Sha W., Malinov S. Titanium Alloys: Modelling of Microstructure, Properties and Applications

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Titanium alloys: modelling of microstructure168

corresponds to the maximum rate of transformation. The area under the

curve from the start to the peak temperatures being more than 50% means

that the transformation rate increases with decreasing temperature.

The DSC results disagree with the published CCT diagram for Ti-6Al-4V

(Sieniawski et al., 1996), for the end of the β to α + β transformation. The

end of transformation from the DSC is in the range from 820 to 865 °C,

depending on the cooling rate (see Table 7.1), while for the same cooling

rates, according to the CCT diagrams by Sieniawski et al. (1996), the end of

transformation is 670 to 690 °C. The following microscopy data clarify this

discrepancy. The microstructure of the samples quenched from 970, 940,

890 and 860 °C is a mixture of α and α′ (martensite). Figure 7.2a is for a

sample quenched from 860 °C, but the microstructure is the same in nature

for samples quenched from 970, 940, 890 and 860 °C, so the micrographs for

samples quenched from the other three temperatures (970, 940 and 890 °C)

are not shown to avoid repetition. The amount of α′ decreases, naturally,

with lower quenching temperature. α′ means that the β phase transformation

is incomplete. The microstructure of the samples quenched from 800 and

750 °C (Fig. 7.2b) consists of only acicular α phase, implying that the

transformation is completed above 800 °C. It can be concluded that the end

of the β to α + β transformation at the cooling rate of 20 °C/min is between

800 and 860 °C. This conclusion supports the DSC data rather than the

published CCT diagrams (Sieniawski et al., 1996). The difference between

the DSC data and those by Sieniawski et al. (1996) may be due to the

difference in the composition of the alloys. For example, impurity and

oxygen levels have a dramatic influence on the transformation kinetics

(Chapter 14).

7.2.2 Ti-6Al-2Sn-4Zr-2Mo-0.08Si

A start temperature of 990 °C is appropriate for all cooling curves, slightly

higher than the start temperature for the Ti-6Al-4V alloy. The reasons for

this difference could be both thermodynamic and kinetic in nature. The β-

transus temperature for both alloys for commercial use is 1000±15 °C, but

can vary depending on the exact chemical compositions. The β-transus

temperatures based of their real compositions are 1000 °C for Ti-6Al-2Sn-

4Zr-2Mo-0.08Si and 995 °C for Ti-6Al-4V alloys, calculated using the Thermo-

Calc software and the titanium database. This difference may influence the

start of the β to α phase transformation in continuous cooling.

The area under the DSC curve from the start to the peak temperatures

ranges from 74 to 80% of the entire area from the start to the end temperatures

(Table 7.1). The peak temperatures are very similar to the corresponding

peak temperatures for the Ti-6Al-4V alloy. So, the temperature of the maximum

speed of the β to α transformation in both alloys is about the same, and the

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Johnson–Mehl–Avrami method adapted to continuous cooling 169

Table 7.1

Calorimetry peak parameters for Ti-6Al-4V (first number), Ti-6Al-2Sn-4Zr-2Mo-0.08Si (second number), Ti-6Al-7Nb (third number)

and Ti-46Al-2Mn-2Nb (fourth number except for 15 °C/min)

Cooling rate (°C/min) Start (°C) Peak (°C) End (°C) Area from start Enthalpy (J/g)

to peak (%)

10 970/990/960/1303 908/908/926/1280 865/870/901/1236 61.4/79.7/58.4/48.0 24/28.4

15 (Ti-46Al-2Mn-2Nb) 1296 1269 1221 46.8

20 970/990/960/1298 894/894/914/1267 850/850/887/1214 62.2/74.0/53.5/43.2 25/29.6

30 970/990/960 883/883/907 841/830/871 63.6/74.9/60.7 26/33.2

40 970/990/960 873/873/895 830/815/862 63.7/75.0/68.4 27/32.9

50 970/990/960 867/867/890 820/800/850 62.4/74.5/65.1 */42.3*

*The cooling rate of 50 °C/min is too fast to allow accurate determination of the enthalpy.

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Titanium alloys: modelling of microstructure170

kinetics of the transformation on continuous cooling with cooling rates ranging

from 5 to 50 °C/min in the alloys are similar.

