Determination of the Elastic Tensor of a Textured Low-Carbon Steel

Abstract

The components of the elastic stiffness tensor of hot rolled low-carbon steel were determined using an ultrasonic pulse-echo-method. They were also calculated on the basis of X-ray texture measurements using the Hill approximation. The maximum deviation between experimental and calculated values is 3.5%. An influence of the slightly anisotropic grain structure on the elastic anisotropy could not be seen. and position of each crystallite is known, then the boundary conditions in the grain boundaries can be strictly taken into account and the polycrystal properties can be calculated straight foreward. However, this is usually not the case. Certain statistical assumptions must then be made which lead to various approximative models for the polycrystal constants. In the Reuss model (Reuss, 1929), constant stress is assumed whereas the Voigt model (Voigt, 1928) assumes constant strain throughout the polycrystal. The polycrystal constants are then the simple volume averages of the components of the stiffness and compliance tensor of the individual crystallites, respectively. These assumptions are limiting cases, the actual values must lie between them. In a first approximation, knowing nothing about the microstructure, the average of both these assumptions can be taken, corresponding to the Hill approximation (Hill, 1952). It has been found that this approximation, although theoretically unsatisfactory, agrees with the experimen- tal results within a few percent, which is sufficient for most practical purposes. A theoretically much more satisfactory model was developed by Kr6ner (Kr6ner, 1958). In this model a spherical grain is embedded in a polycrystalline matrix