Nizhny Novgorod State Technical University named after R. E. Alekseev, Nizhny Novgorod, Russia:

Yu. G. Kabaldin, Dr. Eng., Prof., Dept. of Technology and Equipment of Mechanical Engineering
M. S. Anosov, Cand. Eng., Associate Prof., Dept. of Technology and Equipment of Mechanical Engineering, e-mail: anosov-maksim@list.ru
M. A. Chernigin, Post-graduate Student, Engineer, Dept. of Technology and Equipment of Mechanical Engineering, e-mail: honeybadger52@yandex.ru

The features of accumulation of structural damage of alloys 09G2C and 07Cr25Ni13 obtained by additive electric arc surfacing have been studied. To assess the accumulation of damage during fatigue loading, a series of microstructural studies was carried out, followed by fractal analysis of the obtained microstructures at various stages of the test and at different stress amplitudes in the cycle. In the process of fatigue loading in the microstructure of the analyzed alloys, the appearance of a large number of sliding strips is observed, already at the initial stages of testing, after which an increase in their number and total area is observed, which quantitatively shows a change in the fractal dimension of the microstructure image. According to the results of the study, a significant influence of the scale of the analyzed image on the result of the fractal dimension assessment was established. The most intense structural changes are observed at the level of individual most favorably located grains. The values of the increment of the fractal dimension of the image -0.0075, -0.009 and -0.0175 for magnifications ×100, ×200 and ×500 and more, respectively, can be taken as a criterion for the formation of a macro crack for the 09G2C alloy. The origin of the macro-crack was observed when the values of the fractal dimension of the microstructure image were reached, of the order D_F =1.863±0.007. When analyzing changes in the fractal dimension for alloy 07Cr25Ni13, it was found that the area in which microcracks originated later and the appearance of a macrocrack was observed had the lowest values of the fractal dimension of the image. The origin of microcracks was observed when the values of the fractal dimension of the microstructure image were reached, of the order D_F =1.87±0.006, while the image scale for the alloy under study practically does not affect the specified criterion. Based on the data obtained, an algorithm for assessing structural damage based on the fractal dimension of the image of the microstructure of alloys obtained on the basis of additive surfacing is proposed. This algorithm and software can be used to estimate the residual life and the stage of deformation and destruction of materials.
The study was supported by the Russian Science Foundation grant No. 22-79-00095 "Development of scientific and technological foundations for the structure formation of structural materials obtained by additive electric arc growth for the formation of mechanical properties under fatigue using artificial intelligence approaches".