A comparison of the DSC results with published CCT diagrams for Ti-

6Al-2Sn-4Zr-2Mo-0.08Si alloy reveals some discrepancies. Mitchell (1991)

proposed a set of CCT diagrams where the start of the β to α transformation

was 820–840 °C (Fig. 7.3), and the end of the transformation was 790–

810 °C. Cias (1991) proposed similar CCT diagrams where the start of the

transformation was 950–980 °C and the end was 600–650

°C. Both were for

cooling rates of 5–50 °C/min. However, the temperatures and shape of the

curve depend heavily on the exact chemistry of the alloy, the heat treatment

history and the experimental technique used.

α’

50 µm

(a)

50 µm

(b)

7.2

Microstructure of Ti-6Al-4V after continuous cooling at 20 °C/min

and quenching from (a) 860 and (b) 750 °C.

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Johnson–Mehl–Avrami method adapted to continuous cooling 171

7.2.3 Ti-6Al-7Nb

The start temperature of the β to α phase transformation in continuous cooling

for this alloy is estimated at around 960 °C (Fig. 7.1c and Table 7.1), slightly

lower as compared to both Ti-6Al-2Sn-4Zr-2Mo-0.08Si and Ti-6Al-4V alloys.

The reason for the lower temperature is most likely in the kinetics of the α

phase nucleation, because the β-transus temperature for Ti-6Al-7Nb is in

fact slightly higher as compared to the other two alloys (see Chapter 5). On

the other hand, the peak and the end temperatures for Ti-6Al-7Nb are slightly

higher as compared to the above two alloys. This means a narrower temperature

range for the transformation. The area under the DSC curve from the start to

the peak temperatures ranges from 53 to 68% of the entire area from the start

to the end temperatures, with a tendency for higher values at higher cooling

rates (Table 7.1).

The Ti-Nb alloy exhibits a far less exothermic reaction during phase

transformation than the other two titanium alloys. A possible reason is problems

with the equipment. We had difficulties at the time of the experiment with

the equipment calibration. Therefore, quantitatively, the DSC curves may

not be quite correct in terms of enthalpy, but the shape of the curves should

still trace the kinetics of the phase transformation, and this in fact is what we

need and use.

α+β

Transus

Beta

Ti-6Al-2Sn-4Zr-2Mo

α′

1 10 100

Time – seconds

Temp – F

1800

1700

1600

1500

1400

1300

1200

7.3

Continuous-cooling-transformation diagram for Ti-6Al-2Sn-4Zr-

2Mo by Mitchell (1991).

β→α+β

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Titanium alloys: modelling of microstructure172

7.2.4 Ti-46Al-2Mn-2Nb

The model to be discussed later in this chapter is based on published

experimental results by Butler (1995) of a DTA study of the phase

transformations in the Ti-46Al-2Mn-2Nb alloy. Data for the formation of the

γ phase upon cooling are used (Fig. 7.1d). The DTA curves for all the cooling

rates have a similar asymmetry, with a tail at low temperatures, corresponding

to the end of the transformation. The area under the curve from the start to

the peak temperatures ranges from 43 to 48% of the entire area.

7.3 X-ray diffraction

X-ray diffraction of Ti-6Al-2Sn-4Zr-2Mo-0.08Si cooled with different cooling

rates shows the presence of α phase only, with no residual β phase (Fig. 7.4).

This means that the transformation can be regarded as 100%β to100%α.

Small amounts (up to, say, 4%) of β phase are possible which are not detectable

with a conventional X-ray facility. Using X-ray diffraction for determining

the β volume fraction is problematic, especially when using laboratory X-

ray diffraction. Laboratory X-ray diffraction is not a good method for

determining β volume fraction accurately. On the other hand, there are many

publications that clearly demonstrate that Ti-6242 always contains a small

Intensity (arbitrary unit)

350

300

250

200

150

100

32 37 42 47 52 57 62 67 72

2θ (°)

50 °C/min

30 °C/min

5 °C/min

{100}α

{002}α

{101}α

{102}α

{110}α

{103}α

7.4

X-ray diffraction patterns of Ti-6Al-2Sn-4Zr-2Mo-0.08Si after

cooling with different rates. For clarity, the diffraction patterns are

shifted along the vertical axis with respect to each other.

