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

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Titanium alloys: modelling of microstructure128

6.3.3 Ti 8-1-1 alloy

First, a very small amount, about 9%, of separate α phase crystals is found

in the alloy exposed at 950 °C and then quenched. At 925 °C, the amount of

the α phase increases to about 29%. In both cases, the α phase is observed

as thin layers, covering β grain boundaries (Fig. 6.5a). Decreasing the

temperature of isothermal holding, down to 900 °C, causes formation of

coarser grain-boundary α phase and appearance of the first small portions of

α crystals growing from this grain-boundary phase using it as a nucleating

site (Fig. 6.5b). The total amount of the α phase at 900 °C is about 46%.

Further decrease of the holding temperature down to 850 °C leads to a

change of the mechanism of the α phase formation. An α phase nucleated

and grown homogeneously inside the former β grains is observed (Fig. 6.5c

and d). A substantial increase in the total amount of the α phase (up to 70%)

is detected. The grain-boundary α phase at 850 °C (Fig. 6.5c) is thinner as

compared to the grain-boundary α phase at 900 °C (Fig. 6.5b). It is possible

that the thin α layer covering the β grain boundary at 850 °C is formed on

cooling from the β solution temperature to the temperature of isothermal

exposure (note that the cooling rate was not high enough to depress completely

the β phase decomposition).

A decrease of the temperature down to 800 and 750 °C (Figs. 6.5e and f,

respectively) causes further increase of the amount of α phase up to 88 and

98%, respectively. The mechanism of the α phase formation remains the

same. The main part of the α phase is homogeneously formed within the

former β grains as packets of lamellar α phase. Additionally, a small amount

of α phase covering β grain boundary is observed which is probably precipitated

on cooling from solid solutioning to the holding temperatures.

In summary, at temperatures of exposure above 900 °C, the predominant

place for α precipitation is the β grain boundary, whereas at lower temperatures,

most α lamellae precipitate rather homogeneously inside the β grains. Optical

microscopy quantitative data are in good agreement with the contents of α

phase calculated from resistivity work.

6.4 X-ray diffraction

X-ray diffraction is not usually used for quantitative study of α and α + β

titanium alloys. The reason for this is that in these alloys a martensite

transformation may take place and it is difficult to distinguish between the α

and the α′ (martensite) phases. In the β21s alloy, the martensite start temperature

is below room temperature. Hence, mainly α and β phases in different ratios,

depending on the processing and heat treatment conditions, exist. These two

phases are easily detectable and distinguishable by X-ray diffraction. The

equilibrium amount of the α phase should increase when the temperature is

lower (see also Section 6.6).

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The Johnson–Mehl–Avrami method 129

After the resistivity experiments, β21s samples can be cooled to room

temperature and studied by X-ray diffraction. The results from the samples

after isothermal exposure for two hours at different temperatures are given in

Fig. 6.6. The amount of the α phase can be calculated from the fitted diffraction

patterns using the direct comparison method. In order to avoid error due to

preferred orientation (crystallographic texture that usually is present in

Relative intensity

30 35 40 45 50 55 60 65 70 75

2θ (°)

750 °C

700 °C

650 °C

600 °C

500 °C

{110}β

{200}β

{211}β

{101}α

{100}α

{002}α

{102}α

{110}α

{103}α

6.6

X-ray diffraction patterns and profile fits (dotted lines) in the

range of 30 to 75° 2

(Cu K

radiation) of β21s after isothermal

exposure at different temperatures for two hours. The intensities are

given relative to the maximum, {110}β reflection. For clarity, the

diffraction patterns are shifted with respect to each other along the

vertical axis.

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Titanium alloys: modelling of microstructure130

thermomechanically processed titanium alloys), the quantitative analysis should

be based on the entire diffraction pattern instead of using single reflections.

The principle of ‘averaging the integral intensities’ should be applied. All α

and β reflections observed should be used.

X-ray analysis of the alloy after different temperatures of isothermal exposure

shows different quantities of the α phase. The total amount of the α phase

precipitated after isothermal exposure at 750 °C is estimated at about 12%.

Decreasing of the temperature of isothermal holding down to 700 and

650 °C results in an increase of the α phase fraction (see Fig. 6.6). The

amounts of the α phase at 700 and 650 °C are 19 and 35%, respectively.

Further decrease of the temperature of isothermal exposure down to 600 and

500 °C leads to decrease of the total amount of the α phase to 32 and 13%,

respectively.

