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

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Titanium alloys: modelling of microstructure108

Table 5.1

Aluminium and molybdenum equivalent values of

some titanium alloys

Alloy Aluminium Molybdenum

equivalent (wt.%) equivalent (wt.%)

Ti 8-1-1 8 1.7

IMI 834 7.5 0.6

Ti 6-2-4-2 7.4 2

Ti 6-4 6 2.7

IMI 367 5.5 1.8

Ti 10-2-3 3 11.7

β21s 3 15

Phase amount (wt.%)

100

700 800 900 1000 1100 1200 1300 1400

(°C)

(a)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Phase amount (wt.%)

100

700 800 900 1000 1100 1200 1300 1400

(°C)

(b)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

5.8

Calculated equilibrium β phase fractions versus temperature for

different oxygen levels for (a) Ti 8-1-1, (b) IMI 834, (c) IMI 367, and (d)

Ti 10-2-3 alloys.

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Thermodynamic modelling 109

of alloying elements. Some calculated data are compared with experimental

measurements by atom probe microanalysis.

Previous attempts to study TiAl systems include the α-transus temperatures

of various γ-TiAl based alloys, which are in good agreement with experimental

data. Phase diagrams of the multi-component systems were also calculated.

The following features calculations in binary and multi-component TiAl

based systems. The concentration in this section is in at.%.

5.8

Continued

Phase amount (wt.%)

100

700 800 900 1000 1100 1200 1300 1400

(°C)

(c)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Phase amount (wt.%)

100

500 600 700 800 900 1000 1100

(°C)

(d)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

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Titanium alloys: modelling of microstructure110

5.3.1 TiAl-DATA

TiAl-DATA has the following elements included: Ti, Al, Cr, Mn, Mo, Nb, Si,

Ta, V, W, Zr, B, and O, with data for the following phases: liquid, γ-TiAl, α

Al, B2, bcc (β), hcp (α), Al

(Ti,Mo,Nb,V…), Laves C14, Laves C15, σ-

(Nb,Ta)

Al, Ti

, TiZrSi, TiB, TiB

, and Al

. This database includes

features which allow, uniquely, the inclusion of oxygen in the α

-Ti

Al and

γ-TiAl phases and the incorporation of new models to allow for the important

(°C)

1400

1300

1200

1100

1000

900

800

700

100% beta

50% beta

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Oxygen content (wt.%)

(a)

(°C)

1400

1300

1200

1100

1000

900

800

700

100% beta

50% beta

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Oxygen content (wt.%)

(b)

5.9

Variation of characteristic transformation temperatures with

oxygen content for (a) Ti 8-1-1, (b) IMI 834, (c) IMI 367, and (d) Ti 10-

2-3 alloys.

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Thermodynamic modelling 111

bcc to B2 transformation to be reproduced in multi-component alloys. The

database has been constructed using a combination of published information,

unique proprietary data and newly developed extrapolation methods. It was

designed for use with γ-TiAl alloys but can, to a certain degree, also be used

with super α

-Ti

Al based alloys.

5.3.2 Ti-46Al

Since industrial multi-component alloys are based on the Ti–Al binary system,

it is important to have a good understanding of phase transformations in

(°C)

1400

1300

1200

1100

1000

900

800

700

100% beta

50% beta

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Oxygen content (wt.%)

(c)

(°C)

1200

1100

1000

900

800

700

600

500

400

100% beta

50% beta

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Oxygen content (wt.%)

(d)

5.9

Continued

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Titanium alloys: modelling of microstructure112

binary alloys. Table 5.2 gives the calculated values, from Thermo-Calc, of

both the phase fraction and element partition.

5.3.3 Ti-48Al-2Cr-2Nb

The phase constitution and element distribution in this alloy are shown in

Table 5.3. α

contains more chromium. TC calculation also shows that the

5.10

Calculated driving force for formation of α phase in (a) Ti 6-4

alloy at different temperatures and vanadium concentrations, and (b)

Ti 6-2-4-2 alloy at different temperatures and molybdenum

concentrations.

Driving force (∆G/kT)

0.1

0.08

0.06

0.04

0.02

(°C)

750

800

850

900

950

1000

Vanadium (wt. %)

(a)

Driving force (∆G/kT)

0.1

0.08

0.06

0.04

0.02

(°C)

750

800

850

900

950

1000

Molybdenum (wt. %)

(b)

Table 5.2

Calculated phase constitution and element

distribution in a Ti-46Al alloy at 1000°C

Phase Ti Al %

γ 51.3 48.7 73.2

61.4 38.6 26.8

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Thermodynamic modelling 113

B2 phase seems to be more stable than the α

phase, which implies that long-

time ageing will eventually result in a mixture of γ and B2 phases.

5.3.4 Ti-48Al-2Cr-0.175O

The influence of oxygen on phase fraction and element distribution is studied.

The composition of the studied alloy is Ti-48Al-2Cr-0.175O-0.055C. Carbon

is neglected in the calculation, since it is not included in the TiAl database.

