Comparative study of cavitation erosion resistance of austenitic steels with different levels of metastability

Vol. 24 No. 1 2022 3 EDITORIAL COUNCIL EDITORIAL BOARD EDITOR-IN-CHIEF: Anatoliy A. Bataev, D.Sc. (Engineering), Professor, Rector, Novosibirsk State Technical University, Novosibirsk, Russian Federation DEPUTIES EDITOR-IN-CHIEF: Vladimir V. Ivancivsky, D.Sc. (Engineering), Associate Professor, Department of Industrial Machinery Design, Novosibirsk State Technical University, Novosibirsk, Russian Federation Vadim Y. Skeeba, Ph.D. (Engineering), Associate Professor, Department of Industrial Machinery Design, Novosibirsk State Technical University, Novosibirsk, Russian Federation Editor of the English translation: Elena A. Lozhkina, Ph.D. (Engineering), Department of Material Science in Mechanical Engineering, Novosibirsk State Technical University, Novosibirsk, Russian Federation The journal is issued since 1999 Publication frequency – 4 numbers a year Data on the journal are published in «Ulrich's Periodical Directory» Journal “Obrabotka Metallov” (“Metal Working and Material Science”) has been Indexed in Clarivate Analytics Services. We sincerely happy to announce that Journal “Obrabotka Metallov” (“Metal Working and Material Science”), ISSN 1994-6309 / E-ISSN 2541-819X is selected for coverage in Clarivate Analytics (formerly Thomson Reuters) products and services started from July 10, 2017. Beginning with No. 1 (74) 2017, this publication will be indexed and abstracted in: Emerging Sources Citation Index. Journal “Obrabotka Metallov” (“Metal Working & Material Science”) has entered into an electronic licensing relationship with EBSCO Publishing, the world's leading aggregator of full text journals, magazines and eBooks. The full text of JOURNAL can be found in the EBSCOhost™ databases. Novosibirsk State Technical University, Prospekt K. Marksa, 20, Novosibirsk, 630073, Russia Tel.: +7 (383) 346-17-75 http://journals.nstu.ru/obrabotka_metallov E-mail: metal_working@mail.ru; metal_working@corp.nstu.ru

OBRABOTKAMETALLOV Vol. 24 No. 1 2022 4 EDITORIAL COUNCIL EDITORIAL COUNCIL CHAIRMAN: Nikolai V. Pustovoy, D.Sc. (Engineering), Professor, President, Novosibirsk State Technical University, Novosibirsk, Russian Federation MEMBERS: The Federative Republic of Brazil: Alberto Moreira Jorge Junior, Dr.-Ing., Full Professor; Federal University of São Carlos, São Carlos The Federal Republic of Germany: Moniko Greif, Dr.-Ing., Professor, Hochschule RheinMain University of Applied Sciences, Russelsheim Florian Nürnberger, Dr.-Ing., Chief Engineer and Head of the Department “Technology of Materials”, Leibniz Universität Hannover, Garbsen; Thomas Hassel, Dr.-Ing., Head of Underwater Technology Center Hanover, Leibniz Universität Hannover, Garbsen The Spain: Andrey L. Chuvilin, Ph.D. (Physics and Mathematics), Ikerbasque Research Professor, Head of Electron Microscopy Laboratory “CIC nanoGUNE”, San Sebastian The Republic of Belarus: Fyodor I. Panteleenko, D.Sc. (Engineering), Professor, First Vice-Rector, Corresponding Member of National Academy of Sciences of Belarus, Belarusian National Technical University, Minsk The Ukraine: Sergiy V. Kovalevskyy, D.Sc. (Engineering), Professor, Vice Rector for Research and Academic Affairs, Donbass State Engineering Academy, Kramatorsk The Russian Federation: Vladimir G. Atapin, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Victor P. Balkov, Deputy general director, Research and Development Tooling Institute “VNIIINSTRUMENT”, Moscow; Vladimir A. Bataev, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Vladimir G. Burov, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Aleksandr N. Gerasenko, Director, Scientifi c and Production company “Mashservispribor”, Novosibirsk; Sergey V. Kirsanov, D.Sc. (Engineering), Professor, National Research Tomsk Polytechnic University, Tomsk; Aleksandr N. Korotkov, D.Sc. (Engineering), Professor, Kuzbass State Technical University, Kemerovo; Evgeniy A. Kudryashov, D.Sc. (Engineering), Professor, Southwest State University, Kursk; Dmitry V. Lobanov, D.Sc. (Engineering), Associate Professor, I.N. Ulianov Chuvash State University, Cheboksary; Aleksey V. Makarov, D.Sc. (Engineering), Corresponding Member of RAS, Head of division, Head of laboratory (Laboratory of Mechanical Properties) M.N. Miheev Institute of Metal Physics, Russian Academy of Sciences (Ural Branch), Yekaterinburg; Aleksandr G. Ovcharenko, D.Sc. (Engineering), Professor, Biysk Technological Institute, Biysk; Yuriy N. Saraev, D.Sc. (Engineering), Professor, Institute of Strength Physics and Materials Science, Russian Academy of Sciences (Siberian Branch), Tomsk; Alexander S. Yanyushkin, D.Sc. (Engineering), Professor, I.N. Ulianov Chuvash State University, Cheboksary

