery strain

R1 :12.5 mm

Load Load

t :1 mmspecimen

R2

l

Fig. 1 Schematic diagram illustrating recovery strain measurement.

exot

herm

icheating

coolingMs

As

Temperature, T/K

Hea

t flo

w (

W/g

)

Fig. 2 DSC curve of Ti72Nb15Zr10Al3 alloy quenched in water aftersolution treatment.

Non-Monotonic Aging Temperature Dependence of Superelasticity of Ti72Nb15Zr10Al3 Quaternary Alloys 1503

diffraction spots corresponding to ½ phase became clearer asthe aging temperature was increased.

3.2 Effects of aging temperature on mechanical proper-ties

The Vickers hardness values (Hv) of Ti72Nb15Zr10Al3alloys were measured after aging for 3.6 ks at severaltemperatures; a summary of Hv as a function of agingtemperature is shown in Fig. 5. The hardness increased withincreasing aging temperature when the specimen was agedbetween 403 and 603K. When the specimen was agedbetween 803 and 973K, the hardness decreased withincreasing aging temperature. Once the aging temperaturereached 973K or higher, the aged specimens showed similarhardness to that of the unaged sample.

Figure 6 shows a series of stress­strain curves forTi72Nb15Zr10Al3 alloy, measured before and after aging for3.6 ks at various temperatures from 403 to 653K. ·y and ¾brwere derived as shown in Fig. 6. The ·y of the specimens

aged at 403K is similar to that of the specimen before aging.·y increased with increasing aging temperature for agingtemperatures between 453 and 653K. However, for this same

30° 40° 50° 60° 70° 80° 90°

Before aging453K

753K703K

653K603K

553K503K

Inte

nsity

( a

. u. )

Angle, 2θ

αω

α” phaseβ phaseω phaseα phase

Fig. 3 X-ray diffraction patterns of aged Ti72Nb15Zr10Al3 alloy.

1 μm 1 μm

1 μm

ω1 ω2

[111]β // [0001]ω

110β

110β

002β

1 μm

(a)

(d)

(b) (c)

(e)

Fig. 4 TEM micrograph and SADP of Ti72Nb15Zr10Al3 alloy (a) solution treated (b) aged at 453K, (c) aged at 503K, (d) aged at 553Kand (e) indexed diffraction pattern.

Vic

kers

har

dnes

s

Aging temperature, T / K

ω phase precipitation

Fig. 5 Variation of Vickers Hardness of Ti72Nb15Zr10Al3 alloy for agingtemperature.

H. Tada, T. Yamamoto, X. Wang and H. Kato1504

aging temperature region, the ¾br decreased with increasingaging temperature.

3.3 Effects of aging temperature on shape memory andsuperelastic properties

The bending test results used to measure the amount ofrecovery strain due to shape memory and superelasticity aregiven in Table 1. The total recovery strain (¾tot) decreased asthe aging temperature increased from 403 to 503K. Whenthe specimen was aged between 503 and 603K, the totalrecovery strain increased with increasing aging temperature.It decreased for specimen aged at 653K, compared with thespecimen aged at 603K. The greatest residual strain after thebending test was obtained for the specimen aged at 503K for3.6 ks.

Figure 7 shows the results of loading-unloading tests forTi72Nb15Zr10Al3 alloys aged at different temperatures (be-tween 403 and 653K), along with the unaged alloy forcomparison. Slight superelastic behavior was observed forthe specimen aged at 403K. Specimens aged at 453, 553, 605and 653K showed a 3% or more total recovery strain, whichincludes recovery because of superelastic behavior. It shouldbe noted here that neither shape memory nor superelasticbehavior was seen for the specimen aged at 503K.

