Linear analysis of texture–property relationships using process-based representations of Rodrigues space

Techniques for exploring texture–property–process relationships in various deformation processes are derived from a reduced-order model of texture evolution. The orientation distribution function (ODF) in polycrystals is represented over the Rodrigues space in a discrete form using finite element interpolation techniques. Linear programming algorithms are developed for retrieving ODFs with extremal or optimal properties from the complete ODF space. The relationship of optimal textures with processing is addressed by representing texture evolution in a space of reduced basis coefficients called the process plane. This involves generation of orthogonal basis functions for representing spatial variations of the ODF in a given process using proper orthogonal decomposition. These basis functions are found to work in interpolatory and extrapolatory processing modes and allow representation of texturing for deviations in the process variables. Optimization problems are posed in the reduced space for retrieving textures with desired properties. A graphical technique is discussed that allows identification of optimal processing paths for reaching desired textures in association with process plane databases.