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

O.A. Krymskaya ORCID logo , M.G. Isaenkova, E.S. Zharikov, V.A. Fesenko show affiliations and emails
Received 30 August 2024; Accepted 15 October 2024;
Citation: O.A. Krymskaya, M.G. Isaenkova, E.S. Zharikov, V.A. Fesenko. 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. Lett. Mater., 2024, 14(4) 412-418
BibTex   https://doi.org/10.48612/letters/2024-4-412-418

Abstract

In our graphical abstract we tried to summarize the algorithms and show the main diargam of calculations.  
We hope that it's not very complicated for the perception)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.

References (30)

1. M. G. Isaenkova, Yu. A. Perlovich, Regularities of the development of crystallographic texture and substructural heterogeneity in zirconium alloys during deformation and heat treatment, NRNU MEPhI, 2014, 528 p. (in Russian) [М. Г. Исаенкова, Ю. А. Перлович, Закономерности развития кристаллографической текстуры и субструктурной неоднородности в циркониевых сплавах при деформации и термообработке, НИЯУ МИФИ, Москва, 2014, 528 с.].
8. D. Douglass, The metallurgy of zirconium, International atomic energy agency, Vienna, 1971, 466 p.
10. P. F. Prasolov, Anisotropy of elastic-plastic deformation of textured zirconium alloys: Prof. thesis, Moscow, Russia, 1992, 444 p. (in Russian) [П. Ф. Прасолов, Анизотропия упругопластического деформирования текстурованных сплавов циркония: дисс. на соискание ученой степени д. т. н., Москва, 1992, 444 с.].
11. H.-J. Bunge, N.-J. Park, H. Klein, Physical properties of Textured Materials, Cuviller Verlag, Gottingen, 1993, 150 p.
12. U. F. Kocks, C. N. Tome, H. R. Wenk Texture and anisotropy, Cambridge University Press, 1998, 675 p.
13. S. I. Novikova, Teplovoe racshirenie tverdyh tel, Nauka, Moscow, 1974, 294 p. (in Russian) [С. И. Новикова, Тепловое расширение твердых тел, Наука, Москва, 1974, 294 с.].
18. Z. L. Liu, High-efficiency calculation of elastic constants enhanced by the optimized strain-matrix sets (arXiv:2002.00005), Luoyang, China, 2020, 8 p.
19. High-performance computing center of NRNU MEPhI, Website: https://it.mephi.ru/hpc (accessed 9 August, 2024).
20. ISO 14577-1 Metallic materials-Instrumented indentation test for hardness and materials parameters. Part 1: Test Method, 2015, 46 p.
22. MTEX - Open software for analyzing and modeling crystallographic textures by means of EBSD or pole figure data, TU Chemnitz, Germany, Website: https://mtex-toolbox.github.io (accessed 9 August, 2024).

Funding

1. Ministry of Science and Higher Education of Russian Federation - 075-15-2021-1352