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

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Nitriding: modelling of hardness profiles and the kinetics 523

described in Section 18.2.2, solves the moving-boundary diffusion problem

(Schuh, 2000) and considers the simultaneous diffusion of nitrogen in α-Ti

and development of a compound layer consisting of TiN and Ti

Boundary conditions from third order (see above) are used to model the

nitrogen mass transfer from the nitrogen containing medium to the solid.

The intrinsic diffusion coefficient is assumed to be independent of the nitrogen

concentration. The growth is described in terms of mass balance between

phases in thermodynamic equilibrium. The model is capable of predicting

the nitrogen distribution, layer thickness and incubation times for the formation

of layers.

The finite element method is used for solving the diffusion equation on

the domains occupied by different phases. The elements chosen have dimensions

in both space and time. This allows easy determination of the position of the

interface between different phases. The method is essentially an implicit

time stepping technique and is therefore stable even for a relatively large

time step.

The problem to be solved involves diffusion through two adjacent single

phases ‘a’ and ‘b’, which are separated by a moving boundary. In general,

the diffusivities in each phase D

and D

are not equal, and the concentration

has a discontinuity across the boundary. A local equilibrium is assumed at

the interface, and the interfacial compositions of both phases are calculated

from the equilibrium phase diagrams. The interface may move in either

direction normal to it as the reaction proceeds. The moving velocity of the

interface is calculated from flux balance equations.

Mass transfer from the diffusant-containing media to the solid occurs as

a result of the reactions at the diffusant–solid interface. The mass transfer

reactions determine the surface boundary conditions of the process. For

conventional gaseous nitriding, the surface boundary conditions from third

order must be applied:

–

(,)

= ( – (,))

Cxt

Ka Cxt

∂

[18.6]

where C(x, t) is the concentration at depth x and time t, D is the diffusion

coefficient, K is the reaction rate coefficient and a is the diffusant potential

in the atmosphere.

In the single-phase region, the usual diffusion model is used. Fick’s first

law, relating flux and concentration gradient in the case of isothermal, isobaric

diffusion, is expressed as:

= –

∂

[18.7]

The conservation of solute in the solid then requires:

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Titanium alloys: modelling of microstructure524

∂

J = (– )

[18.8]

A mass balance must be maintained at the interface, which is determined by

the relation of the inward and outward flux through the interface:

– = ( – )

∂

ξξ

[18.9]

where D

, D

, C

and C

are the diffusion coefficients and interface

concentrations in the corresponding phases, ξ is the interface position, and

∂

indicates the layer’s growth rate. The speed of the displacement of the

discontinuity

∂

is determined by Eq. [18.9]. There will be one flux balance

equation for each interface and the solution of the second Fick’s equation is

necessary.

Input parameters

The model based on the numerical simulations is used to develop user-

friendly software for monitoring the process of surface nitriding in titanium

and titanium alloys under various processing conditions. On input of the

processing temperature, parameters for the diffusion coefficient (activation

energy and pre-exponential term) and concentration limits of the different

phases, the nitriding process can be monitored. In this way, the model can be

used for simulation of surface nitriding not only in pure titanium but in

titanium alloys, if the diffusion coefficients of nitrogen are known.

The frequency factor A and the activation energy Q are changed for each

alloy, to obtain results close to the experimental results in terms of thickness

of the compound and the diffusion layers. Then, for each alloy the best-fit

diffusion data are found (see Table 18.2).

Finite element modelling test and performance

The model performance is tested comparing simulation results with

experimental data. Figure 18.16 illustrates one example of the numerical

model simulations. The calculated results are compared with experimental

data on microhardness in Ti-8Al-1Mo-1V after nitriding for the same

temperature and time. These results can also be compared with the neural

network predictions of microhardness profiles made by the models described

in Section 18.1 and, in particular, Model 2 (see Fig. 18.16c). A good

correspondence between the numerical simulations, experimental results and

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Nitriding: modelling of hardness profiles and the kinetics 525

Table 18.2

Diffusion data obtained from the modelling of Ti–Ti

N–TiN system

Alloy α-Ti Ti

NTiN

, m

, kJ/mole

, m

, kJ/mole

, m

, kJ/mole

Ti (Metin and Inal, 1989) 9.6 × 10

–5

215 2.7 × 10

–7

150 4.4 × 10

–9

153

Ti-8Al-1Mo-1V 1.1 × 10

–3

225 2.0 × 10

–7

160 1.0 × 10

–7

160

Ti-6Al-2Sn-4Zr-2Mo 0.5 × 10

–3

225 1.0 × 10

–7

165 6.0 × 10

–7

163

Ti-6Al-4V 0.5 × 10

–3

225 1.0 × 10

–7

165 6.0 × 10

–7

163

Ti-10V-2Fe-3Al 1.0 × 10

–3

210 2.0 × 10

–7

155 5.0 × 10

–8

145

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Titanium alloys: modelling of microstructure526

0 50 100 150 200 250 300

Distance from the surface (µm)

(a)

Nitrogen concentration (wt.%)

0 50 100 150 200 250 300

Distance from the surface (µm)

(b)

Hardness (HK0.05)

800

700

600

500

400

300

1 h

3 h

5 h

18.16

(a) Numerical simulations for the evolution of the surface layer

after nitriding of Ti-8Al-1Mo-1V at 950 °C for 1, 3 and 5 hours,

compared with (b) experimental microhardness profiles of the same

alloy after nitriding at the same conditions and (c) neural network

predictions of microhardness profiles for the same alloy.

