Preface ...................................................... XVII
List of Contributors .......................................... XXI
Part I General ................................................. 1
1 Microstructure and Properties of Engineering Materials ....... 3
Helmut Clemens and Christina Scheu
1.1 Introduction ............................................ 3
1.2 Microstructure .......................................... 5
1.2.1 Crystal Defects .................................. 8
1.2.2 Grain (Phase) Boundaries and Twins ............... 8
1.2.3 Precipitates and Dispersions ..................... 9
1.3 Microstructure and Properties .......................... 12
1.4 Microstructural Characterization ....................... 15
References .................................................. 20
2 Internal Stresses in Engineering Materials .................. 21
Anke Rita Pyzalla
2.1 Definition ............................................. 21
2.1.1 Stress Tensor, Strain Tensor, and Elasticity
Tensor .......................................... 21
2.1.1.1 Stress Tensor .......................... 21
2.1.1.2 Strain Tensor .......................... 22
2.1.2 Definitions, Residual Stresses .................. 24
2.1.2.1 Stress Equilibrium ..................... 24
2.1.2.2 Residual Macro- and Microstresses ...... 25
2.2 Origin of Residual Macro- and Microstresses ............ 27
2.2.1 Residual Stress Formation in Primary Forming
Processes ....................................... 29
2.2.2 Residual Stress Formation in Heat Treatment
Processes ....................................... 30
2.2.2.1 Residual Stresses in a Material
without Phase Transformation (Pure
Cooling Residual Stresses) ............. 30
2.2.2.2 Residual Stresses in a Material with
Phase Transformation ................... 31
2.2.2.3 Residual Stress Formation in Surface
Hardening Processes (Nitriding,
Carbo-Nitriding, and Case Hardening) ... 33
2.2.3 Residual Stress Formation in Forming
Processes ....................................... 34
2.2.3.1 Deep-Rolling Residual Stresses ......... 35
2.2.3.2 Cold Extrusion Residual Stresses ....... 37
2.2.4 Residual Stress Formation in Metal Cutting
Manufacturing ................................... 39
2.2.4.1 Grinding Residual Stresses ............. 40
2.2.5 Residual Stress Formation in Joining
Processes ....................................... 42
2.2.6 Residual Stress Formation in Coatings ........... 46
2.3 Relevance .............................................. 48
2.3.1 Failure due to Residual Stress Formation or
Residual Stress Relief Induced by Temperature
Changes ......................................... 49
2.3.2 Influence of Residual Stresses on Component
Failure Under Static and Dynamic Mechanical
Loads ........................................... 50
2.3.3 Influence of Residual Stresses on Component
Failure in Corrosive Environments ............... 53
2.3.4 Influence of Residual Stresses on Wear .......... 53
References .................................................. 55
3 Texture and Texture Analysis in Engineering Materials ....... 57
Heinz-Cünter Brokmeier and Sang-Bong Yi
3.1 Introduction ........................................... 57
3.2 Pole Figures ........................................... 60
3.3 Texture Measurements on Laboratory Scale ............... 62
3.3.1 X-ray Diffraction ............................... 62
3.3.2 Electron Diffraction ............................ 63
3.4 Texture Measurements at Large-Scale Facilities ......... 65
3.4.1 Neutron Diffraction ............................. 65
3.4.1.1 Texture of Semifinished Products ....... 68
3.4.2 Texture Analysis Using Synchrotron X-rays ....... 70
3.4.2.1 Local Texture Measurement in an
Extruded Mg Rod ........................ 73
3.4.2.2 Global Texture in Cu Wire .............. 74
3.4.2.3 In situ Texture Measurement at
Elevated Temperatures .................. 74
3.4.2.4 In situ Texture Measurement Under
Loading ................................ 75
References .................................................. 76
4 Physical Properties of Photons and Neutrons ................. 79
Andreas Schreyer
4.1 Introduction ........................................... 79
4.2 Interaction of X-Ray Photons and Neutrons with
Individual Atoms ....................................... 80
4.2.1 Neutrons ........................................ 81
4.2.2 X-Rays .......................................... 83
4.3 Scattering of X-Ray Photons and Neutrons from
Ensembles of Atoms ..................................... 86
References .................................................. 89
5 Radiation Sources ........................................... 91
5.1 Generation and Properties of Neutrons .................. 91
Wolfgang Knop, Philipp Klaus Pranzas, and Peter
Schreiner
5.1.1 Introduction .................................... 91
5.1.2 Generation of Neutrons .......................... 91
5.1.2.1 Research Reactors ...................... 91
