Sha W., Malinov S. Titanium Alloys: Modelling of Microstructure, Properties and Applications
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Neural network models and applications 351
Molybdenum is another very important and frequently used alloying element
in titanium alloys, and its influence is also illustrated by using the model.
The well known commercial alloy Ti-5Al-4Cr-4Mo-2Sn-2Zr was chosen.
TTT diagrams were calculated assuming different molybdenum contents
(Fig. 14.18). They do not show any clear tendency for the influence of the
T
(°C)
950
900
850
800
750
700
650
Ti-xAl-4V
4% Al
6% Al
8% Al
β to α + β
β
M
s
10
0
10
1
10
2
Time (sec)
(a)
T
(°C)
1000
950
900
850
800
750
700
650
600
550
500
Ti-6Al-xV
2% V
4% V
6% V
β to α + β
β
M
s
10
0
10
1
10
2
Time (sec)
(b)
14.16
Calculated TTT diagrams for start of β to α + β transformation
in Ti-Al-V alloy assuming different (a) aluminium and (b) vanadium
contents.
Titanium alloys: modelling of microstructure352
Ti-6Al-4V-xO
T
(°C)
1000
950
900
850
800
750
700
650
600
550
β to α + β
β
M
s
10
0
10
1
10
2
10
3
Time (sec)
14.17
Calculated TTT diagrams for start of β to α + β transformation
in Ti-6Al-4V alloy with different oxygen levels: 䊐, 0.05; 䊊, 0.10; ✳,
0.20 wt.% O. Bold line is experimental result.
T
(°C)
800
750
700
650
600
550
500
450
400
β
10
1
10
2
10
3
Time (sec)
Ti-5Al-4Cr-xMo-2Sn-2Zr
2% Mo
4% Mo
6% Mo
8% Mo
10% Mo
15% Mo
β to α + β
Experimental for Ti-
5Al-4Cr-4Mo-2Sn-2Zr
14.18
Calculated TTT diagrams for start of β to α + β transformation
in Ti-5Al-4Cr-
x
Mo-2Sn-2Zr alloy assuming different molybdenum
content.
Neural network models and applications 353
molybdenum content on the C-curve shifting. The influence is more or less
unsystematic. For example, the temperature of the nose point first decreases
at low content and then increases with increasing molybdenum content. The
trend of the incubation time variations is also unclear. A similar, apparently
erratic influence of molybdenum was reported for binary Ti–Mo alloys. This
effect is most probably due to the complex and dual influence of molybdenum
on the thermodynamic and the kinetic parameters. The significant changes
of the C-curve shape in these cases confirm this duality.
The model was used to study the influence of other typical and commonly
used alloying elements in titanium alloys. The influence of tin and chromium
on the isothermal transformation kinetics is simulated. TTT diagrams are
calculated by the NN model assuming increased and decreased contents of
tin and chromium in the Ti-5Al-4Cr-4Mo-2Sn-2Zr alloy. With the increasing
of either tin or chromium contents, the C-curve is shifted to lower temperatures
and longer times (Fig. 14.19). Hence, these two elements have similar influence
to vanadium. There is a good correspondence between the neural network
simulations and the experimental TTT diagram for the Ti-5Al-2Sn-2Zr-4Mo-
4Cr alloy.
Figure 14.20 demonstrates further examples of the use of the model
developed to simulate the influence of zirconium (Fig. 14.20a) and iron (Fig.
14.20b) on the start of the β to α + β transformation in Ti 6-2-4-2 and Ti 10-
2-3 alloys, respectively. TTT diagrams are calculated, assuming increased
and decreased contents of zirconium and iron from their usual contents (4
wt.% zirconium in Ti 6-2-4-2 alloy and 2 wt.% iron in Ti 10-2-3 alloy). The
increase of the zirconium amount shifts the C-curve to longer times, probably
due to the decrease in diffusivity. At the same time, there is no appreciable
effect of zirconium on shifting of the curve along the temperature scale. This
simulation result is in agreement with the binary Ti–Zr phase diagram, where
an increase of zirconium from 0 to 5 wt.% causes only slight decrease of the
β-transus temperature, about 15 °C. The increase of iron in Ti 10-2-3 alloy
causes a shift in the TTT diagram to lower temperatures and longer times
(Fig. 14.20b). The nose point is shifted down by about 150 °C when the iron
content is increased from 0 to 4 wt.%. Again, this simulation result is in
agreement with the binary Ti–Fe phase diagram, according to which increase
of iron from 0 to 4 wt.% causes decrease of the β-transus temperature by
more than 100 °C. The shift of the C-curve to longer times is due to decrease
in diffusivity because (i) the phase transformation takes place at lower
temperatures and (ii) the presence of an alloying element decreases the diffusion
coefficient. Figure 14.20b also shows good correspondence between the
model simulations and experimental data for the usual composition of Ti 10-
2-3 alloy. In addition, there is good correspondence between the neural
network model simulations of the TTT diagram and same diagrams obtained
by other methods.
Titanium alloys: modelling of microstructure354
T
(°C)
800
750
700
650
600
550
500
450
400
10
1
10
2
10
3
Time (sec)
(b)
Ti-5Al-2Sn-2Zr-4Mo-4Cr Experimental
Ti-5Al-2Sn-2Zr-4Mo-4Cr Neural Network
Ti-5Al-2Sn-2Zr-4Mo-2Cr Neural Network
Ti-5Al-2Sn-2Zr-4Mo-6Cr Neural Network
T
(°C)
800
750
700
650
600
550
500
450
400
10
1
10
2
10
3
Time (sec)
(a)
Ti-5Al-2Sn-2Zr-4Mo-4Cr Experimental
Ti-5Al-2Sn-2Zr-4Mo-4Cr Neural Network
Ti-5Al-1Sn-2Zr-4Mo-4Cr Neural Network
Ti-5Al-3Sn-2Zr-4Mo-4Cr Neural Network
14.19
Calculated TTT diagrams for start of β to α + β transformation in Ti-5Al-2Sn-2Zr-4Mo-4Cr alloy assuming different
(a) tin and (b) chromium contents.
