Skip to main content
Top

2016 | OriginalPaper | Chapter

4. Fractal Kinetics of Fracture

Authors : Ahad Kh. Janahmadov, Maksim Y. Javadov

Published in: Synergetics and Fractals in Tribology

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Fractals are called geometric objects: line, surface, spatial body having very jagged shape, and self-similarity.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference B.B. Mandelbrot, Fractals: forme, chance and dimension (Freeman, San Fracisko, 1977), p. 362 B.B. Mandelbrot, Fractals: forme, chance and dimension (Freeman, San Fracisko, 1977), p. 362
2.
go back to reference A.V. Korolenko, M.S. Maganova, A.V. Mesniankin, Innovatsionnye metody analiza stokhasticheskikh protsessov i struktur v optike. Fraktal’nye i mul’tifraktal’nye metody, veivlet-preobrazovaniia. Uchebnoe posobie (MGU im. M.V.Lomonosova, NII iadernoi fiziki im. D.V. Skobel’tsyna, Moscow, 2004), p. 82 A.V. Korolenko, M.S. Maganova, A.V. Mesniankin, Innovatsionnye metody analiza stokhasticheskikh protsessov i struktur v optike. Fraktal’nye i mul’tifraktal’nye metody, veivlet-preobrazovaniia. Uchebnoe posobie (MGU im. M.V.Lomonosova, NII iadernoi fiziki im. D.V. Skobel’tsyna, Moscow, 2004), p. 82
3.
go back to reference B.F. Timofeev, Fraktal. Fizika tverdogo tela (Nauk. Dumka, Kiev, 1998), 2, 460–461 B.F. Timofeev, Fraktal. Fizika tverdogo tela (Nauk. Dumka, Kiev, 1998), 2, 460–461
4.
go back to reference A.F. Bulat, V.I. Dyrda, Fraktaly v geomekhanike (Nauk. Dumka, Kiev, 2005), p. 357 A.F. Bulat, V.I. Dyrda, Fraktaly v geomekhanike (Nauk. Dumka, Kiev, 2005), p. 357
5.
go back to reference J.E. Hutchinson, Fractals and self similarity. Indiana Univ. Math. J. 30(5), 713–747 (1981) J.E. Hutchinson, Fractals and self similarity. Indiana Univ. Math. J. 30(5), 713–747 (1981)
6.
go back to reference M. Barnsley, Fractals everywhere (Academic Press, Boston, 1988)MATH M. Barnsley, Fractals everywhere (Academic Press, Boston, 1988)MATH
7.
go back to reference R.M. Kronover, Fraktaly i khaos v dinamicheskikh sistemakh. Osnovy teorii. per. s angl (Postmarket, Moscow, 2000), pp. 0–352 R.M. Kronover, Fraktaly i khaos v dinamicheskikh sistemakh. Osnovy teorii. per. s angl (Postmarket, Moscow, 2000), pp. 0–352
8.
go back to reference V.E. Rokotian, Avtomodel’nost’. Fizicheskaia entsiklopediia, vol. 1 (SE, Moscow, 1988), pp. 19–20 V.E. Rokotian, Avtomodel’nost’. Fizicheskaia entsiklopediia, vol. 1 (SE, Moscow, 1988), pp. 19–20
9.
go back to reference Iu.M. Maksenko, Masshtabnaia invariantnost’ (skeiling). Fizicheskaia entsiklopediia, vol. 3 (BRE, Moscow, 1992), pp. 60–61 Iu.M. Maksenko, Masshtabnaia invariantnost’ (skeiling). Fizicheskaia entsiklopediia, vol. 3 (BRE, Moscow, 1992), pp. 60–61
10.
go back to reference V.L. Vinetskii, Avtomodel’nost’, Fizika tverdogo tela. Entsiklopedicheskii slovar’, vol. 1 (Nauk. Dumka, Kiev, 1996), p. 16 V.L. Vinetskii, Avtomodel’nost’, Fizika tverdogo tela. Entsiklopedicheskii slovar’, vol. 1 (Nauk. Dumka, Kiev, 1996), p. 16
11.
