The Development of Deformation Textures Described by an Orientation Flow Field

The mean orientation change δg of crystals of the orientation g in a polycrystalline material due to plastic deformation can be described (under certain assumptions) by an orientation flow field δg(g) = dη·ν(g) where dη is the absolute value of a small deformation step. The flow field ν(g) is a vector field in the orientation space g = {φ1, Φ, φ2} which must obey a continuity equation. The flow field describes the texture changes due to plastic deformation. The components of the flow vector, as a function of the orientation g, can be represented in terms of a series expansion which must obey certain symmetry conditions. As an example, the flow field calculated according to the Taylor theory for {111}〈110〉 glide was calculated in 5-degree steps in the orientation space.