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

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Neural network models and applications in property studies 381

The effects of the most commonly used heat treatments for titanium alloys

are shown in Fig. 15.8. A very good agreement between predicted and

experimental tensile strength is illustrated. The neural network has been

trained to understand the influence of the heat treatment on the microstructure,

and, therefore, on the properties of titanium alloys. It must be noted, however,

that the approach used is not quantitative regarding the heat treatment. The

particular heat treatment parameters such as temperature of heating, time,

heating/cooling rates are not taken into account in the model. The assumption

is that all data are at optimal heat treatment conditions for the corresponding

heat treatment procedure (α + β annealing, solution treatment and ageing,

etc.) and alloy.

The model would be more accurate and precise if the particular

characteristics of the microstructure (type of phases present, grain size and

grain shape, morphology and distribution of the fine microstructure, e.g. α +

β colonies and texture) were involved as input parameters instead of simply

the type of heat treatment. However, at present, in the literature, there are not

enough data for training of such a neural network.

Additionally, the influence of the ageing temperature on the mechanical

properties can be modelled. The tendency towards decreasing tensile strength

was simulated when the ageing temperature was raised, but the accuracy of

prediction was not acceptable. Apparently, more data for mechanical properties

after ageing at different temperatures are needed to train the neural network

to understand this effect.

NN prediction

Experimental

Ti-8Al-1Mo-1V

Tensile strength (MPa)

1400

1200

1000

800

600

400

200

Annealing

(α)

Annealing

(α + β)

STA

(α + β)

Double

annealing

15.8

Neural network predictions and experimental tensile strength of

Ti-8Al-1Mo-1V alloy after different heat treatments.

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Titanium alloys: modelling of microstructure382

15.1.5 Prediction of mechanical properties for

different alloy compositions

The influence of aluminium (Fig. 15.9a,c) and vanadium (Fig. 15.9b,d) for

one of the most popular titanium systems (Ti–Al–V) is modelled. Attention

Strength (MPa)

1200

1100

1000

900

800

700

600

500

Tensile strength

Yield strength

Ti-xAl-4V

2 4 6 8 10 12

Al (wt.%)

(a)

Strength (MPa)

1200

1100

1000

900

800

700

600

500

Tensile strength

Yield strength

Ti-6Al-xV

2 4 6 8 10 12

V (wt.%)

(b)

15.9

Neural network predictions of the influence of the alloy

composition on the mechanical properties for the Ti-

Al-

V system:

(a) tensile and yield strength for Ti-

Al-4V; (b) tensile and yield

strength for Ti-6Al-

V; (c) elongation for Ti-

Al-4V; (d) elongation and

reduction of area for Ti-6Al-

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Neural network models and applications in property studies 383

is paid to this system since Ti-6Al-4V alloy is the most widely used titanium

alloy. The mechanical properties are computed assuming increased and

decreased contents of aluminium and vanadium from the Ti-6Al-4V

composition, in an α + β annealing condition.

With increasing aluminium content, both tensile strength and yield strength

are increased appreciably (Fig. 15.9a). Simultaneously, a very high influence

of aluminium on the elongation (especially when the aluminium exceeds

Elongation (%)

–5

–10

Ti-xAl-4V

2 4 6 8 10 12

Al (wt.%)

(c)

15.9

Continued

Elongation or reduction of area %

Ti-6Al-xV

2 4 6 8 10 12

V (wt.%)

(d)

Elongation

Reduction of area

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Titanium alloys: modelling of microstructure384

8 wt.%) is found. A very small increase of the aluminium content causes a

significant decrease of the elongation (see Fig. 15.9c), approaching a value

of zero when the aluminium content is as high as 11 wt.%. The predicted

effect of a significant decrease of the ductility properties can be explained

from the metallurgical point of view with the formation of the Ti

Al phase.

The influence of vanadium on the mechanical properties shows a similar

tendency. With increasing vanadium content, tensile strength and yield strength

are increased (Fig. 15.9b), while the plasticity properties (elongation and

reduction of area) are decreased (Fig. 15.9d). The vanadium influence on the

tensile strength is much weaker as compared to the influence of aluminium.

The predicted dependencies on aluminium and vanadium are in accordance

with the well-established influence of the above elements over the mechanical

properties. From the metallurgical point of view, it is also not surprising that,

in general, substitutional elements increase the strength properties in titanium

alloys. The simulation is therefore consistent with what is expected from the

metallurgical theory and the practice of the titanium alloys.