4. Discussion

4.1 Non-monotonic aging temperature dependence ofsuperelasticity

To investigate the aging temperature dependence ofsuperelasticity in more detail, the ¾tot values from bending

and load-unload tests were summarized in Fig. 8. Therecovery strain was classified into that due to stress-inducedmartensite (¾M) and that due to elastic deformation (¾d), as afunction of aging temperature. ¾d increased slightly andmonotonically with increasing aging temperature. Mean-while, ¾M did not change monotonically with increasingaging temperature. As a result, total shape recovery strains(defined as ¾tot = ¾M + ¾d) of 3% or more were measuredfor specimens aged at or below 453K. ¾tot then abruptlydecreased to 2% for the specimen aged at 503K, before ¾totagain reached 3% or more for the specimens aged at 553 and603K. After that, it decreased gradually with further increasesin aging temperature. It is obvious that ¾tot is significantlyaffected by changes in the martensitic transformation. Thespecimen aged at 503K seems to be deformed plasticallybefore stress-induced martensitic transformation occurs.

This led us to investigate the influence of isochronal agingon martensitic transformation of Ti72Nb15Zr10Al3 alloy.Figure 9 shows the critical stress for inducing martensite(·M), along with ·max and ¾br, for specimens aged at 403­653K. ·max increased and ¾br decreased with increasing agingtemperature. While both ·max and ¾br changed monotonicallywith aging temperature, ·M did not. Instead, ·M increasedwith increasing aging temperature between 403 and 503K,decreased between 503 and 553K, and then increased againat 603K and above. Here, we attempt to interpret these

Stre

ss, σ

/ MPa

Strain, ε

before aging

403 K 453 K 503 K553 K

603 K653 K

Fig. 6 Stress­strain curves of aged Ti72Nb15Zr10Al3 alloy.

Table 1 Result of bending tests.

Aging temp.T (K)

Residual strain¾r (%)

Total recovery strain¾tot (%)

® 0 3.8

403 0 3.8

453 0.3 3.5

503 2.4 1.4

553 1.8 2.8

603 0.4 3.4

653 1.2 2.6

Stre

ss, σ

/ MPa

Strain, ε

before aging403 K

453 K503 K 553 K

603 K653 K

Fig. 7 Stress­strain curves obtained upon loading and unloading forTi72Nb15Zr10Al3 alloy aged at various temperatures.

Rec

over

y st

rain

, ε

Aging temperature, T / K

Fig. 8 Variation of recovery strain of Ti72Nb15Zr10Al3 alloy for agingtemperature.

Non-Monotonic Aging Temperature Dependence of Superelasticity of Ti72Nb15Zr10Al3 Quaternary Alloys 1505

interesting phenomena in terms of the ordering of disordered¢ phase, phase separation of ¢ phase and the volume fractionof ½ phase.

4.2 Ordering of disordered ¢ phaseAt first, the possibility of ordering of ¢ phase in the

Ti72Nb15Zr10Al3 specimen aged at 503K is discussed. TheTEM observations revealed that fine ½iso particles beginprecipitating at aging temperatures around 403K. Hvincreased with increasing aging temperature from 403 to603K, which implies that the ½iso particles grow continu-ously up until 603K. Therefore, the superelastic behaviormay have disappeared because of ordering of the ¢ phasewhen the specimen aged at 503K. However, the XRDmeasurement for the specimen aged at 503K shows onlydiffraction peaks from ¢ phase (Fig. 3). No striking dif-ferences were observed between the patterns from thespecimens aged at 453, 503 and 553K. Therefore orderingof disordered ¢ phase is not the cause of the non-monotonicaging temperature dependence of superelasticity.

