Preface ....................................................... vii
Acknowledgements ............................................... ix
Acronyms ....................................................... xv
1 Nanomaterials ................................................ 1
1.1 Length Scales and Nanotechnology ........................ 1
1.2 What are Nanomaterials? ................................. 3
1.3 Classes of Materials .................................... 5
1.4 Making Nanomaterials .................................... 6
1.4.1 Making dn Materials .............................. 6
1.4.2 Health Risks Associated with Nanoparticles ....... 7
1.4.3 Making Bulk Nanomaterials ........................ 8
1.5 Closing ................................................ 17
1.6 Suggestions for Further Reading ........................ 18
1.7 Problems and Directions for Research ................... 18
References .................................................. 19
2 Fundamentals of Mechanics of Materials ...................... 21
2.1 Review of Continuum Mechanics .......................... 21
2.1.1 Vector and Tensor Algebra ....................... 21
2.1.2 Kinematics of Deformations ...................... 25
2.1.3 Forces, Tractions and Stresses .................. 29
2.2 Work and Energy ........................................ 34
2.3 Field Equations of Mechanics of Materials .............. 35
2.4 Constitutive Relations, or Mathematical Descriptions
of Material Behavior ................................... 35
2.4.1 Elasticity ...................................... 36
2.4.2 Plastic Deformation of Materials ................ 43
2.4.3 Fracture Mechanics .............................. 53
2.5 Suggestions for Further Reading ........................ 57
2.6 Problems and Directions for Research ................... 57
References .................................................. 59
3 Nanoscale Mechanics and Materials: Experimental
Techniques .................................................. 61
3.1 Introduction ........................................... 61
3.2 NanoMechanics Techniques ............................... 62
3.3 Characterizing Nanomaterials ........................... 64
3.3.1 Scanning Electron Microscopy or SEM ............. 64
3.3.2 Transmission Electron Microscopy or ТЕМ ......... 65
3.3.3 X-Ray Diffraction or XRD ........................ 66
3.3.4 Scanning Probe Microscopy Techniques ............ 66
3.3.5 Atomic Force Microscopy or AFM .................. 68
3.3.6 In situ Deformation ............................. 68
3.4 Nanoscale Mechanical Characterization .................. 71
3.4.1 Sample and Specimen Fabrication ................. 71
3.4.2 Nanoindentation ................................. 72
3.4.3 Microcompression ................................ 74
3.4.4 Microtensile Testing ............................ 82
3.4.5 Fracture Toughness Testing ...................... 86
3.4.6 Measurement of Rate-Dependent Properties ........ 86
3.5 Suggestions for Further Reading ........................ 91
3.6 Problems and Directions for Research ................... 91
References .................................................. 91
4 Mechanical Properties: Density and Elasticity ............... 95
4.1 Density Considered as an Example Property .............. 95
4.1.1 The Rule of Mixtures Applied to Density ......... 96
4.1.2 The Importance of Grain Morphology ............. 101
4.1.3 Density as a Function of Grain Size ............ 103
4.1.4 Summary: Density as an Example Property ........ 105
4.2 The Elasticity of Nanomaterials ....................... 106
4.2.1 The Physical Basis of Elasticity ............... 106
4.2.2 Elasticity of Discrete Nanomaterials ........... 107
4.2.3 Elasticity of NanoDevice Materials ............. 110
4.3 Composites and Homogenization Theory .................. 1ll
4.3.1 Simple Bounds for Composites, Applied to
Thin Films ..................................... 113
4.3.2 Summary of Composite Concepts .................. 116
4.4 Elasticity of Bulk Nanomaterials ...................... 117
4.5 Suggestions for Further Reading ....................... 118
4.6 Problems and Directions for Research .................. 118
References ................................................. 119
5 Plastic Deformation of Nanomaterials ....................... 121
5.1 Continuum Descriptions of Plastic Behavior ............ 121
5.2 The Physical Basis of Yield Strength .................. 122
5.3 Crystals and Crystal Plasticity ....................... 128
5.4 Strengthening Mechanisms in Single Crystal Metals ..... 132
5.4.1 Baseline Strengths ............................. 133
5.4.2 Solute Strengthening ........................... 133
5.4.3 Dispersoid Strengthening ....................... 134
5.4.4 Precipitate Strengthening ...................... 135
5.4.5 Forest Dislocation Strengthening ............... 135
5.5 From Crystal Plasticity to Polycrystal Plasticity ..... 136
5.5.1 Grain Size Effects ............................. 138
5.5.2 Models for Hall-Petch Behavior ................. 138
5.5.3 Other Effects of Grain Structure ............... 150
5.6 Summary: The Yield Strength of Nanomaterials .......... 154
