THE EVOLUTION OF THE ANISOTROPY OF A POLYCRYSTALLINE AGGREGATE

THE MACROSCoPIc properties of a polycrystalline aggregate depend upon the orientational distribution of the single crystals. Here we determine how this distribution of orientations is established for a single crystal whose deformation is assumed to be identical to that of the aggregate. We first derive the equation of evolution for the orientation of a single crystal of arbitrary type that deforms through the mechanism of rate independent crystallographic slip. We then introduce an orientational distribution function to characterize how the orientations of the single crystals are distributed, and derive the equation of evolution for this function. We further consider an approximate representation of the orientational distribution function and derive the linear, first-order ordinary differential equations for the evolution of the coefficients associated with the anisotropic term of the representation. Solutions to these equations can be obtained numerically. These may be used, for example, to describe the development of anisotropy in numerical simulations of metal forming processes.