Physics:Tribo-Fatigue

From HandWiki

Tribo-Fatigue – section of Mechanics,[1][2] in which[3][4] wear-fatigue damage (WFD) and destruction of Tribo-Fatigue systems are studied. Tribo-Fatigue was created[5][6][7][8][9][10] at the junction of Tribology and Mechanical fatigue (Figure 1).

Figure 1 – The main effects in Tribo-Fatigue: DE – direct effect; BE – back effect; Λσ\τ – effect of Λ-interactions (conventionally indicated by arrows) of damage caused by stresses (σ, τw) of different types (hexagon – Tribo-Fatigue logo)

Objects for study

Tribo-Fatigue system is called any mechanical system in which the process of friction in any of its manifestations takes place (during rolling, sliding, slipping, impact, erosion, etc.) and which simultaneously perceives and transmits voluntarily repeated variable (in particular cyclic) load.[5][6][8][9] As a rule, these are products of responsible purpose. Thus, in the wheel / rail system, the rail head is additionally subjected to repeated bending, therefore, the performance of this system is determined by the complex WFD – mechano-rolling fatigue.[5][6][11] In the crankshaft / connecting rod system shaft is simultaneously subjected to bending with torsion, therefore, its performance is determined by the complex WFD – mechano-sliding fatigue.[5][6][12] In a variety of shaft / hub joints, the shaft is additionally subjected to bending with rotation. And their performance is determined by the complex WFD – fretting-fatigue.[5][6][13] If we study the pipe / fluid (oil) system, the pipe is simultaneously loaded with alternating internal pressure. Therefore, its performance is determined by the complex WFD – mechano-corrosion (or corrosion-erosion) fatigue.[5][6][14][15] Similarly, radiation-mechanical fatigue is characteristic of the primary circuit pipes of the nuclear power plant.[16]

Thus, essentially, a tribo-fatigue system is any pair of friction, at least one of the elements of which is additionally and simultaneously loaded with a volume (non-contact) load. Virtually every modern machine (car, tank, airplane, machine tool, and many others) there is at least one tribo-fatigue system, which, as a rule, is heavily loaded, and it largely determines the operational reliability of the product. It follows that the great technical and economic significance for the modern technology of friction and wear problems (studied in Tribology, on the one hand, and problems of fatigue damage and destruction (studied in Mechanical fatigue, on the other hand, repeatedly increases when particular damaging phenomena (fatigue, friction and wear) are realized simultaneously and jointly in the form of complex WFD (studied in Tribo-Fatigue).[1]

Main content

Table 1 summarizes the main content of Tribo-Fatigue in comparison with Tribology and Mechanical fatigue, which are its sources. Figure 1 shows the three main effects established and studied in Tribo-Fatigue.[5][6][7][8][9][10] Direct effect[6][17][18][19]: the influence of processes and conditions of friction and wear on the change in the characteristics of fatigue resistance of the tribo-fatigue system and / or its elements. It was established experimentally that friction and wear can both dramatically reduce (by 3-7 times or more) and significantly (by 30–40%) increase[6][19] fatigue limit σ−1 of structural elements (Figure 2).

The back effect[6][17][18][20]: the effect of alternating stresses on the change in the characteristics of friction and wear of the tribo-fatigue system and / or its elements. It was established experimentally that cyclic stresses from a volume load, excited in the contact zone, can, depending on the conditions, either reduce or increase the wear resistance of a friction pair (by 10–60% or more).

Table 1 – Comparison of the methodologies of scientific disciplines
Discipline Object of study Basic methods of studies Tasks
experimental theoretical
Tribo-Fatigue Tribo-Fatigue system Wear-fatigue tests Mechanics of wear-fatigue damage Optimal management of complex wear-fatigue damage processes of tribo-fatigue systems in order to reduce labor, equipment and materials costs in their production and operation
Tribology Friction pair Tribotesting Contact mechanics Combating wear (up to wear-free friction) and preventing jamming of a friction pair
Fatigue Structural element Fatigue tests Mechanics of deformation and fracture Reducing the rate of accumulation of damage and preventing fatigue failure of structural elements
Figure 2 – Diagram explaining the main features Λ-interactions with the direct effect (p0 is the highest stress on the contact pad during rolling; τw is the frictional stress during sliding; q is the contact pressure in the fretting zone)

