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On the distribution of the breaking strain of a bundle of brittle elastic fibers

Part of: Special processes Survival analysis and censored data Applications

Published online by Cambridge University Press:  01 July 2016

James U. Gleaton  and
James D. Lynch
James U. Gleaton*
Affiliation:
University of North Florida
James D. Lynch*
Affiliation:
University of South Carolina
*
∗ Postal address: Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL 32224, USA.
∗∗ Postal address: Center for Reliability and Quality Sciences, Department of Statistics, University of South Carolina, Columbia, SC 29208, USA. Email address: [email protected]
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Abstract

The maximum-entropy formalism developed by E. T. Jaynes is applied to the breaking strain of a bundle of fibers of various cross-sectional areas. When the bundle is subjected to a tensile load, and it is assumed that Hooke's law applies up to the breaking strain of the fibers, it is proved that the survival strain distribution for a fiber in the bundle is restricted to a certain class consisting of generalizations of the log-logistic distribution. Since Jaynes's formalism is a generalization of statistical thermodynamics, parallels are drawn between concepts in thermodynamics and in the theory of inhomogeneous bundles of fibers. In particular, heat transfer corresponds to damage to the bundle in the form of broken fibers, and the negative reciprocal of the parameter corresponding to thermodynamic temperature is the resistance of the bundle to damage.

Keywords

Max entropybreaking strainlog-logistic distributionthermodynamicsbundle of fiberstensile loadtemper

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62N05: Reliability and life testing 62P35: Applications to physics
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 1 , March 2004 , pp. 98 - 115
Copyright
Copyright © Applied Probability Trust 2004 

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Footnotes

Research partially supported by NSF Grants DMS 9877107 and NSF DMS 0243594.

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