go back to reference B.B. Mandelbrot, The fractal geometry of nature (W.H. Frecman, New York, 1982)MATH B.B. Mandelbrot, The fractal geometry of nature (W.H. Frecman, New York, 1982)MATH
12.
go back to reference R.F. Voss, Random fractal forgeries. in Fundamental algorithms in computer graphics, ed. by R.A. Earnshaw (Springer, Berlin, 1985), pp. 805–835 R.F. Voss, Random fractal forgeries. in Fundamental algorithms in computer graphics, ed. by R.A. Earnshaw (Springer, Berlin, 1985), pp. 805–835
13.
go back to reference R.F. Voss, Random fractals. Characterization and measurement, in Scalling phenomena disordered systems, ed. by R. Pynn, A. Skjeltorp (Plenum Press, New York, 1985), pp. 1–11 R.F. Voss, Random fractals. Characterization and measurement, in Scalling phenomena disordered systems, ed. by R. Pynn, A. Skjeltorp (Plenum Press, New York, 1985), pp. 1–11
14.
go back to reference E. Feder, Fraktaly, per. s angl (Mir, Moscow, 1991), p. 254 E. Feder, Fraktaly, per. s angl (Mir, Moscow, 1991), p. 254
15.
go back to reference B.B. Mandelbrot, Self-affine fractal sets, in Fractals in Physics, ed. by L. Pietronero, E. Tosatti (North Holland, Amsterdam, 1986), pp. 3–28 B.B. Mandelbrot, Self-affine fractal sets, in Fractals in Physics, ed. by L. Pietronero, E. Tosatti (North Holland, Amsterdam, 1986), pp. 3–28
16.
go back to reference A.I. Olemskoi, A.A. Katsnel’son, Sinergetika kondensirovannoi sredy, Izd 2-e (Editorial URSS, Moscow, 2010), p. 336 A.I. Olemskoi, A.A. Katsnel’son, Sinergetika kondensirovannoi sredy, Izd 2-e (Editorial URSS, Moscow, 2010), p. 336
17.
go back to reference V.E. Egorushkin, V.E. Panin, E.V. Savushkin, Iu.A. Khon, Sil’novozbuzhdennye sostoianiia v kristallakh. Izv. vuzov. Fizika 1, 9–33 (1987) V.E. Egorushkin, V.E. Panin, E.V. Savushkin, Iu.A. Khon, Sil’novozbuzhdennye sostoianiia v kristallakh. Izv. vuzov. Fizika 1, 9–33 (1987)
18.
go back to reference V.E. Panin, V.E. Egorushkin, Iu.A. Khon, T.F. Elsukova, Atomnovakansionnye sostoianiia v kristallakh. Izv. vuzov., Fizika, №12 (1982) V.E. Panin, V.E. Egorushkin, Iu.A. Khon, T.F. Elsukova, Atomnovakansionnye sostoianiia v kristallakh. Izv. vuzov., Fizika, №12 (1982)
19.
go back to reference V.E. Panin, Iu.V. Griniaev, V.E. Egorushkin i dr. Spektr vozbuzhdennykh sostoianii i vikhrevoe mekhanicheskoe pole v deformiruemom kristalle. Izv. vuzov., Fizika, №1 (1987) V.E. Panin, Iu.V. Griniaev, V.E. Egorushkin i dr. Spektr vozbuzhdennykh sostoianii i vikhrevoe mekhanicheskoe pole v deformiruemom kristalle. Izv. vuzov., Fizika, №1 (1987)
20.
go back to reference V.E. Panin, V.A. Likhachev, Iu.V. Griniaev, Strukturnye urovni deformatsii tverdykh tel (Nauka, Sib.otd-nie, Novosibirsk, 1985), p. 229 V.E. Panin, V.A. Likhachev, Iu.V. Griniaev, Strukturnye urovni deformatsii tverdykh tel (Nauka, Sib.otd-nie, Novosibirsk, 1985), p. 229
21.
