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Probability distributions for the strength of fibrous materials under local load sharing I: Two-level failure and edge effects

Published online by Cambridge University Press:  01 July 2016

D. Gary Harlow  and
S. Leigh Phoenix
D. Gary Harlow*
Affiliation:
Drexel University
S. Leigh Phoenix*
Affiliation:
Cornell University
*
∗Postal address: Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, PA 19104, U.S.A.
∗∗Postal address: Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, U.S.A.
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Abstract

The focus of this paper is on obtaining a conservative but tight bound on the probability distribution for the strength of a fibrous material. The model is the chain-of-bundles probability model, and local load sharing is assumed for the fiber elements in each bundle. The bound is based upon the occurrence of two or more adjacent broken fiber elements in a bundle. This event is necessary but not sufficient for failure of the material. The bound is far superior to a simple weakest link bound based upon the failure of the weakest fiber element. For large materials, the upper bound is a Weibull distribution, which is consistent with experimental observations. The upper bound is always conservative, but its tightness depends upon the variability in fiber element strength and the volume of the material. In cases where the volume of material and the variability in fiber strength are both small, the bound is believed to be virtually the same as the true distribution function for material strength. Regarding edge effects on composite strength, only when the number of fibers is very small is a correction necessary to reflect the load-sharing irregularities at the edges of the bundle.

Keywords

SERIES-PARALLEL STRUCTURESSTRENGTH OF COMPOSITE MATERIALSLOCAL LOAD SHARINGPROBABILITY BOUNDSWEIBULL DISTRIBUTION
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 1 , March 1982 , pp. 68 - 94
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Research supported by the U.S. Department of Energy under Contract DE-AC02-76-ER04027.

References

Argon, A. S. (1972) Fracture of composites. In Treatise on Materials Science and Technology, ed. Herman, H., Academic Press, New York, 79–114.Google Scholar
Daniels, H. E. (1945) The statistical theory of the strength of bundles of threads. Proc. R. Soc. London A 183, 405–435.Google Scholar
Harlow, D. G. and Phoenix, S. L. (1978a) The chain-of-bundles probability model for the strength of fiberous materials I: Analysis and conjectures. J. Composite Materials 12, 195–214.Google Scholar
Harlow, D. G. and Phoenix, S. L. (1978b) The chain-of-bundles probability model for the strength of fibrous materials II: A numerical study of convergence. J. Composite Materials 12, 314–334.Google Scholar
Harlow, D. G. and Phoenix, S. L. (1979) Bounds on the probability of failure of composite materials. Internat. J. Fracture 15, 321–336.CrossRefGoogle Scholar
Karlin, S. and Studden, W. J. (1966) Tchebycheff Systems: With Application in Analysis and Statistics. Wiley, New York.Google Scholar
Rosen, B. W. (1964) Tensile failure of fibrous composites. AIAA J. 2, 1985–1991.Google 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
Selby, R. L. (1980) Standard Mathematical Tables. Chemical Rubber Co., Cleveland.Google Scholar
Smith, R. L. (1980) A probability model for fibrous composites with local load sharing. Proc. R. Soc. London A 372, 539–553.Google Scholar
Zweben, C. (1968) Tensile failure analysis of fibrous composites. AIAA J. 6, 2325–2331.Google Scholar
Zweben, C. and Rosen, B. W. (1970) A statistical theory of material strength with application to composite materials. J. Mech. Phys. Solids 18, 189–206.CrossRefGoogle Scholar