The Development of Deformation Textures Described by an Orientation Flow Field

H J Bunge,E Dahlem,H Klein,C Esling

doi:10.1155/tsm.6.181

Abstract

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.

Highlights

If a polycrystalline material is being deformed plastically this generally leads to the development of a deformation texture or, more generally speaking, to the modification of the existing texture of the material
If one takes the strain continuity and stress equilibrium conditions in the grain boundaries into account this leads to an inhomogenous distribution of the activated glide systems, to inhomogeneous strains and to inhomogeneous orientation changes from grain to grain and within each grain
One does not consider the individual grain but only the statistical mean value of the behaviour of a great number of grains a mean orientation change of all grains having the same orientation can be defined. It is represented by an orientation flow field in the orientation space

Summary

Textures Described by an Orientation Flow Field

The mean orientation change dig of crystals of the orientation g in a polyerystalline. Material due to plastic deformation can be described (under certain assumptions) by an orientation flow field dig(g) dr/.v(g) where dr/is the absolute value of a small deformation step. The flow field v(g) is a vector field in the orientation space g {(pl, 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. The flow field calculated according to the Taylor theory for. 111}(110) glide was calculated in 5-degree steps in the orientation space

INTRODUCTION

Calculation of the flow field according to the Taylor theory

Symmetries of the flow field

Numerical calculation of the flow field