4.3 Phase separationSecondly, let us discuss the possibility of ¢ phase

separation for Ti72Nb15Zr10Al3 alloy when aged at 553K orabove. There are several reports on the phase separation of¢-type Ti alloys which affect the mechanical properties.27,28)

As we mentioned before, ½iso formation was detected in theTi72Nb15Zr10Al3 alloy aged at 453K. The growth of ½iso

precipitates inhibits the martensitic transformation, both as aresult of composition change and also because the precip-itates can act as obstructions to transformation. In our presentalloy, the superelastic behavior disappeared for the specimenaged at 503K, because ·M became comparable to ·Y. Whenthe specimen is aged at 553K, ·M increased further, meaningthat superelastic behavior should not occur; however,superelastic behavior was in fact seen for the specimen agedat 553K. One possible explanation for this is that the ¢ phaseis separated into two phases upon aging at 553K or highertemperature; one phase contains a low concentration (¢1),and the other a high concentration (¢2), of ¢-stabilizingelements. This would allow the stress-induced martensitictransformation to reappear in the ¢1 phase. However, noXRD peak broadening, splitting or separation was found(Fig. 3), which makes this mechanism unlikely. Thus we do

not believe that the reason for the non-monotonic agingtemperature dependence of superelastic behavior is ¢ phaseseparation.

4.4 Non-monotonic variation in volume fraction of ½iso

phase with aging temperature4.4.1 Relationship between stress required to induce

martensitic transformation and volume fractionof ½iso phase

It has been reported that the concentration of ¢-stabilizingelement changes and that internal strain is induced as a resultof ½iso phase precipitation.27) ·M is, in turn, altered by thesechanges.

We will first consider the effect of ¢-stabilizing element(Nb in this alloy). In the ¢-type Ti alloy, ½iso phase grows andejects ¢-stabilizing element. Thus, the concentration of the ¢-stabilizing element in the parent phase is increased by theformation of ½iso phase. The free energy for martensitictransformation decreases when the concentration of ¢-stabilizing element increases, that is, the martensitic trans-formation start (Ms) temperature is decreased and ·M isincreased. Here, we assume that the ½iso phase (volumefraction, Vf ) is formed in unit volume of ¢ phase; theconcentration of ¢-stabilizing element in ¢ phase (C¢) can beexpressed as:

C¢ ¼C0 � Vf � C½

1� Vf

; ð3Þ

where C0 is the concentration of ¢-stabilizing element beforeaging, and C½ is the concentration of ¢-stabilizing elementin ½ phase. S. Neelakantan has reported the concentrationdependence of Ms temperature for Ti­X binary systems.28)

In Ti­Nb alloys, it has been empirically expressed as:

MS ¼ 1104þ 6832XNb1=2; ð4Þ

where XNb is concentration of the alloying element. From thisequation, the change in the MS temperature (�MS) can bedescribed as:

�MS ¼ 6832� ½ðC0Þ1=2 � ðC¢Þ1=2�Nb ðat%Þ: ð5ÞIn addition, taking the Clausius-Clapeyron relationship intoconsideration, �·M is proportional to �MS Thus:

�·M ¼ B��MS; ð6Þwhere B is a constant which depends on the alloycomposition. In Ti­26 at% Nb alloy, H. Y. Kim et al.reported that the relationship between ·M and change oftemperature can be expressed as: d·/dT = 4.4MPa/K.17)

By applying this constant to our alloy, and consolidatingthe above equations, �·M can be described as:

�·M ¼ 4:4� 6832� ðC0Þ1=2 �C0 � Vf � C½

1� Vf

� �1=2" #

;

ð7ÞThis equation implies that �·M can be determined from theNb concentrations of the alloy before aging and of the½iso phase, and the volume fraction of the ½iso phase. Theconcentration of Nb in Ti72Nb15Zr10Al3 alloy is 15 at%. Theconcentration of ¢-stabilizing element in ½iso phase has beenreported to be independent of alloy composition; for Ti­Nb

Aging temperature, T / K

Stre

ss, σ

/ MPa

Frac

ture

str

ain,

εbr

0

200

400

600

800

1000

0.05

0.10

0.15

0.20

0.25

0.30

400 450 500 550 600 650

Fig. 9 Influence of aging temperature on mechanical properties.

