Statistics of Microstructure, Peak Stress and Interface Damage in Fiber Reinforced Composites

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.