Stress and strain

Popa, N.C.

doi:10.1107/97809553602060000967

International Tables for Crystallography (2019). Vol. H. ch. 5.2, pp. 538-554
https://doi.org/10.1107/97809553602060000967

Chapter 5.2. Stress and strain

5.2. Stress and strain (pp. 538-554) | html | pdf | chapter contents |
N. C. Popa
- 5.2.1. The importance of determining stress and the diffraction method (p. 538) | html | pdf |
- 5.2.2. Strain and stress in single crystals, elastic constants and transformations (p. 538) | html | pdf |
- 5.2.3. Strain and stress in polycrystalline samples (pp. 540-542) | html | pdf |
  - 5.2.3.1. Types of strains and stresses, and the strain/stress orientation distribution function (pp. 540-541) | html | pdf |
  - 5.2.3.2. The mean and variance of the observable strain, the peak shift and broadening (pp. 541-542) | html | pdf |
- 5.2.4. Determining the strain/stress by diffraction (pp. 542-543) | html | pdf |
  - 5.2.4.1. Determining the macrostrain/stress (pp. 542-543) | html | pdf |
  - 5.2.4.2. Determining the microstrain (p. 543) | html | pdf |
- 5.2.5. Macrostrain/stress in isotropic samples: classical approximations (pp. 543-546) | html | pdf |
  - 5.2.5.1. The Voigt model (p. 544) | html | pdf |
  - 5.2.5.2. The Reuss model (pp. 544-545) | html | pdf |
  - 5.2.5.3. The Hill average (p. 545) | html | pdf |
  - 5.2.5.4. The Kroner model (p. 545) | html | pdf |
  - 5.2.5.5. The `sin²Ψ' method (pp. 545-546) | html | pdf |
  - 5.2.5.6. Determining the single-crystal elastic constants (p. 546) | html | pdf |
- 5.2.6. The hydrostatic state in isotropic polycrystals (pp. 546-547) | html | pdf |
- 5.2.7. Calculating the macroscopic strain/stress using spherical harmonics (pp. 547-552) | html | pdf |
  - 5.2.7.1. Strain expansion in generalized spherical harmonics: the Popa and Balzar approach (pp. 547-548) | html | pdf |
  - 5.2.7.2. The selection rules for all Laue classes (p. 548) | html | pdf |
  - 5.2.7.3. Generalized spherical harmonics of real type, and the WSODF index (pp. 548-549) | html | pdf |
  - 5.2.7.4. Determining the macrostrain/stress state of the sample (pp. 549-550) | html | pdf |
  - 5.2.7.5. Simplified (`short') harmonics representation of the peak shift, and the `mixed' representation (p. 550) | html | pdf |
  - 5.2.7.6. Implementation in Rietveld codes (pp. 550-551) | html | pdf |
  - 5.2.7.7. An application: determining the averaged macroscopic strain and stress tensors in a rolled uranium plate from time-of-flight neutron diffraction data (pp. 551-552) | html | pdf |
  - 5.2.7.8. Limitations of the spherical-harmonics approach and possible further developments (p. 552) | html | pdf |
- 5.2.8. The spherical-harmonics approach to strain broadening (pp. 552-553) | html | pdf |
  - 5.2.8.1. Ignoring the macrostrain variance (p. 552) | html | pdf |
  - 5.2.8.2. The double-dependent anisotropic strain breadth (DDASB) (pp. 552-553) | html | pdf |
  - 5.2.8.3. The `classical' limit of the DDASB (p. 553) | html | pdf |
- References | html | pdf |
- Tables
  - Table 5.2.1. The matrix C for all Laue groups represented by specific constraints (p. 540) | html | pdf |
  - Table 5.2.2. Quadratic and quartic forms for symmetries higher than triclinic (p. 545) | html | pdf |
  - Table 5.2.3. Assignment of functions $[T_l^\nu (\Phi, \beta \semi \Psi, \gamma)]$ to the coefficients $[g_{il}^\nu]$ (p. 549) | html | pdf |
  - Table 5.2.4. The real generalized spherical harmonics (p. 549) | html | pdf |
  - Table 5.2.5. The monomials j_μl(a₁, a₂, a₃) for l = 2, 4, 6 (p. 550) | html | pdf |
  - Table 5.2.6. The complete set of polynomials J_μl for l = 2, 4, 6 for all Laue groups (p. 551) | html | pdf |

Chapter 5.2. Stress and strain

Contents