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The asymptotic distribution for the time to failure of a fiber bundle

  • S. Leigh Phoenix (a1)
Abstract

A model is developed for the failure time of a bundle of fibers subjected to a constant load. At any time, all surviving fibers share the bundle load equally while all failed fibers support no load. The bundle may collapse immediately or fibers may fail randomly in time, possibly more than one at a time. The failure time of the bundle is the failure time of the last surviving fiber. For a single fiber, the c.d.f. for the failure time is assumed to be a specific functional of an arbitrary load history. The model is developed using a quantile process approach. In the most important case the failure time of the bundle is shown to be asymptotically normal with known parameters. The bundle failure model has the features of both static strength and fatigue failure of earlier analyses, and thus is more realistic than earlier models.

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Postal address: Sibley School of Mechanical and Aerospace Engineering, Upson and Grumman Halls, Cornell University, Ithaca N.Y. 14853, U.S.A.
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This research was supported in part by the United States Department of Energy under Contract No. EY-76-S-02-4027 and in part by the Office of Naval Research under grant N00014-76-C-0790.

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References
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Coleman, B. D. (1958) Statistics and time dependence of mechanical breakdown in fibers. J. Appl. Phys. 29, 968983.
Daniels, H. E. (1945) The statistical theory of strength of bundles of threads. Proc. R. Soc. London A183, 405435.
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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