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Nitriding: modelling of hardness profiles and the kinetics 527

0 50 100 150 200 250 300

Distance from the surface (µm)

(c)

900

800

700

600

500

400

300

1 h

3 h

5 h

18.16

Continued

the NN results is found. The use of the best-fit diffusion parameters for each

alloy makes it possible for the model to predict nitrogen concentration profiles

and the thickness of the layers for new situations within the used experimental

time and temperature range.

Furthermore, the model can be used to optimise the processing parameters

(temperature and time) of nitriding in order to achieve a desirable surface

layer thickness. Figure 18.17 demonstrates an example of model simulations

and monitoring of the evolution of nitrided layers. The simulations are for

Ti-8Al-1Mo-1V, temperature of nitriding 840 and 920 °C and using the

diffusion data of nitrogen in different phases from Table 18.2.

The layer’s thickness increases with increase of the time and the temperature

of nitriding, in agreement with the diffusion theory and the experimental

results.

There is a higher concentration of nitrogen in the nitrided layer after

longer saturation time, leading to an effective production of thicker nitrided

layers with higher values of the microhardness.

From Figs. 18.16a and 18.17, the thickness of the sub-compound layer

that consists of Ti

N is very small. This is because the concentration profile

in this phase is very steep, which leads to a very short incubation time for the

formation of the Ti

N phase. This thickness is achieved by verifying the

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Titanium alloys: modelling of microstructure528

diffusion data used for the simulation by the time an insignificant thickness

of this phase is obtained. It is desirable to obtain such a small thickness of

this phase because, from the experimental results (Chapter 16), no Ti

phase is observed on the surface after nitriding under different thermodynamic

conditions.

Nitrogen concentration (wt.%)

TiN

α-Ti(N)

100

150

100

200

300

Depth (µm)

(a)

Time (min)

Nitrogen concentration (wt.%)

TiN

α-Ti(N)

100

150

100

200

300

Depth (µm)

(b)

Time (min)

18.17

Numerical model simulations for the evolution of the surface

layer during nitriding at (a) 840 and (b) 920 °C for Ti-8Al-1Mo-1V.

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Nitriding: modelling of hardness profiles and the kinetics 529

Another example can be given for Ti-6Al-2Sn-4Zr-2Mo nitrided at

840 °C using the diffusion data from Table 18.2 (see Fig. 18.18).

The simulation of Ti-10V-2Fe-3Al during nitriding at 790 °C is shown in

Fig. 18.19. Using the diffusion data from Table 18.2, a good agreement

Nitrogen concentration (wt.%)

TiN

α-Ti(N)

100

150

100

200

300

Depth (µm)

Time (min)

18.18

Numerical model simulations for the evolution of the surface

layer during nitriding at 840 °C for Ti-6Al-2Sn-4Zr-2Mo.

18.19

Numerical model simulations for the evolution of the surface

layer during nitriding at 790 °C for Ti-10V-2Fe-3Al.

Nitrogen concentration (wt.%)

TiN

α-Ti(N)

100

150

100

200

300

Depth (µm)

Time (min)

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Titanium alloys: modelling of microstructure530

between the fundamental diffusion theory and the experimental results can

be seen.

18.2.6 Summary of numerical modelling of the

nitrided layer growth

Models for simulation and monitoring of the evolution of the surface layers

during gas nitriding of titanium alloys are based on analytical and numerical

solutions of the diffusion equation. The temperature and time of gas nitriding

can be varied for each of the titanium alloys. The growth of the nitrided

layers can be observed and monitored.

These numerical models, together with the NN models, are able to give a

complete picture of the nitrided layers of titanium alloys after thermo-chemical

treatment of nitriding and can be useful tools for titanium users and the

titanium industry in general for optimising the processing parameters of

nitriding to obtain the desirable surface properties and characteristics of the

titanium alloys for various applications.

The best-fit diffusion data for each of the Ti-8Al-1Mo-1V, Ti-6Al-2Sn-

4Zr-2Mo, Ti-6Al-4V and Ti-10V-2Fe-3Al titanium alloys are shown. Using

these data, numerical simulations and predictions of the nitrogen distribution,

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

of the layers can be made for new thermodynamic conditions.

