Conclusions
1. The stress distribution over the individual bonds at the end of a crack is taken into account on the basis of fracture mechanics using the Bartenev-Razumovskaya-Rebinder kinetic model for polymeric glasses.
2. The rate of growth of a transverse edge crack in a strip subjected to tensile stresses is obtained as a function of the parameter σ√l; this dependence is similar to that observed experimentally.
3. The time characteristics of the strength are calculated numerically with reference to polymethyl methacrylate.
4. An approximate analytic expression is obtained for the lifetime of a strip of polymeric glass; at σo<σ<σk this expression coincides with the exact result calculated on a computer.
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Literature cited
V. V. Panasyuk, Limit Analysis of Brittle Bodies with Cracks [in Russian], Kiev (1968).
A. K. Malmeister, V. P. Tamuzh, and G. A. Teters, Strength of Rigid Polymeric Materials [in Russian], Riga (1972).
G. P. Cherepanov, Mechanics of Brittle Fracture [in Russian], Moscow (1974).
L. M. Kachanov, Fundamentals of Fracture Mechanics [in Russian], Moscow (1974).
S. N. Zhurkov and B. N. Narzullaev, "Time dependence of the strength of solids," Zh. Tekh. Fiz.23, 1677–1689 (1953).
S. N. Zhurkov, "A problem of the strength of solids," Vestn. Akad. Nauk SSSR, No. 11, 78–82 (1957).
S. N. Zhurkov and É. E. Tomashevskii, "Investigation of the strength of solids," Zh. Tekh. Fiz.,25, No. 1, 66–73 (1955).
S. N. Zhurkov and T. P. Sanfirova, "Study of the time and temperature dependence of strength," Fiz. Tverd. Tela,11, No. 6, 1033–1039 (1960).
A. M. Leksovskii and V. R. Regel', "Study of the growth of main cracks in polymers under static and cyclic tension," Mekh. Polim., No. 2, 253–265 (1970).
V. R. Regel', "Kinetic theory of strength as a scientific basis for predicting the life of polymers under load," Mekh. Polim., No. 1, 98–112 (1971).
V. R. Regel', A. I. Slutsker, and É. É. Tomashevskii, Kinetic Nature of the Strength of Solids [in Russian], Moscow (1974).
G. M. Bartenev, "Time and temperature dependence of the strength of solids," Izv. Akad. Nauk SSSR. Otd. Tekh. Nauk, No. 9, 53–64 (1955).
G. M. Bartenev, I. V. Razumovskaya, and P. A. Rebinder, "Theory of spontaneous dispersion of solids," Kolloidn. Zh.,20, 654–664 (1958).
G. M. Bartenev, "Present position and prospects for development of the physical theory of the brittle strength of polymers," Mekh. Polim., No. 5, 700–721 (1966).
V. E. Gul', Structure and Strength of Polymers [in Russian], Moscow (1971).
G. I. Barenblatt, V. M. Entov, and R. L. Salganik, "Crack propagation kinetics. Fracture criterion and long-term strength," Inzh. Zh., Mekh. Tverd. Tela, No. 6, 76–81 (1966).
G. I. Barenblatt, V. M. Entov, and R. L. Salganik, "Crack propagation kinetics. Fluctuation fracture," Inzh. Zh., Mekh. Tverd. Tela, No. 1, 122–129 (1967).
V. M. Entov and R. L. Salganik, "On the Prandtl brittle fracture model," Inzh. Zh., Mekh. Tverd. Tela, No. 6, 87–99 (1968).
R. L. Salganik, "Investigation of fracture kinetics and crack development in polymeric materials," Doctoral Dissertation, Moscow (1971).
A. I. Gubanov and A. D. Chevychelov, "Theory of breaking strength of rigid polymers," Fiz. Tverd. Tela,4, No. 4, 928–933 (1962).
V. P. Pukh, S. A. Laterner, and V. N. Ingal, "Kinetics of crack growth in glass," Fiz. Tverd. Tela,12, No. 4, 1128–1132 (1970).
V. P. Pukh, S. A. Laterner, and V. N. Ingal, "Kinetics of fracture development in glass and estimation of the theoretical strength of glass," in: Proceedings of the First All-Union Symposium on the Mechanical and Thermal Properties and Structure of Inorganic Glasses [in Russian], Moscow (1972), pp. 74–80.
V. P. Pukh, Strength and Fracture of Glass [in Russian], Leningrad (1973).
I. N. Goodier, "Mathematical theory of equilibrium cracks," in: Fracture, Vol. 2, New York-London (1968), pp. 1–67.
P. Paris and J. Si, "Analysis of the state of stress around cracks," in: Applied Problems of Fracture Toughness [Russian translation], Moscow (1968), pp. 64–142.
I. N. Goodier and M. Kanninen, "Crack propagation in continuum model with nonlinear atomic separation law," Tech. Rep., No. 165, 156, Div. Eng. Mecha., Stanford University (1966).
G. M. Bartenev and Yu. S. Zuev, Strength and Fracture of Rubberty Materials [in Russian], Moscow (1964).
P. Manogg, "Schattenoptische Messung der spezifischen Bruchenergie wahrend des Bruchvorgangs bei Plexiglas," in: Physics of Non-Crystalline Solids. Proceedings of the International Conference, Delft, July, 1964, Amsterdam (1965), pp. 481–490.
A. S. Vavakin, R. V. Gol'dshtein, R. L. Salganik, and N. S. Yushchenko, "Determination of lifetime characteristics from crack growth kinetics data," Mekh. Polim., No. 4, 634–640 (1973).
V. S. Kuksenko, A. I. Slutsker, and A. A. Yastrebinskii, "Occurrence of submicroscopic cracks in oriented amorphous-crystalline polymers under load," Fiz. Tverd. Tela,9, No. 8, 2390–2399 (1967).
V. S. Ryskin, M. A. Gezalov, V. S. Kuksenko, V. A. Marikhin, and A. I. Slutsker, "Study of submicroscopic cracks by diffraction methods," Fiz. Tverd. Tela,13, 784–788 (1971).
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Institute of Physical Chemistry, Academy of Sciences of the USSR, Moscow. Moscow Engineering Physics Institute. Translated from Mekhanika Polimerov, No. 1, pp. 3–11, January–February, 1977.
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Bartenev, G.M., Tulinov, B.M. Kinetic theory of brittle fracture of polymeric glasses. Polymer Mechanics 13, 1–8 (1977). https://doi.org/10.1007/BF00857271
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DOI: https://doi.org/10.1007/BF00857271