Statistical Theory of the Strength of Fiber Bundles

[+] Author and Article Information
L. N. McCartney

Division of Materials Applications, National Physical Laboratory, Teddington, Middlesex, U.K.

R. L. Smith

Department of Mathematics, Imperial College of Science and Technology, London SW7 2BZ, U.K.

J. Appl. Mech 50(3), 601-608 (Sep 01, 1983) (8 pages) doi:10.1115/1.3167097 History: Received November 01, 1981; Revised December 01, 1982; Online July 21, 2009


Following a review of statistical models of the failure of single fibers and bundles of these fibers, algebraic recurrence formulas are derived that generate expressions for the failure probabilities of bundles of classical fibers. One of these recurrence relations is suitable for the accurate numerical calculation of failure probabilities of bundles consisting of up to 500 single fibers. It is shown how account can be taken of the effect of defect-free fibers having finite strength. Numerical results are compared to three asymptotic analytic approximations, two of which have been proposed in the statistical literature and are now applied to fiber problems for the first time.

Copyright © 1983 by ASME
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