18.3 References

Fromm E and Gebhardt E (1980), Gasi and Uglerod in Metallah, Moscow: Metallurgia.

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

plasma nitrided Ti–6Al–5kpalloy in neutral NaCl solution’, Surf Coat Technol, 145

(1–3), 121–31.

Keong K G, Sha W and Malinov S (2004), ‘Artificial neural network modelling of

crystallization temperatures of the Ni–P based amorphous alloys’, Mater Sci Eng A,

365 (1–2), 212–18.

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

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

Li M, Liu X and Xiong A (2002a), ‘Prediction of the mechanical properties of forged

TC11 titanium alloy by ANN’, J Mater Process Technol, 121 (1), 1–4.

Li M, Xiong A, Huang W, Wang H, Su S and Shen L (2002b), ‘Microstructural evolution

and modelling of the hot compression of a TC6 titanium alloy’, Mater Charact, 49 (3),

203–09.

Li M Q and Xiong A M (2002), ‘New model of microstructural evolution during isothermal

forging of Ti-6Al-4V alloy’, Mater Sci Technol, 18 (2), 212–14.

Malinov S, Zhecheva A and Sha W (2003), ‘Modelling the nitriding in titanium alloys’,

in: Popoola O, Dahotre N B, Iroh J O, Herring D H, Midea S and Kopech H (eds),

Surface Engineering Coatings and Heat Treatments, Materials Park, OH: ASM

International, 344–52.

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Nitriding: modelling of hardness profiles and the kinetics 531

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.

Metin E and Inal O T (1989), ‘Kinetics of layer growth and multiphase diffusion in ion-

nitrided titanium’, Metall Trans A, 20 (9), 1819–32.

Öhl G, Matias V, Vieira A and Barradas N P (2003), ‘Artificial neural network analysis of

RBS data with roughness: Application to Ti

0.4

0.6

N/Mo multilayers’, Nuclear Inst

and Methods in Physics Research B, 211 (2), 265–73.

Samsonova G V (ed) (1976), Svoistva Elementov: Fizicheskie Svoistva, Moscow: Metallurgia.

Schuh C (2000), ‘Modeling gas diffusion into metals with a moving-boundary phase

transformation’, Metall Mater Trans A, 31 (10), 2411–21.

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.

Smithells C J, Brandes E A and Brook G B (eds) (1992), Smithells Metals Reference

Book, 7th edn, Oxford: Butterworth-Heinemann.

Song J, Kim S, Jeon Y and Kim K (2002), ‘Improvements in surface properties of Ti-6Al-

4V by ion nitriding’, J Kor Inst Met Mater, 40 (3), 285–90.

Spies H J, Reinhold B, Wilsdorf K (2001), ‘Gas nitriding – Process control and nitriding

non-ferrous alloys’, Surf Eng, 17 (1), 41–54.

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532

Aluminising: fabrication of Al and Ti–Al

coatings by mechanical alloying

Abstract: During mechanical alloying (MA) processing, aluminium is better

deposited on the surface in the presence of titanium particles. MA technique

produces titanium/aluminium coatings with thickness of ca. 200 µm and

aluminium coatings with thickness of ca. 50 µm after two hours at room

temperature. As-synthesized coatings show a structure with high apparent

density and no porosity. Annealing at temperatures ranging between 600 and

1100 °C gives different aluminide phases on the samples. In the case of the

aluminium coating, Al

Ti and Ti

Al compounds are observed upon heating.

In the case of the titanium/aluminium coating, Al

Ti, Al

Ti, TiAl and Ti

are formed on the surface.

Key words: coating, mechanical alloying, titanium aluminides, phase

transformation, microstructure.

19.1 Introduction

A surface mechanical attrition treatment technique has been developed for

obtaining nanostructured surface layers of various metals (Tao et al., 2003;

Wang et al., 2003). The surface layer of the metal substrate is subject to

repeated ball collisions in the absence or presence of a second metal in the

form of a powder and as a result the structure at the surface becomes refined

into a nanometre scale. In the absence of a metal powder, a nanostructured

surface layer with a thickness of 10–50 µm is obtained. In the presence of an

Al or Al/Ti powder, coatings on Ti or Ti–Al substrates can be obtained by

this mechanical alloying (MA) method. The structural formation of aluminised

layer during subsequent annealing is described.

By the MA method, coatings of aluminium or titanium and aluminium

can be deposited on the substrates (Fig. 19.1). The metal substrate piece(s)

and the powder along with the steel balls are placed into the chamber and are

vibrated by the mechano-reactor for two hours. The milling process can be

carried out in air, though the chamber should be sealed to limit the amount

of available oxygen and nitrogen. The temperature of the chamber walls

during MA processing does not exceed 100 °C. During mechano-activation

processing, the metal surface is impacted by a large number of flying balls

along with particles of powder. The repeated ball collisions with the metal

result in deposition of powder on the surface.

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