Abstract
A new derivation of the scale effect equation for polymer fibers is proposed. The equation is: σ ∼ σAL −β, where σ is the average strength of the fiber; L is the length of the fiber; A and β are coefficients. The equation was obtained from the general premises of scale effect theory without indication of the concrete form of the probability function F(S).
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References
F. T. S. Pierce, J. Text. Inst., 17, 355 (1926).
Zav. Lab., 26, 319, 1104 (1960); 27, 318 (1961).
B. B. Chechulin, The Scale Factor and Statistical Nature of the Strength of Metals [in Russian], Mashgiz, Moscow (1963), p. 203.
R. E. Pitt and S. L. Phoenix, Text. Res. J., 51, 408 (1981).
H. E. Daniels, Proc. Roy. Soc., 183A, 405 (1945).
G. Korten, in: Modern Composite Materials, Addison-Wesley, Reading, Massachusetts (1967) [Russian translation], Mir, Moscow (1970), pp. 130–141].
B. Rosen, in: Fibrous Composite Materials [Russian translation], Mir, Moscow (1967), pp. 55–96.
W. Weibull, J. Appl. Mech., 18, 293 (1951).
V. P. Tamuzh and V. S. Kuksenko, Micromechanism of Failure of Polymeric Materials [in Russian], Zinatne, Riga (1978).
V. A. Petrov and A. V. Savitskii, Dokl. Akad. Nauk, 224, 806–809 (1975).
A. V. Savitskii, B. Ya. Levin, I. A. Gorshkova, and G. N. Smikk, Mekh. Polim., No. 5, 925–931 (1977).
W. F. Knoff, J. Mater. Sci., 22, 1024–1030 (1977).
Ya.I. Frenkel', Introduction to the Theory of Metals [in Russian], Nauka, Leningrad (1972).
B. Wunderlich, Physics of Macromolecules [Russian translation], Mir, Moscow (1979).
A. N. Orlov, Introduction to the Theory of Defects in Crystals [in Russian], Vysshaya Shkola, Moscow (1983).
Fibrous Composite Materials [Russian translation], Mir, Moscow (1967).
M. A. Evgrafov, Asymptotic Estimations and Entire Functions [in Russian], Nauka, Moscow (1979).
Additional information
Ukrainian Scientific-Research Institute of Polymer Fibers, Kiev. Translated from Khimicheskie Volokna, No. 4, pp. 34–36, July–August, 1992.
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Nosov, M.P., Zabashta, Y.F. Phenomenological model of the scale effect of the strength of polymer fibers. Fibre Chem 24, 291–295 (1993). https://doi.org/10.1007/BF00550855
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DOI: https://doi.org/10.1007/BF00550855