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Johnson–Mehl–Avrami method adapted to continuous cooling 173

amount of β phase unless it is very rapidly quenched (Lütjering and Williams,

2003).

Examination of the patterns can reveal increase in the relative intensities

of the {hk0} planes and decrease in the relative intensities of the {00l}

planes with increased cooling rate. This effect may be associated with preferable

crystallographic orientation of the α phase growth when different cooling

rates are applied. Such an effect should also depend strongly on the original

alloy processing.

The a and c lattice parameters of the hexagonal structure are calculated

from the intercept and the slope of plots of

hkl

versus l

, using the reflections

{100}, {101}, {102} and {103}. An influence of cooling rate is shown in

Fig. 7.5. When the cooling rate increases from 10 to 50 °C/min, both lattice

parameters increase. A higher level of residual stress is a plausible explanation

for the increase in lattice parameters. The formation of a lamellar structure

generates high levels of residual stresses, due to lattice mismatches between

the α and the β phases. The coefficient of thermal expansion of the different

orientations of the hcp α phase and those between the α and the β phases are

different, leading to a higher level of residual stresses at a higher cooling

rate. Moreover, at a relatively slow cooling rate, redistribution of solute

elements during β to α transformation may ease the level of residual stresses.

In addition to residual stresses, it is also likely that chemical changes will

affect the lattice spacing, since high cooling rates will avoid any partitioning

of the α and β stabilisers.

(Å)

4.700

4.696

4.692

4.688

4.684

0102030405060

Cooling rate (°C/min)

2.954

2.950

2.946

2.942

2.938

(Å)

7.5

Lattice parameters of the α phase of Ti-6Al-2Sn-4Zr-2Mo-0.08Si

after cooling with different cooling rates.

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Titanium alloys: modelling of microstructure174

7.4 Microstructure and hardness

The microstructures consist of grain boundary α phase and α plate colonies,

and are fully lamellar (Figs. 7.6 and 8.1). The Widmanstätten microstructure

7.6

Microstructure of (a) Ti-8Al-1Mo-1V, (b) IMI 834 and (c) IMI 367

after cooling at different cooling rates.

(a)

5 °C/min 10 °C/min

50 µm

100 µm

40 °C/min 50 °C/min

100 µm

20 °C/min 30 °C/min

50 µm 50 µm

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Johnson–Mehl–Avrami method adapted to continuous cooling 175

5 °C/min 10 °C/min

100 µm

20 °C/min

30 °C/min

100 µm

40 °C/min 50 °C/min

100 µm

(b)

7.6

Continued

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Titanium alloys: modelling of microstructure176

40 °C/min 50 °C/min

50 µm

20 °C/min 30 °C/min

50 µm 50 µm

5 °C/min 10 °C/min

50 µm

7.6

Continued

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Johnson–Mehl–Avrami method adapted to continuous cooling 177

nucleates from β grain boundary (Mythili et al., 2005), but this happens only

if cooling rates are sufficiently small. The difference from cooling with

various rates is in the α plate thickness. Thinner α plates are produced as the

cooling rate increases (see Figs. 7.6, 7.7, 7.8a and 8.1). This naturally results

in increase of the hardness at higher cooling rates, where the microstructure

is finer (Figs. 7.8b and 7.9).

The percentage of α-stabilising element aluminium is higher in the α

regions (Fig. 7.10 and Table 7.2). Conversely, the percentages of β-stabilising

elements molybdenum and vanadium are higher in the β regions. This

demonstrates that the mode of transformation in the Ti-8Al-1Mo-1V alloy,

and by inference other titanium alloys, when continuously cooled from the

β phase field, is that of diffusion. At the slow cooling rate, all of the β-

stabilising elements have diffused out of the α portion.

These findings support the theory describing the transformation from β

to α on cooling from the β single phase field. Under equilibrium conditions,

the composition of the phases changes with the temperature (see Chapter 5).

As the temperature is reduced to below β

, the β-stabilising elements

diffuse out of the growing α lamellae, into the retained β portion of the

microstructure.

05 °C/min

10 °C/min

20 °C/min

30 °C/min

40 °C/min

50 °C/min

Lamellar width (µm)

Occurrence

200

180

160

140

120

100

7.7

Variation of lamellar thickness with cooling rate for IMI 834.

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