On the interpretation of diffraction line-shift measurements on textured cubic materials

Applied SciencesApplied Science

Evaluation of the Integral ??1+1?Plm,n(x)Plm?2,n(x)?dx

Integrals of the type indicated can be evaluated using the Fourier-series development of the Jacobi-polynomials. An alternative procedure is given yielding an analytical expression in terms of l, m and n.Mechanical Maritime and Materials Engineerin

Cubic Invariant Spherical Surface Harmonics in Conjunction With Diffraction Strain Pole-Figures

Four kinds of cubic invariant spherical surface harmonics are introduced. It has been shown previously that these harmonics occur in the equations relating measured diffraction (line-shift) elastic strain and macro-stresses generating these strains for the case of textured cubic materials. As a consequence, these harmonics are important for the determination of unknown macro-stress tensor components if the o.d.f. expansion coefficients are known. On the other hand, they play a role in the determination of unknown o.d.f. expansion coefficients if the macro-stresses are known using for instance, a tensile test device on the diffractometer. Then, even the odd-order o.d.f. expansion coefficients can be obtained. In this paper, special attention is given to the mathematical construction of the cubic harmonics, the physical symmetry requirements they are subject to and some examples are given exhibiting both even and odd order harmonics.Mechanical Maritime and Materials Engineerin