An analysis of texture and plastic spin for planar polycrystals

Abstract

A major source of induced anisotropy in metals undergoing large strain is the preferential reorientation of single crystals. We present a macroscopic description of this textural anisotropy for an idealized planar aggregate of single crystals with two slip systems. We derive an analytical expression for the plastic spin associated with crystallographic slip and use it to obtain an equation of evolution for the single crystal orientation. The single microstructural parameter that appears in this equation is defined in terms of the slip system geometry. We introduce a continuous distribution function to describe orientation of crystals in an aggregate and obtain analytical solutions to the conservation equation governing its evolution. Such solutions are either monotonic or periodic, depending upon the relative magnitudes of stretching, spin and the microstructural parameter. Using an orientation average, we determine the average plastic spin in terms of the microstructural parameter and a second rank tensor related to the anisotropy in the orientation distribution. Finally, for constant velocity gradients, we show that the eigenvectors of this tensor rotate with half the difference between the macroscopic and average plastic spins.