Crystal Elasticity - Pascal Gadaud

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Résumé :

Introduction ix

Part 1. Crystal Elasticity: Dimensionless and Multiscale Representation 1

Chapter 1. Macroscopic Elasticity: Conventional Writing 3

1.1. Generalized Hooke's law 3

1.1.1. Cubic symmetry 4

1.1.2. Hexagonal symmetry 8

1.2. Theory and experimental precautions 10

Chapter 2. Macroscopic Elasticity: Dimensionless Representation and Simplification 13

2.1. Cubic symmetry: cc and fcc metals 14

2.2. Hexagonal symmetry 19

2.3. Other symmetries 27

2.4. Problem posed by cubic sub-symmetries 27

Chapter 3. Crystal Elasticity: From Monocrystal to Lattice 31

3.1. Discrete representation 31

3.2. Continuous representation for cubic symmetry 34

3.3. Continuous representation for the hexagonal symmetry 37

Chapter 4. Macroscopic Elasticity: From Monocrystal to Polycrystal 43

4.1. Homogenization: several historical approaches and a simplified approach 43

4.2. Choice of ideal data sets and comparison of various approaches 47

4.3. Two-phase materials, inverse problem and textured polycrystals 51

4.3.1. Two-phase materials 51

4.3.2. Reverse problem 52

4.3.3. Textured materials 54

Chapter 5. Experimental Macroscopic Elasticity: Relation with Structural Aspects and Physical Properties 57

5.1. A high-performance experimental method 57

5.2. Elasticity of nickel-based superalloys 60

5.2.1. Single-grained superalloy 61

5.2.2. Passage from cubic symmetry to transverse isotropic symmetry 62

5.2.3. Rafting 65

5.2.4. Precipitation in Inconel 718 66

5.3. Elasticity and physical properties 69

5.3.1. Phase transformations 69

5.3.2. Magneto-elasticity 72

5.3.3. Ferroelectricity and phase transformation 74

5.4. Influence of porosity and damage on elasticity 75

5.4.1. Isotropic porosity 75

5.4.2. Anisotropic porosity 77

5.4.3. Micro-cracks and extreme porosity 78

5.5. The mystery of the diamond structure 79

5.6. What about amorphous materials? 81

5.7. Inelasticity and fine structure of crystals 84

5.7.1. Relaxation of substitutional defects 85

5.7.2. Relaxation of interstitial defects 87

Part 2. Lagrangian Theory of Vibrations: Application to the Characterization of Elasticity 91

Introduction to Part 2 93

Chapter 6. Tension-Compression in a Cylindrical Rod 95

6.1. Tension-compression without transverse deformation 95

6.2. Tension-compression with transverse deformation 97

6.3. Determination of E and v of isotropic and anisotropic materials 98

Chapter 7. Beam Bending 101

7.1. Homogeneous beam bending without shear 101

7.2. Homogeneous beam bending with shear 103

7.2.1. Homogeneous beam bending with shear (rotation) 103

7.2.2. Homogeneous beam bending with shear (deformation) 107

7.2.3. Homogeneous beam bending with shear (comparison) 112

7.3. Application to the characterization of the elasticity of bulk materials 113

7.4. Composite beam bending (substrate + coating) 114

7.5. Composite beam bending (substrate + sandwich coating) 117

7.6. Application to the characterization of single coatings 117

7.7. Three-layer beam bending 120

7.8. Multi-layered and with gradient in elastic properties of materials 123

Chapter 8. Plate Torsion 127

8.1 Torsion of homogeneous cylinder 127

8.2. Torsion of homogeneous plate 128

8.3. Determination of the shear modulus and Poisson's ratio for bulk materials 131

8.4. Torsion of composite plate 134

Biographie:

Pascal Gadaud is a researcher at Institut P' at the French CNRS in Poitiers, where he has worked since 1989. This book covers his main research activities undertaken since 1997, namely the characterization of elasticity.