Fiber-fiber interactions in the elastic properties of short-fiber composites

A decomposition method for predicting the elastic properties of randomly-oriented short-fiber composites has been developed and tested. The method uses analytical techniques to develop an expression giving a composite\u27s effective stiffness tensor in terms of an infinite series in integral powers of the fiber volume fraction, $\phi$. This expression is exact and requires no simplifying assumptions other than those associated with the conventional linear elastic theory. The coefficients of the individual terms have distinct physical interpretations. In particular, the first order term specifically accounts for the effects of all interactions occurring between pairs of fibers. These are expected to exert a significant influence on the composite\u27s effective elastic properties and have never been adequately quantified. There is no technique available by which any of the terms in the series can be evaluated analytically. They must be treated numerically. In this project, the boundary element code, BEASY$\sp{\rm TM}$, was used to solve the models required to evaluate the zero and first order terms in the series. The series was truncated after the first order term resulting in predictions with errors of order $0(\phi\sp3$). The results of the numerical modeling are used to generate a set of composite interaction functions. These are valid for all composites made from the same matrix and fiber stock, and thus only need to be calculated once. To make a prediction for any particular composite, these functions are ensemble averaged, according to that composite\u27s fiber orientation and aspect ratio distributions, to yield the coefficients in the decomposition series. The predictions of the decomposition method were compared to two experimental systems. First, a series of idealized macro-scale test specimens was fabricated and tested. Their designs were such that the effects of fiber-fiber interactions could be definitively isolated and examined. These were found to be significant and were correctly predicted by the decomposition method. In the second experiment, a series of injection molded Nylon$\sp{\rm TM}$/carbon composite specimens was fabricated, characterized and tested. The experimental results were found to agree closely with the predictions made by the decomposition method