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

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Titanium alloys: modelling of microstructure158

In addition, TTT diagrams available in previous literature are plotted in

the same figures. From the resistivity data, we find that the kinetics of the β

to α + β transformation at isothermal conditions in Ti 6-4 and Ti 6-2-4-2

alloys are very similar in the temperature range of 800–900 °C (Fig. 6.19a

and b). However, the previously published TTT diagrams by VanderVoort

(1991) for these alloys are very different, especially in regard to the end of

the transformation. For the Ti 6-2-4-2 alloy, the end of the transformation in

the above temperature range is at 5–10 s (see dot line in Fig. 6.19b), while

for the Ti 6-4 alloy, it is at longer than 500 s (see dot line in Fig. 6.19a). Such

a large difference in the kinetics of the β to α + β transformation in these two

alloys under isothermal conditions can hardly be justified. In this respect, it

is worth mentioning that the Ti 6-2-4-2 and the Ti 6-4 alloys have very

similar kinetics of the β to α + β transformation under continuous cooling

(Chapter 7).

The curves presenting the end of the β to α + β transformation show a

small deviation from the usual ‘C-shape’ of such diagrams for both alloys.

This may be due to incomplete transformations at high temperatures (>900 °C).

Probably, a very slow process of transformation would still occur if the time

were prolonged. However, this process is beyond the accuracy of the

Beta 21s

Experimental

Calculated

650 °C

600 °C

700 °C

500 °C

750 °C

0 600 1200 1800 2400 3000 3600

Time (sec)

Amount of α phase (vol. %)

6.18

Experimental and calculated kinetics of the β to α + β

transformation at different temperatures for β21s alloy.

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The Johnson–Mehl–Avrami method 159

1 10 100 10

Time (sec)

α + β

(°C)

1000

950

900

850

800

750

700

Start of transformation (5%)

End of transformation (95%)

20% alpha

(a)

1 10 100

Time (sec)

(°C)

1000

950

900

850

800

750

700

Start of transformation (5%)

End of transformation (95%)

20% alpha

α + β

(b)

6.19

Calculated time–temperature–transformation diagrams for (a) Ti-

6Al-4V and (b) Ti-6Al-2Sn-4Zr-2Mo-0.08Si alloys plotted together with

TTT diagrams published in previous literature (dot lines)

(VanderVoort, 1991).

40% alpha

60% alpha

70% alpha

Ti-6Al-4V

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

40% alpha

60% alpha

70% alpha

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Titanium alloys: modelling of microstructure160

experimental technique used. For the Ti 6-4 alloy, no ‘nose’ point for the

start of the transformation is found. Two possible reasons are suggested:

(i) The vanadium content of the alloy studied is higher than the norm for

the Ti 6-4 alloy. Vanadium causes a decrease of the β-transition temperature,

which itself will cause a shifting-down of the TTT diagrams (Chapter

14). Hence, before the nose point appears, the mechanism of the

transformation is altered from pure diffusional (above 800–850 °C) to

diffusional with partial participation of diffusionless (shifting) processes.

In titanium alloys, there is not a sharp boundary between diffusional and

diffusionless (martensitic) transformations.

(ii) Pre-processing and even early stages of the transformation may take

place on cooling from the β-region to the temperature of the isothermal

exposure. This is more likely to happen at lower holding temperatures.

Since the incubation period for the transformation is very short (a few

seconds), this effect may contribute to the experimental absence of the

nose point.

For the Ti 6-2-4-2 alloy, a TTT diagram is calculated on the basis of an

artificial neural network model (Chapter 14). Good agreement between the

data obtained in different ways is found (Fig. 6.20).

1 10 100

Time (sec)

(°C)

1000

900

800

700

600

α + β

Transformation start (Resistivity)

Transformation start (Neural network)

6.20

Calculated start of the β to α + β transformation in Ti-6Al-2Sn-

4Zr-2Mo-0.08Si alloy (TTT diagram) from resistivity experiments and

from artificial neural network predictions.

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

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The Johnson–Mehl–Avrami method 161

6.8.2 Ti 8-1-1

An isothermal transformation diagram is designed (Fig. 6.21). The end of

the transformation is difficult to be determined reliably, because the sensitivity

of the resistivity technique at very final stages of the transformation is not

high enough.

The cooling rate used (300 °C s

–1

) corresponds to a time of 1.5 s for

cooling from the β homogenisation temperature (1200 °C) to a temperature

of 750 °C. This time is of the same magnitude as the incubation period for

the transformation in this alloy. Nevertheless, we believe that the constructed

TTT diagram can be used in the heat treatment practice for Ti 8-1-1 alloy. No

previously published TTT diagram is available for comparison.

6.8.3 β21s

A time–temperature–transformation (TTT) diagram is designed based on the

data from the resistivity, additional ageing and the quantitative X-ray analyses

TTT Ti 8-1-1

α + β

(°C)

1000

950

900

850

800

750

700

1 10 100

Time (sec)

Start of transformation (5%)

20% alpha

40% alpha

6.21

Calculated time–temperature–transformation diagrams for

Ti-8Al-1Mo-1V alloy.

