From MMGWiki
Spectral formulation of Microstructure Sensitive Design (MSD) is able to reproduce the essential predictive capabilities of the Taylor-type model for polycrystals. It is demonstrated that it is possible to tremendously speed up the crystal plasticity calculations in metals by implementing a database approach that is combined with a local spectral interpolation using Discrete Fast Fourier Transform (DFFT) methods. Specifically, it was seen that the stresses, the lattice spins, and the strain hardening rates predicted by the Taylor-type crystal plasticity model for individual grains in an arbitrary deformation mode can be efficiently stored as a function of their lattice orientation. The approach revealed tremendous savings in the computational time, and provides a significant incentive for incorporation into the finite element simulations of bulk deformation processing operations. The significantly improved computational speed of the DFFT method also provided a remarkable reduction in the computational time involved in the delineation of the uniform ductility-ultimate tensile strength closures. Figures a) below show a typical comparison of the predicted texture (shown as pole figures) corresponding to a true compressive strain of -1.0 in plane strain compression and strain of 1.0 in simple shear obtained from the spectral crystal plasticity framework described above and the corresponding predictions from a Taylor-type model. It is seen that these two predictions are in excellent agreement with each other. The corresponding predictions of the stress-strain responses are shown in the figure (b).