go back to reference V.E. Panin, Iu.V. Griniaev, V.I. Danilov i dr. Strukturnye urovni plasticheskoi deformatsii i razrusheniia. (Nauka. Sib. Otd-nie, Novosibirsk, 1990), p. 255 V.E. Panin, Iu.V. Griniaev, V.I. Danilov i dr. Strukturnye urovni plasticheskoi deformatsii i razrusheniia. (Nauka. Sib. Otd-nie, Novosibirsk, 1990), p. 255
22.
go back to reference V.E. Panin, V.E. Egorushkin, P.V. Makarov i dr., Fizicheskaia mezomekhanika i komp’iuternoe konstruirovanie materialov. V 2t. (Nauka. Sib. Izdat. firma RAN, Novosibirsk, 1995), p. 298 V.E. Panin, V.E. Egorushkin, P.V. Makarov i dr., Fizicheskaia mezomekhanika i komp’iuternoe konstruirovanie materialov. V 2t. (Nauka. Sib. Izdat. firma RAN, Novosibirsk, 1995), p. 298
23.
go back to reference Iu.V. Grinaev, N.V. Chertova, Opisanie polzuchesti v ramkakh polevoi teorii defektov. Prikladnaia mekhanika i tekhnicheskaia fizika. 41(3), 177–183 (2000) Iu.V. Grinaev, N.V. Chertova, Opisanie polzuchesti v ramkakh polevoi teorii defektov. Prikladnaia mekhanika i tekhnicheskaia fizika. 41(3), 177–183 (2000)
24.
go back to reference Trenie, iznashivanie i smazka, Spravochnik v 2-kh kn., pod red. I.V.Krachel’skogo, V.V.Anisina (Mashinostroenie, Moscow, 1978), Kn. 1, p. 400 Trenie, iznashivanie i smazka, Spravochnik v 2-kh kn., pod red. I.V.Krachel’skogo, V.V.Anisina (Mashinostroenie, Moscow, 1978), Kn. 1, p. 400
25.
go back to reference A.Kh. Janahmadov, Termomekhanicheskaia teoriia iznosa (Elm, Baku, 1997), p. 28 A.Kh. Janahmadov, Termomekhanicheskaia teoriia iznosa (Elm, Baku, 1997), p. 28
26.
go back to reference A.Kh. Janahmadov, Neftianaia tribologiia (Elm, Baku, 2003), p. 326 A.Kh. Janahmadov, Neftianaia tribologiia (Elm, Baku, 2003), p. 326
27.
go back to reference A.Kh. Janahmadov, Tribotekhnicheskie problemy v neftegazovom oborudovanii (Elm, Baku, 1998), p. 216 A.Kh. Janahmadov, Tribotekhnicheskie problemy v neftegazovom oborudovanii (Elm, Baku, 1998), p. 216
28.
go back to reference A.Kh. Janahmadov, M.Y. Javadov, O.A. Dyshin, Diagnosis of the contact interaction of solid bodies at friction using fractal analysis methods. J. Sci. Appl. Eng. Q. 04, 5–16 (2014) A.Kh. Janahmadov, M.Y. Javadov, O.A. Dyshin, Diagnosis of the contact interaction of solid bodies at friction using fractal analysis methods. J. Sci. Appl. Eng. Q. 04, 5–16 (2014)
29.
go back to reference A.I. Olemskoi, A.Ia. Flat, Ispol’zovanie kontseptsii fraktala v fizike kondensirovannoi sredy. Usp. Fiz. Nauk., 163(12), 1–50 (1993) A.I. Olemskoi, A.Ia. Flat, Ispol’zovanie kontseptsii fraktala v fizike kondensirovannoi sredy. Usp. Fiz. Nauk., 163(12), 1–50 (1993)
30.
