Crystal Elasticity. Pascal Gadaud

      

Table of Contents

      1  Cover

      2  Dedication

      3  Title Page

      4  Copyright

      5  Introduction

      6  PART 1: Crystal Elasticity: Dimensionless and Multiscale Representation 1 Macroscopic Elasticity: Conventional Writing 1.1. Generalized Hooke‘s law 1.2. Theory and experimental precautions 2 Macroscopic Elasticity: Dimensionless Representation and Simplification 2.1. Cubic symmetry: cc and fcc metals 2.2. Hexagonal symmetry 2.3. Other symmetries 2.4. Problem posed by cubic sub-symmetries 3 Crystal Elasticity: From Monocrystal to Lattice 3.1. Discrete representation 3.2. Continuous representation for cubic symmetry 3.3. Continuous representation for the hexagonal symmetry 4 Macroscopic Elasticity: From Monocrystal to Polycrystal 4.1. Homogenization: several historical approaches and a simplified approach 4.2. Choice of “ideal” data sets and comparison of various approaches 4.3. Two-phase materials, inverse problem and textured polycrystals 5 Experimental Macroscopic Elasticity: Relation with Structural Aspects and Physical Properties 5.1. A high-performance experimental method 5.2. Elasticity of nickel-based superalloys 5.3. Elasticity and physical properties 5.4. Influence of porosity and damage on elasticity 5.5. The mystery of the diamond structure 5.6. What about amorphous materials? 5.7. Inelasticity and fine structure of crystals

      7  PART 2: Lagrangian Theory of Vibrations: Application to the Characterization of Elasticity Introduction to Part 2 6 Tension-Compression in a Cylindrical Rod 6.1. Tension-compression without transverse deformation 6.2. Tension-compression with transverse deformation 6.3. Determination of E and v of isotropic and anisotropic materials 7 Beam Bending 7.1. Homogeneous beam bending without shear 7.2. Homogeneous beam bending with shear 7.3. Application to the characterization of the elasticity of bulk materials 7.4. Composite beam bending (substrate + coating) 7.5. Composite beam bending (substrate + “sandwich” coating) 7.6. Application to the characterization of single coatings 7.7. Three-layer beam bending 7.8. Multi-layered and with gradient in elastic properties of materials 8 Plate Torsion 8.1. Torsion of homogeneous cylinder 8.2. Torsion of homogeneous plate 8.3. Determination of the shear modulus and Poisson’s ratio for bulk materials 8.4. Torsion of composite plate 9 Thin Plate Bending 9.1. Bending vibrations of a homogeneous thin plate 9.2. Application to the characterization of thin plate elasticity 10 Vibration Measurements and Macroscopic Internal Stresses 10.1. Experimental evidence of the relaxation of the internal stresses of bulk materials 10.2. Internal stresses and homogeneous beam vibration 10.3. Analysis of the profile of internal stresses of coated materials (static case) 10.4. Influence of internal stresses on the vibrations of coated materials 10.5. Application to the determination of internal stresses of coated materials

      8  Conclusion

      9  References

      10  Index

      11  End User License Agreement

      List of Tables

      1 Chapter 4Table 4.1. Discrete data of the elasticity of cubic symmetry (Cij in GPa, Sij in...Table 4.2. Discrete data of the elasticity