Kinetic characteristics of polymers with cracks under mechanical and thermal loads


Аuthors

Kartashov E. M.1, 2*, Tishaeva I. R.3, Solomonova E. V.3

1. MIREA — Russian Technological University (Lomonosov Institute of Fine Chemical Technologies), 78, Vernadsky prospect, Moscow, 119454, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
3. MIREA ,

*e-mail: professor.kartashov@qmail.com

Abstract

The article presents theoretical relationships of important kinetic characteristics for brittle polymers with cracks under mechanical and thermal impacts, being fundamental of thermo-kinetics studies of polymer destruction process in terms of the time dependence theory of strength-durability. Straight (internal and surface) cracks in plate-type samples and internal circular (disc-shaped) cracks in polymer fibers were considered. Two test modes were considered sequentially: constant tensile stress, constant absolute temperature, the unchanging structure, inactive medium, as well as a more complex mode of purely thermal loading, namely the least developed case in the theory of fracture. Calculated ratios of a number of limiting characteristics and parameters of the destruction process are given. They are safe and critical stress; the initial length of a micro-crack and its relative critical length; safe and critical tension; local stress at the crack tip (in the fluctuation volume); the amount of free surface energy. The above mentioned relations are the basis for the development of the theory of time dependence of strength-durability. Prospects for the further development of the corresponding theories were formulated, with account for the relaxation processes in polymers, as well as their chemical structure and supermolecular organization.

Keywords:

brittle polymers; fracture cracks; kinetic characteristics of strength; durability

References

  1. Askadsky A.A., Khokhlov A.R. Introduction to Physical Chemistry of Polymers. Moscow: Scientific World, 2009, 380 p. In Russ.

  2. Kartashov E.M. Modern concepts of the kinetic thermofluctuation theory of polymer strength. Results of Science and Technology. A series of chemistry and technology of macromolecular compounds. Moscow: VINITI, 1991, vol. 27, pp. 3‒111. In Russ.

  3. Regel V.R., Slutsker A.I., Tomashevsky E.E. The kinetic nature of the strength of solids. Moscow: Nauka, 1974, 560 p. In Russ.

  4. Bartenev G.M. Strength and degradation mechanisms of polymers. Moscow: Chemistry, 1984. 280 p. In Russ.

  5. Valishin A.A., Kartashov E.M. Energy effects in the kinetics of fracture of solids. Izvestiya RАN. Energetika — Proceedings of the Russian Academy of Sciences. Power Engineering, 2006, no. 4, pp. 150‒160.

  6. Gul V.E., Kuleznev V.N. Structure and mechanical properties of polymers. Moscow: Higher school, 1976. 352 p.

  7. Irwin G.R. Analysis of stresses and strains near the and of a crack traversinq a plate. Appl. Mech., 1957, vol. 24, no. 3, pp. 361‒364.

  8. Panasyuk V.V., Savruk M.P., Datsishin A.P. Stress distribution around cracks in plates and shells. Kiev: Naukova Dumka, 1976. 446 p.

  9. C. On the singular character of temperature stresses at the crack tip. Applied Mechanics, 1962, vol. 29, no. 3, pp. 157‒159.

  10. Muskhelishvili N.I. Some Basic Problems of the Mathematical Theory of Elasticity. Moscow: Nauka, 1966. 708 p.

  11. Kartashov E.M., Kudinov V.A. Analytical theory of thermal conductivity and applied thermoelasticity. Moscow: URSS, 2012. 655 p.

  12. Si, Paris, Erdogan. Coefficients of stress concentration at the crack tip under plane tension and bending of plates. Applied Mechanics (translated by the Proceedings of the American Society of Mechanical Engineers), 1962, T29-E, no. 2, pp. 101‒108.

  13. Savruk M.P. Stress intensity factors in bodies with cracks. Fracture Mechanics, vol. 2. Kiev: Naukova Dumka, 1988. 620 p.

  14. Bartenev G.M. State and prospects for the development of the physical theory of the brittle strength of polymers. Mechanics of polymers, 1966, no. 5, pp. 700‒721.

  15. Kartashov E.M. Griffith’s Energy Problem for Brittle Polymers. Engineering Physics Journal, 2007, vol. 80, no. 1, pp. 156‒165.

  16. Finkel V.M. Physical bases of inhibition of destruction. Moscow: Metallurgy, 1977. 360 p.

  17. Kartashov E.M. Analytical methods in the theory of thermal conductivity of solids. Moscow: Higher school, 2001. 540 p.

  18. Kartashov E.M., Kudinov V.A. Analytical methods of the theory of heat conduction and its applications. Moscow: URSS, 2017. 1080 p.

  19. Bartenev G.M., Zelenev Yu.V. Relaxation Phenomena in Polymers. Leningrad: Khimiya, 1972. 376 p.

  20. Kartashov E.M. Model representations of thermal shock in dynamic thermoelasticity. Russian technological journal, 2020, vol. 8, no. 2, pp. 85‒108.

  21. Kartashov E.M. Originals of operational images for generalized problems of unsteady heat conduction. Fine chemical technologies, 2019, vol. 14, no. 4, p. 77‒86.

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