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

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Surface gas nitriding: mechanical properties, morphology 493

breaks the oxide film and the nitrided compound layers, leading to a significant

increase of weight loss.

1.8

M H

Surface gas nitriding worsens the corrosion resistance of Ti-6Al-2Sn-4Zr-

2Mo in 1.8

M H

at 20 and 80 °C solutions (Fig. 17.26). At a solution

temperature of 40 °C, the untreated and nitrided alloys are quite similar.

Surface gas nitriding worsens the corrosion resistance of Ti-8Al-1Mo-1V

in 1.8

M H

at room temperature. After holding the same alloy at higher

medium temperatures of 40 and 80 °C, the alloy in the nitrided condition has

better corrosion resistance than that in the untreated condition. The weight

loss of the nitrided Ti-8Al-1Mo-1V increases with the time prolongation,

and with the increase of the temperature from 40 to 80 °C. There is no clear

tendency in the corrosion behaviour of Ti-8Al-1Mo-1V in 1.8

M H

At 40 °C, the untreated Ti-6Al-2Sn-4Zr-2Mo has better corrosion resistance

in comparison with the untreated Ti-8Al-1Mo-1V.

At 80 °C, the nitrided Ti-8Al-1Mo-1V shows better performance than Ti-

6Al-2Sn-4Zr-2Mo and the opposite tendency can be seen for the untreated

alloys.

17.4.3 Influence of the corrosive medium

The corrosive medium is an important parameter determining the corrosion

behaviour of the materials. The corrosion behaviour of nitrided Ti-6Al-2Sn-

4Zr-2Mo and Ti-8Al-1Mo-1V in three different corrosive media at three

different temperatures is compared.

At room temperature, the Ti-6Al-2Sn-4Zr-2Mo alloy nitrided at 950 °C

for 5 hours has better corrosion resistance in sulfuric acid solution than in

hydrochloric acid solution. At 40 °C, the alloy shows a very good corrosion

resistance in 0.5

M NaCl. The corrosion resistance worsens in 1.8M H

and the weight loss dramatically increases in 4.9M HCl. A similar tendency

exists at the higher solution temperature of 80 °C.

The Ti-8Al-1Mo-1V alloy nitrided at 950 °C for 5 hours is very resistant

to 0.5

M NaCl at 40 and 80 °C. The overall corrosion response is different

from the nitrided Ti-6Al-2Sn-4Zr-2Mo alloy.

17.4.4 Influence of the media temperature

In 0.5M NaCl solution, as mentioned earlier, the weight loss values of Ti-

6Al-2Sn-4Zr-2Mo after nitriding at 950 °C for 5 hours are very small. In

4.9

M HCl solution, the weight loss values are quite similar at 20 and 40 °C,

and they increase with the increase of the temperature to 80 °C. The same

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Titanium alloys: modelling of microstructure494

17.26

Weight loss versus time of Ti-6Al-2Sn-4Zr-2Mo and Ti-8Al-1Mo-

1V, untreated and nitrided (950 °C for 5 hours), after holding them in

1.8

M H

at (a) room temperature, (b) 40 and (c) 80 °C.

Weight loss (g/cm

)

0.004

0.003

0.002

0.001

0 1000 2000 3000 4000

Time (h)

(a)

Ti-6242, nitrided

Ti-6242, untreated

Ti-811, nitrided

Ti-811, untreated

Weight loss (g/cm

)

0.008

0.006

0.004

0.002

0 400 800 1200 1600

Time (h)

(b)

Ti-6242, nitrided

Ti-6242, untreated

Ti-811, nitrided

Ti-811, untreated

Weight loss (g/cm

)

0.01

0.008

0.006

0.004

0.002

0 500 1000 1500

Time (h)

(c)

Ti-6242, nitrided

Ti-6242, untreated

Ti-811, nitrided

Ti-811, untreated

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Surface gas nitriding: mechanical properties, morphology 495

tendency exists in 1.8M H

solution. The sudden jumps in the weight loss

values in both reducing acid solutions at 80 °C are probably due to the

breaking of the surface oxide and nitride layer.

As described by Galvanetto et al. (2002), the failure of the compound

layer is probably due to local dissolution of the layer, which leads to penetration

by the solution and then the fast corrosion of the inner titanium matrix,

eventually causing cracking and removal of the fragile compound layer.

There is a difference between the surface morphology of the untreated

and nitrided Ti-6Al-2Sn-4Zr-2Mo before and after the corrosion test, probably

due to an increase of surface roughness caused by the aggressive attack of

the corrosive medium.

Nitrided Ti-8Al-1Mo-1V has a similar tendency to the one for Ti-6Al-

2Sn-4Zr-2Mo. Ti-8Al-1Mo-1V has better corrosion resistance in all cases.