go back to reference Sinergetika i ustalostnoe razrushenie metallov (Nauka, Moscow, 1980), p. 246 Sinergetika i ustalostnoe razrushenie metallov (Nauka, Moscow, 1980), p. 246
31.
go back to reference A.I. Olemskoi, E.A. Toropov, Teoriia nizkotemperaturnoi evoliutsii ortorombicheskoi fazy vysokotemperaturnykh sverkhprovodiashchikh oksidov. Fizika metallov. Metallovedenie, 7, 32–40 (1991) A.I. Olemskoi, E.A. Toropov, Teoriia nizkotemperaturnoi evoliutsii ortorombicheskoi fazy vysokotemperaturnykh sverkhprovodiashchikh oksidov. Fizika metallov. Metallovedenie, 7, 32–40 (1991)
32.
go back to reference D. Adelman, C.P. Burmester, L.T. Wille, P.A. Stern, R. Gronsky, J. Phys. Condens. Matter 4, 585 (1992)ADSCrossRef D. Adelman, C.P. Burmester, L.T. Wille, P.A. Stern, R. Gronsky, J. Phys. Condens. Matter 4, 585 (1992)ADSCrossRef
33.
go back to reference R. Rammal, G. Toulouse, M.A. Virasova, Ultrametricity for physicists. Rev. Mod. Phys. 58, 765, 788 (1986) R. Rammal, G. Toulouse, M.A. Virasova, Ultrametricity for physicists. Rev. Mod. Phys. 58, 765, 788 (1986)
34.
go back to reference S.L. Ginzburg, Neobratimye iavleniia v spinovykh steklakh (Nauka, Moscow, 1989) S.L. Ginzburg, Neobratimye iavleniia v spinovykh steklakh (Nauka, Moscow, 1989)
35.
go back to reference K. Binder, A.P. Jeung, Rev. Mod. Phys. 58, 801 (1986) K. Binder, A.P. Jeung, Rev. Mod. Phys. 58, 801 (1986)
36.
go back to reference V.S. Ivanova, V.F. Terent’ev, Priroda ustalosti metallov (Metallurgiia, Moscow, 1975), p. 456 V.S. Ivanova, V.F. Terent’ev, Priroda ustalosti metallov (Metallurgiia, Moscow, 1975), p. 456
37.
go back to reference A.I. Olemskoi, I.I. Naumov, Fraktal’naia kinetika ustalostnogo razrusheniia. V sb.: Sinergetika i ustalostnoe razrushenie metallov. (Nauka, Moscow, 1989), pp. 200–215 A.I. Olemskoi, I.I. Naumov, Fraktal’naia kinetika ustalostnogo razrusheniia. V sb.: Sinergetika i ustalostnoe razrushenie metallov. (Nauka, Moscow, 1989), pp. 200–215
39.
go back to reference A.I. Olemskoi, Fraktal’naia kinetika perestroiki kristallicheskoi struktury. Fizika metallov. Metallovedenie, 68(1), 56–65 (1989) A.I. Olemskoi, Fraktal’naia kinetika perestroiki kristallicheskoi struktury. Fizika metallov. Metallovedenie, 68(1), 56–65 (1989)
40.
go back to reference A.M. Pashaev, A.Kh. Janahmadov, O.A. Dyshin, Fraktal’naia razmernost’ i ee sviaz’ s mekhanicheskimi svoistvami metallov i splavov v usloviiakh predrazrusheniia. Vestnik Azerbaidzhanskoi Inzhenernoi Akademii 2(2), 13–24 (2010) A.M. Pashaev, A.Kh. Janahmadov, O.A. Dyshin, Fraktal’naia razmernost’ i ee sviaz’ s mekhanicheskimi svoistvami metallov i splavov v usloviiakh predrazrusheniia. Vestnik Azerbaidzhanskoi Inzhenernoi Akademii 2(2), 13–24 (2010)
41.
