MODELING CRYSTALLOGRAPHIC TEXTURE EVOLUTION WITH FINITE-ELEMENTS OVERNEO-EULERIAN ORIENTATION SPACES

A novel methodology is presented for the modeling of crystallographic texture based on the application of finite elements to represent and c ompute the orientation distribution function (ODF) over explicit discr etizations of orientation space. Various orientation spaces are examin ed for this purpose. The neo-Eulerian axis angle spaces of Frank are p referred over the conventional Euler angle spaces for their superior p roperties. Properties of the neo-Eulerian spaces required by the model ing are derived. These include the reduction of the spaces under cryst al symmetries to fundamental regions, the consequent boundary symmetry relationships, and the various Riemannian metrical properties of the spaces. The structure of crystal flow generated under the uniaxial ext ension of FCC crystals is examined over the cubic fundamental region o f Rodrigues' space. Stabilized finite element schemes for the ODF cons ervation equation, developed previously for the texturing of planar po lycrystals, are extended to the three-dimensional texturing considered . Properties of the schemes are illustrated by application to the text uring of FCC polycrystals over Rodrigues' space.