Some mechanical properties are computed assuming increased and decreased

content of aluminium from the Ti-6Al-6V-2Sn composition (Fig. 15.10).

With increasing aluminium content, the impact strength is decreased

appreciably. Simultaneously, the increase of the aluminium content causes

an increase in the hardness. Higher operation temperature results in higher

20 °C

200 °C

400 °C

Ti-xAl-6V-2Sn alloy; solution treatment

(alpha+beta) + ageing

120

100

Impact strength, Charpy (J)

234 5678

Al (wt.%)

(a)

15.10

Neural network predictions for the influence of the aluminium

content on (a) impact strength, (b) Rockwell hardness, and (c) yield

strength of Ti-

Al-6V-2Sn alloy at different temperatures.

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Neural network models and applications in property studies 385

impact strength and lower hardness. This is a classical example for optimisation

of the alloy composition in order to maximise a property or group of properties.

In similar ways, the models can be used to give quantitative predictions for

all outputs in Fig. 13.1, at different alloy compositions, processing conditions

and temperatures. For example, the trained neural network can be used for

optimisation of the alloy composition, such as Mo, Sn, Zr, Fe and oxygen

content, in order to obtain the desired combination of mechanical properties.

20 °C

300 °C

Ti-xAl-6V-2Sn alloy; solution treatment

(alpha+beta) + ageing

Rockwell hardness

234 5678

Al (wt.%)

(b)

20 °C

200 °C

400 °C

Ti-xAl-6V-2Sn alloy; solution treatment

(alpha+beta) + ageing

1200

1100

1000

900

800

700

600

500

400

Yield strength (MPa)

234 5678

Al (wt.%)

(c)

15.10

Continued

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Titanium alloys: modelling of microstructure386

15.1.6 Optimisation of alloy composition and

processing parameters

In this mode, the input parameters of the program are the optimisation criteria

under any conditions. Loops are for alloy composition, heat treatment and

temperature (Fig. 15.11). For each combination of inputs (alloy composition,

heat treatment and temperature), the output values are predicted from the

neural network and compared with the input criteria. As a result of computation,

the best solution in respect of alloy composition and/or heat treatment

corresponding to the desired properties is obtained at the output. In the

following, one example simulated from the program is demonstrated:

Find: Alloy composition with maximal tensile strength (Rm) at 420 °C.

Fix: Heat treatment = α + β annealing; T = 420 °C; zero amount of Sn,

Cr, Fe, Si, Nb, Mn; O = 0.12;

Vary: Al, Mo, Zr, V;

15.11

Block diagram of computer program for optimisation of the

alloy composition and heat treatment conditions as functions of the

desired properties and working temperature.

Optimisation

criteria

Loops for heat

treatment

Trained

neural

network

Loops for

temperature

Loops for alloy

composition

Solution

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Neural network models and applications in property studies 387

Solution: The optimal composition is Al = 5.8 wt.%, Mo = 7.3 wt.%, Zr =

5.2 wt.%, V = 0 wt.%. This composition gives tensile strength at

420 °C Rm = 932 MPa. The other mechanical properties at

420 °C are: Rp = 665 MPa; E = 10%; ME = 94 GPa; R

–1

= 448

MPa; K

= 101 MPa m

1/2

The above program can be used to find a solution for the best alloy composition

and processing parameters for arbitrary optimisation criteria or combination

of optimisation criteria.

15.1.7 Graphical user interface

On input of the chemical composition of the titanium alloy, temperature

interval and the heat treatment, the chosen mechanical property is simulated

and plotted (Fig. 15.12). In this way, the user can very easily obtain the

temperature dependence of any from the nine mechanical properties involved

in the model, for any heat treatment conditions and arbitrary alloy composition.

An option is incorporated, where the mechanical properties can be calculated

and plotted versus the amount of a chosen alloying element at any fixed

temperature. The GUI also allows easy switch between the different heat

treatments and mechanical properties. In this way, the user can analyse the

15.12

Graphical user interface for prediction of mechanical properties

of titanium alloys as functions of alloy composition, heat treatment

and operating temperature.

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Titanium alloys: modelling of microstructure388

influence of the different factors (heat treatment and alloy composition) on

the various mechanical properties, at different operating temperatures. It

should be noted here that the program will work with appropriate accuracy

within the range of the data set used for training of the neural network.

15.1.8 Summary

An artificial neural network model has been developed for the prediction of

the mechanical properties of titanium alloys, as functions of the alloy

composition, heat treatment condition and working temperature. The model

has been used to study the influence of different factors on the mechanical

properties in titanium alloys.