H. Tada, T. Yamamoto, X. Wang and H. Kato1506

alloy, the concentration of ¢-stabilizing element in ½iso phaseis almost 9% Nb.19) By substituting these values into eq. (8),the �·M caused by the change of ¢-stabilizing elementconcentration can be shown quantitatively as a function of Vf.

The effect of the internal strain, caused by the formation of½iso phase, on ·M will now be discussed. When the ½iso phaseis precipitated within the matrix, internal strain developsbecause of the volume difference between the parent phaseand the ½iso phase. The internal stress associated with thestrain affects the martensitic transformation. Under suchconditions, the shear strain (£) at distance R from the ½iso

particle can be expressed as:

£ ¼ ¾� r

R

� �3; ð8Þ

where r is the particle radius of ½iso phase and ¾ is internalstrain.29) Assuming that there are N particles of ½iso phase inunit volume of ¢ phase, then there will be 1=ð

ffiffiffiffiN3

pÞ particles,

on average, along any unit length. Therefore, the straingenerated at distance R ¼ 1=ð2 ffiffiffiffi

N3p Þ from the ½iso particle can

be regarded as the average shear strain. Meanwhile, therelationship between volume fraction ðVfÞ and particle radius(r) of ½iso phase is:

Vf ¼4

3³r3 �N; ð9Þ

so the average shear strain ( �£) can be approximated as:

�£ ¼� 2¾Vf : ð10ÞConsequently, the average shear stress (· i) can be expressedas:

· i ¼ ®� 2¾ð¢�½ÞVf ; ð11Þwhere ® is the rigidity modulus and ¾ð¢�½Þ is the internalstrain developed from the volume difference between theparent phase and the ½iso phase. Table 2 shows the resultsof computation of the specific volume per atom for anelementary cell of both ¢ and ½iso phases in the Ti72Nb15-Zr10Al3 alloy. The shear strain can be calculated as:

¾ð¢�½Þ ¼ffiffiffiffiffiffiV¢

3p � ffiffiffiffiffiffi

V½3p

ffiffiffiffiffiffiV¢

3p ¼� 0:0030; ð12Þ

where V¢ and V½ are the specific volumes of ¢ and ½iso

phases, respectively. Substituting this value, along with thegeneral value of the rigidity modulus of ¢ Ti alloy(® = 30GPa) into eq. (12), yields the following relationshipbetween · i and Vf:

· i ¼ 90ðMPaÞ � Vf : ð13ÞTherefore, the influences of both the concentration of ¢-stabilizing element and the internal strain on �·M can beexpressed as a function of Vf as shown in Fig. 10. Theinfluence of ¢-stabilizing element increases as Vf increases.Additionally, the volume of ½iso phase is less than that of ¢phase, which means that ¢ phase is strained in a tensilemanner by ½iso phase precipitation. Thus, this strain assistsmartensitic transformation. The relative influence of internalstrain decreases as Vf increases. Overall, ·M changes by up toseveral hundred MPa, depending on the volume fraction of½iso phase.

4.4.2 Relationship between volume fraction of ½iso phaseand aging temperature

The relationship between Vf and ·M was expressed in theprevious section. Assuming that the ½ phase precipitationbehavior in this study satisfies the general C-type curve,a lot of ½iso phase is precipitated by isochronal aging nearthe nose temperature, because the incubation period is short.The nose temperature would be estimated around 603Kfrom Fig. 5. However, ·M in Fig. 9 is monotonicallyincreased with increasing aging temperature from 553K orabove. The ·M is varied depending on the volume fraction of½iso phase (Vf ). Therefore, in this section, the relationshipbetween Vf and aging temperature is discussed in more detailto interpret the non-monotonic aging temperature dependenceof ·M.