Neural network models and applications 355
The NN model was developed based only on collected experimental TTT
diagrams published by other authors. Chapter 6 has discussed experimental
study of the kinetics of the β to α + β phase transformation in popular
titanium alloys at isothermal conditions. Using resistivity techniques,
microscopical examinations and X-ray measurements, we have designed
TTT diagrams for Ti-6Al-4V, Ti-6Al-2Sn-4Zr-2Mo, Ti-8Al-1Mo-1V and
T
(°C)
900
850
800
750
700
650
10
0
10
1
10
2
Time (sec)
(a)
Ti-6Al-2Sn-xZr-2Mo
3% Zr
4% Zr
5% Zr
T
(°C)
800
700
600
500
400
300
10
0
10
2
10
4
Time (sec)
(b)
Ti-10V-xFe-3Al
0 wt% Fe
Experimental for
Ti-10V-2Fe-3Al
2 wt% Fe
4 wt% Fe
14.20
Calculated TTT diagrams for start of β to α + β transformation
in (a) Ti-6Al-2Sn-4Zr-2Mo alloy assuming increased and decreased
zirconium content, and (b) Ti-10V-2Fe-3Al alloy assuming increased
and decreased iron content.
Titanium alloys: modelling of microstructure356
β21s. These experimental TTT diagrams are compared with those predicted
from the NN model (Fig. 14.21) and a good correspondence is observed.
14.2.3 Prediction of TTT diagrams for commercial alloys
TTT diagrams for some commercial alloys have been calculated (see Fig.
14.22). Some of the most popular titanium alloys are chosen for which no
TTT diagrams are available in the literature. In the computation of all TTT
diagrams in Fig. 14.22, an oxygen level of 0.1 wt.% is assumed. When iron
is not an alloying element, its content is assigned as 0.15 wt.%. The simulated
TTT diagrams are consistent with what might be expected from a knowledge
of the phase transformation in titanium alloys.
The diagrams in Fig. 14.22 could be used for explaining the transformation
kinetics during cooling for corresponding alloys. In Fig. 14.23, TTT diagrams
are shown for an additional set of titanium alloys for which no TTT diagrams
are available in the literature, namely Ti-2.5Cu (IMI 230), Ti-12V-2.5Al-
2Sn-2Zr and Ti-13V-2.7Al-7Sn-2Zr.
14.21
Calculated and experimental TTT diagrams for start of β to
α + β transformation in Ti-6Al-2Sn-4Zr-2Mo and β21s titanium alloys.
T
(°C)
1000
900
800
700
600
500
1 10 100 1.10
3
1.10
4
Time (sec)
Ti-6Al-2Sn-4Zr-2Mo Experimental
Ti-6Al-2Sn-4Zr-2Mo Neural network
Beta21s Experimental
Beta21s Neural network
Neural network models and applications 357
T
(°C)
900
850
800
750
700
650
600
550
500
10
0
10
1
10
2
Time (sec)
(a) Ti-7Al-4Mo
T
(°C)
800
750
700
650
600
550
500
450
400
10
0
10
1
10
2
10
3
Time (sec)
(b) Ti-4Al-3V-2Mo-2Fe
T
(°C)
800
750
700
650
600
550
500
10
0
10
1
10
2
Time (sec)
(c) Ti-4.5Al-3Mo-1V
14.22
Calculated TTT diagrams for start of β to α + β transformation
in some commercial titanium alloys.
Titanium alloys: modelling of microstructure358
T
(°C)
850
800
750
700
650
600
550
10
0
10
1
10
2
10
3
Time (sec)
(d) Ti-5Al-1.5Fe-1.4Cr-1.2Mo (Ti-155A)
T
(°C)
950
900
850
800
750
700
650
10
0
10
1
10
2
Time (sec)
(e) Ti-6.4Al-1.2Fe (RMI Low-cost alloy)
T
(°C)
650
600
550
500
450
400
350
10
0
10
1
10
2
10
3
Time (sec)
(f) Ti-2Fe-2Cr-2Mo
14.22
Continued
Neural network models and applications 359
T
(°C)
650
600
550
500
450
400
10
2
10
3
10
4
Time (sec)
(g) Ti-15V-3Cr-3Al-3Sn
T
(°C)
650
600
550
500
450
400
10
1
10
2
10
3
10
4
Time (sec)
(h) Ti-8Mo-8V-2Fe-3Al
T
(°C)
600
550
500
450
400
350
10
2
10
3
Time (sec)
(i) Ti-15Mo-5Zr
14.22
Continued
Titanium alloys: modelling of microstructure360
14.2.4 Summary
A model for prediction of TTT diagrams for titanium alloys has been created,
based on a neural network analysis, using data from the published literature.
T
(°C)
650
600
550
500
450
400
(j) Ti-15Mo-5Zr-3Al
10
2
10
3
Time (sec)
14.22
Continued
14.23
Calculated TTT diagrams for start of β to α + β transformation
in additional commercial titanium alloys.
Ti-2.5Cu (IMI 230)
Ti-12V-2.5Al-2Sn-2Zr
Ti-13V-2.7Al-7Sn-2Zr
10
0
10
1
10
2
10
3
10
4
Time (sec)
T
(°C)
900
850
800
750
700
650
600
550
500
450