Microstructures; Polycrystalline; Probability and statistics
This paper focuses on the application of statistical continuum mechanics to the prediction of mechanical response of polycrystalline materials and microstructure evolution under large plastic deformations. A statistical continuum mechanics formulation is developed by applying a Green's function solution to the equations of stress equilibrium in an infinite domain. The distribution and morphology of grains (crystals) in polycrystalline materials is represented by a set of correlation functions that are described by the corresponding probability functions. The elastic deformation is neglected and a viscoplastic power law is employed for crystallographic slip in single crystals. In this formulation, two- and three-point probability functions are used. A secant modulus-based formulation is used. The statistical analysis is applied to simulate homogeneous deformation processes under uniaxial tension, uniaxial compression and plane strain compression of an FCC polycrystal. The results are compared to the well-known Taylor upper bound model and discussed in comparison to experimental observations.