The effect of Λ-interactions[6] damage (ωσ, ωτ) is due to normal stresses (index σ) from non-contact volume loads (fatigue) and frictional stresses (index τw) (friction and wear) and is illustrated by the rule:

Tribo-fatigue-3.jpg

According to this rule, damages from various (contact and volume) loads are not summed, but interact dialectically. This means that Λ-functions should take three classes of values (Λ>1, Λ<1, Λ=1)[6] to describe not only unity and struggle, but also the direction of the physical hardening-softening processes in the system (see Figure 2). Formulas for calculating the limiting stresses with direct (σ−1τ) and back (τfσ) effects are obtained with allowance for Λ-interactions of damages:[6][21]

Tribo-fatigue-4-2.jpg

Taking into account the above three effects, it is possible to pose and practically solve the problems of optimal (taking into account economic responsibility) management of the WFD processes of tribo-fatigue systems. See Table 1 and these references:[6][7][8][9][10]

A number of new results, including fundamental results, have been obtained in Tribo-Fatigue.

  • Theoretically formulated[7][22] and experimentally confirmed[6][7][23][24] the generalized law of friction: in the general case, the friction force is proportional to both the contact and the volume load, if the latter excites cyclic stress (±σ) in the contact area. It has been established that the friction coefficient in the tribo-fatigue system is fσ>fs, fσ<fs, fσ=fs (where fs is the friction coefficient in the analogous friction pair according to the classical Amonton – Coulomb law). If friction is realized in the tension zone (with volume loading), then fσ<fs, and if in the compression zone, then fσ>fs. The difference between fσ and fs reaches 10-30% or more, depending on the loading conditions.[23]
  • A mechanical-mathematical model of the combined stress-strain state of the tribo-fatigue system has been developed:[6][7][10]:[25]
Tribo-fatigue-5.jpg

where σij(n), σij(τ),σij(b) are the stresses caused respectively by the normal contact load, the tangential contact load, the non-contact loads, and the superscripts M, N, and Q correspond to the internal moment, the longitudinal and transverse forces. This model underlies the formulation and solution of a new class of contact problems, supplemented by the action of various non-contact forces,[7][26] and the creation of a new section of the theory of elasticity, supplemented by taking into account local effects in the load application area.[7][27]

  • Based on the statistical model of a deformable solid,[28] a new and effective measure has been proposed for the volume damage of friction pairs and tribo-fatigue systems[7][29]
Tribo-fatigue-6.jpg

where σ*min is the lower limit of the scattering of the limiting stress for a given object, P is the probability of damage (determined with a confidence probability γ). With the help of this measure, practical problems of analyzing the scale effect and the calculated and experimental assessment of wear are solved, since the latter is implemented within a dangerous volume VPγ.[30] A systematization and classification of dangerous volumes in friction pairs and tribo-fatigue systems is given, depending on the criteria for assessing damage.[7]

  • The energy theory[6][21][31][32] of limiting states of tribo-fatigue systems was developed, with which one can predict the occurrence of failures according to various performance criteria (fatigue failure, unacceptable wear, critical density of pittings, etc.).
  • Principles were formulated and methods[6][10][33] were developed for calculating tribo-fatigue systems for strength, durability, reliability, durability, taking into account the risk (safety) of operation.[34] This means that in Tribo-Fatigue they move away from the traditional calculation of individual parts and proceed to the calculation and design of mechanical systems.[1]
  • Experimental and theoretical studies in a new and promising field of knowledge allowed us to formulate 9 tribo-fatigue surprises,[35][36][37] which «before tribo-fatigue» «scientists could not see, understand, imagine or analytically describe».[35] So, surprise S3 (tribo-fatigue bomb[35]) – anomalously low resistance to fracture during fretting-fatigue, due to the strong interaction of the complex of weak damages. It turned out that such a surprise is found in the rotor of a unique turbine with a unit capacity of 1200 MW, in a fusion reactor with a strong magnetic field, in a rocket engine with hydrogen fuel, in an installation for drilling ultra-deep wells.[1] Surprise S5 (the Troppy phenomenon[35]) – the formation of irregular residual surface undulating damage as a result of non-stationary process of elastoplastic deformation in the area of contact interaction during rolling friction. This phenomenon turned out to be implemented in the wheel / rail system as wavy damage that occurs on the tread surface under severe operating conditions.[38]
  • As is known, in thermodynamics, entropy is a characteristic of energy dissipation. And in Tribo-Fatigue, a similar characteristic of its absorption was proposed:[39]
Tribo-fatigue-7.jpg

