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

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Neural network models and applications in property studies 371

performance is achieved in the neural networks for the other mechanical

properties.

Additionally, the performance accuracy can be verified by the way of the

analysis shown in Fig. 15.3. For the test data set, neural network predictions

Data points

Best linear fit

A = T

Training

R = 0.97

0 500 1000 1500 2000 2500

Experimental (

)

(a)

Data points

Best linear fit

A = T

2500

2000

1500

1000

500

Neural network predictions (

)

Test

R = 0.963

0 500 1000 1500 2000 2500

Experimental (

)

(b)

2500

2000

1500

1000

500

Neural network predictions (

)

15.2

Predicted tensile strength (MPa) from the neural network versus

experimental values for (a) training and (b) test data sets.

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Titanium alloys: modelling of microstructure372

are calculated. These are compared with the corresponding experimental

values. Thereafter, the relative errors (in %) are calculated using

Error =

–

100

Exp NN

Exp

Rm Rm

[15.1]

where Rm

Exp

is the experimental (measured) tensile strength and Rm

is the

predicted value from the neural network.

The error has a classical Gaussian distribution around the zero value. For

more than 95% of the test data set, the error of prediction is within ±10%, so

the model can predict with sufficient accuracy for the practice.

Comparison of the prediction from the model and experimental data

Some of the results are compared with experimental data from the literature.

All comparisons between neural network predictions and experimental data

are for data pairs which have not been involved in the training process.

The tensile strengths for some of the most popular commercial titanium

alloys are calculated (see Fig. 15.4) using the model. The neural network

predictions are in good agreement with the experimental data. Similar

–30 –20 –10 0 10 20 30

Error (%)

Number

200

150

100

Min. = –27.13

Max. = 22.02

Mean = 0.53

StDev = 7.11

15.3

Statistical analysis of the error of the neural network predictions

for tensile strength.

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Neural network models and applications in property studies 373

correspondences are observed for the other mechanical properties. In fact,

the accuracy of the neural network predictions is higher for the tensile test

properties, because the number of training data pairs is larger for the tensile

properties as compared with the other mechanical properties (see Table 15.3).

However, the accuracy of the neural network predictions is within acceptable

error range for all other properties. Some uncertainty exists only regarding

the prediction of the fracture toughness.

15.1.2 Prediction of mechanical properties at

room temperature

Since most of the data pairs used are for mechanical properties at room

temperature, the highest accuracy of the neural network is expected for the

prediction of room temperature properties. The calculation results are compared

with experimental data published in different sources (Fig. 15.5).

There is a very good agreement between the predicted values from the

neural network and the experimental data for the various properties (Fig.

15.5). The difference between the neural network predictions and the

experimental data is comparable with the difference between experimental

data published in different sources. This shows the accuracy of the predictions

from the model.

15.4

Neural network predictions and experimental tensile strengths

for different alloys, heat treatments and operating temperatures.

NN Prediction

Experimental

Tensile strength (MPa)

1400

1200

1000

800

600

400

200

Ti-6Al-4V (Grade 5)

Annealing (α + β)

at 20 °C

21s

STA (β)

at 20 °C

Ti-8Al-1Mo-1V

Annealing (β)

at 427 °C

Ti-15V-3Cr-3Sn-3Al

STA (β)

at 427 °C

VT-8

STA (α + β)

at 500 °C

Ti-5Al-2.5 Sn(low O)

Annealing (α + β)

at 20 °C

Ti-5Al-5Sn-2Zr-2Mo-0.25Si

STA (α + β)

at 427 °C

VT 14

STA (α + β)

at 500 °C

VT 3-1

STA (α + β)

at 450 °C

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

Double annealing

at 316 °C

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Titanium alloys: modelling of microstructure374

Ti 6-4 Ti 8-1-1 Ti 6-2-4-2 Ti 10-2-3 Beta21s

(a)

Tensile strength (MPa)

1100

1000

900

800

700

600

Ti 6-4 Ti 8-1-1 Ti 6-2-4-2 Ti 10-2-3 Beta21s

(b)

Yield strength (MPa)

1100

1000

900

800

700

600

NN prediction

Experimental

Ti 6-4 Ti 8-1-1 Ti 6-2-4-2 Ti 10-2-3 Beta21s

(c)

Elongation (%)

15.5

Neural network predictions of mechanical properties at room

temperature for different titanium alloys after α + β annealing: (a)

tensile strength; (b) yield strength; (c) elongation; (d) reduction of

area; (e) hardness; (f) modulus of elasticity.

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Neural network models and applications in property studies 375

Ti 6-4 Ti 8-1-1 Ti 6-2-4-2 Ti 10-2-3 Beta21s

(d)

Reduction of area (%)

Ti 6-4 Ti 8-1-1 Ti 6-2-4-2 Ti 10-2-3 Beta21s

(e)

Rockwell hardness, HRC

Ti 6-4 Ti 8-1-1 Ti 6-2-4-2 Ti 10-2-3 Beta21s

(f)

Modulus of elasticity (GPa)

140

120

100

15.5

Continued

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Titanium alloys: modelling of microstructure376

15.1.3 Prediction of mechanical properties at

high and low temperatures

Since operating temperature is a very important factor in the application of

titanium alloys, its influence is demonstrated by using the model. The well-

known high-temperature commercial alloys Ti-6Al-2Sn-4Zr-2Mo (Western)

and VT-8 (Russian) are chosen. Their mechanical properties are calculated

in the temperature range from –200 to 800 °C (Fig. 15.6).