5.7 Plastic Strain and Dislocation Motion ................. 155
5.8 The Physical Basis of Strain Hardening ................ 156
5.8.1 Strain Hardening in Nanomaterials .............. 158
5.9 The Physical Basis of Rate-Dependent Plasticity ....... 160
5.9.1 Dislocation Dynamics ........................... 160
5.9.2 Thermal Activation ............................. 162
5.9.3 Dislocation Substructure Evolution ............. 166
5.9.4 The Rate-Dependence of Nanomaterials ........... 167
5.10 Case Study: Behavior of Nanocrystalline Iron .......... 172
5.11 Closing ............................................... 175
5.12 Suggestions for Further Reading ....................... 175
5.13 Problems and Directions for Research .................. 176
References ................................................. 176
6 Mechanical Failure Processes in Nanomaterials .............. 179
6.1 Defining the Failure of Materials ..................... 180
6.2 Failure in the Tension Test ........................... 183
6.2.1 Effect of Strain Hardening ..................... 184
6.2.2 Effect of Rate-Sensitivity ..................... 186
6.2.3 Multiaxial Stresses and Microscale Processes
Within the Neck ................................ 188
6.2.4 Summary: Failure in the Simple Tension Test .... 189
6.3 The Ductility of Nanomaterials ........................ 190
6.4 Failure Processes ..................................... 193
6.4.1 Nucleation of Failure Processes ................ 194
6.4.2 The Growth of Failures ......................... 195
6.4.3 The Coalescence of Cracks and Voids ............ 196
6.4.4 Implications of Failure Processes in
Nanomaterials .................................. 196
6.5 The Fracture of Nanomaterials ......................... 197
6.6 Shear Bands in Nanomaterials .......................... 201
6.6.1 Types of Shear Bands ........................... 203
6.6.2 Shear Bands in Nanocrystalline bcc Metals ...... 203
6.6.3 Microstructure Within Shear Bands .............. 207
6.6.4 Effect of Strain Rate on the Shear Band
Mechanism ...................................... 210
6.6.5 Effect of Specimen Geometry on the Shear Band
Mechanism ...................................... 210
6.6.6 Shear Bands in Other Nanocrystalline Metals .... 211
6.7 Suggestions for Further Reading ....................... 211
6.8 Problems and Directions for Research .................. 211
References ................................................. 212
7 Scale-Dominant Mechanisms in Nanomaterials ................. 215
7.1 Discrete Nanomaterials and Nanodevice Materials ....... 215
7.1.1 Nanoparticles .................................. 215
7.1.2 Nanotubes ...................................... 222
7.1.3 Nanofibers ..................................... 225
7.1.4 Functionalized Nanotubes, Nanofibers, and
Nanowires ...................................... 226
7.1.5 Nanoporous Structures .......................... 226
7.1.6 Thin Films ..................................... 227
7.1.7 Surfaces and Interfaces ........................ 227
7.2 Bulk Nanomaterials .................................... 228
7.2.1 Dislocation Mechanisms ......................... 228
7.2.2 Deformation Twinning ........................... 230
7.2.3 Grain Boundary Motion .......................... 235
7.2.4 Grain Rotation ................................. 236
7.2.5 Stability Maps Based on Grain Rotation ......... 251
7.3 Multiaxial Stresses and Constraint Effects ............ 256
7.4 Closing ............................................... 256
7.5 Suggestions for Further Reading ....................... 256
7.6 Problems and Directions for Research .................. 257
References ................................................. 257
8 Modeling Nanomaterials ..................................... 261
8.1 Modeling and Length Scales ............................ 261
8.2 Scaling and Physics Approximations .................... 267
8.3 Scaling Up from Sub-Atomic Scales ..................... 268
8.3.1 The Enriched Continuum Approach ................ 269
8.3.2 The Molecular Mechanics Approach ............... 269
8.4 Molecular Dynamics .................................... 274
8.5 Discrete Dislocation Dynamics ......................... 277
8.6 Continuum Modeling .................................... 278
8.6.1 Crystal Plasticity Models ...................... 278
8.6.2 Polycrystalline Fracture Models ................ 279
8.7 Theoretically Based Enriched Continuum Modeling ....... 280
8.8 Strain Gradient Plasticity ............................ 287
8.9 Multiscale Modeling ................................... 289
8.10 Constitutive Functions for Bulk Nanomaterials ......... 292
8.10.1 Elasticity ..................................... 292
8.10.2 Yield Surfaces ................................. 293
8.11 Closing ............................................... 294
8.12 Suggestions for Further Reading ....................... 295
8.13 Problems and Directions for Future Research ........... 295
References ................................................. 296
References .................................................... 299
Index ......................................................... 311
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