Effects of interactions among crystals on the inhomogeneous deformations of polycrystals

The deformations of model fcc polycrystals are studied using finite element simulations in which each element of the discretization is treated as a single crystal. The extent to which interactions between a crystal and its neighbors influence its deformation is examined by conducting a series of simulations. For each of these simulations the model polycrystal is constructed using a different spatial arrangement of the same set of crystals, so as to alter the neighborhood of each crystal. The deformation rate data for all the crystals obtained from these simulations are analyzed using the method of empirical eigenfunctions and using statistical methods. Variation of the deformation rate data with the Taylor factors of the crystal orientations as well as over three-dimensional space of Rodrigues' parameters is examined to study the dependence on orientation. The results show that interactions among crystals play a crucial role in determining the distribution of the applied deformation among them. Such interactions should be incorporated in averaging assumptions of polycrystal plasticity models to obtain improved predictions of crystallographic texture evolution.