DOI:10.52150/2522-9117-2026-40-031
M. Yu. Ambrazhei1,*, Ph. D. Student, ORCID 0000-0002-6564-4312
1 Iron and Steel Institute of Z. I. Nekrasov NAS of Ukraine
* Corresponding author: ambrazhey@gmail.com
METHOD FOR EVALUATING THE FINE STRUCTURE EVOLUTION
OF LOW-CARBON STEEL DURING THE PRODUCTION OF STABILIZED COLD-DEFORMED REINFORCING STEEL
Abstract. A method for estimating the parameters of the fine structure of low-carbon steel SAE1018 during complex combined processing is proposed. The method of X-ray structural analysis of diffraction line profiles is chosen as the main tool for conducting research. A comparative analysis of two methods for separating the influence of dimensional and deformation effects on the true physical broadening of diffraction maxima is performed. It is established that the classical method of Warren-Averbach harmonic analysis has certain limitations for highly textured steel, which is due to the occurrence of systematic mathematical artifacts (false zeroing of microstrains) due to the inversion of Fourier amplitude coefficients. It is shown that for the correct quantitative estimation of the parameters of the substructure of steel SAE1018, which is characterized by a pronounced texture, it is necessary to apply the Halder-Wagner method, which takes into account the integral characteristics of the X-ray profile and is much more resistant to the influence of the anisotropy of the structure. Automation of mathematical processing of diffraction data arrays, deconvolution of Stokes profiles and approximation by Gauss and Lorentz functions is implemented using the author’s algorithm developed in the Python programming language using the NumPy and SciPy libraries. The evolution of the fine structure of low-carbon steel SAE1018 at different technological stages of manufacturing stabilized cold-deformed reinforcement in coils is studied and described. It is shown that after thermal strengthening of wire rod from SAE1018 steel, a multiphase structure with a high density of dislocations on the surface of the rolled product and significant microdeformations of the crystal lattice in the central part is formed. It is established that cold plastic deformation of the wire rod with subsequent profiling of its surface leads to an increase in microdeformations and elongation of grains and subgrains along the drawing direction, and the final stabilizing mechanocyclic treatment initiates various mechanisms of structural relaxation along the cross-section of the reinforcing steel. In the surface layers of reinforcement, which undergo sign-changing deformation with maximum amplitude, a decrease in the level of microstrains is observed simultaneously with a decrease in the size of coherent scattering regions, which indicates the formation of a subgrain structure and the redistribution of dislocations from the internal volumes of subgrains to their boundaries. In the axial zone of reinforcing steel, microstrains remain quite high, but the size of the blocks increases, which is obviously associated with the enlargement of substructural elements due to the possible coalescence of subgrains. The combined effect of both processes obviously contributes to an increase in the macroscopic plasticity of cold-deformed reinforcement and its ability to relax local stress redistribution due to an increase in the mean free path of mobile dislocations.
Keywords: low-carbon steel, reinforcing steel, deformation, mechanical properties, structure, heat treatment, cooling, drawing, modeling.
For citation: Ambrazhey, M. Yu. (2026). Method for evaluating the fine structure evolution of low-carbon steel during the production of stabilized cold-deformed reinforcing steel. Fundamental and Applied Problems of Ferrous Metallurgy, 40, 525-547. https://doi.org/10.52150/2522-9117-2026-40-031
1. Ivchenko, A. V., Ambrazhei, M. Yu., Mamaev, A. V., Gun’kin, I. A., Bashlii, I. F. Production of high-strength rolled steel for the manufacture of B500S cold-deformed periodic rebar. Steel Transl. 41, 1014–1018 (2011).
https://doi.org/10.3103/S0967091211120072
2. Gorlovsky M. B., Merkachev V. N. (1993). Spravochnik volochilshchika provoloki [Wire Drawer’s Handbook]. Metallurgiya. [In Russian].
3. Perlin I. L., Ermanok M. Z. (1971). Teoriya volocheniya [Theory of Drawing]. 2nd ed., Metallurgiya. [In Russian].
4. Bitkov V. V. (2004). Tekhnologiya i mashiny dlya proizvodstva provoloki [Technology and machines for wire production]. In-t mashinovedeniya UrO RAN. [In Russian].
5. Kireev, E. M., Shulyak, M.N. & Stolyarov, A.V. Influence of final alternating flexure on the mechanical properties of cold-drawn reinforcement. Steel Transl. 39, 270–272 (2009). https://doi.org/10.3103/S0967091209030218
6 Harris, Frank W. (1928). Distribution of tensile strength in hard drawn copper wire. AIME Technical Publication, 518–543.
7. Kruzel, R., & Suliga, M. (2013). The effect of multiple bending of wire on the residual stresses of high carbon steel wires. Metalurgija, 52(1), 93-95.