go back to reference R.G. Palmer, D.L. Stein, E. Abrahams et al., Models of hieracheally constrained dynamics for glassy relaxation. Phys. Rev. Let. 53(10), 958–961 (1984)ADSCrossRef R.G. Palmer, D.L. Stein, E. Abrahams et al., Models of hieracheally constrained dynamics for glassy relaxation. Phys. Rev. Let. 53(10), 958–961 (1984)ADSCrossRef
42.
go back to reference V.V. Zosimov, L.M. Liamshev, Fraktaly v volnovykh protsessakh. Uspekhi fizicheskikh nauk 165(4), 361–401 (1995)CrossRef V.V. Zosimov, L.M. Liamshev, Fraktaly v volnovykh protsessakh. Uspekhi fizicheskikh nauk 165(4), 361–401 (1995)CrossRef
43.
go back to reference A.Kh. Janahmadov, O.A. Dyshin, Synergetic and fractal dimensions in tribology. J. Friction Wear 32(1), 61–71 (2011) A.Kh. Janahmadov, O.A. Dyshin, Synergetic and fractal dimensions in tribology. J. Friction Wear 32(1), 61–71 (2011)
44.
go back to reference S.N. Zhurkov, Dilatonnyi mekhanizm prochnosti tverdykh tel. Fizika tverdogo tela 25(10), 3119–3123 (1983) S.N. Zhurkov, Dilatonnyi mekhanizm prochnosti tverdykh tel. Fizika tverdogo tela 25(10), 3119–3123 (1983)
45.
go back to reference Dzh. Gilman, V. Dzhonston, Vozniknovenie dislokatsii v kristallakh LiF pri nizkikh napriazheniiakh. Dislokatsii i mekhanicheskie svoistva kristallov. (Inostr. lit., Moscow, 1960), pp. 393–394 Dzh. Gilman, V. Dzhonston, Vozniknovenie dislokatsii v kristallakh LiF pri nizkikh napriazheniiakh. Dislokatsii i mekhanicheskie svoistva kristallov. (Inostr. lit., Moscow, 1960), pp. 393–394
46.
go back to reference V.E. Panin, V.A. Likhachev, Iu.V. Griniaev, Strukturnye urovni deformatsii tverdykh tel (Nauka, Novosibirsk, 1985), p. 163 V.E. Panin, V.A. Likhachev, Iu.V. Griniaev, Strukturnye urovni deformatsii tverdykh tel (Nauka, Novosibirsk, 1985), p. 163
47.
go back to reference A.I. Olemskoi, I.A. Skliar, Evoliutsiia defektnoi struktury tverdogo tela v protsesse plasticheskoi deformatsii. Uspekhi fizicheskikh nauk 162(6), 29–79 (1992)CrossRef A.I. Olemskoi, I.A. Skliar, Evoliutsiia defektnoi struktury tverdogo tela v protsesse plasticheskoi deformatsii. Uspekhi fizicheskikh nauk 162(6), 29–79 (1992)CrossRef
48.
go back to reference U. Nikolis, I. Prigozhin, Samoorganizatsiia v neravnovesnykh sistemakh. (Mir, Moscow, 1979), p. 300 U. Nikolis, I. Prigozhin, Samoorganizatsiia v neravnovesnykh sistemakh. (Mir, Moscow, 1979), p. 300
49.
go back to reference A.M. Pashaev, A.Sh. Mekhtiev, A.Kh. Janahmadov, O.A. Dyshin, Avtomodel’nost’ i fraktal’naia mekhanika razrusheniia. Vestnik Azerbaidzhanskoi Inzhenernoi Akademii 1(1), 93–103 (2009) A.M. Pashaev, A.Sh. Mekhtiev, A.Kh. Janahmadov, O.A. Dyshin, Avtomodel’nost’ i fraktal’naia mekhanika razrusheniia. Vestnik Azerbaidzhanskoi Inzhenernoi Akademii 1(1), 93–103 (2009)
50.