5.1.2.2 Spallation Sources ..................... 93
5.1.3 Instrumentation ................................. 96
References ............................................. 97
5.2 Production and Properties of Synchrotron Radiation ..... 97
Rolf Treusch
5.2.1 Introduction .................................... 97
5.2.2 Properties of Synchrotron Radiation ............ 100
5.2.3 Sources of Synchrotron Radiation ............... 105
5.2.3.1 Bending Magnets ....................... 106
5.2.3.2 Wigglers and Undulators ............... 107
5.2.4 Outlook: Free Electron Lasers .................. 109
5.2.5 Summary ........................................ 111
References ................................................. 112
Part II Methods .............................................. 113
6 Introduction to Diffraction Methods for Internal Stress
Analyses ................................................... 115
Walter Reimers
6.1 General Aspects ....................................... 115
6.2 Principles of Diffraction Methods ..................... 116
6.3 Principles of Strain Determination by Diffraction
Methods ............................................... 118
6.4 Determination of the Stress-Free Interplanar Lattice
Distance do ........................................... 121
6.5 sin2Ψ -Technique ...................................... 122
6.6 Nonlinear Lattice Strain Distributions ................ 123
6.6.1 Anisotropy ..................................... 123
6.6.2 Strain/Stress Gradients ........................ 125
6.6.3 Shear Strains/Stresses ......................... 127
6.7 Diffraction Elastic Constants ......................... 128
6.7.1 Calculation of DEC ............................. 129
6.7.2 Experimental Determination of the DEC .......... 129
6.8 Experimental Set-up and Measuring Procedures .......... 130
6.8.1 Experimental Set-up ............................ 130
6.8.1.1 Diffractometers ....................... 130
6.8.1.2 Diaphragms ............................ 132
6.8.1.3 Detectors ............................. 132
6.8.2 Measuring Procedures ........................... 132
6.9 Overview on In-depth and Local Residual Stress
Analysis .............................................. 133
References ................................................. 134
7 Stress Analysis by Angle-Dispersive Neutron Diffraction .... 137
Peter Staron
7.1 Introduction .......................................... 137
7.2 Diffractometer for Residual Stress Analysis ........... 138
7.2.1 Set-up of a Diffractometer for Strain
Scanning ....................................... 138
7.2.2 Monochromator .................................. 139
7.2.3 Slit System .................................... 140
7.2.4 Sample Positioning ............................. 141
7.2.5 Detector ....................................... 141
7.3 Measurement and Data Analysis ......................... 142
7.3.1 Gauge Volume and Sample Positioning ............ 142
7.3.2 Data Reduction and Analysis .................... 144
7.3.2.1 Data Reduction and Peak Fitting ....... 144
7.3.2.2 Calculation of Stresses ............... 145
7.3.2.3 Macro and Microstresses ............... 247
7.3.2.4 Stress-Free Reference ................. 147
7.4 Examples .............................................. 148
7.4.1 Residual Stresses in Friction Stir Welded
Aluminum Sheets ................................ 148
7.4.2 Residual Stresses in Water-Quenched Turbine
Discs .......................................... 150
7.5 Summary and Outlook ................................... 152
References ................................................. 152
8 Stress Analysis by Energy-Dispersive Neutron Diffraction ... 155
Javier Roberto Santisteban
8.1 Introduction .......................................... 155
8.2 Time-of-Flight Neutron Diffraction .................... 155
8.2.1 TOF Peak Shape and Data Analysis Packages ...... 157
8.3 TOF Strain Scanners ................................... 159
8.3.1 Counting Times and Resolution .................. 160
8.3.2 Neutron Optics and Time Focusing ............... 163
8.4 A Virtual Laboratory for Strain Scanning .............. 164
8.5 Evolution of Intergranular Stresses ................... 168
8.6 TOF Transmission Analysis ............................. 170
8.6.1 Bragg Edges .................................... 172
8.6.2 Strain Mapping ................................. 172
8.6.3 Quantitative Phase Analysis .................... 172
8.6.4 Other Applications ............................. 174
8.7 Conclusions ........................................... 174
References ................................................. 175
9 Residual Stress Analysis by Monochromatic High-Energy
X-rays ..................................................... 177
René Valéry Martins
9.1 Basic Set-ups ......................................... 177
9.2 Principle of Slit Imaging and Data Reconstruction ..... 180
9.3 The Conical Slit ...................................... 181
9.3.1 Working Principle .............................. 181
