Premium
A general treatment of X‐ray (residual) macro‐stress determination in textured cubic materials: General expressions, cubic invariancy and application to X‐ray strain pole figures
Author(s) -
Brakman C. M.
Publication year - 1985
Publication title -
crystal research and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.377
H-Index - 64
eISSN - 1521-4079
pISSN - 0232-1300
DOI - 10.1002/crat.2170200503
Subject(s) - orthorhombic crystal system , isotropy , crystallography , cubic crystal system , pole figure , monoclinic crystal system , lattice (music) , materials science , diffraction , condensed matter physics , residual stress , geometry , texture (cosmology) , crystallographic point group , orientation (vector space) , crystal structure , mathematics , physics , optics , chemistry , composite material , image (mathematics) , artificial intelligence , computer science , acoustics
An expression in terms of general hkl and orientation distribution functions for the relationship between the elastic lattice strain measured by means of X‐ray diffraction methods and the (residual) elastic stress is given for cubic textured materials. In practice the socalled sin 2 Ψ‐method is often used to determine these macro stresses. Then, for the case of textured specimens the quasi‐isotropic X‐ray elastic constants (depending on hkl only) become complicated functions of the crystallographic texture (J. Appl. Crystallogr. 16 , 325 (1983)). Results are given for both orthorhombic and monoclinic specimen symmetry in terms of general (b.c.c. or f.c.c.) hkl and allow every permutation possible for a given hkl combination. From this cubic invariancy some new cubic invariant spherical surface harmonics are derived which are represented on a basis consisting of the 4‐fold symmetry axes of the cubic crystals. Special textures and special stress‐states are discussed. For a given texture of a cold‐rolled production steel sheet values of the predicted elastic strains are given in terms of “X‐ray strain pole figures”.