Tribo-fatigue entropy (surprise S7[35]) generates irreversible damages ωΣ in dangerous volumes VPγ of moving and deformable solids interacting with each other and / or with the medium. Here TΣ ≥ T is the temperature caused by all sources (T is the medium temperature), γ1(w) is the pressure (stress) that causes damage to a dangerous volume of a unit value, UΣeff is the effective (absorbed) energy caused by loads of a different nature. Using the notion of tribo-fatigue entropy, the general law of entropy increase[40][41] was formulated and analytically recorded for the first time. This law, like the concept of entropy itself, is useful for cosmological studies.[42][43][44] We also point out the surprise S8 (tribo-fatigue life[35]), according to which life is a special way of the existence of protein bodies evolving from inevitable damage states. This concept is based on the phenomenoanalysis of the phenomena of fatigue, wear, biochemical, and other damage characteristic of a living organism, and it has proved useful for describing the characteristics of life of Homo Sapiens,[45] as well as in philosophy and social studies.[46][47]

Testing machines

Within the framework of Tribo-Fatigue, a new class of test equipment has been created on the basis of a number of inventions – SI-series machines for wear-fatigue testing of materials, models of friction pairs and tribo-fatigue systems.[6][24][48][49][50] The main feature of such machines is the use of standardized sizes of test objects (Figure 3). This provides a correct comparison of the results of tests conducted in different conditions.

Figure 3 – Scheme of the test machine and the formation of methods of wear-fatigue testing (ICS – information-control system)

The SI-series machines are equipped with the research laboratories of the JSC «Gomselmash», JSC «GOMELTRANSNEFT DRUZHBA, Belarusian-Russian University (Mogilev), Belarusian State University (Minsk), etc. Technical characteristics of the SI-series machines are regulated by the re-quirements of the interstate standard GOST 30755-2001 «Tribo-Fatigue. Wear-fatigue tests machines. General technical requirements». The main test methods are standardized.[51]

In 2018, on the basis of the SI-series machines as a result of their miniaturization, a prototype personal desktop test center (PTC)[52] was manufactured by the State Program of the Republic of Belarus. It is planned that such a center can serve as a peripheral device for PC (Figure 4) in universities. Such a test complex is designed for the production of a modern laboratory workshop for students and undergraduates as part of the disciplines of the mechanical cycle (Theoretical mechanics, Strength of materials, Design of machines, Tribo-Fatigue, etc.).

Figure 4 – Original peripheral device PTC for PC: ТМ – compact modular test center for desktop use; ICS – information-control system

Tribo-Fatigue as an academic discipline

In several universities of the Republic of Belarus (since 1996) and China (since 2018) the course of Tribo-Fatigue has been introduced into the curricula. There is a complete teaching and methodological support,[10][53][54][55][56] an electronic lecture course on Tribo-Fatigue, officially registered in the Republic of Belarus in the established order[57] has been created and effectively used. For 20 years, the course was attended by more than 3,500 students and undergraduates, which contributed to improving the quality of training of mechanical engineers and mechanics and mathematicians.[58][59][60]

From the history

The term Tribo-Fatigue (tribo (Greek) – friction, fatigue (Fr., Eng.) – fatigue) was first proposed in a letter of L. А. Sosnovskiy to K. V. Frolov dated September 30, 1984,[1] adopted in the interstate standard[5] and included in the Belarusian Encyclopedia[3] and the Great Encyclopedic Dictionary.[4]

The initial stage of development (1985–1993) is believed to have ended with the (first) International Symposium on Tribo-Fatigue (ISTF 1993), the preparatory materials for which were published in[2][61][62][63] and many more, and are summarized, for example, in[64][65] and many others. In four countries (Republic of Belarus, Russia, China, Ukraine) seven International Symposiums (ISTF) have been held, the works of which have been published in these countries (see, for example,[66][67][68][69][70][71]) . More than 2,500 scientists and specialists took part in the symposiums, and 147 authors from many countries (including 16 Belarusian scientists) were awarded the Honorary Diploma «For contribution to the development of Tribo-Fatigue». In 2010, 25 scientists and organizers of science from different countries were awarded the Honorary Jubilee Badge «TRIBO-FATIGUE-25» (photo).