The phase constitution and element distribution in this alloy are shown in

Table 5.4.

5.3.5 Ti-47Al-2Cr-1Nb-1V

Precipitation and partition of alloying elements in a Ti-47Al-2Cr-1Nb-1V

alloy were investigated using a position sensitive atom probe (Qin et al.,

2000). The alloy was held at 800 °C for 216 hours. The phase identity,

fraction and element distribution in different phases are listed in Table 5.5,

where experimental data are also given. Only the composition of the γ phase

was measured.

Table 5.3

Calculated phase constitution and element distribution in a Ti-48Al-2Cr-

2Nb alloy at 1000°C

Phase Ti Al Cr Nb Mol.%

γ 47.8 48.2 2.0 2.0 98.0

57.8 37.8 2.9 1.5 2.0

Table 5.4

Calculated phase constitution and element distribution in a Ti-48Al-2Cr-

0.175O alloy at 1000°C

Phase Ti Al Cr O Mol.%

γ 48.9 49.1 2.0 0.06 91.7

60.2 36.1 2.2 1.5 8.3

Table 5.5

Calculated phase constitution and element distribution in a Ti-47Al-2Cr-

1Nb-1V alloy at 1000°C (with data after 216 hours at 800 °C from atom probe

measurement in parentheses)

Phase Ti Al Cr Nb V Mol.%

γ 47.3 (49.8) 48.7 (45.3) 0.9 (1.0) 2.1 (3.0) 1.0 (0.8) 86.5

60.0 35.9 1.5 1.4 1.2 13.5

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Titanium alloys: modelling of microstructure114

5.3.6 Ti-47Al-2Cr-1.8Nb-0.2W-0.15B

The TC calculated data at 900 °C are shown in Table 5.6. The majority of

boron is in a variety of borides such as TiB

, TiB, and Ti

B. Due to a

limitation of the database, the partition of boron in α

and γ phases is not

predicted. The boride from the TC calculation is of the form of TiB

. TiB and

B may be phases formed before the equilibrium is reached. TC calculation

also indicates the existence of the B2 phase at this temperature, which is

enriched in chromium, niobium and tungsten. One may argue that these

elements may segregate at interface boundaries. However, only tungsten was

found to segregate to inter-phase boundaries. Experimental measurement

implies the existence of a chromium-rich phase.

The phase identity, fraction and element partition of the alloy after ageing

at 800 °C are listed in Table 5.6. Apart from the experimentally observed α

and γ phases and the boride, TC calculation predicts the existence of a Laves

phase. This phase is enriched in chromium and tungsten. Its existence can

explain why the amounts of chromium in both α

and γ phases are lower than

the nominal concentration. Indeed, a Ti(Cr,Al)

Laves phase is observed in

a similar alloy system (see next section).

5.3.7 Ti-47Al-2Cr-1Nb-0.8Ta-0.2W-0.15B

TC calculation gives B2 at 900 °C, and Laves phase at 800 °C (Table 5.7).

The former was not observed through atom probe. However, the latter phase

was found and identified as Ti(Cr,Al)

. Calculation shows that Ta partitions

to the α

phase.

Table 5.6

Calculated phase constitution and element distribution in a Ti-47Al-2Cr-

1.8Nb-0.2W-0.15B alloy

Temperature Phase Ti Al Cr Nb W B Mol.%

(°C)

900 γ 48.1 48.4 1.6 1.8 0.14 0 88.9

59.1 37.0 2.5 1.3 0.19 0 7.4

B2 48.0 36.2 11.5 2.5 1.84 0 3.5

TiB

33.3 0 0 0 0 66.7 0.2

800 γ 48.4 48.6 1.0 1.9 0.19 0 89.5

60.7 36.1 1.6 1.3 0.28 0 7.6

Laves 32.0 29.0 37.4 1.2 0.4 0 2.7

(Ti(Cr, Al)

)

TiB

33.3 0 0 0 0 66.7 0.23

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Thermodynamic modelling 115

5.3.8 Summary

Thermo-Calc calculation can help identify the existence of some phases

which are not readily observed experimentally, such as B2 or Ti(Cr,Al)

some titanium aluminides. It can be used as a guide in alloy design of the γ-

TiAl based alloys.

5.4 References

Andersson J-O, Helander T, Hoglund L, Shi P and Sundman B (2002), ‘Thermo-Calc &

DICTRA, computational tools for materials science’, Calphad, 26 (2), 273–312.

Davies R H, Dinsdale A T, Gisby J A, Robinson J A J and Martin S M (2002), ‘MTDATA

– thermodynamic and phase equilibrium software from the National Physical Laboratory’,

Calphad, 26 (2), 229–71.

Dore X, Combeau H and Rappaz M (2000), ‘Modelling of microsegregation in ternary

alloys: Application to the solidification of Al-Mg-Si’, Acta Mater, 48 (15), 3951–62.

Ekroth M, Dumitrescu L F S, Frisk K and Jansson B (2000), ‘Development of a

thermodynamic database for cemented carbides for design and processing simulations’,

Metall Mater Trans B, 31B (4), 615–19.

