X-Ray Investigation of Deformation of Polycrystalline Metals

On the Effect of Fiber Texture on the Elastic Constants

Abstract

There have been a number of methods proposed, of calculating the elastic constants of polycrystalline material from those of its constituent crystals. As the most fundamental boundary conditions of these methods, Reuß proposed an assumption that stress is uniform throughout the aggregate. On the other hand, Voigt proposed another assumption that it is strain that is uniform. They treated only those cases in which the constituent crystals are randomly oriented. However, most polycrystalline metals contain crystals with lattice orientations that are not random, but instead are aligned to some degree about a particular orientation or about a set of orientations because of the mechanical and thermal history of the metals. The elastic constants of a single crystal are generally anisotropic, and therefore, the elastic constants of a polycrystalline metal should be influenced by its preferred orientation or texture.
In the present paper, a method of estimating the bulk elastic constants of a polycrystalline metal with fiber texture is proposed, and the calculated results of a polycrystalline α-iron with [110] texture are presented as an example. Two kinds of bulk elastic constants are treated here. One is termed the mechanical elastic constant which is the constant averaged over all the crystals constituting polycrystalline aggregate. The other is termed the X-ray elastic constant which is the constant averaged over only the select crystals that are in the correct direction to satisfy Bragg's condition.
It is found from the results of α-iron that the X-ray elastic constants calculated on the basis of the Reuß condition are reduced about 20 percent by the development of [110] fiber texture. On the other hand, neither the X-ray elastic constants based on the Voigt condition nor the mechanical elastic constants are estimated to be decreased more than 5 percent by fibering.