The increased total amount of the α phase when the temperature is decreased

from 750 to 650 °C is in agreement with what is expected from the

thermodynamics of this phase transformation. However, the lower amounts

of the α phase after isothermal exposure at lower temperatures contradict the

thermodynamic equilibria for titanium alloys. It is likely that, at lower

temperatures (600 and 500 °C), the β to α + β transformation has slow

kinetics, and phase equilibria are not reached during the two-hour exposure.

In order to check this assumption, experiments involving additional prolonged

ageing are necessary.

6.5 Additional ageing

In order to check the completeness of the phase transformation after the

resistivity experiments at 650, 600 and 500 °C, the β21s samples were re-

heated and held at the same temperatures for longer times. Additional ageing

for two hours was applied to the sample after resistivity experiments at 650

°C. The diffraction patterns after resistivity and after the additional ageing

were identical. The identical amounts of α and β phases before and after this

additional ageing mean that the phase transformation was completed before

the additional ageing and a phase equilibrium had been reached.

Additional ageing of 8 and 14 hours was applied for the sample at 600 °C

(note that the total time of isothermal exposure was 10 and 16 hours,

respectively). The diffraction pattern after additional ageing for 8 hours (10

hours in total) showed an increased amount of α phase (see Fig. 6.7a). The

amount of the α phase was increased from 32% after the resistivity experiment

to 36% after the additional ageing. The phase transformation at this temperature

was incomplete after the resistivity experiments. A slow transformation process

was still in progress upon additional ageing, but it was undetectable with the

resistivity technique used. Further increase of the ageing time to 16 hours

did not show any change in the diffraction pattern. So, the β to α + β

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The Johnson–Mehl–Avrami method 131

600 °C

2 h

10 h

Profile fit 2 h

Profile fit 10 h

500 °C

36.5 37 37.5 38 38.5 39 39.5 40 40.5 41 41.5

2θ (°)

(a)

Relative intensity

0.8

0.6

0.4

0.2

2 h

18 h

54 h

Profile fit 2 h

Profile fit 18 h

Profile fit 54 h

36.5 37 37.5 38 38.5 39 39.5 40 40.5 41 41.5

2θ (°)

(b)

Relative intensity

0.8

0.6

0.4

0.2

6.7

X-ray diffraction patterns in the range of 36.5 to 41.5° 2

and

profile fits of the {101}α reflection for β21s after isothermal exposure

at (a) 600 and (b) 500 °C for different periods of time. The intensities

are given relative to the maximum, {110}β reflection.

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Titanium alloys: modelling of microstructure132

transformation at this temperature has completed at or before 10 hours of

isothermal exposure.

After the resistivity experiments at 500 °C, the sample was re-heated and

aged for additional times of 16, 40 and 52 hours (note that these correspond

to total times of isothermal exposure of 18, 42 and 54 hours). The additional

ageing at this temperature also resulted in increase of the amount of α phase

(see Fig. 6.7b). The amount of α phase increased from 13% after the resistivity

experiments for two hours to 25% after additional ageing for 16 hours (18

hours in total). The ageing time prolongation resulted in further increase of

the amount of α phase to 33 and 40% after additional ageing for 40 and 52

hours (42 and 54 hours in total), respectively. At this temperature, the β to α

+ β phase transformation may still not have completed even after 52 hours

additional ageing.

In addition, the X-ray diffraction patterns after exposure at different

temperatures and times showed a tendency in the full width half maximum

(FWHM) values of the α reflections. The FWHM values were higher when

the temperature was lower, implying that the precipitated α phase at lower

isothermal temperatures possesses a larger degree of inhomogeneity. On the

other hand, the time prolongation resulted in decrease of the FWHM values,

indicating α phase homogenisation. The change in FWHM could also be

related to α grain or precipitate size, with large values indicating small sizes.

In summary, for the β alloy β21s, more dependable data can be obtained

using quantitative X-ray analysis, giving linear dependency between resistivity

signal and α volume fraction. This can then be employed to convert resistivity

data into curves for α phase amount versus time of isothermal exposure (Fig.

6.2d). At the same time, it is established that samples exposed at 500 and

600 °C do not reach equilibrium α + β condition after two hours resistivity

experiments. Equilibrium is not reached at 500 °C even after 52 hours additional

ageing.

6.6 Thermodynamic equilibria

From the fundamental theory of the phase transformations, when an alloy is

held at a certain temperature for a long time it tends towards and possibly

reaches a thermodynamic equilibrium. If this principle is applied here, it can

be assumed that in the final stage, when the transformation has been completed,

phase equilibria at the corresponding temperatures have been achieved. This

means equilibrium amounts of α and β phases as well as equilibrium

composition of both phases.