1. Borodin А. N., Borodin Е. М. Analysis of non-destructive methods for testing metal structures. Nauchno-metodicheskiy elektronny zhurnal "Kontsept". 2016. Vol. 11. pp. 2246–2250.
2. Abed Al-Zobayde A. М., Chigareva Yu. А. Fractal model of damage accumulation in solids. Nauka i tekhnika. 2014. No. 6. pp. 42–48.
3. Yakovleva S. P., Buslaeva I. I., Makharova S. N., Levin А. I. Structural damage of spring steel after operation in a cold climate zone. Fundamentalnye issledovaniya. 2017. No. 10-3. pp. 530–535.
4. Terentyev V. F., Korableva S. А. Fatigue of metals. Moscow: Nauka, 2015. 484 p.
5. Koneva N. А., Teplyakova L. А., Sosnin О. V., Tsellermayer V. V., Kovalenko V. V. Dislocation substructures and their transformation under fatigue loading (review). Izvestiya vuzov. Fizika. 2002. No. 3. pp. 87–98.
6. Savenkov G. G., Barakhtin B. K. Relation of the fractal dimension of the fracture surface with a set of standard tension characteristics of the material. Applied Mechanics and Technical Physics. 2011. Vol. 52. pp. 997–1003.
7. Carney L. R., Mecholsky J. J. Relationship between fracture toughness and fracture surface fractal dimension in AISI 4340 steel. Materials Sciences and Applications. 2013. Vol. 4. No. 4. DOI: 10.4236/msa.2013.44032
8. Ivanova V. S., Balankin А. S., Bunin I. Zh. et al. Synergetics and fractals in materials science. Moscow: Nauka, 1994. 384 p.
9. Hilders O. A., Zambrano N., Caballero R. Microstructure, strength, and fracture topography relations in AISI 316L stainless steel, as seen through a fractal approach and the hall-petch law. International Journal of Metals. 2015. Vol. 2015. 624653. DOI: 10.1155/2015/624653
10. Kabaldin Y. G., Anosov M. S., Shatagin D. A. Evaluation of the mechanism of the destruction of metals based on approaches of artificial intelligence and fractal analysis. IOP Conf. Series: Materials Science and Engineering. 2020. Vol. 709. 033076. DOI: 10.1088/1757-899X/709/3/033076
11. Williams S., Filomeno M., Adrian A., Jialuo D., Pardal G., Colegrove P. Wire+arc additive manufacturing. Materials Science and Technology. 2016. Vol. 32, Iss. 7. pp. 641–647. DOI: 10.1179/1743284715Y.0000000073
12. Jackson M. A., Van Asten A., Morrow J. D., Min S., Pfefferkorn F. E. Energy consumption model for additive-subtractive manufacturing processes with case study. International Journal of Precision Engineering and Manufacturing-Green Technology. 2018. No. 5 (4). pp. 459-466. DOI: 10.1007/s40684-018-0049-y
13. Pinto-Lopera J. E. et al. Real-time measurement of width and height of weld beads in GMAW processes. Sensors. 2016. Vol. 16 (9). 1500. DOI: 10.3390/s16091500
14. Johnnieew Zhong Li, Mohd Rizal Alkahari, Nor Ana Rosli. Review of wire arc additive manufacturing for 3D metal printing. International Journal of Automation Technology. 2019. Vol. 13 (3). pp. 346–353. DOI: 10.20965/ijat.2019.p0346
15. Oskolkov А. А., Matveev Е. V., Bezukladnikov I. I., Trushnikov D. N., Krotova Е. L. Advanced technologies of additive manufacture of metal products. Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mashinostroenie, materialovedenie. 2018. Vol. 20. No. 3. pp. 90–105. DOI: 10.15593/2224- 9877/2018.3.11
16. Williams S. Large scale metal wire + arc additive manufacturing of structural engineering parts. WAAM. Available at: https://waammat.com/documents/s-williams-large-scale-metal-wirearc-additive-manufacturing-of-structural-engineering-parts. Accessed: 12.01.2023.
17. WAAM vs machining from solid – a cost comparison. WAAM. Available at: https://waammat.com/documents/waam-vs-machining-from-solid-a-cost-comparison. Accessed: 12.01.2023.
18. Cunningham C. R., Wikshåland S., Xu F. et al. Cost modelling and sensitivity analysis of wire and arc additive manufacturing. Procedia Manufacturing. 2017. Vol. 11. pp. 650–657. DOI: 10.1016/j.promfg.2017.07.163
19. Kabaldin Yu. G., Shatagin D. А., Anosov М. S., Kolchin P. V., Kisilev А. V. Diagnostics of the 3D printing process on a CNC machine using machine learning approaches. Vestnik mashinostroeniya. 2021. No. 1. pp. 55–59.
20. Kabaldin Yu. G., Anosov M. S., Shatagin D. A., Ryabov D. A., Kolchin P. V., Kisilev A. V. Study of the influence of 3D printing modes on the structure and cold resistance of 08G2S steel. Vestnik Magnitogorskogo gosudarstvennogo tekhnicheskogo universiteta imeni G. I. Nosova. 2021. Vol. 19. No. 4. pp. 64–70. DOI: 10.18503/1995-2732-2021-19-4-64-70
21. Kim V. A., Mokritskii B. Y., Morozova A. V. Multifractal analysis of microstructures after laser treatment of steels. Solid State Phenomena. 2020. Vol. 299SSP. pp. 926–932.
22. Kabaldin Yu. G., Anosov M. S., Zhelonkin M. V., Shatagin D. A., Mikhaylov A. M. Program for assessing the indicators of microstructure and structural damage of materials. Certificate of registration of the computer program. 2022676932, 12.09.2022. Application No. 2022366406 dated 09/07/2022.
23. Kesireddy A., McCaslin S. Application of image processing techniques to the identification of phases in steel metallographic specimens. In: Elleithy K., Sobh T. (eds) New Trends in Networking, Computing, E-learning, Systems Sciences, and Engineering. Lecture Notes in Electrical Engineering. 2015. Vol. 312. pp. 425–430. DOI: 10.1007/978-3-319-06764-3_53
24. Gadalov V. N., Bashkov O. V., Vornacheva I. V., Filonovich A. V. Digital image processing of metallographic microstructures in MATLAV environment. Methodology. 2015. No. 12 (21). pp. 43–46.
25. GOST 25.502–79. Methods of mechanical testing of metals. Fatigue testing methods. Introduced: 01.01.1981.
26. Gonchar A. V., Kurashkin K. V., Andreeva O. V., Anosov M. S., Klyushnikov V. A. Fatigue life prediction using acoustic birefringence and characteristics of persistent slip bands. Fatigue Fract. Eng. Mater. Struct. 2022. No. 45 (1). pp. 101–112. DOI: 10.1111/ffe.13586
27. Gonchar А. V., Anosov М. S., Ryabov D. А. Assessment of structural degradation of the heat-affected zone during fatigue failure of a welded joint. Defektoskopiya. 2022. No. 9. pp. 25–34. DOI: 10.31857/S0130308222090032