Calculation of X-Ray Stress Factors Using Vector Parameterization and Irreducible Representations for SO(3) Group
In the presence of texture, the concept of X-ray elastic constants as well as Sin2ψ law is inapplicable and the X-ray stress factors (XSF) connecting average strain and stress have to be used [1-2]. The SO(3) vector parameterization with smart composition law [3-4] proved to be a powerful tool for handling transformations between reference systems used in XSF calculation. Decomposition of the 4-th rank elastic constant tensor on the SO(3) irreducible representations (IR) allows one to highlight the symmetry properties and to separate isotropic and anisotropic parts. Joint use of the vector parameterization and IR decomposition enables to obtain transparent analytical expressions for XSF in case of textures described by preferred spherical/fiber components.
Paolo Scardi and Cristy L. Azanza Ricardo
A. Benediktovich et al., "Calculation of X-Ray Stress Factors Using Vector Parameterization and Irreducible Representations for SO(3) Group", Materials Science Forum, Vol. 681, pp. 387-392, 2011