A Ti database which allows phase equilibria calculations to be performed

for multi-component, conventional titanium alloys is available. The phase

equilibria can be calculated for the compositions and the temperature range

used. The calculations are carried out with Thermo-Calc software and using

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The Johnson–Mehl–Avrami method 133

the above-mentioned Ti database, for the actual alloy compositions, taking

into account the Al, V, Mo, Nb, Si, Fe and O contents. The C, N and H

contents are not taken into account in the calculations, except in the case of

β21s when C and N are taken into account. The experimental (from the

resistivity study) and calculated results are compared in Table 6.1 for

Ti-6Al-4V and Ti-6Al-2Sn-4Zr-2Mo-0.08Si and Table 6.2 for Ti-8Al-1Mo-

1V, respectively.

6.6.1 Ti-6Al-4V and Ti-6Al-2Sn-4Zr-2Mo-0.08Si

A good agreement between the experimental and calculated phase compositions

is found for the Ti 6-4 alloy (Table 6.1). The correspondence is better at

lower temperatures (750–800 °C). At higher temperatures (850–900 °C) the

calculated equilibrium α amount is slightly lower than that experimentally

observed. The differences between the experimental and calculated phase

compositions for Ti 6-4 are within the acceptable error range.

The differences between the calculated amount of equilibrium α phase

and the amount experimentally detected by the resistivity experiments are

significant for the Ti 6-2-4-2 alloy, which has a more complicated composition

than Ti 6-4 (Table 6.1). No reasonable explanation for this observation could

be found. In order to clarify this discrepancy, additional experiments were

carried out. Samples from both alloys were treated according to the same

heat treatment process. Thereafter, the samples were studied by means of

quantitative metallography (Fig. 6.8). Again, acceptable correspondence for

the Ti 6-4 alloy was observed (Fig. 6.8a). For the Ti 6-2-4-2 alloy the

experimental results from the metallography were in agreement with the

experimental results of the resistivity and in disagreement with the calculated

phase equilibria (Fig. 6.8b). Thus, it is reasonable to believe that the

experimentally observed α-amounts were the correct ones and the calculated

values for Ti 6-2-4-2 were unrealistically high. It should be noted that the

curve tracing the kinetics at a high temperature (see curve corresponding to

930 °C in Fig. 6.2b) has a tendency to increase with the time prolongation.

This may indicate that the transformation at this temperature is still incomplete.

Possibly, a very slow transformation process is still in progress, but it is

undetectable with the experimental technique used. Nevertheless, it is very

unlikely that even when the time is significantly prolonged, the experimental

amount of α phase (current data value 15%) will reach the amount calculated

(65%). One may conclude that for both Ti-6Al-4V and Ti-6Al-2Sn-4Zr-

2Mo-0.08Si alloys, there is a better correspondence between the calculated

and experimentally observed α amounts at lower temperatures.

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Titanium alloys: modelling of microstructure134

Table 6.1

Experimental and calculated phase compositions for Ti-6Al-4V and Ti-6Al-2Sn-4Zr-2Mo-0.08Si alloys at various temperatures

Alloy

Experimental Calculated

(°C) αβα β Al in Al in V in V in Sn in Sn in Zr in Zr in Mo in Mo in

αβαβαβαβαβ

(vol.%) (vol.%) (mol.%) (mol.%) (wt.%) (wt.%) (wt.%) (wt.%) (wt.%) (wt.%) (wt.%) (wt.%) (wt.%) (wt.%)

Ti-6Al-4V 950 22.5 77.5 – – – – – – – – – – – –

900 43.7 56.3 35.9 64.1 6.9 5.8 2.0 6.7 – – – – – –

850 68.9 31.1 62.2 37.8 6.6 5.5 2.4 9.2 – – – – – –

800 79.5 20.5 76.9 23.1 6.5 5.3 2.8 12.2 – – – – – –

750 85.1 14.9 85.0 15.0 6.4 5.1 3.1 15.8 – – – – – –

Ti-6Al-2Sn- 930 14.9 85.1 65.8 34.2 6.7 5.1 – – 1.8 2.1 3.8 4.3 0.56 4.5

4Zr-2Mo- 900 42.7 57.3 78.9 21.1 6.5 4.9 – – 1.9 1.9 3.9 4.3 0.71 6.4

0.08Si 850 68.2 31.8 89.5 10.5 6.3 4.8 – – 2.0 1.3 3.9 4.2 0.95 10.0

800 82.9 17.1 94.2 5.8 6.3 4.6 – – 2.0 0.81 4.0 4.0 1.1 14.2

750 87.3 12.7 96.4 3.6 6.2 4.4 – – 2.0 0.45 4.0 3.6 1.2 18.9

735 97.7 2.3 96.8 3.2 6.2 4.3 – – 2.0 0.37 4.0 3.44 1.3 20.4

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The Johnson–Mehl–Avrami method 135