Tribo-fatigue-10 EN.jpg

In 2015, a bibliographic index[72] was published, which included 930 works on Tribo-Fatigue, including about 40 books and 12 state and interstate standards developed based on the results of research in a new field of knowledge. To date, their number is more than 1,100 items.

The stages of development of Tribo-Fatigue are described in more detail in this reference.[73]

References

  1. ↑ 1.0 1.1 1.2 1.3 1.4 Word on Tribo-Fatigue / Strazhev V. I., Frolov К. V., Vysotsky М. S., Troshchenko V. Т., Sosnovskiy L. А., Makhutov N. А., Kuharev А. V., Gruntov P. S., Starovoitov E. И., Marchenko V. А., Koreshkov V. N., Shurinov V. А., Botvina L. R., Drozdov Yu. N., Gorbatsevich M. I., Pavlov V. G., Efros D. G.Botvina L. R. / ed.-com. А. V. Bogdanovich. – Gomel, Minsk, Moscow, Kiev  : Remika, 1996. – 132 p. (in Russian).
  2. ↑ 2.0 2.1 Tribo-Fatigue: New ideas in a promising direction / K. V. Frolov [et al.]. – Gomel : BIRE, 1990. – 7 р. (in Russian).
  3. ↑ 3.0 3.1 Tribo-Fatigue // Belarusian encyclopedia. – Minsk : Belarusian encyclopedia, 2002. – V. 15. – P. 542. (in Belarusian).
  4. ↑ 4.0 4.1 Tribo-Fatigue // Big Belarusian Encyclopedic Dictionary / Ed. by : T. V. Belova (chairman) [et al.]. – Minsk : Belarusian encyclopedia named after P. Brouka, 2011. – P. 354. (in Belarusian).
  5. ↑ 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 GOST 30638–99. Tribo-Fatigue. Terms and definitions (interstate standard). – Intr. 1999–06–17. – Minsk : Interstate Council on Standardization, Metrology, and Certification, 1999. – 17 р. (in Russian).
  6. ↑ 6.00 6.01 6.02 6.03 6.04 6.05 6.06 6.07 6.08 6.09 6.10 6.11 6.12 6.13 6.14 6.15 6.16 6.17 6.18 Sosnovskiy, L. A. Wear-fatigue mechanics / L. A. Sosnovskiy. – Gomel : BelSUT, 2007. – 434 p. (in Russian).
  7. ↑ 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 Sherbakov, S. S. Mechanics of Tribo-Fatigue systems / S. S. Sherbakov, L. A. Sosnovskiy. – Minsk : BSU, 2010. – 407 р. (in Russian).
  8. ↑ 8.0 8.1 8.2 8.3 Sosnovskiy, L. A. Tribo-Fatigue. Wear-fatigue damage and its prediction / L. A. Sosnovskiy // Series : Foundations of Engineering Mechanics, Springer, 2005. – 424 p.
  9. ↑ 9.0 9.1 9.2 9.3 摩擦疲劳学 磨损 – 疲劳损伤及其预测. L. A. 索斯洛-夫斯基著, 高万振译 – 中国矿业大学出版社, 2013. – 324 p.
  10. ↑ 10.0 10.1 10.2 10.3 10.4 10.5 Sosnovskiy, L. А. Fundamental and applied tasks of Tribo-Fatigue: lectures / L. А. Sosnovskiy, М. А. Zhuravkov, S. S. Sherbakov. – Minsk : BSU, 2010. – 488 p. (in Russian).
  11. ↑ Sosnovskiy, L. A. Mechano-rolling fatigue: the main laws (summary article) / L. A. Sosnovskiy, N. A. Makhutov, V. A. Shurinov // Industrial laboratory. Diagnostics of materials. – 1992. – № 11. – P. 44–61. (in Russian).
  12. ↑ Sosnovskiy, L. A. Mechano-sliding fatigue: the main laws (summary article) / L. A. Sosnovskiy, N. A. Makhutov, V. A. Shurinov // Industrial laboratory. Diagnostics of materials. – 1992. – № 9. – P. 46–63. (in Russian).
  13. ↑ Sosnovskiy, L. A. Fretting-fatigue: the main laws (summary article) / L. A. Sosnovskiy, N. A. Makhutov, V. A. Shurinov // Industrial laboratory. Diagnostics of materials. – 1992. – № 8. – P. 45–62. (in Russian).
