Representation of the orientation distribution function and computation of first-order elastic properties closures using discrete Fourier transforms

The orientation distribution function (ODF) is most commonly described in the Bunge–Euler space using generalized spherical harmonics (GSH) as a Fourier basis. In this paper, we explore critically the relative advantages and disadvantages of using an alternate description of the ODF using the much more readily accessible discrete Fourier transforms (DFTs). Appropriate protocols to address the consideration of crystal and sample symmetries in the DFT representations of ODFs have been developed and validated in this paper. It was also observed that the representation of first-order texture-elastic property linkages using DFTs needed a higher number of terms compared to the GSH representations. However, the use of DFT representations resulted in major computational economy in producing the ODF plots as well as the delineation of the property closures. It is shown that the improved computational efficiency facilitated the delineation of the first-order elastic property closures involving the normal–shear coupling stiffness coefficients.