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The Influence of Cylindrical Geometry on X‐ray Stress Tensor Analysis. I. General Formulation
Author(s) -
François M.,
Dionnet B.,
Sprauel J. M.,
Nardou F.
Publication year - 1995
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889895006868
Subject(s) - diffraction , tensor (intrinsic definition) , translation (biology) , geometry , cauchy stress tensor , symmetry (geometry) , rotation (mathematics) , plane stress , stress (linguistics) , plane (geometry) , infinitesimal strain theory , texture (cosmology) , strain rate tensor , x ray , materials science , orientation (vector space) , physics , mathematical analysis , optics , mathematics , computer science , finite element method , chemistry , image (mathematics) , thermodynamics , biochemistry , linguistics , philosophy , artificial intelligence , messenger rna , gene
Stress analysis by X‐ray diffraction, usually performed on a specimen with plane geometry, becomes very difficult on more complex surfaces. A model is proposed to calculate the six independent components of the stress tensor for cylindrical symmetry. The mathematical approach described highlights two distinct effects that modify values of measured strain by X‐ray diffraction, a rotation effect and a translation effect. The X‐ray absorption by the material is taken into consideration and two models are proposed to undertake the mathematical processing on thick materials and thin layers. It is equally possible to take into account, for example, crystallographic texture and experimental features as ϕψ oscillations., Examples and applications will be given in paper II [Dionnet, François, Sprauel & Nardou (1995). In preparation].