  14. ↑ Sosnovsky, L. A. On a multidisciplinary approach to the analysis and prediction of operational damageability and resource life of linear sections of the pipeline from the standpoint of tribo-fatigue / L. A. Sosnovskiy, Yu. V. Lisin, A. N. Kozik // Mechanics of machines, mechanisms and materials. – 2017. – № 3 (40). – P. 75–84. (in Russian).
  15. ↑ Sosnovskiy, L. A. Mechano-corrosion fatigue: the main laws (summary article) / L. A. Sosnovskiy, N. A. Makhutov, V. A. Shurinov // Industrial laboratory. Diagnostics of materials. – 1993. – № 7. – P. 33–44. (in Russian).
  16. ↑ Troshchenko, V. Т. Fatigue resistance of metals and alloys: handbook : in 2 volumes / V. Т. Troshchenko, L. А. Sosnovskiy. – Kiev : Naukova dumka, 1987. – V. 2. – P. 320–325. (in Russian).
  17. ↑ 17.0 17.1 Vysotsky, М. S. New Word in Mechanics / M. S. Vysotsky // Science and Innovations. – 2010. – № 9 (91). – P. 17–19. (in Russian).
  18. ↑ 18.0 18.1 Sosnovskiy, L. A. Sliding-mechanical fatigue. Direct and back effects / L. A. Sosnovskiy, A. V. Marchenko // Proceedings of the World Tribology Congress (London, Sept. 8–12, 1997). – London, 1997. – P. 569.
  19. ↑ 19.0 19.1 Serensen, S. V. The problem of fatigue and wear resistance of machine parts (brief overview) / S. V. Serensen // In book : Increased wear resistance and machine life. – Кiev : Ukrainian Academy of Science Publishing, 1960. – V. 1. – P. 10–14. (in Russian).
  20. ↑ Sharay, V. Т. Comprehensive study of wear and fatigue in steels / V. T. Sharay. – Kiev : Ukrainian Publishing of technical literature, 1959. – 32 p. (in Russian).
  21. ↑ 21.0 21.1 Bogdanovich, A. V. Prediction of limiting states of tribo-fatigue systems / A. V. Bogdanovich. – Grodno : Grodno State University, 2008. – 372 p. (in Russian).
  22. ↑ Sherbakov, S. S. The change in the force and coefficient of friction under the action of non-contact load (theoretical analysis) / S. S. Sherbakov // Bulletin of BelSUT. – 2016. – № 1 (32). – P. 110–115. (in Russian).
  23. ↑ 23.0 23.1 Sosnovskiy, L. A. The law of (external) friction and its generalization: theory and experiment / L. A. Sosnovskiy, S. S. Sherbakov, V. V. Komissarov // Bulletin of BelSUT. – 2016. – № 1 (32). – P. 91–101. (in Russian).
  24. ↑ 24.0 24.1 Sosnovskiy, L. A. Methods and main results of tribo-fatigue tests / L. A. Sosnovskiy, A. V. Bogdanovich, O. M. Yelovoy, S. A. Tyurin, V. V. Komissarov, S. S. Sherbakov // International Journal of Fatigue. – 2014. – V. 66. – P. 207–219.
  25. ↑ Vityaz, P. А. New approaches in the mechanics of deformable systems / P. А. Vityaz, L. А. Sosnovskiy, S. S. Sherbakov // Proc. of Belarusian National Academy of Sciences. – 2009. – V. 53. – № 4. – P. 102–110. (in Russian).
  26. ↑ Sosnovskiy, L. A. Special class of contact problems and the calculation of the state of stress of wheel / rail system elements (CM105) / L. A. Sosnovskiy, S. S. Sherbakov // Proc. of the 7th International Conference on Contact Mechanics and Wear of Rail / Wheel Systems (Brisbane, Australia, Sept. 24–27, 2006). – Brisbane, 2006. – V. 1. – P. 93–104.
  27. ↑ Sherbakov, S. S. Contact interaction, volume damageability and multicriterial limiting states of multielement Tribo-Fatigue systems / S. S. Sherbakov, M. A. Zhuravkov, L. A. Sosnovskiy // Selected Problems on Experimental Mathematics / R. Witula [et al.]. – Gliwice : Wydawnictwo Politechniki Slaskiej, 2017. – P. 17–38.
  28. ↑ Sosnovskiy, L. A. Statistical mechanics of fatigue fracture / L. A. Sosnovskiy. – Minsk : Nauka i Tekhnika, 1987. – 288 p. (in Russian).
