N-site modeling of a 3D viscoplastic polycrystal using Fast Fourier Transform

We present a formulation to compute the local response of elastic and viscoplastic anisotropic 3D polycrystals based on the Fast Fourier Transform (FFT) algorithm. This formulation is conceived for periodic heterogeneous microstructures and also for materials with random spatial distribution of heterogeneities. The approach is of the n-site kind, provides an exact solution of the equilibrium equation and has better numerical performance than small-scale FEM. The viscoplastic FFT formulation combined with an ad-hoc microstructure updating scheme is used to predict local states, morphology and texture evolution of ideal f.c.c. polycrystals. The model predicts strain localization, intragranular misorientation and subgrain formation and overall textures which are smoother than those obtained with classical 1-site schemes, in better agreement with experiments.