go back to reference V.S. Ivanova, Sinergetika: Prochnost’ i razrushenie metallicheskikh materialov (Nauka, Moscow, 1992), p. 160 V.S. Ivanova, Sinergetika: Prochnost’ i razrushenie metallicheskikh materialov (Nauka, Moscow, 1992), p. 160
51.
go back to reference V.S. Ivanova, A.S. Balankin, I.Zh. Bunin i dr. Sinergetika i fraktaly v materialovedenii (Nauka, Moscow, 1994), p. 383 V.S. Ivanova, A.S. Balankin, I.Zh. Bunin i dr. Sinergetika i fraktaly v materialovedenii (Nauka, Moscow, 1994), p. 383
52.
go back to reference V.S. Ivanova, Problemy prochnosti. 5, 91–98 (1982) V.S. Ivanova, Problemy prochnosti. 5, 91–98 (1982)
53.
go back to reference V.S. Ivanova, S.A. Kunavin, Izv. AN SSSR. Metally 4, 148–153 (1984) V.S. Ivanova, S.A. Kunavin, Izv. AN SSSR. Metally 4, 148–153 (1984)
55.
go back to reference A.R. Rosenfeld, Ibid 21(11), 1339–1361 (1987) A.R. Rosenfeld, Ibid 21(11), 1339–1361 (1987)
56.
go back to reference A.S. Balankin, A.A. Liubomudrov, I.T. Sevriukov, Zhurnal tekhnicheskoi fiziki. 59(12), 102–104 (1989) A.S. Balankin, A.A. Liubomudrov, I.T. Sevriukov, Zhurnal tekhnicheskoi fiziki. 59(12), 102–104 (1989)
57.
go back to reference V.A. Kuz’menko, Razvitie predstavlenii o protsesse deformirovaniia materialov (UkrNIITI, Kiev, 1968), p. 47 V.A. Kuz’menko, Razvitie predstavlenii o protsesse deformirovaniia materialov (UkrNIITI, Kiev, 1968), p. 47
58.
go back to reference O.D. Khlopotov, Metallovedenie i termicheskaia obrabotka materialov. №12, 12–14 (1974) O.D. Khlopotov, Metallovedenie i termicheskaia obrabotka materialov. №12, 12–14 (1974)
59.
go back to reference A.S. Balankin, V.S. Ivanova, V.P. Breusov, Dokl. AN SSSR. 322(6), 1080–1085 (1992) A.S. Balankin, V.S. Ivanova, V.P. Breusov, Dokl. AN SSSR. 322(6), 1080–1085 (1992)
60.
go back to reference V.E. Panin, Iu.V. Griniaev, V.I. Danilov i dr. Strukturnye urovni plasticheskoi deformatsii i razrusheniia (Nauka, Sib.otd-e, Novosibirsk, 1990), p. 255 V.E. Panin, Iu.V. Griniaev, V.I. Danilov i dr. Strukturnye urovni plasticheskoi deformatsii i razrusheniia (Nauka, Sib.otd-e, Novosibirsk, 1990), p. 255
61.
go back to reference M. Feigenbaum, Universal’nost’ v povedenii nelineinykh sistem. UFN 141(2), 343–374 (1983)CrossRef M. Feigenbaum, Universal’nost’ v povedenii nelineinykh sistem. UFN 141(2), 343–374 (1983)CrossRef
62.
go back to reference V.A. Chernomorets, S.K. Gorbunov, Printsipy identifikatsii determinirovannoi osnovy v khaoticheskom povedenii sistem. Problemy uprvleniia i informatiki, №6, 24–33 (2005) V.A. Chernomorets, S.K. Gorbunov, Printsipy identifikatsii determinirovannoi osnovy v khaoticheskom povedenii sistem. Problemy uprvleniia i informatiki, №6, 24–33 (2005)
Metadata
Title
Fractal Kinetics of Fracture
Authors
Ahad Kh. Janahmadov
Maksim Y. Javadov
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-28189-6_4

Premium Partner