60% alpha

70% alpha

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Titanium alloys: modelling of microstructure162

(Fig. 6.22). The nose point of the TTT curves is around 600 °C (for the start

curve), and it gradually shifts to higher temperatures for higher amounts of

α phase and the end curve.

No previously published TTT diagram for the β21s alloy is available in

the literature for comparison. A TTT diagram is calculated for the composition

of the alloy on the basis of an artificial neural network model (Chapter 14).

The temperature interval studied is commonly used for ageing in the heat

treatment practice of metastable β titanium alloys and particularly of β21s

alloy.

6.9 Summary

Study of the thermodynamics of β to α + β transformation shows good

agreement between the experimental and the calculated phase equilibria for

the Ti-6Al-4V and disagreement for the Ti-6Al-2Sn-4Zr-2Mo-0.08Si, the Ti-

8Al-1Mo-1V and the β21s alloys.

The kinetics of β to α + β transformation in titanium alloys of different

kinds can be quantified under isothermal conditions using resistivity, optical

6.22

Calculated time–temperature–transformation diagrams for β21s

alloy. The percentage numbers mean the amount of α phase.

Beta 21s

α + β

(°C)

800

750

700

650

600

550

500

450

Start

10% alpha

15% alpha

20% alpha

25% alpha

30% alpha

35% alpha

End

Start NN

Time (min)

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The Johnson–Mehl–Avrami method 163

microscopy and X-ray techniques. Based on data from these techniques, the

kinetics of the β to α + β transformation can be modelled in the theoretical

frame of the Johnson–Mehl–Avrami (JMA) theory. The JMA kinetic parameters

are derived for the different alloys, temperatures and mechanisms of the

transformation. A good agreement between the calculated and the

experimentally measured transformed fractions is established.

Two different mechanisms of the β to α + β transformation under isothermal

conditions are observed and suggested in four different alloys, depending on

the temperature. In the near-α and α + β Ti-6Al-4V, Ti-6Al-2Sn-4Zr-2Mo-

0.08Si, and Ti-8Al-1Mo-1V alloys, at temperatures below 900 °C, the main

part of the α phase microstructure is formed via homogeneously nucleated

and grown plate-like lamellae. For temperatures above 900 °C, the mechanism

of transformation is dominated with α phase nucleating on β grain boundaries

and growing in lamellae form from these boundaries in the Ti-6Al-4V and

the Ti-6Al-2Sn-4Zr-2Mo-0.08Si alloys, while the mechanism of the

transformation alters during the course of the transformation in the case of

the Ti-8Al-1Mo-1V alloy. Grain boundary α phase is formed firstly, followed

by α phase amount increase in conditions of decreasing nucleation rate and

α plates nucleating and growing from the grain boundaries.

In the β21s alloy, for temperatures above about 650 °C, mainly grain

boundary α phase is nucleated and grown. For temperatures below about

650 °C, the mechanism of the transformation alters during the course of the

transformation. The initial stage of transformation mainly consists of α phase

nucleation, followed by diffusional growth of fine lamellae, which is mainly

controlled by a diffusional redistribution of molybdenum between the α and

the β phases.

Time–temperature–transformation diagrams are designed for the β to α +

β transformation in titanium alloys, with iso-lines tracing the amounts of the

α phase.

6.10 References

Boyer R, Welsch G and Collings E W (eds) (1994), Materials Properties Handbook:

Titanium Alloys, Materials Park, OH: ASM International.

Filip P and Mazanec K (2001), ‘On precipitation kinetics in TiNi shape memory alloys’,

Scr Mater, 45 (6), 701–07.

Janlewing R and Koster U (2001), ‘Nucleation in crystallization of Zr–Cu–Ni–Al metallic

glasses’, Mater Sci Eng A, 304–306A, 833–38.

Kempen A T W, Sommer F and Mittemeijer E J (2002), ‘Determination and interpretation

of isothermal and non-isothermal transformation kinetics: The effective activation

energies in terms of nucleation and growth’, J Mater Sci, 37 (7), 1321–32.

Malinov S, Markovsky P, Sha W and Guo Z (2001), ‘Resistivity study and computer

modelling of the isothermal transformation kinetics of Ti-6Al-4V and Ti-6Al-2Sn-

4Zr-2Mo-0.08Si alloys’, J Alloy Compd, 314 (1–2), 181–92.

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Titanium alloys: modelling of microstructure164

Malinov S, Markovsky P and Sha W (2002), ‘Resistivity study and computer modelling

of the isothermal transformation kinetics of Ti–8Al–1Mo–1V alloy’, J Alloy Compd,

333 (1–2), 122–32.

Malinov S, Sha W and Markovsky P (2003), ‘Experimental study and computer modelling

of the β⇒α+β phase transformation in β21s alloy at isothermal conditions’, J Alloy

Compd, 348 (1–2), 110–18.

Markovsky P E, Malinov S and Sha W (2004), ‘Experimental study and computer modeling

of the isothermal beta to alpha transformation kinetics in titanium alloys’, in: Luetjering

G and Albrecht J (eds), Ti-2003, Science and Technology, Proceedings of the 10th

World Conference on Titanium, Vol. 2, Weinheim: Wiley-VCH Verlag GmbH, 1131–

38.

