Development of the calculating algorithms for elastic properties, linear thermal expansion coefficients and yield stresses of textured Zr-Nb alloys taking into account the substructural inhomogeneity

Currently, most calculations of the anisotropy of the physical and mechanical properties of textured products are based on the properties of the single crystal and the actual information about the texture of the material, that is, the orientation distribution function. On the other hand, it is known that grains of different crystallographic orientations have different subsubstructure parameters, including the degree of crystalline lattice distortion (b) and the magnitude of elastic microstrains (∆d / d). Determination of these parameters is possible with the X-ray method of Generalized Pole Figures, consisting in the registration of the whole X-ray reflection profile for every point of orientation space, which can be realized under the pole figure recording. The presence of such substructural heterogeneity affects the stored elastoplastic (viscoelastic) energy of the polycrystalline material and, consequently, the value of such properties as elastic moduli, coefficients of linear thermal expansion, yield stresses and others. Previously, the authors proposed an algorithm for taking into account lattice microstrains when calculating the elastic properties and linear thermal expansion coefficients, based on minimizing elastic energy, the effectiveness of which was demonstrated on samples of the Zr-2.5 % Nb alloy. However, the possible influence of the additional bcc-(Nb, Zr) phase, which is present in this alloy, was not taken into account. In this work, we further develop the methodology for calculating the anisotropy of elastic properties, thermal expansion coefficients and yield stresses for the case of dual-phase zirconium products on the basis of generalized direct pole figures and the database of different properties for single crystals of α- and β-phases in Zr-Nb alloy.