The elastic constants of randomly oriented fiber composites: a new approach to prediction

Abstract

This article proposes a new and simple technique to predict the elastic material constants for a random fiber composite, including tensile and shear moduli and the Poisson's ratios for both 2-D and 3-D cases. Through a simple example how the Rule of Mixtures is derived for a unidirectional composite, the present author first demonstrates that what differentiates a random fiber composite from a unidirectional one lies in the fiber orientation, which can be best reflected from the relationship between the system fiber volume fraction Vf and the fiber area fraction Af at a given direction of the composite. By establishing a general relationship between Vf and Af using the fiber orientation density function, the author has developed a simple method based on the Rule of Mixtures to calculate the elastic properties of a random fiber composite. The new model is compared to several existing models derived using more complicated mechanistic and mathematical theories. Previously published experimental data are also employed to verify the predictions of the new model. The results are found to be reasonably satisfactory.