9.3.2 Capabilities ................................... 182
9.3.3 Example ........................................ 183
9.4 The Spiral Slit ....................................... 184
9.4.1 Functional Principle ........................... 184
9.4.2 Capabilities ................................... 186
9.4.3 Example ........................................ 186
9.5 Simultaneous Strain Measurements in Individual Bulk
Grains ................................................ 188
9.6 Coarse Grain Effects .................................. 189
9.7 Analysis of Diffraction Data from Area Detectors ...... 191
9.8 Matrix for Comparison and Decision Taking Which
Technique to Use for a Specific Problem ............... 193
References ................................................. 193
10 Residual Stress Analysis by White High Energy X-Rays ....... 195
10.1 Reflection Mode ....................................... 195
Christoph Cenzel
10.1.1 Motivation ..................................... 195
10.1.2 Basic Relations in Depth-Resolved Energy-
Dispersive X-Ray Stress Analysis (XSA) in
Reflection Geometry ............................ 196
10.1.3 Experimental Set-up ............................ 199
10.1.4 Example for Depth-Resolved Residual Stress
Analysis by ED Diffraction ..................... 200
10.1.5 Concluding Remarks and Prospects ............... 205
References ................................................. 206
10.2 Transmission Mode ..................................... 207
Anke Rita Pyzalla
10.2.1 Motivation ..................................... 207
10.2.2 Experiment Set-up and Experimental Details .......... 208
10.2.2.1 Penetration Depth .......................... 208
10.2.2.2 Gauge Volume and Spatial Resolution ........ 209
10.2.2.3 Example for an Experiment Set-up ........... 211
10.2.3 Data Evaluation ..................................... 213
10.2.4 Examples ............................................ 214
10.2.5 Conclusions ......................................... 218
References ................................................. 218
11 Diffraction Imaging for Microstructure Analysis ............ 221
Thomas Wroblewski
11.1 Introduction, the Principle of Diffraction Imaging .... 221
11.2 The MAXIM Experiment at HASYLAB Beamline G3 ........... 222
11.3 Data Structure ........................................ 223
11.4 Strategies for Data Reduction and Visualization ....... 224
11.5 Outlook, Bulk Imaging ................................. 226
References ................................................. 228
12 Basics of Small-Angle Scattering Methods ................... 229
Philipp Klaus Pranzas
12.1 Common Features of a SAS Instrument ................... 229
12.2 Contrast .............................................. 230
12.3 Scattering Curve ...................................... 230
12.4 Power Law/Scattering by Fractal Systems ............... 232
12.5 Guinier and Porod Approximations ...................... 233
12.6 Macroscopic Differential Scattering Cross Section ..... 234
12.7 Model Calculation of Size Distributions ............... 235
12.8 Magnetic Structures ................................... 236
References ................................................. 237
13 Small-Angle Neutron Scattering ............................. 239
Philipp Klaus Pranzas
13.1 Nanocrystalline Magnesium Hydride for the Reversible
Storage of Hydrogen ................................... 240
13.2 Precipitates in Steel ................................. 242
13.3 SiO2 Nanoparticles in a Polymer Matrix - an
Industrial Application ................................ 245
13.4 Green Surfactants ..................................... 246
References ................................................. 248
14 Decomposition Kinetics in Copper-Cobalt Alloy Systems:
Applications of Small-Angle X-ray Scattering ............... 249
Günter Coerigk
14.1 Introduction .......................................... 249
14.2 ASAXS Fundamentals .................................... 249
14.3 Results of ASAXS Experiments Characterizing the
Decomposition in Copper-Cobalt Alloys ................. 252
14.4 Outlook ............................................... 255
14.5 Summary ............................................... 255
References ................................................. 256
15 B3 Imaging ................................................. 257
Wolfgang Treimer
15.1 Radiography ........................................... 257
15.1.1 Fundamentals ................................... 257
15.1.2 Interactions of Neutrons with Matter ........... 259
15.1.3 Geometries ..................................... 261
15.1.4 Resolution Functions ........................... 264
15.1.5 Image Degradation .............................. 267
15.1.6 Other Imaging Techniques ....................... 269
15.2 Tomography ............................................ 274
15.2.1 Mathematical Introduction ...................... 274
