Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .VIII
1 Material Properties for High Temperature Applications . . . 1
1.1 Technical Demands and Historical Outline . . . . . . . . . . . . . . . . . . 1
1.2 Mechanical and Thermal Properties of Materials for High
Temperature Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Macroscopic (Effective) Properties of Two-Phase Composites . . 11
2 Thermodynamics of Constitutive Modelling of Damaged
Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Effect of Damage on the Mechanical and Thermal Properties
of Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Heat Conduction in Damaged Materials . . . . . . . . . . . . . . 13
2.1.2 Effect of Damage on the Elastic Stiffness of Materials . . 15
2.2 Thermodynamic Framework for Constitutive Modelling of
Elasto-Plastic-Damage Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 State Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Dissipation Coupling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.3 State and Dissipation Equations for Elasto-Plasticity
Coupled with Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.4 Unilateral Damage Concepts . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.5 Continuous Damage Deactivation. . . . . . . . . . . . . . . . . . . . 29
3 Developing and Implementing Selected Constitutive
Models for Elasto-Plastic-Damage Materials . . . . . . . . . . . . . . . 33
3.1 The Constitutive Model of Elastic-Damage Material . . . . . . . . . 33
3.1.1 Incremental Formulation of the Constitutive Equations . 33
XII Contents
3.1.2 Numerical Simulation of Damage and Fracture in
Plane Concrete Structure in the Presence of an Initial
Crack using the Local Approach. . . . . . . . . . . . . . . . . . . . . 40
3.1.3 Nonlocal Formulation of the Constitutive Equations . . . 45
3.1.4 Numerical Simulation of the Nonlocal Damage and
Fracture in a Double-Notched Plane-Stress Concrete
Specimen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.1.5 Numerical Simulation of Fracture in a Double-Notched
Plane-Stress Concrete Specimen by use of the
Nonlocal Equivalent Crack Concept. . . . . . . . . . . . . . . . . . 58
3.2 Constitutive Models of Elasto-Plastic-Damage Materials . . . . . . 61
3.2.1 The Modified Hayakawa–Murakami Constitutive
Model of Thermo-Elasto-Plastic-Damage Materials . . . . 61
3.2.2 Application to Monotonic and Cyclic Uniaxial Loading
Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.2.3 Prediction of Damage and Plastic Evolution in the
Plane notched FCD400 Cast Iron Specimen . . . . . . . . . . . 77
3.2.4 Low Cycle Fatigue of Specimen Made of 316L Stainless
Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.2.5 Influence of Unilateral Damage on the Yield Potential . . 90
4 Developing and Implementing Constitutive Models for
Specific FGM Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.1 Simulation Methodology for Properties Gradation in FGMs . . . 93
4.2 Application of the Concept of FGMs to Simple
Thermo–elasto–plastic Structures . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.2.1 Study of CrN/W300 TBC System Under Cyclic
Thermal Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.2.2 Stability Analysis Against the Hot-spots in a FG
Thermo–elastic Brake Disc . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.2.3 Modelling of FGM Al/ZrO2+Y2O3 Engine Pistons . . . . 117
4.3 Developing and Implementing Models of the Coupled
Thermo–elasto–plastic–damage FGMs for Thermomechanical
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.3.1 Extension of the Thermo–elasto–plastic–damage
Model by the FGMs Concept . . . . . . . . . . . . . . . . . . . . . . . 134
4.3.2 Prediction of Damage in the Plane-stress Notched
Specimen by use of FGMs Under Mechanical Loading . . 140
4.3.3 Analysis of a Problem with the ZrO2/FCD400
TBC/FGM/S System Under Thermal Loading . . . . . . . . 145
5 Microstructural Analysis and Residual Stress
Determination based on Scattering of Neutrons and
X-ray Synchrotron Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.1 Introduction to the Scattering of X-rays and Neutrons . . . . . . . 151
Contents XIII
