Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-27T18:08:52.469Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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

References

Coleman, E. D. (1957) A stochastic process model for mechanical breakdown. Trans. Soc. Rheol. 1, 153–168.CrossRefGoogle Scholar
Coleman, B. D. (1958) Statistical and time dependence of mechanical breadkown in fibres. J. Appl. Phys. 29, 968–983.CrossRefGoogle Scholar
Daniels, H. E. (1945) The statistical theory of the strength of bundles of threads, I. Proc. R. Soc. London A 183, 405–435.Google Scholar
Fukuda, H. and Kawata, K. (1976) On the stress concentration factor in fibrous composites. Fibre Sci. Technol. 9, 189–203.Google Scholar
Harlow, D. G. (1977) Probabilistic Models for the Tensile Strength of Composite Materials. , Cornell University.Google Scholar
Harlow, D. G. and Phoenix, S. L. (1981a) Probability distributions for the strength of composite materials I: Two-level bounds. Internat. J. Fracture. CrossRefGoogle Scholar
Harlow, D. G. and Phoenix, S. L. (1981b) Probability distributions for the strength of composite materials II: A convergent sequence of tight bounds. Internat. J. Fracture. CrossRefGoogle Scholar
Hedgepeth, J. U. and Van Dyke, P. (1967) Local stress concentrations in imperfect filamentary composite materials. J. Composite Materials 1, 294–309.Google Scholar
Kelley, R. P. (1978) Further Examination and a Local Load Sharing Extension of Coleman's Time to Failure Model for Fiber Bundles. , Cornell University.Google Scholar
Phoenix, S. L.(1978a) Stochastic strength and fatigue of fiber bundles. Internat. J. Fracture 14, 327–344.CrossRefGoogle Scholar
Phoenix, S. L.(1978b) The asymptotic time to failure of a mechanical system of parallel members. SIAM J. Appl. Math. 34, 227–246.Google Scholar
Phoenix, S. L. (1979) The asymptotic distribution for the time to failure of a fibre bundle. Adv. Appl. Prob. 11, 153–187.Google Scholar
Pitt, R. E. (1980) The Statistical Strength of Fibrous Materials as Influenced by Fiber Load-Sharing and Geometric Configuration. , Cornell University.Google Scholar
Rosen, D. W. (1964) Tensile failure of fibrous composites. AIAA J. 2, 1985–1991.CrossRefGoogle Scholar
Scop, P. M. and Argon, A. S. (1969) Statistical theory of strength of laminated composites II. J. Composite Materials 3, 30–47.Google Scholar
Smith, R. L. (1979) Limit Theorems for the Reliability of Series-Parallel Load-Sharing Systems. , Cornell Univeristy.Google Scholar
Smith, R. L. (1981) A probability model for the strength of fibrous composites with local load sharing. Proc. R. Soc. London A 372, 539–553.Google Scholar
Tierney, L. (1980) Limit Theorems for the Failure Time of Bundles of Fibers under Unequal Load Sharing. , Cornell University.Google Scholar
Tierney, L. (1981) The asymptotic time to failure of a bundle of fibers with random slacks. Adv. Appl. Prob. 13, 548–566.Google Scholar
Watson, G. S. (1954) Extreme values in samples from M-dependent stationary stochastic processes. Ann. Math. Statist. 25, 798–800.Google Scholar