15.2.2 Slice Theorem, Shannon Theorem ................. 276
15.2.3 Image Reconstruction ........................... 277
15.3 New Developments in Neutron Tomography ................ 281
References ................................................. 285
16 Neutron and Synchrotron-Radiation-Based Imaging for
Applications in Materials Science - From Macro- to
Nanotomography ............................................. 287
Felix Beckmann
16.1 Introduction .......................................... 287
16.1.1 Attenuation-Contrast Projections ............... 287
16.1.2 Phase-Contrast Projections ..................... 288
16.1.3 Phase-Enhanced Projections ..................... 289
16.1.4 Direct Phase-Contrast Projections .............. 289
16.1.5 Indirect Phase-Contrast Projections ............ 290
16.2 Parallel-Beam Tomography .............................. 290
16.2.1 Measurement and Reconstruction ................. 291
16.2.2 Density Resolution and Detector Quality ........ 292
16.2.3 Data Evaluation and Visualization ............... 295
16.3 Macrotomography Using Neutrons ........................ 296
16.3.1 Experimental Set-up ............................ 296
16.3.2 Measurements and Results ....................... 297
16.4 Microtomography Using Synchrotron Radiation ........... 300
16.4.1 Beamline Optics ................................ 300
16.4.2 Experimental Set-up ............................ 301
16.5 Summary and Outlook ................................... 306
References ................................................. 306
17 μ-Tomography of Engineering Materials ...................... 309
Astrid Haibel
17.1 Advantages of Synchrotron Tomography .................. 309
17.2 Applications and 3D Image Analysis .................... 310
17.2.1 Discharging Processes in Alkaline Cells ........ 310
17.2.2 Microstructural Investigations of Nb3Sn
Multifilamentary Superconductor Wires .......... 312
17.2.3 Influence of the Foaming Agent on Metallic
Foam Structures ................................ 314
17.3 Image Artifacts ....................................... 316
17.3.1 Ring Artifacts ................................. 316
17.3.2 Image Noise .................................... 317
17.3.3 Edge Artifacts ................................. 318
17.3.4 Motion Artifacts ............................... 318
17.3.5 Centering Errors of the Rotation Axis .......... 319
References ................................................. 320
18 Diffraction Enhanced Imaging ............................... 323
Michael Lohmann
18.1 Introduction .......................................... 324
18.1.1 Basics ......................................... 324
18.1.2 Extinction Contrast ............................ 325
18.1.3 Principles of DEI .............................. 326
18.2 Experimental Set-up ................................... 328
18.3 Examples .............................................. 329
18.3.1 Complete Set of DEI Images ..................... 329
18.3.2 Material Science ............................... 329
18.3.3 Example of Mineralogical Investigations ........ 331
18.4 Conclusions ........................................... 332
References ................................................. 332
Part III New and Emerging Methods ............................ 333
19 3D X-ray Diffraction Microscope ............................ 335
Henning Friis Poulsen, Wolfgang Ludwig, and Søren Schmidt
19.1 Basic Set-up and Strategy ............................. 336
19.1.1 The 3DXRD Microscope ........................... 338
19.2 Indexing and Characterization of Average Properties
of Each Grain ......................................... 339
19.2.1 Application I: Nucleation and Growth Studies ... 340
19.2.2 Application II: Plastic Deformation ............ 341
19.2.3 Application III: Studies of Subgrains and
Nanocrystalline Materials ...................... 342
19.3 Mapping of Grains and Orientations .................... 343
19.3.1 Mode III: Mapping Grains in Undeformed
Specimens ...................................... 343
19.3.2 Mode IV: Mapping Orientations in Deformed
Specimens ...................................... 345
19.3.3 Application I: Recrystallization ............... 346
19.3.4 Application II: Grain Growth ................... 347
19.4 Combining 3DXRD and Tomography ........................ 348
19.4.1 Grain Mapping by Tomography .................... 349
19.5 Outlook ............................................... 350
References ................................................. 350
20 3D Micron-Resolution Laue Diffraction ...................... 353
Gene E. Ice
20.1 Introduction .......................................... 353
20.1.1 The Need for Polychromatic Microdiffraction .... 353
20.2 Theoretical Basis for Advanced Polychromatic
Microdiffraction ...................................... 355
20.2.1 Modified Ewald's Sphere Description of Laue
Diffraction .................................... 355
20.2.2 Qualitative Information: Phase, Texture,
