Physical Mesomechanics

, Volume 22, Issue 1, pp 5–12 | Cite as

The Benefits and Challenges of Interdisciplinary Research

  • L. R. BotvinaEmail author


This brief review takes a look at our joint research with Prof. G.I. Barenblatt and at some outcomes of his interdisciplinary initiatives. The research covers the issues of self-similarity in fatigue fracture, jump-like growth of fatigue cracks, and damage accumulation on different scales.


similarity self-similarity fatigue fracture analogy damage ultrasonic attenuation scaling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barenblatt, G.I. and Botvina, L.R., Similarity Methods in the Fatigue Crack Growth Study, in Proc. of the IV All–Union Conference on Fracture Physics, Kiev, 1980, pp. 398–399.Google Scholar
  2. 2.
    Barenblatt, G.I. and Botvina, L.R., Incomplete Self–Similarity of Fatigue in the Linear Range of Crack Growth, FatigueEng. Mater. Struct., 1980, vol. 3, no. 3, pp. 193–202.CrossRefGoogle Scholar
  3. 3.
    Barenblatt, G.I. and Botvina, L.R., Application of the Similarity Methods to Damage Accumulation and Fatigue Crack Growth Studies, in Defects and Fracture: Proc. I Int. Symp., Tuczno, Poland, 1980, 1982, pp. 71–79.Google Scholar
  4. 4.
    Barenblatt, G.I. and Botvina, L.R., A Note Concerning Power–Type Constitutive Equations of Deformation and Fracture of Solids, Int. Eng. Sci., 1982, vol. 20, no. 2, pp. 187–191.CrossRefzbMATHGoogle Scholar
  5. 5.
    Barenblatt, G.I. and Botvina, L.R., Self–Similarity of Fatigue Failure: Damage Accumulation, Izv. ANSSSR. MTT, 1983, no. 2, pp. 88–92.Google Scholar
  6. 6.
    Botvina, L.R. and Barenblatt, G.I., Self–Similarity of Damage Accumulation, Probl. Prochn., 1985, no. 12, pp. 17–24.Google Scholar
  7. 7.
    Barenblatt, G.I. and Botvina, L.R., Self–Oscillatory Modes of Fatigue Fracture and the Formation of Self–Similar Structures at the Fracture Surface, Proc. Roy. Soc. Lond., 1993, vol. 442, pp. 489–494.ADSCrossRefzbMATHGoogle Scholar
  8. 8.
    Alabuzhev, P.M. and Minkevich, L.M., Fundamentals of the Theory of Similarity and Modeling, Novosibirsk: Institute of Hydrodynamics SB USSR AS, 1965.Google Scholar
  9. 9.
    Ivanova, V.S. and Botvina, L.R., Strength Problems and Prediction of Mechanical Properties of Metals, Izv. AN USSR. Metals, 1972, no. 6, pp. 26–33.Google Scholar
  10. 10.
    Barenblatt, G.I., Similarity, Self–Similarity, Intermediate Asymptotics, Leningrad: Gidrometeoizdat, 1982.zbMATHGoogle Scholar
  11. 11.
    Barenblatt, G.I., Dimensional Analysis, New York: Gordon and Breach, 1987.Google Scholar
  12. 12.
    Paris, P.C. and Erdogan, F., A Critical Analysis of Crack Propagation Laws, J. Basis Eng., 1963, vol. 85, no. 4, pp.528–534.Google Scholar
  13. 13.
    Barenblatt, G.I., Scaling Phenomena in Fatigue and Fracture, Int. J. Fracture, 2006, vol. 138, pp. 19–35.CrossRefzbMATHGoogle Scholar
  14. 14.
    Barenblatt, G.I., Flow, Deformation and Fracture, Cambridge: Cambridge University Press, 2014.CrossRefzbMATHGoogle Scholar
  15. 15.
    Botvina, L.R., Ivanskoy, V.A., Maloletnev, A.Ya., Lvov, Yu.B., and Novikov, I.I., Kinetic Regularities of Fracture of Carbon Steels under Cyclic Shock Loading, Probl. Prochn., 1986, no. 9, pp. 11–16.Google Scholar
  16. 16.
    Ciavarella, M., Paggi, M., and Carpinteri, A., One, No One, and One Hundred Thousand Crack Propagation Laws: A Generalized Barenblatt and Botvina Dimensional Analysis Approach to Fatigue Crack Growth, J. Mech. Phys. Solids, 2008, vol. 56, no. 12, pp. 3416–3432.ADSzbMATHGoogle Scholar
