Computational modeling of crystallographic texture evolution over cubochoric space

Abstract

The present work addresses representation of texture evolution in face-centered cubic (fcc) microstructures in cubochoric orientation space. The microstructure is quantified with the orientation distribution function (ODF), which models volume density in the fundamental region of crystallographic space. The ODF is discretized using a finite element scheme in the cubochoric fundamental region. This scheme shows superior features over the classical techniques in global spaces, such as spherical harmonics or Fourier space solutions, since it can represent a large variety of textures, including very sharp textures such as a single crystal. The texture evolution during a particular deformation process is associated with the evolution of the ODF in time, which is governed by the conservation equation and crystal constitutive relations. The transformation in between cubochoric space and other popular angle-axis representation such as Rodrigues space is performed with a two-step approach including the transformations from Rodrigues domain to homochoric domain, and homochoric domain to cubochoric domain through a numerical scheme. The ODF evolution in an fcc material during different deformation processes, such as tension, plane strain compression and shear, is compared across both Rodrigues and cubochoric spaces, and similar patterns are observed.