Tensile strength

Ti 6-2-4-2 NN prediction

Ti 6-2-4-2 Experimental data

VT 8 NN prediction

VT 8 Experimental data

–200 0 200 400 600 800

(°C)

(a)

Rm (MPa)

1750

1500

1250

1000

750

500

250

Yield strength

Ti 6-2-4-2 NN prediction

Ti 6-2-4-2 Experimental data

VT 8 NN prediction

VT 8 Experimental data

–200 0 200 400 600 800

(°C)

(b)

Rp (MPa)

1750

1500

1250

1000

750

500

250

15.6

Neural network predictions of the influence of the temperature

on the mechanical properties for Ti-6Al-2Sn-4Zr-2Mo and VT-8 alloys

after double annealing heat treatment.

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Neural network models and applications in property studies 377

Elongation

Ti 6-2-4-2 NN prediction

Ti 6-2-4-2 Experimental data

VT 8 NN prediction

VT 8 Experimental data

–200 0 200 400 600 800

(°C)

(c)

Elongation (%)

Reduction of area

Ti 6-2-4-2 NN prediction

Ti 6-2-4-2 Experimental data

VT 8 NN prediction

VT 8 Experimental data

–200 0 200 400 600 800

(°C)

(d)

Reduction of area (%)

100

15.6

Continued

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Titanium alloys: modelling of microstructure378

The predicted tensile and yield strength is not affected much when the

temperature is increased from room temperature to 500 °C, for both alloys

(see Fig. 15.6a,b). When the temperature is increased to above 600 °C,

tensile and yield strength decreases significantly. The maximum operating

temperature at which the strength properties are still kept stable is around

550 °C, which is in agreement with the recommendations in the literature for

the temperature range of use for these alloys.

Charpy impact toughness

Ti 6-2-4-2 NN prediction

Ti 6-2-4-2 Experimental data

VT 8 NN prediction

VT 8 Experimental data

–200 0 200 400 600 800

(°C)

(e)

KCU (J)

140

120

100

Fatigue strength (10

cycle, unnotched)

Ti 6-2-4-2 NN prediction

Ti 6-2-4-2 Experimental data

VT 8 NN prediction

VT 8 Experimental data

–200 0 200 400 600 800

(°C)

(f)

–1

(MPa)

700

600

500

400

300

15.6

Continued

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Neural network models and applications in property studies 379

On the other hand, an increase in temperature results in significant increasing

of the elongation (especially above 600 °C, see Fig. 15.6c), the reduction of

area (Fig. 15.6d), and the impact toughness (Fig. 15.6e).

At sub-zero temperatures, naturally, the influence is the opposite. The

strength properties are increased (Fig. 15.6a,b,f), while the plasticity and the

toughness of the alloys are significantly decreased (Fig. 15.6c,d,e). The

effect of the temperature calculated from the trained neural network on the

mechanical properties is consistent with what is expected from a metallurgical

point of view.

The predicted temperature dependency of the different mechanical properties

matches well with the experimental data.

Further examples are demonstrated for use of the model to predict

mechanical properties in different alloys and conditions. Quantitative

simulations of the Ti–Al–Fe system are generated (Fig. 15.7). The model

simulations show decreasing of the tensile strength and increasing of the

elongation with the temperature increase. There is a critical temperature at

around 450–500 °C; above that, the temperature influence in these directions

is stronger. The tendency in the results for these alloys is similar to earlier

modelled outcome (Fig. 15.6). The results are also consistent with a knowledge

of the influence of temperature on the Young’s modulus.

Heat treatment: Alpha+beta annealing

Ti-5Al-2.5Fe

Ti-6.4Al-1.2Fe RMI low-cost alloy

Ti-8Al-2Fe

0 100 200 300 400 500 600 700

(°C)

(a)

Tensile strength (MPa)

1400

1200

1000

800

600

400

200

15.7

Neural network predictions of the influence of the temperature

on (a) tensile strength, (b) elongation, and (c) Young’s modulus for

Ti-5Al-2.5Fe, Ti-6.4Al-1.2Fe and Ti-8Al-2Fe alloys.

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Titanium alloys: modelling of microstructure380

15.1.4 Prediction of mechanical properties under

different heat treatment conditions

The method of heat treatment is a significant process parameter. The

optimisation of the heat treatment in order to achieve desirable mechanical

properties has major importance in titanium alloys practice. In the following,

the neural network predictions of the influence of heat treatment on mechanical

properties is discussed.

Heat treatment: Alpha+beta annealing

Ti-5Al-2.5Fe

Ti-6.4Al-1.2Fe RMI low-cost alloy

Ti-8Al-2Fe

0 100 200 300 400 500 600 700

(°C)

(b)

Elongation(%)

Heat treatment: Beta annealing

Ti-5Al-2.5Fe

Ti-6.4Al-1.2Fe

RMI low-cost alloy

Ti-8Al-2Fe

0 100 200 300 400 500 600 700

(°C)

(c)

Young’s modulus (GPa)

120

110

100

15.7

Continued

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