Nanomaterials Book

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 TEM 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 FurtherReading 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 111

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