A kinematics perspective on the micro-to-macro transition in anisotropic plasticity modeling of polycrystalline solids

Abstract

Anisotropic plastic deformation of a polycrystalline solid involves processes spanning over a wide range of length and time scales (atomistic, dislocations dynamics, single crystal grains, and polycrystalline aggregates). At the microscopic level (discrete single crystal grains), the material is structurally heterogeneous, while at the macroscopic level, it is treated as a homogenous continuum element. A theoretical modeling methodology of using a discrete set of macroscopic slips is proposed for formulating phenomenological anisotropic plasticity flow theories. By viewing the major differences between a crystal plasticity (microscopic) model and an effective macroscopic plasticity model of a polycrystalline solid in terms of kinematical degrees of freedom, it is shown that effective macroscopic plasticity models can be developed, using an approach analogous to the crystallographic slips in single crystals. A simple anisotropic plastic flow model of monoclinic poly crystals under uniaxial tension is presented in the chapter to illustrate the new modeling methodology of macroscopic slips.