  29. ↑ Sosnovskiy, L. A. The method of strength calculation in volume fracture and surface damage / L. A. Sosnovskiy // Proceedings of the World Tribology Congress III (Washington, 12–16 September 2005). –Washington, 2005. – 2 p.
  30. ↑ Sherbakov, S. S. New wear model / S. S. Sherbakov, L. A. Sosnovskiy // Bulletin of BelSUT. – 2016. – № 1 (32). – P. 74–82. (in Russian).
  31. ↑ Sosnovskiy, L. A. Generalized theory of limiting states of tribo-fatigue systems / L. A. Sosnovskiy, S. S. Sherbakov // News of the National Academy of Sciences of Belarus, Physical and Technical Series. – Minsk, 2008. – №. 4. – P. 17–23. (in Russian).
  32. ↑ Sosnovskiy, L. A. Theory of the limiting states of active systems / L. A. Sosnovskiy, A. V. Bogdanovich // Proceedings of the World Tribology Congress III (Washington, 12–16 September 2005). –Washington, 2005. – 2 p.
  33. ↑ Elovoy, О. М. To development of regulatory methods for calculating and designing of tribo-fatigue systems. Parts 1 and 2 / О. М. Elovoy, А. V. Bogdanovich // Mechanics of machines, mechanisms and materials. – 2017. – № 4 (41). – P. 82–88; – 2018. – № 1 (42). – P. 58–66. (in Russian).
  34. ↑ Sosnovskiy, L. A. L-Risk (Mechanothermodynamics of irreversible damages) / L. A. Sosnovskiy. – Gomel : BelSUT, 2004. – 317 p. (in Russian).
  35. ↑ 35.0 35.1 35.2 35.3 35.4 35.5 Sosnovskiy, L. A. Surprises of Tribo-Fatigue / L. A. Sosnovskiy, S. S. Sherbakov. – Gomel : BelSUT, 2005. – 192 p. (in Russian).
  36. ↑ Nine Tribo-Fatigue surprises (selection of articles) // Science and Innovations. – 2010. – № 9 (91). – P. 5–28. (in Russian).
  37. ↑ Sosnovskiy, L. A. Surprises of Tribo-Fatigue / L. A. Sosnovskiy, S. S. Sherbakov. – Minsk : Magic Book, 2009. – 200 p.
  38. ↑ Grassie, S L. Rail corrugation: characteristics, causes, and treatments / S L Grassie // Proc. of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 2009 223:581 / DOI: 10.1234/09544097JRRT264.
  39. ↑ Sosnovskiy, L. A. On one type of entropy as a measure of the absorption of energy spent on the production of damage in a mechanothermodynamic system / L. A. Sosnovskiy // Reports of the National Academy of Sciences of Belarus. – 2007. – V. 51. – № 6. – P. 100–104. (in Russian).
  40. ↑ Sosnovskiy, L. A. Mechanothermodynamics (about combining great competitors: 1850-2015) / L. A. Sosnovskiy // Mechanics of machines, mechanisms and materials. – 2016. – № 4 (37). – P. 19–41. (in Russian).
  41. ↑ Sosnovskiy, L. А. Fundamentals of the theory of the evolution of inorganic and organic systems, the number of living and reasonable / L. А. Sosnovskiy, S. S. Sherbakov, А. А. Lazarevich // National philosophy in a global world : proc. of the First Belarusian Congress of Philosophy, Minsk, oct. 18–20, 2017. – Minsk : Belarusian science, 2018. – P. 155–178. (in Russian).
  42. ↑ Bekenstein, J. D. Black holes and entropy // Physical Review, 1973, D 7, p. 2333–2346.
  43. ↑ Peter V. Coveney. The second law of thermodynamics: entropy, irreversibility and dynamics // Nature. Vol. 333 1988. – P. 409–415.
  44. ↑ Bardeen, J. M., Carter, B., Hawking, S. W. The four laws of black hole mechanics // Communications in Mathematical Physics, 1973, 31, – P. 161–170.