Mittemeijer E J and Sommer F (2002), ‘Solid state phase transformation kinetics: A

modular transformation model’, Z Metallkd, 93 (5), 352–61.

Starink M J (2001), ‘On the meaning of the impingement parameter in kinetic equations

for nucleation and growth reactions’, J Mater Sci, 36 (18), 4433–41.

Suñol J J, Clavaguera-Mora M T and Clavaguera N (2002), ‘Thermally activated

crystallization of two FeNiPSi alloys’, J Therm Anal, 70 (1), 173–79.

VanderVoort G F (ed) (1991), Atlas of Time–Temperature Diagrams for Nonferrous Alloys,

Materials Park, OH: ASM International.

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165

The Johnson–Mehl–Avrami method

adapted to continuous cooling

Abstract: This chapter describes in detail how differential scanning

calorimetry measurements can be used for quantitative analysis of the phase

transformation in titanium alloys and how continuous-cooling-transformation

diagrams can be constructed. It shows how the Johnson–Mehl–Avrami

theory can be adapted to model diffusion controlled phase transformation in

two-phase titanium alloys during continuous cooling. The size of area from

the start to the peak temperatures in a DSC curve is identified and explained.

The low start transformation temperature is clarified for Ti-6Al-2Sn-4Zr-

2Mo (Ti-6242). Experimental aspects of calorimetry and X-ray diffraction

are discussed.

Key words: kinetics, phase transformation, Johnson–Mehl–Avrami,

continuous-cooling-transformation diagrams, calorimetry.

7.1 Introduction

Microstructures are formed through phase transformations during heat treatment

and thermo-mechanical processing. In contrast to the large volume of

experimental work on phase transformations in titanium alloys, including

aluminides (Butler, 1995), calculation and modelling of the kinetics of the

phase transformations have not yet been extensively conducted.

Differential scanning calorimetry (DSC) and differential thermal analysis

(DTA) are widely used experimental techniques for studying phase

transformations. There is much work on calculation and modelling of the

kinetics of phase transformations for various types of material systems based

on calorimetric data.

In this chapter, DSC and DTA experimental data are used to model the

kinetics of β to α phase transformation in titanium alloys and γ phase formation

in titanium aluminide, under continuous cooling conditions. The modelling

is based on the application of the Johnson–Mehl–Avrami theory and aims at

deriving and understanding fundamental kinetic and thermodynamic

parameters. Experimental procedures are described in original research papers

(Malinov and Sha, 2001; Malinov et al., 2001a,b).

7.2 Interpretation of calorimetry data

Figure 7.1 shows some processed experimental DSC or DTA curves. Each

curve represents the average of several different runs using the same cooling

rate and condition.

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Titanium alloys: modelling of microstructure166

50 °C/min

40 °C/min

30 °C/min

20 °C/min

10 °C/min

800 820 840 860 880 900 920 940 960 980 1000

(°C)

(a)

Heat flow (W/gr.)

0.5

0.4

0.3

0.2

0.1

50 °C/min

40 °C/min

30 °C/min

20 °C/min

10 °C/min

800 820 840 860 880 900 920 940 960 980 1000

(°C)

(b)

Heat flow (W/gr.)

0.5

0.4

0.3

0.2

0.1

7.2.1 Ti-6Al-4V

While the temperatures corresponding to the peak and the end of the

transformation are clear and accurately measurable, the temperatures

corresponding to the exact start of the transformation are difficult to determine.

For modelling, a best-fit start temperature of 970 °C is used for all cooling

curves. This assumption agrees with the published continuous-cooling-

transformation (CCT) diagrams for Ti-6Al-4V alloy (Sieniawski et al., 1996).

7.1

Calorimetry curves for (a) Ti-6Al-4V, (b) Ti-6Al-2Sn-4Zr-2Mo-

0.08Si, (c) Ti-6Al-7Nb and (d) Ti-46Al-2Mn-2Nb alloys employing

different cooling rates. Exothermic peaks are shown.



Johnson–Mehl–Avrami method adapted to continuous cooling 167

According to the diagrams by Sieniawski et al. (1996), the start temperature

of the β to α + β transformation in continuous cooling is about the same for

quite a large range of cooling rates, up to 200 °C/min, and it is 970

°C. A

similar result is obtained from the calculation of the incubation times for the

cooling rates used, based on the isothermal incubation times and applying

Scheil’s sum.

The DSC curves for all the cooling rates have a similar asymmetry, with

a tail at high temperatures, at the start of the transformation. The area under

the curve from the start to the peak temperatures ranges from 61 to 64% of

the entire area from the start to the end temperatures. The peak temperature

50 °C/min

40 °C/min

30 °C/min

20 °C/min

10 °C/min

800 820 840 860 880 900 920 940 960 980 1000

(°C)

(c)

Heat flow (W/gr.)

0.20

0.18

0.16

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0.00

1200 1220 1240 1260 1280 1300 1320

(°C)

(d)

20 °C/min

15 °C/min

10 °C/min

Temperature difference,

arbitrary units

1.5

0.5

7.1

Continued

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