Re-evaluation of formulae for X-ray stress analysis in polycrystalline specimens with fibre texture

Abstract

The stress–strain relation presented by Tanaka, Akiniwa, Ito & Inoue [Jpn Soc. Mech. Eng. Int. J. Ser. A, (1999),42, 224–234] for X-ray stress analysis for polycrystalline specimens with fibre texture is re-examined. By introducing the symmetry of reciprocal lattices for constituent crystallites, the physical meaning of taking an average of the strains observed by X-ray diffraction and the validity of the approximation used are made clear. By applying the present treatment to a cubic specimen in the m{\overline 3}m point group,hklBragg reflections withh≠k≠lsplit into doublets owing to the existence of crystallites with two different orientations. The formulae derived for cubic polycrystalline specimens with 〈111〉 fibre texture in the biaxial state in the Reuss model are in good agreement with those given previously. This technique is applicable to polycrystalline specimens of any symmetry with fibre texture.