  45. ↑ Sosnovskiy, L. A. Tribo-Fatigue : the dialectics of life / L. A. Sosnovskiy. – Ed. 2nd. – Gomel : BelSUT, 1999. – 116 p. (in Russian).
  46. ↑ Sosnovskiy, L. А. Philosophy and Tribo-Fatigue / L. А. Sosnovskiy, А. А. Lazarevich // Tribo-Fatigue : proc. of VI Intern. Symposium on Tribo-Fatigue ISTF 2010, Minsk, oct. 25 – Nov. 1, 2010. : in 2 p. / Belarusian State University ; ed. board. : M. A. Zhuravkov (prev.) [et al.]. – Minsk : BSU Press, 2010. – V. 2. – P. 591–620. (in Russian).
  47. ↑ Lazarevich, A. A. On the possibility of quantitative analysis of good and evil in socio-humanitarian studies / A. A. Lazarevich, L. A. Sosnovskiy // Tribo-Fatigue : proc. of VI Intern. Symposium on Tribo-Fatigue ISTF 2010, Minsk, oct. 25 – Nov. 1, 2010. : in 2 p. / Belarusian State University ; ed. board. : M. A. Zhuravkov (prev.) [et al.]. – Minsk : BSU Press, 2010. – V. 2. – P. 497–500. (in Russian).
  48. ↑ Sosnovskiy, L. А. Wear-fatigue tests / L. А. Sosnovskiy, N. А. Makhutov // Mechanical Engineering : Encyclopedia / Ed. by : К. V. Frolov (chairman) [et al.]. – V. II-1. Physical and mechanical properties. Tests of metallic materials / L. V. Agamirov [et al.]; general edition Е. I. Mamaeva. – М. : Mechanical Engineering, 2010. – P. 354–385. (in Russian).
  49. ↑ SI-series machines for wear-fatigue tests. – Minsk, 2009. – 62 p.
  50. ↑ Sosnovskiy, L. A. Methods and machines for wear-fatigue tests of materials and their standardization / L. A. Sosnovskiy, V. N. Koreshkov, O. M. Yelovoy // Proceedings of the World Tribology Congress (London, Sept. 8–12, 1997). – London, 1997. – P. 723.
  51. ↑ Koreshkov, V. N. Standardization in the field of Tribo-Fatigue / V. N. Koreshkov, V. A. Andriyashin, S. A. Tyurin // Proc. of V Intern. Symposium on Tribo-Fatigue ISTF 2005, Irkutsk, oct. 3–7, 2005 / Ed. by A. P. Khomenko. – Irkutsk : Irkutsk State University of Communications, 2005. – V. 1. – P. 204–233. (in Russian).
  52. ↑ Sosnovskiy, L. A. Modern science and multidisciplinary education–science–production system: some achievements / L. A. Sosnovskiy, S. S. Sherbakov, A. V. Bogdanovich // Theoretical and Applied Mechanics. – 2018. – V. 33. – P. 3–11. (in Russian).
  53. ↑ Sosnovskiy, L. A. Fundamentals of Tribo-Fatigue : in 2 pt. / L. A. Sosnovskiy. – Gomel : BelSUT, 2003. – V. 1. – 246 p.; V. 2. – 234 p. (in Russian).
  54. ↑ Bogdanovich, A. V. Laboratory workshop on experimental mechanics: a teaching aid / A. V. Bogdanovich, S. S. Sherbakov, D. E. Marmysh. – Minsk : BSU, 2017. – 107 p. (in Russian).
  55. ↑ Komissarov, V. V. Characterization of resistance to wear-fatigue damage: a teaching aid for the implementation of work in the discipline «Basics of Tribo-Fatigue» / V. V. Komissarov. – Gomel : BelSUT, 2013. – 47 p. (in Russian).
  56. ↑ Senko, V. I. Basic ideas of Tribo-Fatigue and their study at technical university / V. I. Senko, L. A. Sosnovskiy. – Gomel : BelSUT, 2005. – 191 p. (in Russian).
  57. ↑ Electronic educational and methodical complex on academic discipline «Tribo-Fatigue». Registration certificate № 7731816154 on the inclusion in the State Register information resource. (in Russian).
  58. ↑ Senko, V. I. Experience of twenty years of teaching of «Foundations of Tribo-Fatigue» / V. I. Senko, L. A. Sosnovskiy, A. V. Putyato, V. V. Komissarov, E. S. Taranova, S. S. Sherbakov, A. V. Bogdanovich, V. B. Popov // Bulletin of BelSUT. – 2016. –№ 1 (32). – P. 11–31. (in Russian).