Vol. 23 No. 2 2021 5 CONTENTS OBRABOTKAMETALLOV TECHNOLOGY Kuznetsov V.P., Makarov A.V., Skorobogatov A.S., Skorynina P.A., Luchko S.N., Sirosh V.A., Chekan N.M. Normal force infl uence on smoothing and hardening of steel 03Cr16Ni15Mo3Ti1 surface layer during dry diamond burnishing with spherical indenter............................................................................ 6 Gubin D.S., Kisel’A.G. Calculation of temperatures during fi nishing milling of a nickel based alloys.......... 23 EQUIPMENT. INSTRUMENTS Bratan S.M., Roshchupkin S.I., Chasovitina A.S., Gupta K. The effect of the relative vibrations of the abrasive tool and the workpiece on the probability of material removing during fi nishing grinding................. 33 MATERIAL SCIENCE OzolinA.V., Sokolov E.G. Effect of mechanical activation of tungsten powder on the structure and properties of the sintered Sn-Cu-Co-W material................................................................................................................. 48 Korobov Yu.S., Alwan H.L., Makarov A.V., Kukareko V.A., Sirosh V.A., Filippov M.A., Estemirova S. Kh. Comparative study of cavitation erosion resistance of austenitic steels with different levels of metastability................................................................................................................................................... 61 Vologzanina S.A., IgolkinA.F., PeregudovA.A., Baranov I.V., Martyushev N.V. Effect of the deformation degree at low temperatures on the phase transformations and properties of metastable austenitic steels.......... 73 Filippov A.V., Shamarin N.N., Moskvichev E.N., Novitskaya O.S., Knyazhev E.O., Denisova Yu.A., Leonov A.A., Denisov V.V. Investigation of the structural-phase state and mechanical properties of ZrCrN coatings obtained by plasma-assisted vacuum arc evaporation..................................................................... 87 EDITORIALMATERIALS Guidelines for Writing a Scientifi c Paper ............................................................................................................ 103 Abstract requirements ......................................................................................................................................... 107 Rules for authors ................................................................................................................................................. 111 FOUNDERS MATERIALS 119 CONTENTS

OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 24 No. 1 2022 Comparative study of cavitation erosion resistance of austenitic steels with different levels of metastability Yury Korobov 1, a, *, Hussam Alwan 2, b, Aleksey Makarov 1, c, Vladimir Kukareko 3, d, Vitaliy Sirosh 1, е, Michael Filippov 2, f, Svetlana Estemirova 4, g 1 M.N. Miheev Institute of Metal Physics, Ural Branch of the Russian Academy of Sciences, 18 S. Kovalevskoy str., Ekaterinburg, 620108, Russian Federation 2 Ural Federal University named after the fi rst President of Russia B.N. Yeltsin, 19 Mira str., Ekaterinburg, 620002, Russian Federation 3 The Joint Institute of Mechanical Engineering of the National Academy of Sciences of Belarus, 12 Akademicheskaya str., Minsk, 220072, Republic of Belarus 4 Institute of Metallurgy, Ural Branch of the Russian Academy of Sciences, 101 Amundsen str., Ekaterinburg, 620016, Russian Federation a https://orcid.org/0000-0003-0553-918X, yukorobov@gmail.com, b https://orcid.org/0000-0002-2955-204X, lefta.hussam@gmail.com, c https://orcid.org/0000-0002-2228-0643, av-mak@yandex.ru, d https://orcid.org/0000-0003-4283-871X, v_kukareko@mail.ru, e https://orcid.org/0000-0002-8180-9543, sirosh.imp@yandex.ru, f https://orcid.org/0000-0002-0733-4607, fi lma1936@mail.ru, g https://orcid.org/0000-0001-7039-1420, esveta100@mail.ru Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science. 2022 vol. 24 no. 1 pp. 61–72 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2022-24.1-61-72 Obrabotka metallov - Metal Working and Material Science Journal homepage: http://journals.nstu.ru/obrabotka_metallov ART I CLE I NFO Article history: Received: 17 December 2021 Revised: 17 January 2022 Accepted: 28 January 2022 Available online: 15 March 2022 Keywords: Cavitation erosion resistance Metastable austenite Martensitic phase transformation Microstructure Deposited coatings Funding The work was carried out within the framework of the state assignment of the IMF UB RAS on topics No. AAAAA18-118020190116-6, No. AAAAA19-119070490049-8. This study was supported by project No. IRASME-66316 “cladHEA +” under the M-ERA.NET program, Call 2019-II. Acknowledgements Research were partially conducted at core facility “Structure, mechanical and physical properties of materials” ABSTRACT Introduction. Reliability-critical components of equipment working in contact with high-speed liquid media (for example, turbine blades of hydroelectric power stations, pump impellers, ship propellers) are subjected to one of the types of wear – cavitation erosion. The current study aims to select and scientifi cally substantiate the type of coating and its structural-phase state for the effective protection of parts from cavitation erosion. Research methods. The study carries out a comparative analysis of differences in the cavitation erosion resistance of characteristic austenitic steels, in the form of bulk material (316L) and coatings (E308L, 60Cr8TiAl), used for protection against cavitation Arc surfacing, i.e. MMA and MIG, is used for depositing the coatings. The tests are carried out on an original installation for evaluating the cavitation resistance of materials with applying ultrasound and the electrical potential difference. Results and Discussion. The results show that the 60Cr8TiAl has a higher resistance to cavitation erosion than that of E308L and 316L by 4 and 10 times, respectively. The structural factors that determine the resistance to cavitation erosion damage are identifi ed to analyze the reasons for the differences in material resistance. Firstly, a strong dependence of the cavitation erosion resistance of austenitic steels on the intensity of the deformation martensitic transformation, developing under the infl uence of cavitation, is confi rmed. This structural transformation contributes to an increase in cavitation resistance of the surface layer. In metastable austenitic steel, a deformation martensite (α′) is formed in the surface layer during the initial test period. This causes an increase in hardness, dissipation of the energy of external action, and the appearance of compressive stresses that prevent the occurrence of microcracks. Subsequently, additional hardening of the previously formed dispersed crystals of α′-martensite occurs. In 60Cr8TiAl, these effects are signifi cantly stronger than that of E308L and 316L due to the higher level of metastability of austenite and formation of carbon deformation martensite. For citation: Korobov Yu.S., Alwan H.L., Makarov A.V., Kukareko V.A., Sirosh V.A., Filippov M.A., Estemirova S.Kh. Comparative study of cavitation erosion resistance of austenitic steels with different levels of metastability. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2022, vol. 24, no. 1, pp. 61–72. DOI: 10.17212/1994-6309-2022-24.1-61-72. (In Russian). ______ * Corresponding author Korobov Yury S., D.Sc. (Engineering), Head of Laser/Plasma Processing Laboratory M.N. Miheev Institute of Metal Physics, Ural Branch of the Russian Academy of Sciences 18 S. Kovalevskoy str., 620108, Ekaterinburg, Russian Federation Tel.: 8 (919) 379-20-16, e-mail: yukorobov@gmail.com

OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 24 No. 1 2022 Introduction The high-effective machinery parts operating in contact with high-speed liquid media (for example, turbine blades of hydroelectric power plants, pump impellers, ship propellers) are subjected to cavitation erosion [1–5]. During the cavitation process high-pressure shock waves (1,500 MPa [6, 7]) are initiated, and the velocity of emerging liquid microjets can exceed 120 m/s [8–10]. On the surface subjected to cavitation, local plastic deformation occurs, followed by the destruction starting from the surface layers [11, 12]. As a result, defects that appear in this case (micro pits or cavities) lead to reduction of the equipment effi ciency and increasing repair costs [13]. Fig. 1 represents a typical example of cavitation erosion damage occurring in pump impeller blade made of AISI 316L austenitic stainless steel used in power plant-cooling systems. As reported, steel AISI 316 cavitation erosion resistance is not high enough [14]. Fig. 1. Cavitation wear of water pump impeller Surface treatment is promising way for reducing the cavitation damage [15, 16]. Another way to increase the resistance of parts against cavitation erosion is the deposition of coatings by arc surfacing [17–19] and thermal spraying [5, 20, 21]. Arc surfacing is widely used due to low cost and the possibility of formation dense coatings [22]. Particularly, austenitic electrodes/wire of the E308L-17 type (Russian analogue 03Cr19Ni10) has become widespread due to good weldability and adequate cavitation resistance [23, 24]. Metastable austenitic steels (MAS) are potentially promising alternatives to more expensive alloys based on Co and Ni. When the external load is applied to MAS, a phase transformation from austenite to martensite (γ → ʹ) takes place accompanied by synergistic effects. First, an increase in the proportion of the martensite phase leads to an increase in hardness. Second, the energy of the external load, applied to the surface, is dissipated due to the strain induced nucleation of martensite. Also, due to the phase transformation (γ → ʹ), compressive stresses arise in the surface layer of the part, preventing the occurrence of microcracks [25]. As a result, wear resistance is improved under various conditions (for example, abrasive, hydro- and gas-abrasive, erosive, cavitation, adhesive, and fatigue loads) [26, 27]. For 50Ni9Cr5 MAS, it is shown that the phase transformation (γ → ʹ) occurs at a threshold level of external load from 1,000 to 2,500 MPa with an increase in the initial amount of martensite from 15 to 75 %. At strains exceeding the threshold value, the amount of deformation martensite increases linearly with increasing strains [28]. The authors obtained similar results for 50Cr18 MAS deposited coatings under the action of highly dynamic impact loads [29] and for 60Cr8TiAl MAS coatings under abrasive action [30]. The presented external loads correspond to cavitation loads, which exceed 1,500 MPa, as shown above [6-10]. This suggests the possibility of (γ → ʹ) phase transformation in 60Cr8TiAl MAS coating during the cavitation. The purpose of this study is to evaluate the cavitation erosion resistance and analyze structural changes in the deposited coating of steel 60Cr8TiAl in comparison with austenitic steels 316L (bulk workpiece) and E308L-17 (deposited layer).

OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 24 No. 1 2022 Methodology In this work, AISI 316L stainless steel (bulk workpiece) and two coatings (60Cr8TiAl formed by deposition of 1.6 mm fl ux-cored wire and E308L-17 formed by deposition of 2.5 mm electrode) have been studied. The coatings were deposited using Shtorm-LORCH S-series welding machine, (Shtorm, Ekaterinburg, Russia). The chemical compositions of materials, Wt%, according to manufacturers, is shown in Table 1The chemical compositions of materials, Wt%, according to manufacturers, were the following AISI 316L: C ≤ 0.03, Cr 16.5-18.0, Ni 10.0-13.0, Mo 2.0-2.5, Mn ≤ 0.03, P ≤ 0.045, S ≤ 0.03, N ≤ 0.1, Fe balance; 60Cr8TiAl: 0.6 C, 8.0 Cr, 1.5 Al, 1.0 Ti, Fe balance; E308L-17 electrode: 0.04, Cr 17.50, Ni 7.92, Si 0.86, Mn 0.51, Nb 0.30, P 0.03, S 0.01, Fe balance. The 60Cr8TiAl coating was deposited by tungsten inert gas welding (TIG) in the following modes: current 90-110A, voltage 12 V, argon feed rate 12-15 l/min. The E308L-17 coating was deposited by manual metal arc welding (MMA) in the following modes: current 70-75 A, voltage 25 V. The test specimens were prepared in accordance with the requirements of the ASTM G32–10 cavitation erosion test [31], Fig. 2. Surfacing was carried out on specimens of 16 mm and 16 mm high. After that, the specimens were cut out and ground according to Fig. 2. The end part of the specimen 16 mm was subjected to cavitation. a b Fig. 2. Samples for the cavitation tests: a – AISI 316L steel sample, b – the sample with a deposited coating, 1 – deposited layer, 2 – substrate Cavitation erosion was evaluated using an original installation [32], in which the cavitation occurs under the effect of ultrasound on a liquid jet contacting the sample surface, Fig. 3. The constancy of the composition, fl ow pressure and temperature of the liquid is controlled by the feedback algorithm that maintains recycling the liquid. Applying a voltage between the nozzle and the sample contributes to adding an electrochemical effect due to anodic polarization, which increases erosive wear. The voltage value is chosen to be the minimum, at which the effect of erosion acceleration appears. The proposed scheme for cavitation test differs from the standardized one [31] in terms of the location of the sample relative to the water jet as well as the design features mentioned above. This allows speeding up testing, increase the reliability and stability of the results in comparison with analogues [33, 34]. The conditions of carrying out cavitation tests are given in Table 1. The cavitation erosion resistance was evaluated depending on a weight loss criterion. The tests were interrupted at irregular intervals to weigh the test sample. Before and after each interval, the sample was

OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 24 No. 1 2022 Ta b l e 1 Cavitation test modes Parameter Value Vibration frequency, kHz 20 ± 0.1 Peak-to-peak displacement amplitude, μm 53 ± 3.0 Test environment Tap water, pH 7.5 ± 0.20 Applied voltage, V 8.5 Testing time, min 300 Temperature Room Fig. 3. Scheme of the installation for cavitation erosion testing cleaned with acetone, dried with warm air for 30-40 seconds, and weighed on a balance with an accuracy of 0.5 mg. The difference between the initial mass of the sample and the measured mass after cavitation represents the mass loss at each test interval. To study phase transformations occurring during cavitation, X-ray diffraction analysis (XRD) was performed on a Shimadzu XRD-7000 diffractometer (Shimadzu, Japan) in a Cu Kα radiation, graphite monochromator (angular range 2θ from 30˚ to 115˚ with 0.04˚ scanning step for 3 s exposure). The analysis was performed for samples after tests, the duration of which corresponded to the time of measurements of weight loss. Results and discussion The results of cavitation tests are given in Table 2.As seen, the cavitation erosion resistance of 60Cr8TiAl is about 10 and 4 times higher comparing to AISI 316L and E308L-17, respectively.

OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 24 No. 1 2022 Ta b l e 2 Cavitation test results Testing time, min Weight loss, mg AISI 316L E308L-17 60Cr8TiAl 0 0.00 0.00 0.00 5 0.67 0.47 0.10 10 1.10 0.75 0.31 20 1.65 0.90 0.66 40 2.02 1.03 0.87 60 2.90 1.13 0.99 90 5.04 1.57 1.24 120 7.74 2.43 1.48 180 15.44 4.72 1.76 240 22.13 8.07 2.06 300 28.65 12.13 2.49 A noticeable increase in the wear rate for AISI 316L and E308L-17 in comparison with 60Cr8TiAl is observed after 40 and 90 minutes, respectively. According to XRD, Fig. 4, it is noticed that, before cavitation tests, the share of the α-phase in the surface layer was 29.5 % in 60Cr8TiAl, 2 % in AISI 316L, and was not found in E308L-17. The presented combination of austenite and martensite in 60Cr8TiAl is due to the infl uence of alloying elements. Carbon is a strong austenitizer, and at a given C/Cr ratio, the initial martensitic transformation temperature (Ms) decreases. Calculations using predictive equations for the main chemical composition of 0.6 % C and 8 % Cr [35] showed that Ms is in the range of 170–220°C. Aluminum and titanium within the indicated limits induce γ → αʹ transformation, contributing to increasing the number of crystallization centers and obtaining a fi ne-grained structure [36]. As indicated by XRD analysis an increase in the amount of deformation martensite was observed in the surface layer of all samples during the cavitation tests, Fig. 5. In 60Cr8TiAl, the quantity of martensite increased to 73 %, which is much higher than that of E308L-17 and AISI 316L. This indicates a signifi cantly lower austenite stability in 60Cr8TiAl. The deformation martensite causes an increase in hardness, dissipation of the energy of external loading, and development of compressive stresses preventing the formation of microcracks. For 60Cr8TiAl and E308L-17, the slope of the curves for the dependence of the proportion of martensite on the duration of testing changes, which indicates the stabilization of austenite. Therefore, at latest test stage with a slight increase in the quantity of martensite, there is an additional strain hardening of the previously formed dispersed crystals of α’-martensite. For AISI 316L steel, during the fi rst 60 min of cavitation, no noticeable formation of αʹ-martensite was observed. This indicates a high stability of austenite, which is also confi rmed by other studies [26]. Only prolonged for 300 min cavitation exposure led to the formation of 25 % martensite on the metal surface. This means that the formation of α’-martensite occurs in the already hardened austenite of this steel. Comparing the results of cavitation tests and XRD data, it can be concluded that there is a correlation between the erosion resistance of austenitic steels and the intensity of the martensitic transformation. The latter one develops under the infl uence of cavitation, contributing to erosion resistance increase, Fig. 6.

OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 24 No. 1 2022 Fig. 4. XRD patterns of the samples before cavitation tests: a – AISI 316L, b – E308L-17, c – 60Cr8TiAl a b c Fig. 5. Change in the proportion of martensite during cavitation tests

OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 24 No. 1 2022 Fig. 6. Correlation between erosive wear and the intensity of martensitic transformation during cavitation A strong effect of martensitic transformation on cavitation erosion resistance was also shown for austenitic steel 304 [37, 38], which is similar in alloying system to the considered AISI 316 steel and E308L-17 coating. Thus, it can be concluded that cavitation loading of the 60Cr8TiAl coating leads to a phase transformation (γ → αʹ), similar to abrasive action. This causes synergistic effects inherent in metastable austenitic steels, such as increased hardness, energy dissipation, and increased stresses in the surface layer. The result of these effects is increasing the cavitation resistance of 60Cr8TiAl coating in comparison with widespread materials used for parts operating in applications requiring cavitation resistance. Conclusions 1. The mechanism of surface hardening in metastable austenitic steel during cavitation is shown and confi rmed. In the initial period of testing, deformation martensite (α′) is formed in the surface layer. Subsequently, additional strain hardening of previously formed dispersed α’-martensite crystals occurs. 2. Cavitation effect on the surface of metastable austenitic steel leads to the deformation transformation of martensite, as in the cases of previously considered effects on similar steels at highly dynamic impact loads and abrasive wear. This indicates the same level of external specifi c loads for all these types of loading. 3. There is a correlation between the erosion resistance of austenitic steels and the intensity of the martensitic transformation developing under the action of cavitation. The resistance to cavitation of the 60Cr8TiAl coating, having the highest intensity of martensitic transformation, is higher than that of AISI 316L steel and E308L-17 coating by 4 and 10 times, respectively. References 1. Bogachev I.N. Kavitatsionnoe razrushenie i kavitatsionnostoikie splavy [Cavitation destruction and cavitationresistant alloys]. Moscow, Metallurgiya Publ., 1972. 192 p. 2. Singh R., Tiwari S.K., Mishra S.K. Cavitation erosion in hydraulic turbine components and mitigation by coatings: current status and future needs. Journal of Materials Engineering and Performance, 2012, vol. 21, pp. 1539–1551. DOI: 10.1007/s11665-011-0051-9. 3. Adamkowski A., Henke A., Lewandowski M. Resonance of torsional vibrations of centrifugal pump shafts due to cavitation erosion of pump impellers. Engineering Failure Analysis, 2016, vol. 70, pp. 56–72. DOI: 10.1016/j. engfailanal.2016.07.011.

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