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Crystal Elasticity
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Crystal Elasticity
by Pascal Gadaud
Crystal Elasticity
Cover
Dedication
Title Page
Copyright
Introduction
PART 1: Crystal Elasticity: Dimensionless and Multiscale Representation
PART 2: Lagrangian Theory of Vibrations: Application to the Characterization of Elasticity
Conclusion
References
Index
End User License Agreement
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Cover
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Dedication
Table of Contents
Cover
Dedication
Title Page
Copyright
Introduction
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
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
Conclusion
References
Index
End User License Agreement
List of Tables
Chapter 4
Table 4.1. Discrete data of the elasticity of cubic symmetry (Cij in GPa, Sij in...
Table 4.2. Discrete data of the elasticity of hexagonal symmetry (Cij in GPa, Si...
Table 4.3.
Simplified writing of various approaches for the cubic symmetry
Chapter 5
Table 5.1.
Elasticity–pressure coupling for several covalent materials
Chapter 7
Table 7.1.
Study of the scattering of the elasticity of submicron W films
Chapter 10
Table 10.1.
Values of the internal stresses analyzed by two methods
List of Illustrations
Chapter 2
Figure 2.1. Dimensionless representation of the elasticity of fcc and cc metals....
Figure 2.2. Evolution of elasticity with temperature for fcc and cc metals. For ...
Figure 2.3.
Evolution of the anisotropy of several metals with temperature
Figure 2.4. Correlation between the experimental ratio of moduli and dimensionle...
Figure 2.5. Experimental error on Poisson’s ratio. For a color version of this f...
Figure 2.6. Uncertainty on the dimensionless representation of the elasticity of...
Figure 2.7. Correlation with S11 and S33 of the three other constants: a) –S13, ...
Figure 2.8. Angular representation of the dimensionless elasticity of the hexago...
Figure 2.9. Dimensionless representation of the elasticity of all cubic sub-symm...
Chapter 3
Figure 3.1.
Insertion of atomic springs. For a color version of this figure, see
...
Figure 3.2. Simulation of a traction test on the lattice cell. For a color versi...
Figure 3.3. Spatial anisotropy of the representation of dimensionless elasticity...
Figure 3.4. Dependence of c/a ratio on anisotropy (hexagonal symmetry). For a co...
Chapter 4
Figure 4.1. Simulation of a traction test on polycrystal. For a color version of...
Figure 4.2. Dimensionless representation for the cubic symmetry of the elasticit...
Figure 4.3. Dimensionless representation for the hexagonal symmetry of the elast...
Figure 4.4. Anisotropy determination error related to experimental error measure...
Figure 4.5. Elastic anisotropy of five shades of textured copper alloys. For a c...
Figure 4.6.
Elastic anisotropy of a superalloy obtained by the additive method
Chapter 5
Figure 5.1.
Measurement head and its sample for free tests
Figure 5.2. Experimental setup for the dynamic resonant measurement of elasticit...
Figure 5.3. Single-grained superalloy. The vertical and horizontal directions co...
Figure 5.4. Evolution with temperature of the elastic constants of CSMX-4 supera...
Figure 5.5. Passage from the matrix of the pseudo-monocrystal to that of the tra...
Figure 5.6. Angular elasticity of a superalloy elaborated by directional solidif...
Figure 5.7.
Rafting during a creep test (loading along the vertical axis)
Figure 5.8. Evolution after creep of the elasticity of a single-grained superall...
Figure 5.9. Evolution with temperature of the elasticity of an Inconel 718 after...
Figure 5.10. Evolution of elasticity in time during the precipitation at 680°. a...
Figure 5.11.
TTT diagram of an Inconel 718
Figure 5.12. Evolution of the elasticity of CuAlNi during its transformation. Su...
Figure 5.13. Phase transformation of a titanium alloy. a) Evolution of elasticit...
Figure 5.14. Magneto-elastic coupling of pure nickel (Ben Dhia 2016). For a colo...
Figure 5.15. Amplitude of ΔE effect as a function of the stress level. Adapted f...
Figure 5.16. Evolution of the elasticity of PZT ceramics with temperature (Ben D...
Figure 5.17. Observation of the pores on the surface of a sample of porous silve...
Figure 5.18. Evolution of the Young’s modulus of sintered silver depending on po...
Figure 5.19. Young’s modulus of aluminum of additive manufacturing as a function...
Figure 5.20.
Micro-cracked electrolytic chromium
Figure 5.21. Effect of pressure on the Young’s modulus and damping of silicon (B...
Figure 5.22. Elasticity of SeGe system. a) Rough representation. b) Rationalized...
Figure 5.23. Dimensionless elasticity of amorphous materials. For a color versio...
Figure 5.24. Isothermal damping spectra of a γ’-Ni3Al polycrystal (Gadaud and Ch...
Figure 5.25. Arrhenius diagram for the relaxation of Ni in Ni3Al (Gadaud and Cha...
Figure 5.26. Isothermal damping spectra of YBCO superconductor (Gadaud and Kaya ...
Chapter 6
Figure 6.1. Elasticity as a function of temperature for an isotropic titanium al...
Figure 6.2. Elasticity as a function of temperature for an anisotropic superallo...
Chapter 7
Figure 7.1. Relative variation of the Young’s modulus measured during bending by...
Figure 7.2.
Elasticity of a high-entropy alloy depending on its stoichiometry
Figure 7.3. Comparison of the elasticity of porous silver under massive form or ...
Figure 7.4. Influence of thickness on the apparent elasticity of a SiC coating d...
Figure 7.5.
Superalloy + anticorrosive platinum aluminide + thermal barrier
Figure 7.6. Elasticity with temperature of the superalloy + anticorrosive platin...
Figure 7.7. Evolution of elasticity near the surface of nitrided steel. Adapted ...
Figure 7.8. Elasticity profile perpendicular to a welding by friction. Adapted f...
Chapter 8
Figure 8.1. Comparison of dispersion in the measurement of Poisson’s ratio with ...
Figure 8.2. Evolution of Poisson’s ratio with temperature for various materials ...
Figure 8.3. Evolution with temperature of Young’s and shear moduli for a high-en...
Figure 8.4. Evolution with temperature of Young’s and shear moduli of porous bul...
Chapter 9
Figure 9.1. Vibration mode on a quarter of the plate. For a color version of thi...
Chapter 10
Figure 10.1. Evidence of the relaxation of elaboration stresses for an HIP sinte...
Figure 10.2. Evidence of the relaxation of elaboration stresses for rolled steel...
Figure 10.3. Evidence of the relaxation of elaboration stresses of AlPtNi coatin...
Figure 10.4. Evidence of the relaxation of elaboration stresses of a porous silv...
Guide
Cover
Table of Contents
Title Page
Copyright
Introduction
Begin Reading
Conclusion
References
Index
End User License Agreement
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