When ½iso phase is precipitated in ¢ solid solution byaging, the volume fraction of ½iso phase can be estimatedfrom the particle number and size. First, the relationshipbetween particle number and aging temperature must beconsidered. It has been reported that the transformation from¢ phase to ½iso phase occurs by aging accompanied bydiffusion of atoms.5) Thus, the number of ½iso phase particles(N) can be expressed by the general nucleation formula as:

N / B exp ��G� þQd

kT

� �; ð14Þ

where �G� is the activation energy for nucleation, Qd is theactivation energy for diffusion of solute atoms and T is theaging temperature. Eventually, the number of ½iso phaseparticles exhibits a maximum at a certain intermediate agingtemperature.

The second consideration is the relationship between theparticle size and aging temperature. This requires determin-ing the stage or stages of precipitation process that takewithin 3.6 ks. Li et al. reported that the volume of ½iso phase

Table 2 Specific volume and phase parameters for Ti72Nb15Zr10Al3 alloy.

Phase parametersnm

Specific volume of phasesnm3/atom

a¢ a½ c½ V¢ V½

0.3329 0.4690 0.2876 18.44 © 10¹3 18.28 © 10¹3

Volume fraction of ωiso phase, Vf

Eff

ectiv

e st

ress

, / M

Pa

B

AA+B

compression

tension

Fig. 10 Relationship between �·M and Vf; A: effect of compositionchange, B: effect of internal strain.

Non-Monotonic Aging Temperature Dependence of Superelasticity of Ti72Nb15Zr10Al3 Quaternary Alloys 1507

of TiNb24Zr2 alloy is increased with increasing aging time inspecimens aged at 573K for 1.8 to 18 ks.30) The crucial agingtemperatures and period in this study is between 453 and553K for 3.6 ks, which is a lower temperature range than thetemperature which Li et al. used, and a similar aging period.Thus, we expect that the precipitation of ½iso phase inTi72Nb15Zr10Al3 alloy under the aging conditions in thisstudy is also at the nucleation and growth stage. During thenucleation and growth stage, it has been reported thatnucleation of ½iso phase is homogeneous.31) After that, thenuclei start to grow. At this stage, the particle size is greatlyaffected by the diffusion rate and degree of supersaturation ofsolute atoms. The relationship between these parameters canbe given as:

r ¼ KðDtÞ1=2; ð15Þ

K ¼ ðC¢0 � C½1Þ½ðC½2 � C½0ÞðC½2 � C½1Þ�1=2

; ð16Þ

where D is diffusion coefficient of solute atoms, t is agingtime, C¢0 is composition of alloy, and C½1 and C½2 are theconcentrations of solute atoms in ½iso phase and at the ¢ and½iso phase boundary, respectively. At the conditions used inthis study, the particle size of ½iso phase is affected only bythe diffusion coefficient, D, in both stages. Here, D isexpressed by an Arrhenius relationship:

D ¼ D0 � exp � Q

kT

� �; ð17Þ

where D0 is frequency factor, Q is activation energy fordiffusion of solute atoms and T is aging temperature. Theseequations imply that the particle size of the ½iso phaseincreases monotonically with increasing aging temperature.To confirm this, TEM observations were carried out.Figure 11 shows dark-field images of the ½iso phase in thespecimens aged at several temperatures, taken using thediffraction spots of the ½iso phases. The TEM observationssupport the predictions of the equations regarding particlesize.

Finally, let us discuss the relationship between agingtemperature and volume fraction of ½iso phase, based on ourknowledge of particle size and particle number. The particlesize increases monotonically with aging temperature. Thevolume per particle of the ½iso phase is proportional to thecube of the particle radius, r. However, the largest number ofparticles was obtained when the specimen was aged atintermediate temperature. Thus, it can be considered that

the volume fraction of ½iso phase depends on the agingtemperature, but this dependence is not monotonic.4.4.3 Comparison with the experimental data