For untreated and nitrided Ti-6Al-2Sn-4Zr-2Mo and Ti-8Al-1Mo-1V alloys,

the corrosion rate increases with the increase of the temperature. For Ti-6Al-

2Sn-4Zr-2Mo, the corrosion rate in 0.5

M NaCl is up to 0.002 mm/yr and for

Ti-8Al-1Mo-1V is up to 0.006 mm/yr. In 4.9

M HCl, for Ti-6Al-2Sn-4Zr-

2Mo, the corrosion rate varies from 0.013 to 0.26 mm/yr, and for Ti-8Al-

1Mo-1V, it varies from 0.015 to 0.067 mm/yr. In 1.8

M H

, for Ti-6Al-

2Sn-4Zr-2Mo, it varies from 0.007 to 0.13 mm/yr, and for Ti-8Al-1Mo-1V,

it varies from 0.017 to 0.13 mm/yr.

For most of the cases, the corrosion rate is below 0.13 mm/yr, which is the

maximum corrosion rate accepted by designers. The only exception is nitrided

Ti-6Al-2Sn-4Zr-2Mo in 4.9

M HCl at 80 °C, for which the corrosion rate is

0.26 mm/yr. The cases for which we have a corrosion rate below 0.04% can

be considered as fully passive conditions.

17.4.5 Summary of the corrosion resistance of

titanium alloys after gas nitriding

The correlation between the corrosion behaviour of titanium alloys and nitriding

processing parameters, the corrosive conditions and alloy composition is

important for many industrial applications.

The corrosion weight loss tests show that surface gas nitriding does not

change significantly the corrosion resistance properties of titanium alloys.

These properties depend on the corrosive environment and conditions. Titanium

alloys show excellent corrosion resistance in salt solutions. In aggressive

reducing acid solutions, gas nitriding either worsens or improves the corrosion

resistance, depending on the alloy composition, corrosive environment and

the corrosive solution temperature.

Ti-8Al-1Mo-1V has better corrosion resistance in comparison with Ti-

6Al-2Sn-4Zr-2Mo in most of the cases. The weight loss values increase in

most cases with increase of the solution temperatures from 20 to 80 °C and

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Titanium alloys: modelling of microstructure496

time prolongation. The corrosion rate of Ti-6Al-2Sn-4Zr-2Mo and Ti-8Al-

1Mo-1V is below 0.13 mm/yr, with the only exception of nitrided Ti-6Al-

2Sn-4Zr-2Mo in 4.9

M HCl at 80 °C (0.26 mm/yr).

17.5 References

Fleszar A, Wierzchon T, Kim S K and Sobiecki J R (2000), ‘Properties of surface layers

produced on the Ti–6Al–3Mo–2Cr titanium alloy under glow discharge conditions’,

Surf Coat Technol, 131 (1–3), 62–65.

Galliano F, Galvanetto E, Mischler S and Landolt D (2001), ‘Tribocorrosion behavior of

plasma nitrided Ti–6Al–4V alloy in neutral NaCl solution’, Surf Coat Technol, 145

(1–3), 121–31.

Galvanetto E, Galliano F P, Fossati A and Borgioli F (2002), ‘Corrosion resistance properties

of plasma nitrided Ti–6Al–4V alloy in hydrochloric acid solutions’, Corros Sci, 44

(7), 1593–606.

Gokul Lakshmi S, Arivuoli D and Ganguli B (2002), ‘Surface modification and

characterisation of Ti–Al–V alloys’, Mater Chem Phys, 76 (2), 187–90.

Kessler O, Surm H, Hoffmann F and Mayr P (2002), ‘Enhancing surface hardness of

titanium alloy Ti-6Al-4V by combined nitriding and CVD coating’, Surf Eng, 18 (4),

299–304.

Malinova T, Malinov S and Pantev N (2001), ‘Simulation of microhardness profiles for

nitrocarburized surface layers by artificial neural network’, Surf Coat Technol, 135

(2–3), 258–67.

Meletis E I (2002), ‘Intensified plasma-assisted processing: Science and engineering’,

Surf Coat Technol, 149 (2–3), 95–113.

Shashkov D P (2001), ‘Effect of nitriding on the mechanical properties and wear-resistance

of titanium alloys’, Metallovedenie i Termicheskaya Obrabotka Metallov, 6, 20–25.

Takahashi A and Kimura Y (2001), ‘Evaluation of wear corrosion characteristics of Ti-

6Al-4V in quasi-human body environment and improvement of wear corrosion

characteristics by gas nitriding’, in Dominguez J (ed), Computational Methods in

Contact Mechanics V, Southampton: WIT Press, 117–26.

