A 2-D texture study based on a double-slip model of polycrystal plasticity with analysis of thin-walled tubes under torsion

Abstract

Elastic-plastic polycrystals are analyzed by means of a planar double-slip model. The analysis uses Taylor's assumption of uniform strain within all grains. Due to the consideration of elastic behavior, a general planar stress and strain state can be determined. Crystal hardening has been incorporated naturally into the framework of texture evolution. The concept of orientation distribution function (ODF) has been used together with its evolution equation. The overall stress components of the polycrystals are obtained analytically by the orientation (ODF) averaging. This model has then been applied to discuss the texture formation of thin-walled tubular specimens subjected to torsion. The differences between simple shear, simple (fixed-end) torsion, and pure (free-end) torsion are discussed in detail and a unified analytical solution is presented. It has been found that the theoretical axial stress of simple torsion is twice as large as that of simple shear. It has also been discovered that the development of hoop strain is directly related to the texture development during a torsion test of tube. The model also predicts the phenomenon of ‘tilting‘ of the ideal texture orientation, which has been experimentally observed. The theoretical results show very good agreement with experimental data of high purity aluminum. It may be concluded that the present model can provide a reasonable description of the torsion tests in the large strain range.