X-ray Strain Analysis and Elastic Anisotropy of Textured Metals

Abstract

The stress and strain in each grain in a rolled steel during uniaxial elastic deformation were analyzed by the finite element method using a plane model of polycrystals, and the influence of texture on the elastic constants of the bulk specimen and that on the lattice strain in the grains reflecting X-rays were studied. The stress in a grain was affected by the restraint on it and by its shape. In the case of a model with elliptical grains, the mode of deformation was close to the condition of uniform local strain, and the influence of the restraint on the grains was small when the shape of the grains was prolate in the direction of the applied stress. On the other hand, the mode was close to the condition of uniform local stress, and the influence of the restraint was large when the shape was oblate. The elastic constants of the bulk specimen were affected by the texture, their values being dependent on the restraint condition of the grains and on the shape of grains. The lattice strain was not linearly related to sin2 Ψ for those metals with texture in X-ray stress measurements. The relationship between the lattice strain and sin2 Ψ was greatly affected by the texture, and the influence of the deformation behavior of polycrystals was small for the 211 reflection. In the sin2 Ψ diagram, the influences of the restraint and shape of grains were relatively small, and the results calculated by the present model are close to those of the uniform local stress model for the 310 reflection.