Eskin D G (2002), ‘Hardening and precipitation in the Al-Cu-Mg-Si alloying system’,

Mater Sci Forum, 396–402, 917–22.

Gorsse S and Shiflet G J (2002), ‘A thermodynamic assessment of the Cu-Mg-Ni ternary

system’, Calphad, 26 (1), 63–83.

Guo Z and Sha W (2000), ‘Modelling of beta transus temperature in titanium alloys using

thermodynamic calculation and neural networks’, in: Gorynin I V and Ushkov S S

(eds), Titanium’99: Science and Technology, Proceedings of the Ninth World Conference

on Titanium, St. Petersburg, Russia, Central Research Institute of Structural Materials,

61–68.

Jarvis D J, Brown S G R and Spittle J A (2000), ‘Modelling of non-equilibrium solidification

in ternary alloys: Comparison of 1D, 2D, and 3D cellular automaton–finite difference

simulations’, Mater Sci Technol, 16 (11–12), 1420–24.

Qin G W, Smith G D W, Inkson B J and Dunin-Borkowski R (2000), ‘Distribution

Table 5.7

Calculated phase constitution and element distribution in a Ti-47Al-2Cr-

1Nb-0.8Ta-0.2W-0.15B alloy

Temperature Phase Ti Al Cr Nb W Ta B Mol.%

(°C)

900 γ 47.8 48.7 1.6 1.0 0.13 0.7 0 86.2

58.4 37.1 2.4 0.7 0.19 1.3 0 10.1

B2 47.6 36.5 11.0 1.4 1.8 1.7 0 3.5

TiB

33.3 0 0 0 0 0 66.7 0.22

800 γ 48.1 48.9 1.0 1.0 0.19 0.75 0 87.1

59.8 36.2 1.6 0.69 0.28 1.5 0 10.1

Laves 32.4 29.2 37.3 0.68 0.41 0 0 2.6

(Ti(Cr, Al)

)

TiB

33.3 0 0 0 0 0 66.7 0.23

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Titanium alloys: modelling of microstructure116

behaviour of alloying elements in α

(α)/γ lamellae of TiAl-based alloy’, Intermetallics,

8 (8), 945–51.

Sha W (2000), ‘Thermodynamic calculations for precipitation in maraging steels’, Mater

Sci Technol, 16 (11–12), 1434–36.

Zackrisson J, Rolander U, Jansson B and Andren H O (2000), ‘Microstructure and

performance of a cermet material heat-treated in nitrogen’, Acta Mater, 48 (17), 4281–

91.

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117

The Johnson–Mehl–Avrami method:

isothermal transformation kinetics

Abstract: This chapter is concerned with the thermodynamics and kinetics

of metastable β phase decomposition under conditions of isothermal

exposure in a wide temperature range in different types of titanium alloys.

Experimental data are from in situ resistivity techniques, optical microscopy,

and X-ray diffraction analysis. Two predominant mechanisms of α

precipitation are discussed: heterogeneous nucleation and growth on β grain

boundaries at α + β temperatures close to the β-transus, and homogeneous

transformation within β grains at lower temperatures. The kinetics of β to α

transformation are modelled in the framework of the Johnson–Mehl–Avrami

theory.

Key words: kinetics, resistivity, metallography, high temperature alloys,

X-ray diffraction.

6.1 Introduction

The mechanical properties of titanium alloys are very sensitive to the

microstructure and depend on the characteristics of it (Boyer et al., 1994). It

is important to know the thermodynamics and kinetics of the phase trans-

formation, which would allow the optimisation of the processing parameters

(temperature, time, cooling rate) to achieve the desired microstructure.

The thermodynamics of the phase equilibria in titanium alloys is generally

well-studied and known. Most of the binary and ternary titanium phase

equilibrium diagrams are available (Boyer et al., 1994). However, in the past

there was no comprehensive knowledge on the kinetics of the phase

transformations in the variety of the titanium alloys under different time–

temperature regimes. Despite large numbers of papers dedicated to this problem,

the data available were incomplete. There was limited work on the kinetics

and physical modelling of time–temperature–transformation (TTT) diagrams

for titanium alloys based on the Johnson–Mehl–Avrami (JMA) theory. Outside

titanium, models for the kinetics of phase transformations taking place in

different alloys at different time–temperature conditions (Filip and Mazanec,

2001; Janlewing and Koster, 2001; Kempen et al., 2002; Mittemeijer and

Sommer, 2002; Starink, 2001; Suñol et al., 2002) are largely related with the

JMA theory.

In this chapter, we present models for the kinetics of the β to α + β phase

transformation, i.e. β phase decomposition, in the commercial α + β titanium

alloy Ti-6Al-4V, near-α (also called pseudo α) titanium alloys Ti-6Al-2Sn-

4Zr-2Mo-0.08Si and Ti-8Al-1Mo-1V, and β21s metastable β titanium alloy

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