6.6.2 Ti-8Al-1Mo-1V

Significant and unacceptable discrepancy between the experimental and

calculated phase compositions is found, especially at high temperatures. The

agreement is better at lower temperatures (750–800 °C). At higher temperatures,

Ti-6Al-4V

Metallography

Resistivity

Calculated

700 750 800 850 900 950 1000

(°C)

(a)

Amount of α phase (%)

100

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

Metallography

Resistivity

Calculated

700 750 800 850 900 950 1000

(°C)

(b)

100

6.8

Experimental and calculated α phase amounts for (a) Ti-6Al-4V

and (b) Ti-6Al-2Sn-4Zr-2Mo-0.08Si alloys versus temperature.

Amount of α phase (%)

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Titanium alloys: modelling of microstructure136

the calculated equilibrium α amount is significantly higher than that

experimentally observed. In order to clarify this discrepancy, samples quenched

from different temperatures were studied by means of quantitative

metallography. The data obtained from the different ways are plotted in Fig.

6.9, together with the data published by Boyer et al. (1994).

The β-transus temperature for Ti 8-1-1 alloy with normal element contents

is approximately 1040 °C (Boyer et al., 1994). Using Thermo-Calc and the

Ti database, a β-transus temperature of 1039 °C for the composition of the

alloy used is obtained. The results from the calculation show that, at 975 °C,

nearly 70% of the β phase should transform to α phase (see Table 6.2), so the

major part of the transformation is between 1039 and 975 °C. Such an

amount of equilibrium α phase at a temperature so close to the β-transus is

probably unrealistically high. The β to α transformation in titanium alloys is

in a much wider temperature range. Thus, there is reason to believe that the

experimental amounts of the α phase at higher temperatures are the correct

ones.

There is also a difference between the amounts of the α phase in Boyer

et al. (1994) and in the resistivity and metallographic data here. The difference

can be due to different composition of the alloys used. For example, oxygen

level has a dramatic influence on the thermodynamics and kinetics of the

phase transformations in titanium alloy (Chapter 14). The oxygen level of

the Ti-8Al-1Mo-1V alloy used in this chapter was 0.085 wt.%, which is

750 800 850 900 950 1000

(°C)

Amount of α phase (%)

100

Metallography

Resistivity

Calculated

Experimental (Boyer)

6.9

Experimental and calculated α phase amounts for Ti-8Al-1Mo-1V

alloy versus temperature.

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The Johnson–Mehl–Avrami method 137

Table 6.2

Experimental and calculated phase compositions for Ti-8Al-1Mo-1V alloy at various temperatures

(°C) Experimental Calculated

αβαβAl in α Al in β V in α V in β Mo in α Mo in β Fe in α Fe in β O in α O in β

(vol.%) (vol.%) (mol.%) (mol.%) (wt.%) (wt.%) (wt.%) (wt.%) (wt.%) (wt.%) (wt.%) (wt.%) (wt.%) (wt.%)

975 8 92 67.9 32.1 8.47 7.09 0.65 1.67 0.33 2.51 0.012 0.220 0.109 0.036

950 25 75 80.5 19.5 8.31 6.84 0.74 1.96 0.44 3.46 0.018 0.331 0.098 0.031

925 45 55 88.1 11.9 8.21 6.64 0.81 2.21 0.55 4.53 0.025 0.473 0.093 0.028

900 60 40 92.8 7.2 8.14 6.47 0.86 2.43 0.66 5.70 0.034 0.648 0.090 0.025

850 77 23 97.7 2.3 8.07 6.16 0.93 2.80 0.86 8.16 0.055 1.079 0.086 0.021

800 90 10 99.9 0.1 8.02 5.86 0.98 3.13 1.03 10.80 0.078 1.560 0.085 0.016

750 98 2 100 – 8.02 – 0.98 – 1.04 – 0.080 – 0.085 –

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