Determination of volume fraction of the texture components in the Rodrigues fundamental region

The fundamental region of Rodrigues space was discretized with finite elements as Euler space was discretized with 5° cell structures. Texture components were modeled with Gaussian distributions in the Rodrigues fundamental region. Spherical texture components are described by a sphere with a Gaussian distribution centered at its ideal position. Ideal fiber orientations are represented by a straight line or a skeleton line in Rodrigues space. The usual fiber textures are represented by a tube with a Gaussian distribution centered along a fiber line in Rodrigues space. The volume fractions of typical texture components can be collected by misorientation approach. The volume collections of spherical components of interest begin with the calculation of misorientation angles between the ideal components and their adjacent orientations. The radius of the orientation sphere is an angular distance. Adjacent components with smaller misorientation angles than a given criterion or a cut-off value locate inside the sphere and contribute to the volume fraction of the spherical component. For fibers, angular distances between the orientations along a skeleton line and adjacent orientations are compared with a cut-off. In addition, discretization effects of the Rodrigues fundamental region on the ODF and texture analysis were investigated. The volume fractions of texture components measured from a cold-rolled gold sheet and bonding wire were analyzed using the misorientation approach proposed.