The simulation of texture evolution with finite elements over orientation space II. Application to planar crystals Original Research Article

In a companion paper, a new class of finite element schemes was presented for the modeling of arbitrary polycrystalline microstructure. In this work, these schemes are applied to the idealization of a planar microstructure. Reorientation velocities, obtained under particular macro-micro linking hypothesis and crystal constitutive relations, are examined over a range of rate sensitivities, and for a range of planar crystal geometries. It is shown that, under monotonic deformations, equilibria of the reorientation velocity determine the asymptotic structure of the developed reorientation entirely. A one-parameter characterization of reorientations by their asymptotic structures is developed, and exploited to display the entire range of reorientation structures in a set of bifurcation diagrams. Texturing representative of the range of qualitatively distinct reorientation structures is simulated using an updated Lagrangian finite element scheme.