Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T22:45:25.808Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  01 July 2016

S. Leigh Phoenix
S. Leigh Phoenix*
Affiliation:
Cornell University
*
∗Postal address: Sibley School of Mechanical and Aerospace Engineering, Upson and Grumman Halls, Cornell University, Ithaca N.Y. 14853, U.S.A.
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

FIBER BUNDLETIME TO FAILURELOAD SHARINGWEAK CONVERGENCEQUANTILE PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 1 , March 1979 , pp. 153 - 187
Copyright
Copyright © Applied Probability Trust 1979 

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 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.

References

Coleman, B. D. (1958) Statistics and time dependence of mechanical breakdown in fibers. J. Appl. Phys. 29, 968–983.Google Scholar
Daniels, H. E. (1945) The statistical theory of strength of bundles of threads. Proc. R. Soc. London A183, 405–435.Google Scholar
Phoenix, S. L. (1978) The asymptotic time to failure of a mechanical system of parallel members. SIAM J. Appl. Math. 34, 227–246.Google Scholar
Phoenix, S. L. and Taylor, H. M. (1973) The asymptotic strength distribution of a general fiber bundle. Adv. Appl. Prob. 5, 200–216.Google Scholar
Pyke, R. and Shorack, G. (1968) Weak convergence of the two-sample empirical process and a new approach to Chernoff-Savage theorems. Ann. Math. Statist. 39, 755–771.Google Scholar
Shorack, G. (1972a) Functions of order statistics. Ann. Math, Statist. 43, 412–427.Google Scholar
Shorack, G. (1972b) Convergence of quantile and spacings processes with applications. Ann. Math. Statist. 43, 1400–1411.Google Scholar