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497

Nitriding: modelling of hardness

profiles and the kinetics

Abstract: The first half of the chapter shows the reader how results from

microhardness testing can be used to develop artificial neural network

models for the simulation and prediction of microhardness profiles after

nitriding in relation to the type of nitriding, temperature, length of time of

nitriding, gas mixtures and alloy composition. The second half switches to

physical modelling of the evolution of surface layers during gas nitriding.

These models are based on analytical and numerical solutions of the

diffusion equation and calculate the nitrogen distribution, the thickness of

the nitrided layers and the incubation time for the formation of layers on the

surface.

Key words: neural network, microhardness, diffusion, kinetics, numerical

simulations.

18.1 Artificial neural network modelling of

microhardness profiles

Gas and plasma nitriding are among the most widely used thermo-chemical

treatments for improving the surface properties of titanium alloys. There

have been many studies on these types of treatments, especially of titanium

alloys (Galliano et al., 2001; Shashkov, 2001). They are diffusion methods

that can easily increase the hardness of these alloys. Understanding the

correlation between the processing parameters of nitriding and the hardness

of the materials is important, because this would allow an optimisation of the

processing parameters and alloy selection in order to achieve properties

desired for various applications. Artificial neural network (ANN, Chapters

13–15) (Keong et al., 2004; Li and Xiong, 2002; Li et al., 2002a,b; Öhl et

al., 2003) models can be develped and used to help achieve this purpose.

This section will describe artificial neural network modelling for simulation

and prediction of microhardness profiles of titanium and titanium alloys

after gas and plasma nitriding. The basic principles of this modelling technique

are described in Chapter 13. Apart from modelling, ANNs can be applied for

classification, transformation, association and process control (Chapters 13

and 15) (Malinova et al., 2001).

There are two different types of neural networks – hierarchical networks

and auto associators. The choice of the type of neural network depends on

the nature of the problem to be solved. In this section, feed-forward hierarchical

networks are used. The model is shown schematically in Fig. 18.1.

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Titanium alloys: modelling of microstructure498

18.1.1 Model description

Input parameters

The training of an ANN requires a large number of input/output pairs. This

leads to more precise work but also an increase of the training time. The

most important parameters of gas and plasma nitriding used to obtain desirable

surface properties are temperature of the process, time for saturation and gas

atmosphere.

As input parameters for the model, type of nitriding, temperature and time

of nitriding, gas mixtures and the chemistry of the titanium alloys presented

by the following most commonly used alloying elements and impurities: Al,

V, C, Fe, N, O, Sn, H, Ni, Mo, Si, Zr, Cr, B are used. For the design of the

ANN, input/output pairs from the published literature, including data by

Galliano et al. (2001) and Shashkov (2001), as well as the experimental data

in Chapter 17 on gas nitriding, are collected, pre-processed and used.

For the input parameter ‘type of nitriding’, the following notations are

adapted:

• plasma nitriding ‘1’

• gas nitriding ‘2’.

For the input parameter ‘gas mixture’, the following notations are adapted:

= 20,

= 400 µm

(µm)

Microhardness profile of

titanium alloys

Output layer

= 1,

= 1 µm

= 2,

= 4 µm

= 3,

= 9 µm

Hidden

layer

Input

layer

…

Titanium

alloys

composition

Type of nitriding

Temperatue

Time

Gas mixture

18.1

A schematic model of ANN for simulation and prediction of

microhardness profiles of titanium alloys after gas and plasma

nitriding.



Nitriding: modelling of hardness profiles and the kinetics 499

• pure N

‘1’

• 80%N

-20%H

‘2’

• 77%N

-22%H

-1%C ‘3’

• 70%N

-24%H

-6%C ‘4’

• NH

‘5’

• 95%N

-5%H

‘6’

• 80%N

-20%Ar ‘7’.

The output parameter, which in this case is a graph, also has to be converted

to a numerical format. Following this aim, all graphics are scanned, put in

electronic format and rescaled to the same scale. All the values are transformed

to Knoop hardness using the conversion tables. After these procedures, each

microhardness profile is described by a set of numbers giving the hardness

values at distance x from the surface (where x = i

and i =1, 2, 3, 4, …, 20).

In this way, the output, given schematically in Fig. 18.1 as a graph, is actually

presented by a set of 20 output neurons. All the data that are not consistent

are excluded from the dataset, such as methods of nitriding with processing

parameters not covered above or experimental cases not fitting well to the

general database.

