On the Influence of Vibrational Heating on the Fracture Propagation in Polymeric Materials

  • G. I. Barenblatt
  • V. M. Entov
  • R. L. Salganik
Conference paper
Part of the IUTAM Symposia book series (IUTAM)


According to the basic concept of S. N. Zhurkov [1, 2], the fracture of solids is a process which takes place in time under any stress and is controlled by certain kinetics due to thermal fluctuations and is strongly affected by temperature and stress. Let us denote the average sample lifetime at temperature T and tensile stress σ by t 0 = t 0 (σ, T). For the evaluation of the time of failure t 0 * for the case of an alternating stress σ (t), Bailey’s rule of damage summation will be used [3], i.e.
$$\int\limits_0^{t_0^*} {\frac{{dt}}{{{t_0}(\sigma (t),T)}}} = 1$$
following from the assumption that each moment the average rate of the damage process is the same as if the acting stress were constant in time (quasi-stationarity).


Stress Intensity Factor Crack Length Heat Generation Heat Conduction Problem Heating Zone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Zhurkov, S. N., and B. N. Narzullaev: The Time-dependence of Solids Strength. Zhurn. Tekhn. Fiz. 28, No. 10, 167 (1953). [in Russian]Google Scholar
  2. [2]
    Zhurkov, S. N.: Kinetic Concept of the Strength of Solids. Intern. J. Fracture Mech. 1, No. 4 (1965).Google Scholar
  3. [3]
    Bailey, J.: Attempt to Correlate Some Tensile Strength Measurements on Glass. Glass Industry 20, No. 1–4 (1939).Google Scholar
  4. [4]
    Regel, V. R., and A. M. Leksovsky: A Study of Fatigue within the Framework of the Kinetic Concept of Fracture. Intern. J. Fracture Mech. 3, No. 2, 99 (1967).Google Scholar
  5. [5]
    Bartenev, G. M., B. I. Panshin, I. V. Raztjmovskaya and G. N. Finogenov: On Long Time Cyclic Strength of Organic Glass. Izv. AN SSSR, OTN, Mech. i mash. No. 6 (1960). [in Russian]Google Scholar
  6. [6]
    Bland, D. R.: The Theory of Linear Viscoelasticity. London: Pergamon Press. 1960.MATHGoogle Scholar
  7. [7]
    Ferry, J.: Viscoelastic Properties of Polymers. New York: J. Wiley. 1965.Google Scholar
  8. [8]
    Entov, V. M., and R. L. Salganik: On the Cracks in Viscoelastic Solids. Inzh. Zhurn., Mekhanika Tverdogo Tela No. 2 (1968). [in Russian]Google Scholar
  9. [9]
    Sneddon, I. N.: The Distribution of Stress in the Neighborhood of a Crack in an Elastic Solid. Proc. Roy. Soc., A 187, 229–260 (1946).Google Scholar
  10. [10]
    Williams, M. L.: On the Stress Distribution at the Base of Stationary Crack. J. Appl. Mech. 24, 109–114 (1957).MathSciNetMATHGoogle Scholar
  11. [11]
    Irwin, G. R.: Fracture. In: Handbuch der Physik (S. Flugge, ed.), Bd. VI. Berlin-Gottingen-Heidelberg: Springer, 551–590 (1958).Google Scholar
  12. [12]
    Barenblatt, G. I.: The Mathematical Theory of Equilibrium Cracks in Brittle Fracture. Advances in Appl. Mechanics, 7. New York: Academic Press. 1962.Google Scholar
  13. [13]
    Ryzhik, I. M., and I. S. Gradstein: Tables of Integrals, Sums, Series and Products. Gostekhisdat, 1951. [in Russian]Google Scholar
  14. [14]
    Barenblatt, G. I.: The Effects of Small Vibrations at the Deformation of Polymers. PMM 30, 1 (1966).Google Scholar
  15. [15]
    Barenblatt, G. I., V. M. Entov and R. L. Salganik: On the Kinetics of the Crack Propagation. General Concepts. The Nearly Equilibrium Cracks. Inzh. Zhurn., Mekhanika Tverdogo Tela, No. 5 (1966). [in Russian]Google Scholar
  16. [16]
    Barexblatt, G. I., V. M. Entov, and R. L. Salganik: On the Kinetics of the Crack Propagation. Fluctuational Failure. Inzh. Zhurn., Mekhanika Tverdogo Tela No. 1 (1967). [in Russian]Google Scholar
  17. [17]
    Frank-Kamenetskij, D. A.: Diffusion and Heat Transfer in the Chemical Kinetics. Izd. Nauka, 1967. [in Russian]Google Scholar
  18. [18]
    Berry, J. P.: Fracture Processes in Polymeric Materials, II. Tensile Strength of Polysterene. J. Polymer Sci. 50, 313–321 (1961).ADSCrossRefGoogle Scholar
  19. [19]
    Berry, J. P.: Fracture Processes in Polymeric Materials, IV. Dependence of the Fracture Surface Energy on Temperature and Molecular Structure. J. Polymer Sci. Part A 1, 993–1003 (1961).Google Scholar
  20. [20]
    Takayanagi, M.: Viscoelastic Properties of Crystalline Polymers. Mem. Fac. Engng Kyushu Univ., 23, No. 1 (1963).Google Scholar
  21. [21]
    Regel, V. R., and A. M. Leksovsky: Time Dependence of Strength at Static and Cyclic Loads. Fiz. Tv. Tela 4, No. 4 (1962). [in Russian]Google Scholar

Copyright information

© Springer-Verlag/Wien 1970

Authors and Affiliations

  • G. I. Barenblatt
    • 1
  • V. M. Entov
    • 1
  • R. L. Salganik
    • 1
  1. 1.MoscowU.S.S.R.

Personalised recommendations