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Influence of inclusion volume fraction of fibers on static characteristics of composites of random structure

Ivanov D.S., Ivanov S.G.

#### Abstract:

We study static characteristics of a structure of two-component composites, in particular, we analyse the influence of inclusion volume fraction of one component (fibers) *P* on these characteristics. Performing a numerical simulation for uni-directional fibrous composites, we estimate the parameters of the random variable *P*, the inclusion volume fraction, which are determined by averaging its indicative function over a square region of constant size. It is shown that the law of distribution of this random variable is quasi-normal. We obtain an experimental dependency of the coefficient of variation of inclusion volume fraction of fibers *P* on the linear size of the region of averaging. We consider a two-point correlation moment of the indicative function. For statistically homogeneous and isotropic structures, this moment is a function of a distance between points (so-called function of correlation) only. We obtain an analytical expression for the correlation function for rarefied structures at*P* –> 0. Using this relationship, we construct functions for arbitrary *P* in the case of small values of the dependent variable and for constructed statistically isotropic set of realizations on the basis of a periodic structure.

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