  59. ↑ Sosnovskiy, L. A. Tribo-Fatigue in engineering education / L. A. Sosnovskiy, A. S. Shaginyan // Proceedings of the World Tribology Congress (London, Sept. 8–12, 1997). – London, 1997. – P. 639.
  60. ↑ Senko, V. I. Fundamentals ideas of Tribo-Fatigue and their study in Belarus / V. I. Senko, L. A. Sosnovskiy // Proceedings of the International Mechanical Engineering Congress and Exposition (Orlando, 5–11 November 2005). –Orlando, 2005. – 7 p.
  61. ↑ Sosnovskiy, L. A. Tribo-Fatigue : problems and potentials / L. A. Sosnovskiy // Report at Thematic Exhibition of USSR Ac. of Sci. Mathematics and Mechanics – the National Economy. – Gomel : BIRE, 1989. – 65 p. (in Russian).
  62. ↑ Sosnovskiy, L. A. Methodological problems of complex assessment of damage and limiting state of tribo-fatigue systems / L. A. Sosnovskiy, N. A. Makhutov // Industrial Laboratory. Diagnostics of Materials. – 1991. – № 5. – Р. 27–40. (in Russian).
  63. ↑ Sosnovskiy, L. A. Tribo-Fatigue. Basic terms and definitions / L. A. Sosnovskiy // Journal of Friction and Wear. –1992. – № 4. – Р. 728–734. (in Russian).
  64. ↑ Tribo-Fatigue – new ways of improving reliability of machines / M. S. Vysotsky, V. N. Koreshkov, V. A. Marchenko, L. A. Sosnovskiy, V. I. Strazhev // Transactions of Belarusian Academy of Sciences. – 1994. – № 4. – Р. 32–41. (in Russian).
  65. ↑ Starovoitov, E. I. International Symposium on Tribo-Fatigue / E. I. Starovoitov // Strength Problems. – 1994. – № 11. – P. 92–94. (in Russian).
  66. ↑ Abstracts of 1st International Symposium on Tribo-Fatigue / ed. by L. A. Sosnovskiy. – Gomel, 1993. – 121 p. (in Russian).
  67. ↑ Abstracts of 2nd Intern. Symposium on Tribo-Fatigue / ed. by V. A. Andriyashin [et al.]. – Moscow–Gomel : SPAS – TRIBOFATIGUE S&P Group, 1996. – 104 p. (in Russian).
  68. ↑ Proceedings of the III International Symposium on Tribo-Fatigue (ISTF 2000), Beijing, China, Oct. 22–26, 2000 / ed. by Gao Wanzhen and Jian Li. – Beijing : Hunan University Press, 2000. – 653 p.
  69. ↑ ISTF 2002 : Proc. of 4th Intern. Symposium on Tribo-Fatigue, Sept. 23–27, 2002 Ternopol, Ukraine : in 2 pt. / Ternopil Ivan Puluj National Technical University : Rep. Ed. V. T. Troshchenko. – Ternopol : TNTU, 2002. – V. 1. – 530 p. – V. 2. – 324 p. (in Russian).
  70. ↑ Proceedings of V International Symposium on Tribo-Fatigue (ISTF 2005), October 3–7 2005, Irkutsk (Russia) / ed. by A. P. Khomenko. – Irkutsk: Irkutsk State Transport University, 2005. – V. 1. – 497 p.; V. 2. – 383 p.; V. 3. – 388 p. (in Russian).
  71. ↑ Tribo-Fatigue : Proc. of VI Intern. Symposium on Tribo-Fatigue ISTF 2010, Minsk, Oct. 25 – Nov. 1, 2010. : in 2 pt. / Belarusian State University ; ed. board. : M. A. Zhuravkov (prev.) [et al.]. – Minsk : BSU Press, 2010. – V. 1. – 840 p.; V. 2. – 724 p. (in Russian).
  72. ↑ Tribo-Fatigue: bibliographic index (1985-2015) / compiled by S. A. Tyurin; Belarusian State University of Transport. – Gomel : BelSUT, 2015. – 61 p. (in Russian).
  73. ↑ Some events and stages of Tribo-Fatigue development / Compiled by А. V. Kuharev, S. А. Tyurin // Bulletin of BelSUT. – 2015. – № 1 (30). – P. 45–63. (in Russian).

External links




Retrieved from "https://handwiki.org/wiki/index.php?title=Physics:Tribo-Fatigue&oldid=165985"