Elastic Strain, Dislocation Density ............ 356
20.2.2.1 Phase ................................. 356
20.2.2.2 Texture ............................... 357
20.2.2.3 Dislocation Tensor .................... 357
20.2.2.4 Elastic Strain Tensor ................. 357
20.3 Technical Developments for an Automated 3D Probe ...... 357
20.3.1 Source ......................................... 358
20.3.2 Microbeam Monochromator ........................ 359
20.3.3 Nondispersive Focusing Optics .................. 361
20.3.4 Area Detector .................................. 361
20.3.5 Differential Aperture .......................... 361
20.3.6 Software ....................................... 362
20.4 Research Examples ..................................... 363
20.4.1 3D Grain Boundary Networks ..................... 363
20.4.2 Deformation Behavior and Grain Boundaries ...... 364
20.4.3 Deformation in Single Crystals ................. 365
20.4.4 Grain Growth on Surfaces and in Three-
Dimensions ..................................... 366
20.4.5 Anomalous Grain Growth ......................... 367
20.5 Future Prospects and Opportunities .................... 369
References ................................................. 370
21 Quantitative Analysis of Three-Dimensional Plastic Strain
Fields Using Markers and X-ray Absorption Tomography ....... 371
Kristoffer Haldrup and John A. Wert
21.1 Introduction .......................................... 371
21.2 Experimental Approach ................................. 372
21.2.1 Markers ........................................ 372
21.2.2 Particle Tracking and DGT Calculation .......... 372
21.2.3 Spatial Resolution ............................. 373
21.3 Results of Investigations ............................. 373
21.3.1 Homogeneous Deformation ........................ 373
21.3.2 Heterogenous Deformation ....................... 374
21.3.3 Microstructural Effects ........................ 375
21.4 Outlook ............................................... 376
References ................................................. 377
22 Combined Diffraction and Tomography ........................ 379
Anke Rita Pyzalla and Augusta Isaac
22.1 Introduction .......................................... 379
22.2 Experimental Set-up ................................... 380
22.3 Example: Combined Diffraction and Tomography for
Investigating Creep Damage Evolution .................. 381
22.3.1 Scientific Background .......................... 381
22.3.2 Experimental Details ........................... 381
22.3.2.1 Miniature Creep Device ................ 381
22.3.2.2 Tomography and Diffraction ............ 381
22.3.2.3 Material .............................. 382
22.3.3 Results ........................................ 382
22.4 Conclusions and Outlook ............................... 385
References ................................................. 386
Part IV Industrial Applications .............................. 387
23 Diffraction-Based Residual Stress Analysis Applied to
Problems in the Aircraft Industry .......................... 389
Peter Staron, Funda S. Bayraktar, Mustafa Koqak, Andreas
Schreyer, Ulrike Cihak, Helmut Clemens, and Martin Stockinger
23.1 Motivation ............................................ 389
23.2 Residual Stresses in Turbine Disks .................... 390
23.2.1 Introduction ................................... 390
23.2.2 Material ....................................... 391
23.2.3 Finite Element Modeling ........................ 393
23.2.4 Neutron Diffraction ............................ 395
23.2.5 Results ........................................ 396
23.2.5.1 In Situ Tensile Test .................. 396
23.2.5.2 Stresses in a Turbine Disk ............ 397
23.2.5.3 Stresses in a Thin Plate .............. 398
23.2.6 Summary ........................................ 400
23.3 Residual Stresses in Laser-Welded Al Joints ........... 400
23.3.1 Introduction ................................... 400
23.3.2 Materials and Welding .......................... 401
23.3.3 Neutron Diffraction ............................ 404
23.3.4 Stresses in Laser-Welded T-Joints .............. 405
23.3.5 Stresses in Laser-Welded Butt Joints ........... 407
23.3.6 Summary ........................................ 408
23.4 Conclusions ........................................... 409
References ................................................. 410
24 Optimization of Residual Stresses in Crankshafts ........... 413
Anke Rita Pyzalla
24.1 Introduction .......................................... 413
24.2 Experimental Determination of Residual Stresses
in Crankshafts ........................................ 414
24.3 Experimental Results and Implications ................. 416
24.4 Conclusions ........................................... 419
References ................................................. 419
Index ......................................................... 421
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