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Asymptotic bounds on the time to fatigue failure of bundles of fibers under local load sharing

Published online by Cambridge University Press:  01 July 2016

Luke Tierney
Luke Tierney*
Affiliation:
Carnegie-Mellon University
*
∗Postal address: Department of Statistics, Carnegie-Mellon University, Pittsburg, PA 15213, U.S.A.
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Abstract

A fiber bundle is a parallel arrangement of fibers. Under a steady tensile load, fibers fail randomly in time in a manner that depends on how they share the applied load. The bundle fails when all its fibers have failed in a specified region.

In this paper we consider the fatigue failure of such a bundle in a fiber load-sharing setting appropriate for composite materials, that is, to bundles impregnated with a flexible matrix. The bundle is actually modelled as a chain of short bundles, and local load sharing is assumed for the fibers within each short bundle. The chain of bundles fails once all the fibers in one of the short bundles have failed.

Reasonable assumptions are made on the stochastic failure of individual fibers. A general framework for describing fiber bundles is developed and is used to derive the limiting distribution of the time to the first appearance of a set of k or more adjacent failed fibers as the number of fibers in the bundle grows large. These results provide useful bounds on the distribution of the time to total bundle failure. Some implications and extensions of these results are discussed.

Keywords

FIBER BUNDLETIME TO FAILURELOCAL LOAD SHARINGRELIABILITY OF COMPOSITE MATERIALS
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 1 , March 1982 , pp. 95 - 121
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

This research was supported by the U.S. Department of Energy under contract DE-AS02-76ER04027.

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