It was mentioned above that the precipitation of the ½iso

phase within the solute ¢ phase leads to compositionalchanges and internal strain. Thus, XRD peak shifts shouldbe observed, if these changes have occurred. The resultsof XRD measurements at room temperature for specimensbefore and after aging for 3.6 ks at temperatures from 403to 653K are shown in Fig. 12. Peak shifts to higher anglewere observed for specimens aged at temperature up to503K. Then, shifts to lower angle were seen when thespecimen was aged from 553 to 653K. If the peak shift tohigher angle was caused by internal strain, then the directionof strain must be compressive, which is opposite to thedirection expected for internal strain induced by nucleationof ½iso phase. Tahara et al. reported that XRD peaks fromTi­Nb alloys shifted to higher angle, even though the loadwas tensile.32) They explained this phenomenon on thebasis that compressive deformation occurred in a directionperpendicular to the tensile direction. XRD measurement forall specimens in our investigation was carried out from thedirection perpendicular to the rolling direction. The speci-mens before XRD measurement were strongly cold-rolledthen solution treated for a short time followed by aging.Therefore, we would expect the compressive strain to occurin the direction perpendicular to the rolling direction,because of the texture that formed in the direction parallel

(a) 453K, 3.6ks

100 nm

(c) 553K, 3.6ks

100 nm

(b) 503K, 3.6ks

100 nm

Fig. 11 Dark field images of ½iso phase and the corresponding selected area diffraction patterns of aged Ti72Nb15Zr10Al3 alloy (a) aged at453K, (b) aged at 503K and (c) aged at 553K for 3.6 ks. These were taken along the [110]b zone axis.

37° 38° 39° 40°

Inte

nsity

(a.

u.)

Angle, 2θ

before aging453 K

503 K

553 K

603 K

653 K

Fig. 12 The diffraction angle of the (110) peaks of the ¢ phase as afunction of the aging temperature.

H. Tada, T. Yamamoto, X. Wang and H. Kato1508

to the rolling direction. In any case, we found that thevariation of peak position in XRD measurements did nottake the form of monotonic changes; the largest shift wasobserved for the specimen aged at 503K.

Secondly, the variation of ·M was also expressed in termsof the volume fraction of ½iso phase. Because of changes in½iso content, the ·M values of the specimens change byseveral hundred MPa, as shown in Fig. 10. In addition,dependence of the ½iso volume fraction on aging temperatureis not monotonic. Moreover, the largest effect of internalstrain and/or composition change was found for the speci-men aged at 503K. Therefore, Fig. 13 compares the resultsobtained by using the equations to predict the variation of·M with the experimental ·M (circles) and ·Y (squares) dataobtained from tensile tests of Ti72NB15Zr10Al3 alloy. Thevariation predicted based on the effects of the assumedvolume fraction of ½iso phase on ·M is shown by the dashedline. In fact, the variation of data measured by the tensile testis in good agreement with our estimates. The experimental·M increased again because of ¡ phase precipitation as theaging temperature was increased above 603K.

5. Conclusion

In this study, the influences of aging temperature onmechanical properties, especially on the superelastic behaviorfor Ti72Nb15Zr10Al3 alloy, were investigated. Superelasticbehavior was observed for discontinuous ranges of agingtemperature. Several possible explanations were considered,and the following conclusions reached:(1) The influence of aging temperature in superelastic

behavior is neither caused by ordered structures, nor by¢-phase separation.

(2) The relative effect of composition change increased,compared to that of internal strain, when the volumefraction of ½iso phase increased. The change in the stressfor martensitic transformation caused by ½iso phaseprecipitation was estimated to be several hundred MPa.By comparing the size of the XRD peak shifts wefound that the largest volume fraction of ½iso phase wasformed in the specimen aged at 503K. This estimate

was in good agreement with the tensile test results.Therefore, the argument that the increased volumefraction of ½iso phase is responsible for the loss ofsuperelasticity in the sample aged at 503K isreasonable.

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Aging temperature, T / K

Stre

ss, σ

/ MPa

Fig. 13 The result of applying the estimation to experimental data fromtensile test.

Non-Monotonic Aging Temperature Dependence of Superelasticity of Ti72Nb15Zr10Al3 Quaternary Alloys 1509