5.1.1 Unperturbed beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.1.2 Interactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.2 Microstructural Investigations by Small Angle Scattering of
Neutrons and X-rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.2.2 Theoretical Bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.2.3 Experimental Methods and Data Analysis . . . . . . . . . . . . 166
5.2.4 Recent Applications to Materials of Technological and
Industrial Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
5.3 Residual Stress Determination by Neutron and X-ray
Diffraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
5.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
5.3.2 Residual Stress Classification . . . . . . . . . . . . . . . . . . . . . . . 178
5.3.3 Techniques for Residual Stress Determination . . . . . . . . . 178
5.3.4 Elastic Stress–Strain Relations . . . . . . . . . . . . . . . . . . . . . . 179
5.3.5 Principle of Strain Determination . . . . . . . . . . . . . . . . . . . 180
5.3.6 Experimental Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5.3.7 The Stress-free Reference Sample . . . . . . . . . . . . . . . . . . . . 183
5.3.8 Metal Matrix Composites . . . . . . . . . . . . . . . . . . . . . . . . . . 184
5.3.9 AA359 + 20 vol.% SiCp Brake Drum . . . . . . . . . . . . . . . . 185
5.3.10 MMC’s Drive Shaft for Helicopter . . . . . . . . . . . . . . . . . . . 187
5.3.11 Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
5.3.12 Cold Expanded Hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
5.3.13 Shot Peening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
5.3.14 Residual Stress Study of Laser Shock Peening for
Ti-6Al-4V Alloy for Aerospace Application . . . . . . . . . . . 191
5.3.15 Reed Pipe Brass Tongues of Historic Organs . . . . . . . . . . 192
5.4 Three-dimensional Imaging by Microtomography of X-ray
Synchrotron Radiation and Neutrons. . . . . . . . . . . . . . . . . . . . . . . 194
5.4.1 Tissue Engineered Bones . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
5.4.2 Al+4% ZS Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
5.4.3 Sintering of Cu Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
5.4.4 Al Foams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
5.5 Specific Investigations of Functionally Graded Materials
(FGM) Systems for High Temperature Applications . . . . . . . . . . 203
5.5.1 Residual Stresses in W/Cu FMG . . . . . . . . . . . . . . . . . . . . 204
5.5.2 Neutron Strain Mapping within Ni/Al2O3 . . . . . . . . . . . . 205
5.5.3 Residual Stresses in Ni/8Y–ZrO2 FGM. . . . . . . . . . . . . . . 206
5.5.4 Residual Stresses in WC/Co FGM . . . . . . . . . . . . . . . . . . . 206
5.5.5 Small Angle Scattering Experiments . . . . . . . . . . . . . . . . . 207
5.5.6 SAXS on a Thermal Barrier Coating . . . . . . . . . . . . . . . . . 208
5.5.7 Residual Stresses and SANS on Al2O3/Y–ZrO2 FGM . . 208
5.5.8 MicroCT on Al/SiCp FGM . . . . . . . . . . . . . . . . . . . . . . . . . 209
XIV Contents
A Appendix: European Sources of Neutrons and X-ray
Synchrotron Radiation and their Main Instrumentation . . . 211
A.1 Neutron Sources and Laboratories . . . . . . . . . . . . . . . . . . . . . . . . . 211
A.1.1 ILL Grenoble (France) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
A.1.2 ISIS (UK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
A.1.3 Laboratoire L′eon Brillouin (LLB) Saclay (France) . . . . 212
A.1.4 BENSC, Berlin (Germany) . . . . . . . . . . . . . . . . . . . . . . . . . 212
A.1.5 Other European Neutron Sources . . . . . . . . . . . . . . . . . . . . 212
A.2 Synchrotron radiation sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
A.2.1 ESRF Grenoble (France) . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
A.2.2 ELETTRA Trieste (Italy) . . . . . . . . . . . . . . . . . . . . . . . . . . 213
A.2.3 HASYLAB Hamburg (Germany) . . . . . . . . . . . . . . . . . . . . 213
A.2.4 SOLEIL Paris (France). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
A.2.5 DIAMOND Oxford (United Kingdom) . . . . . . . . . . . . . . . 214
A.2.6 Other European synchrotron sources . . . . . . . . . . . . . . . . . 214
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
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