Sha W., Malinov S. Titanium Alloys: Modelling of Microstructure, Properties and Applications
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Titanium alloys: modelling of microstructure, properties
and applications
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ii
Titanium alloys:
modelling of
microstructure,
properties and
applications
Wei Sha and Savko Malinov
CRC Press
Boca Raton Boston New York Washington, DC
W
OODHEAD
PUBLISHING
LIMITED
Oxford Cambridge New Delhi
iii
Published by Woodhead Publishing Limited, Abington Hall, Granta Park, Great Abington,
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First published 2009, Woodhead Publishing Limited and CRC Press LLC
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iv
Contents
Author contact details xi
Preface xiii
1 Introduction to titanium alloys 1
1.1 Introduction 1
1.2 Conventional titanium alloys 2
1.3 Titanium aluminides 4
1.4 Modelling 7
1.5 References 8
Part I Experimental techniques
2 Microscopy 11
2.1 High temperature microscopy of surface oxidation and
transformations 11
2.2 Gamma titanium aluminide 16
2.3 Transmission electron microscopy of microstructural
evolution 25
2.4 References 31
3 Synchrotron radiation X-ray diffraction 33
3.1 Introduction 33
3.2 Measurements at room temperature 34
3.3 Measurements at elevated temperatures 42
3.4 Gamma titanium aluminide 54
3.5 References 68
4 Differential scanning calorimetry and property
measurements 70
4.1 Phase and structural transformations 70
4.2 Mechanical properties of β21S alloy 83
v
4.3 Effects of hydrogen penetration 86
4.4 References 91
Part II Physical models
5 Thermodynamic modelling 95
5.1 Introduction 95
5.2 Conventional titanium alloys 96
5.3 Titanium aluminides 106
5.4 References 115
6 The Johnson–Mehl–Avrami method: isothermal
transformation kinetics 117
6.1 Introduction 117
6.2 Resistivity experiments 118
6.3 Metallography 123
6.4 X-ray diffraction 128
6.5 Additional ageing 130
6.6 Thermodynamic equilibria 132
6.7 Kinetics of the transformation 140
6.8 Time–temperature–transformation diagrams 156
6.9 Summary 162
6.10 References 163
7 The Johnson–Mehl–Avrami method adapted to
continuous cooling 165
7.1 Introduction 165
7.2 Interpretation of calorimetry data 165
7.3 X-ray diffraction 172
7.4 Microstructure and hardness 174
7.5 Calculation of continuous-cooling-transformation
diagrams 178
7.6 Calculation of transformation kinetics 183
7.7 Simulation and monitoring of transformations on
continuous cooling 197
7.8 Summary 200
7.9 References 202
8 Finite element method: morphology of β to α phase
transformation 203
8.1 Introduction 203
8.2 Experimental and modelling methodology 204
Contentsvi
8.3 Experimental observation of the morphology of the phase
transformation 205
8.4 Mathematical formulation in the model for the
microstructure of Ti-6Al-4V 205
8.5 The 1-D model 217
8.6 The 2-D model 222
8.7 Summary of the models for Ti-6Al-4V 232
8.8 Extending to other alloys 232
8.9 Summary 235
8.10 References 235
9 Phase-field method: lamellar structure formation
in γ-TiAl 237
9.1 Introduction 237
9.2 Mathematical formulation 239
9.3 Computer simulation of lamellar structure formation in
γ-TiAl 251
9.4 Summary 255
9.5 References 256
10 Cellular automata method for microstructural
evolution modelling 257
10.1 Introduction 257
10.2 Microstructural evolution of Ti-6Al-4V during
thermomechanical processing 258
10.3 The simulation model 262
10.4 Simulated microstructural evolution during dynamic
recrystallisation 264
10.5 Simulated flow stress–strain behaviour 265
10.6 Summary of the simulation method and its capabilities 266
10.7 References 269
11 Crystallographic and fracture behaviour of titanium
aluminide 270
11.1 Introduction 270
11.2 Single crystal characteristic 271
11.3 Crack path analyses 273
11.4 Transmission electron microscopy 279
11.5 A model for microcracks nucleation in basal slip 281
11.6 Summary 289
11.7 References 289
Contents vii
12 Atomistic simulations of interfaces and dislocations
relevant to TiAl 290
12.1 Introduction 290
12.2 Tasks 291
12.3 Computational procedure 292
12.4 Choice of interatomic potential 295
12.5 References 297
Part III Neural network models
13 Neural network method 301
13.1 Introduction 301
13.2 Software description 302
13.3 Use of the software 319
13.4 Upgrading the software system 326
13.5 Summary 328
13.6 References 328
14 Neural network models and applications in phase
transformation studies 331
14.1 β-transus temperature 331
14.2 Time–temperature–transformation diagrams 343
14.3 An example of MatLab program code for neural network
training 361
14.4 References 363
15 Neural network models and applications in property
studies 365
15.1 Correlation between processing parameters and
mechanical properties 365
15.2 Fatigue stress life (S-N) diagrams 388
15.3 Mechanical properties of gamma-based titanium
aluminides 397
15.4 Reference 409
15.5 Appendix 410
Part IV Surface engineering products
16 Surface gas nitriding: phase composition and
microstructure 413
16.1 Introduction 413
16.2 Near-α Ti-8Al-1Mo-1V 417
Contentsviii
16.3 Near-α Ti-6Al-2Sn-4Zr-2Mo 422
16.4 α + β Ti-6Al-4V 427
16.5 Near-β Ti-10V-2Fe-3Al 431
16.6 β21s 435
16.7 Timetal 205 442
16.8 Ti–Al 446
16.9 Summary of the effect of the parameters of gas nitriding
on the microstructure 449
16.10 References 450
17 Surface gas nitriding: mechanical properties,
morphology, corrosion 451
17.1 Hardness evolution 451
17.2 Tensile properties and fatigue performance after nitriding 468
17.3 Surface morphology and roughness of
Ti-6Al-2Sn-4Zr-2Mo after nitriding 471
17.4 Corrosion behaviour 487
17.5 References 496
18 Nitriding: modelling of hardness profiles and the
kinetics 497
18.1 Artificial neural network modelling of microhardness
profiles 497
18.2 Kinetics of gas nitriding 513
18.3 References 530
19 Aluminising: fabrication of Al and Ti–Al coatings by
mechanical alloying 532
19.1 Introduction 532
19.2 As-synthesised state 533
19.3 Annealing treatment of the aluminium coating 536
19.4 Annealing treatment of titanium/aluminium coating 542
19.5 Summary 547
19.6 References 548
Index 549
Contents ix