Training

Descriptions of the ANN transfer functions, Levenberg–Marquardt training

method and Bayesian regularisation are given in Chapter 13. In order to

determine the optimal architecture, several steps are required. The alloying

elements that are present in a small number of cases are ignored, as well as

the impurities. Only seven alloying elements remain as input parameters and

they are Al, V, Fe, Sn, Mo, Zr and Cr. Training with the dataset of 112 data

was performed. The influence of the number of neurons in the hidden layer

on the NN response, shown by the correlation coefficient (R) for the training

and the whole datasets, is given in Fig. 18.2. For each case, the values for the

R coefficient are the average from five separate training runs under the same

conditions and using a different random distribution of the dataset. When the

number of neurons in the hidden layer is increased from one to three, the R

coefficient for both training and whole datasets increases. A further increase

of the neurons to five makes a further slight improvement of the NN, although

the correlation coefficients remain stable and do not change dramatically.

The best NN architecture is when there are five neurons in the hidden

layer. For this case, 50 runs with different database distributions were performed,

and the best case for the NN architecture and data distribution was found.

The performance for this case is demonstrated in Fig. 18.3. The figures show

a linear regression analysis between the network outputs (predictions) and

the corresponding targets (experimental data) for the different datasets. The

correlation coefficient R values for all cases of training, test and whole



Titanium alloys: modelling of microstructure500

datasets are above 0.88. This means that a good performance of the neural

network is achieved and the network can be used for further simulations and

predictions. The optimum performance of this model has eleven neurons in

the input layer, five neurons in the hidden layer and twenty neurons in the

output layer.

The data for plasma nitriding and the data for nitriding in nitrogen

atmospheres different from pure N

are quite limited. Will including these

data as inputs in the model make it possible for it to predict efficiently

microhardness profiles for new situations for plasma nitriding and nitriding

using different gas mixtures? A second model, excluding all the data for

plasma nitriding and all the data using gas mixtures different from pure N

is created in order to see the influence of these two parameters on the

performance of the NNs. This leads to a decrease of the input parameters

from 11 to 9. The whole dataset is for gas nitriding performed in a pure

nitrogen atmosphere. The training is performed with 9 inputs, 20 outputs and

84 data pairs, with 56 in the training dataset and 28 data for test. The number

of neurons in the hidden layer varies from 1 to 5. Then, the best correlation

coefficients for Bayesian regularisation are selected and these are for 5 neurons.

50 runs were again performed for this case with different database distributions,

and the best case for the new NN architecture and data distribution is given

in Fig. 18.4. The correlation coefficient R values for all cases of training, test

Train

All

0123456

Neurons in hidden layer

Correlation coefficients

0.95

0.9

0.85

0.8

0.75

18.2

Influence of the number of neurons in the hidden layer on the

neural network performance.

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Nitriding: modelling of hardness profiles and the kinetics 501

and whole datasets are above 0.91 which means a good performance of the

neural network, slightly better compared with the first model. The optimum

performance of this second model has nine neurons in the input layer, five

neurons in the hidden layer and twenty neurons in the output layer.

Data points

Best linear fit

A = T

R = 0.95

0 400 800 1200 1600 2000

(T) Experimental microhardness (HK)

(a)

(A) Neural network simulations (HK)

2000

1600

1200

800

400

Data points

Best linear fit

A = T

0 400 800 1200 1600

(T) Experimental microhardness (HK)

(b)

(A) Neural network simulations (HK)

1600

1200

800

400

R = 0.887

18.3

Microhardness values predicted from the first neural network

model versus experimental microhardness for (a) the training, (b)

test and (c) the whole dataset.

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Titanium alloys: modelling of microstructure502

At the end of the NN training, there are two trained models that can be

used for simulation of microhardness profiles of nitrided titanium alloys.

The first model can predict microhardness profiles after gas and plasma

nitriding using different gas mixture. The second model can predict

microhardness profiles after gas nitriding only in a pure nitrogen atmosphere.

These models are compared in the following sections.

Performance and test

The neural networks performance is checked after the training, using the test

dataset and the whole set of the two models. The linear regression presented

in Figs. 18.3b,c and 18.4b,c is a kind of neural network test. Furthermore,

the experimental microhardness profiles and those predicted from the trained

neural networks are compared in Fig. 18.5, where there is no significant

difference between the predictions from the two models. A good agreement

between the experimental microhardness profiles and prediction from the

NNs is shown.

18.1.2 Use of the neural networks for simulations

and predictions

NN modelling gives the correlations between the model inputs (which in this

case are the processing parameters and the alloy compositions) and the model

Data points

Best linear fit

A = T

R = 0.931

0 400 800 1200 1600 2000

(T) Experimental microhardness (HK)

(c)

(A) Neural network simulations (HK)

2000

1600

1200

800

400

18.3

Continued

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