A graphical user interface for the use of the model has been created.

The model is a convenient and powerful tool for practical optimisation of

the alloy composition and processing parameters of titanium alloys in order

to obtain the desired combination of properties at different working

temperatures.

15.2 Fatigue stress life (S-N) diagrams

Jet aircraft manufacturers are the principal consumers of Ti-6Al-4V, which

is often specified for critical parts, the failure of which could result in the

loss of an entire system.

Fatigue stress life is one of the most important properties for Ti-6Al-4V

alloys. Several metallurgical and environmental variables have been identified

during years of research that influence the fatigue behaviour of Ti-6Al-4V.

These variables or conditions can alter and influence the fatigue stress life of

Ti-6Al-4V in beneficial or adverse manners. The main factors and conditions

which influence fatigue stress life S-N curves are microstructure, texture,

environment, temperature, surface treatment, and stress ratio. Experimental

investigation of fatigue stress curves has been carried out extensively, but

computer modelling of fatigue stress life using neural networks has not yet

been widely used for titanium alloys.

This section will demonstrate a model of an artificial neural network for

the prediction and simulation of fatigue stress life S-N diagrams for Ti-6Al-

4V.

15.2.1 Model description

The general scheme of the model is given in Fig. 13.1c. The input parameters

of the neural network are microstructure, texture, environment, temperature,

surface treatment and stress ratio. The microstructure includes the most

common structures, namely bimodal, fine and coarse equiaxed, fine and

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Neural network models and applications in property studies 389

coarse lamellar. The test environments are air, vacuum or an aqueous solution

of 3.5% NaCl. The two major types of texture of Ti-6Al-4V are basal and

transverse, and the test direction is also noted as either the rolling or the

transverse test direction. The surface treatment comprises electrolytically

polished, shot peened, stress relieved, and mechanically polished conditions.

The stress ratio, R, is the ratio of the stress cycles (R = S

min

max

) and ranges

from –1 to 0.54. Table 15.4 shows the complete list of inputs.

The output of the artificial neural network model is the S-N fatigue diagram,

which is plotted for the corresponding conditions inputted into it.

Data set and output parameters

The database was constructed by collecting available fatigue stress life S-N

diagrams for Ti-6Al-4V. In total, 58 available S-N diagrams for Ti-6Al-4V

alloy at different conditions were collected and used in the training procedure.

The stress (S) corresponding to 10

, 10

and 10

cycles to failure (N)

was recorded and used as the output data set.

This model includes six neurons in the input layer, four neurons in the

hidden layer and four neurons in the output layer.

Table 15.4

List of inputs used for training of the neural network for fatigue stress

life

Input Values

Microstructure Bimodal; Fine equiaxed; Fine lamellar; Coarse equiaxed;

Coarse lamellar

Environment Vacuum; Air; 3.5% NaCl

Texture No texture;

B/T-TD = basal-transverse texture, transverse test

direction;

B = basal texture;

B/T-RD = basal-transverse texture, rolling test direction;

T-TD = transverse texture, transverse test direction;

T-RD = transverse texture, rolling test direction

Temperature 20 °C; 200 °C; 500 °C

Surface treatment SP = shot peened;

EP = electrolytically polished;

SP+EP;

SP+SR = shot peened + stress relieved;

SP+SR+EP;

MP = Mechanically polished with 7, 80 and 180 µm

particle size

Stress ratio (

) –1; –0.3; 0; 0.05; 0.1; 0.3; 0.5; 0.54

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Titanium alloys: modelling of microstructure390

15.2.2 Neural network test and performance

The performance is demonstrated in Fig. 15.13.

Further analysis of the performance accuracy can be carried out (Fig.

15.14). For the test data set, neural network predictions are compared with

the corresponding experimental values. For more than 80% of the test data

set, the error of prediction is within ±10%.

Data points

Best linear fit

A = T

R = 0.972

0 250 500 750 1000 1250

Experimental (T)

(a)

Predicted from NN (A)

1250

1000

750

500

250

R = 0.88

0 250 500 750 1000 1250

Experimental (T)

(b)

Predicted from NN (A)

1250

1000

750

500

250

15.13

Performance of the neural network for simulation of fatigue

stress life S-N curves, plotting the neural network versus

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

is the

experimental stress amplitude, in MPa.

is the predicted stress

amplitude from the NN, in MPa.

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