Ideal orientations of BCC crystals under equibiaxial tension loading

Abstract

Ideal orientations are one of the material characteristics of the applied mode of deformation. The transfer of material texture to orientations near specific ideal orientations can improve the mechanical properties of the material. In this paper, we focus on the determination of ideal orientations of BCC crystals under the equibiaxial tension mode of deformation. To do this, an Euler space scanning method based on a crystal plasticity approach is presented. In this method some initial orientations which are evenly spaced in the Euler space are selected and their evolutions into the ideal orientations are tracked. The loading is applied incrementally until all of the lattice spin components become permanently zero. The rate sensitive crystal plasticity model with power law hardening is employed and the resulting nonlinear system of equations is solved by the modified Newton–Raphson method. In order to verify the simulation results, the ideal orientations of rolling textures are calculated. A comparison of the obtained results with the existing experimental data demonstrates that all of the reported ideal orientations are satisfactorily predicted. Afterward, preferred orientations for equibiaxial tension mode of deformation which have not been reported previously in the literature are calculated. This analysis resulted in eight fibers EF1–EF8 together with a plane of ideal orientations for equibiaxial tension loading. The effects of symmetry of the crystal structure and loading on the obtained ideal orientations are finally discussed.