  17. 17.
    Forsyth, P.J.E., Fatigue Damage and Crack Growth in Aluminum Alloys, Acta Met., 1963, vol. 11, no. 7, pp. 703–715.CrossRefGoogle Scholar
  18. 18.
    Forsyth, P.J.E., Some Observation and Measurements on Mixed Fatigue–Tensile Crack Growth in Aluminum Alloys, Scripta Met., 1976, vol. 10, no. 5, pp. 383–386.CrossRefGoogle Scholar
  19. 19.
    Botvina, L.R., Limar, L.V., and Logovikov, B.S., Estimation of Parameters of the Jump–Like Growth of Fatigue Cracks in Compressor Blades of Titanium Alloy VT3–1, Fiz.–Khim. Mekh. Mat., 1981, no. 1, pp. 71–74.Google Scholar
  20. 20.
    Botvina, L.R., Kinetics of Fracture of StructuralMaterials, Moscow: Nauka, 1989.Google Scholar
  21. 21.
    Sadovskii, M.A., Hierarchical Distribution of Solid Materials, Preprint of the IPE RAS, Moscow, 1984, preprint no. 7.Google Scholar
  22. 22.
    Sadovskii, M.A., On the Natural Lumpiness of the Rock Structure, Dokl. AN USSR, 1979, vol. 247, pp. 829–840.Google Scholar
  23. 23.
    Bahat, D., Correlation between Fracture Surface Morphology and Orientation of Cross–Fold Joints in Eocene Chalks around Beer Sheva, Israel, Tectonophysics, 1987, vol. 136, pp. 323–333.ADSCrossRefGoogle Scholar
  24. 24.
    Bahat, D., Tectonofractography, Berlin: Springer–Verlag, 1992.Google Scholar
  25. 25.
    Zhurkov, S.N., Kuksenko, V.S., and Slutsker, A.I., Formation of Submicroscopic Cracks in Polymers under Load, FTT, 1969, vol. 11, no. 1, pp. 296–302.Google Scholar
  26. 26.
    Botvina, L.R. and Soldatenkov, A.P., On the Concentration Criterion of Fracture, Metallofiz. Noveish. Tekhnol., 2017, vol. 39, no. 4, pp. 477–490.CrossRefGoogle Scholar
  27. 27.
    Botvina, L.R., Rotwain, I.M., Keilis–Borok, V.I., and Oparina, I.B., On the Character of the Gutenberg–Richter Relation on Different Stages of Damage Accumulation and Earthquake Generation, Rep. Russ. Acad. Science, 1995, vol. 345, pp. 809–812.Google Scholar
  28. 28.
    Rotwain, I.M., Keilis–Borok, V.I., and Botvina, L.R., Premonitory Transformation of Steel Fracturing and Seismicity, Phys. Earth Planetary Interiors, 1997, vol. 101, pp. 61–71.ADSCrossRefGoogle Scholar
  29. 29.
    Botvina, L.R. and Petersen, T.B., On the Analogy of Acoustic and Seismic Modes at Various Stages of Fracture, Dokl. RAN, 2001, vol. 376, no. 3, pp. 331–334.Google Scholar
  30. 30.
    Botvina, L.R., Fracture: Kinetics, Mechanisms, General Laws, Moscow: Nauka, 2008.Google Scholar
  31. 31.
    Botvina, L.R., Fradkin, L.Ju., and Bridge, B.J., Power Laws and Generalised Dimensional Analysis in Ultrasonic NDE, Nondestr. Test. Eval., 1995, vol. 12, pp. 103–118.CrossRefGoogle Scholar
  32. 32.
    Botvina, L.R. and Michailov, A.V., Ultrasonic Method for Estimating Damages Accumulated in Conditions of Creep, Fatigue and Impact Loading, in Proc. 13th Euro. Conf. Fracture. Fracture Mechanics: Application and Challenges, 6–9 September, 2000, San Sebastian, Spain, Paper no. 106, pp. 1–5.Google Scholar
  33. 33.
    Andreeva, I.V., Radomyselskii, I.D., and Scherban, I.I., Investigation of Powder Compactibility, Porosh. Metallurg., 1975, no. 6, pp. 32–41.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Baikov Institute of Metallurgy and Materials ScienceRussian Academy of SciencesMoscowRussia

Personalised recommendations