Prediction of ideal orientations and lattice rotations of FCC crystals in the equibiaxial tension loading: a rate-dependent crystal plasticity approach

Abstract

This paper focuses on the determination of the complete set of ideal orientations of FCC materials in the equibiaxial tension mode of deformation. The simulations are based on the numerical procedure developed by the authors in which, a rate-sensitive crystal plasticity model with Secant hardening law was employed. The resulting nonlinear system of equations is solved by the modified Newton–Raphson method. An Euler space scanning method is used to obtain the ideal orientations of a deformation mode. 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. To verify the accuracy of the presented Euler space scanning method for FCC crystal structures, the ideal orientations of plane strain compression loading are calculated and compared with the existing experimental results. It is observed that this method can predict all of the reported ideal orientations of this deformation mode accurately. Afterward, by applying this method to the equibiaxial tension mode of deformation, eight lines of ideal orientations E1–E8 are resulted. Finally, the major characteristics of the obtained ideal orientations along with the crystal evolution patterns are thoroughly discussed.