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An application of random packing to the multiple fracture of composite materials

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Alan C. Kimber
Alan C. Kimber*
Affiliation:
University of Surrey
*
∗ Postal address: Department of Mathematical and Computing Sciences, University of Surrey, Guildford, GU2 5XH, UK.
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Abstract

A one-dimensional packing approach is used to obtain limiting results for inter-crack distances after multiple fracture of a long brittle-matrix composite with continuous aligned fibres. The results may also be appropriate for applications of the Rényi car-parking model in which there is a reduced probability of cars parking bumper to bumper.

Keywords

RANDOM PACKINGDISTRIBUTION OF GAPSCAR-PARKING MODELASYMPTOTICBEHAVIOURCOMPOSITE MATERIALS

MSC classification

Secondary: 60K99: None of the above, but in this section
Type
Short Communications
Information
Journal of Applied Probability , Volume 31 , Issue 2 , June 1994 , pp. 564 - 569
Copyright
Copyright © Applied Probability Trust 1994 

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References

Abramowitz, M. and Stegun, I. A., (Eds) (1972) Handbook of Mathematical Functions. Dover, New York.Google Scholar
Dunstan, D. J., Young, S. and Dixon, R. H. (1991) Geometrical theory of critical thickness and relaxation in strained-layer growth. J. Appl. Phys. 70, 3038–3045.CrossRefGoogle Scholar
Feller, W. (1966) An Introduction to Probability Theory and Its Applications, Vol. 2. Chichester: Wiley.Google Scholar
Kimber, A. C. and Keer, J. G. (1982) On the theoretical average crack spacing in brittle matrix composites. J. Mater. Sci. Lett. 1, 353–354.Google Scholar
Komaki, F. and Itoh, Y. (1992) A unified model for Kakutani's interval splitting and Renyi's random packing. Adv. Appl. Prob. 24, 502–505.Google Scholar
Rényi, A. (1958) On a one-dimensional problem concerning random space-filling problem. Publ. Math. Inst. Hungar. Acad. Sci. 3, 109–127.Google Scholar
Solomon, H. and Weiner, H. (1986) A review of the packing problem. Commun. Statist.-Theory Methods, 15, 2571–2607.Google Scholar