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Recursions and limit theorems for the strength and lifetime distributions of a fibrous composite

Published online by Cambridge University Press:  14 July 2016

Chia-Chyuan Kuo  and
S. Leigh Phoenix
Chia-Chyuan Kuo
Affiliation:
Cornell University
S. Leigh Phoenix*
Affiliation:
Cornell University
*
∗∗Postal address: Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA.
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Abstract

A composite material is a parallel arrangement of stiff brittle fibers in a flexible matrix. Under load fibers fail, and the loads of failed fibers are locally redistributed onto nearby survivors through the matrix. In this paper we develop a new technique for computing the probability of failure under a previously studied model of the failure process. A recursion and limit theorem are obtained which apply separately to static strength and fatigue lifetime depending on the composite loading and the probability model for the failure of individual fibers under their own loads. The limit theorem yields an approximation for the distribution function for composite lifetime which is of the form 1 – [1 – W(t)]mn where W(t) is a characteristic distribution function and mn is the composite volume, reflecting a size effect. A similar result holds also for static strength. In both cases such a result was conjectured several years ago. This limit theorem is obtained from the recursion upon applying a key theorem in the theory of the renewal equation. In the proofs three technical conditions arise which must be verified in specific applications. In the case of static strength these conditions are quite easy to verify, but in the case of fatigue lifetime the verification is generally difficult, and entails considerable numerical computation.

Keywords

FAILURE PROCESSFATIGUE LIFETIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 137 - 159
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

∗

Present address: Kendall Company, 95 West St., Walpole, MA 02081, USA.

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