Statistical continuum theory for large plastic deformation of polycrystalline materials

This paper focuses on the application of statistical continuum mechanics to the prediction of mechanical response of polycrystalline materials and mic rostructure evolution under large plastic deformations. A statistical conti nuum mechanics formulation is developed by applying a Green's function solu tion to the equations of stress equilibrium in an infinite domain. The dist ribution and morphology of grains (crystals) in polycrystalline materials i s represented by a set of correlation functions that are described by the c orresponding probability functions. The elastic deformation is neglected an d a viscoplastic power law is employed for crystallographic slip in single crystals. In this formulation, two- and three-point probability functions a re used. A secant modulus-based formulation is used. The statistical analys is is applied to simulate homogeneous deformation processes under uniaxial tension, uniaxial compression and plane strain compression of an FCC polycr ystal. The results are compared to the well-known Taylor upper bound model and discussed in comparison to experimental observations. (C) 2001 Elsevier Science Ltd. All rights reserved.