Vol. 4, No. 6, 2009

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Statistics of microstructure, peak stress and interface damage in fiber reinforced composites

Volodymyr I. Kushch, Sergii V. Shmegera and Leon Mishnaevsky Jr.

Vol. 4 (2009), No. 6, 1089–1107

This paper addresses an effect of the fiber arrangement and interactions on the peak interface stress statistics in a fiber reinforced composite material (FRC). The method we apply combines the multipole expansion technique with the representative unit cell model of composite bulk, which is able to simulate both the uniform and clustered random fiber arrangements. By averaging over a number of numerical tests, the empirical probability functions have been obtained for the nearest neighbor distance and the peak interface stress. It is shown that the considered statistical parameters are rather sensitive to the fiber arrangement, particularly cluster formation. An explicit correspondence between them has been established and an analytical formula linking the microstructure and peak stress statistics in FRCs has been suggested. Application of the statistical theory of extreme values to the local stress concentration study has been discussed. It is shown that the peak interface stress distribution in the fibrous composite with uniform random microstructure follows a Fréchet-type asymptotic distribution rule. Based on the established statistical distributions, a simple microdamage model of FRC is suggested.

Received: 24 November 2008
Revised: 7 April 2009
Accepted: 19 June 2009
Published: 14 September 2009
Volodymyr I. Kushch
National Academy of Sciences of Ukraine
Institute for Superhard Materials
2 Avtozavodskaya St.
Kiev 04074
Sergii V. Shmegera
National Academy of Sciences of Ukraine
Institute for Superhard Materials
2 Avtozavodskaya St.
Kiev 04074
Leon Mishnaevsky Jr.
Technical University of Denmark
Risø National Laboratory for Sustainable Energy
Frederiksborgvej 399
4000 Roskilde