8. Kaiser, R., Hatzenbichler, T., Buchmayr, B., & Antretter, T. (2013). Simulation of the Roller Straightening Process with Respect to Residual Stresses and the Curvature Trend. Materials Science Forum, 768–769, 456–463. https://doi.org/10.4028/www.scientific.net/MSF.768-769.456
9. Dieter, G. E. (1988). Mechanical metallurgy (D. Bacon, ed.; SI Metric Edition). McGraw-Hill Book Company (UK) Limited.
10. Beer, F. P., Johnston, E. R., Jr., DeWolf, J. T., & Mazurek, D. F. (2015). Mechanics of materials (7th ed.). McGraw-Hill Education.
11. Instytut chornoi metalurhii NAN Ukrainy, PAT «ArselorMittal Kryvyi Rih», & Tekhnichnyi komitet 4. (2019). Prokat armaturnyi dlia zalizobetonnykh konstruktsii. Zahalni tekhnichni umovy [Reinforcing steel for concrete structures. General specifications] (DSTU 3760:2019). DP “UkrNDNTS”.
12. Williams, D. B., & Carter, C. B. (2009). Transmission Electron Microscopy. Springer US. https://doi.org/10.1007/978-0-387-76501-3
13. Ham, R. K., & Sharpe, N. G. (1961). A systematic error in the determination of dislocation densities in thin films. Philosophical Magazine, 6(69), 1193–1194. https://doi.org/10.1080/14786436108239683
14. Hull, D., & Bacon, D. J. (2011). Chapter 8 – Origin and multiplication of dislocations. Introduction to dislocations (fifth edition) (Fifth Edition, Р. 157–169). Butterworth-Heinemann. https://doi.org/10.1016/B978-0-08-096672-4.00008-6
15. Ham, R. K. (1961). The determination of dislocation densities in thin films. Philosophical Magazine, 6(69), 1183–1184. https://doi.org/10.1080/14786436108239679
16. Rachinger, W. A. (1948). A Correction for the α1α2 Doublet in the Measurement of Widths of X-ray Diffraction Lines. Journal of Scientific Instruments, 25(7), 254–255. https://doi.org/10.1088/0950-7671/25/7/125
17. Wojdyr, M. (2010). Fityk: A general-purpose peak fitting program. Journal of Applied Crystallography, 43(5), 1126–1128. https://doi.org/10.1107/S0021889810030499
18. Warren, B. E., & Averbach, B. L. (1952). The Separation of Cold-Work Distortion and Particle Size Broadening in X-Ray Patterns. Journal of Applied Physics, 23(4), 497. https://doi.org/10.1063/1.1702234
19. Eastabrook, J. N., & Wilson, A. J. C. (1952). The Diffraction of X-Rays by Distorted-Crystal Aggregates III: Remarks on the Interpretation of the Fourier Coefficients. Proceedings of the Physical Society. Section B, 65(1), 67–75. https://doi.org/10.1088/0370-1301/65/1/310
20. Williamson, G. K., & Hall, W. H. (1953). X-ray line broadening from filed aluminium and wolfram. Acta Metallurgica, 1(1), 22–31. https://doi.org/10.1016/0001-6160(53)90006-6
21. Cullity, B. D., & Stock, S. R. (2001). Elements of X-ray diffraction, 3rd edition. Prentice Hall.
22. Stokes, A. R., & Wilson, A. J. C. (1942). A method of calculating the integral breadths of Debye-Scherrer lines. Mathematical Proceedings of the Cambridge Philosophical Society, 38(3), 313–322. https://doi.org/10.1017/S0305004100021988
23. Warren, B. E. (1990). X-ray Diffraction. Dover Publications.
24. Halder, N. C., & Wagner, C. N. J. (1966). Separation of particle size and lattice strain in integral breadth measurements. Acta Crystallographica, 20(2), 312–313. https://doi.org/10.1107/S0365110X66000628
25. Klug, H. P., & Alexander, L. E. (1974). X-ray Diffraction Procedures: For Polycrystalline and Amorphous Materials, 2nd Edition. Willey, New York, EUA.
26. Scherrer, P. (1918). Bestimmung der Grösse und der inneren Struktur von Kolloidteilchen mittels Röntgenstrahlen [Determination of the size and internal structure of colloidal particles using X-rays]. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 1918(2), 98–100.
27. Stokes, A. R., & Wilson, A. J. C. (1944). The diffraction of X rays by distorted crystal aggregates – I. Proceedings of the Physical Society, 56(3), 174–181. https://doi.org/10.1088/0959-5309/56/3/303
28. Suryanarayana, C., & Norton, M. G. (1998). X-Ray Diffraction. Springer US. https://doi.org/10.1007/978-1-4899-0148-4
29. Williamson, G. K., & Smallman, R. E. (1956). III. Dislocation densities in some annealed and cold-worked metals from measurements on the X-ray debye-scherrer spectrum. Philosophical Magazine, 1(1), 34–46. https://doi.org/10.1080/14786435608238074
Рукопис надійшов до редакції / Received 01.04.2026
Рекомендовано до друку / Accepted 28.05.2026
Опубліковано / Published 30.05.2026
