On the Elastic Property Prediction of Randomly Oriented Fiber Composites

A new and simple technique to predict the tensile modulus of a random fiber composite for both 2-D and 3-D cases is developed in this report. Through a simple example how the Rule of Mixtures is derived for a unidirectional laminate composite, the present author first demonstrates that what differentiates a random fiber composite from a unidirectional one lies in 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 favorably to several existing models derived using more complicated mechanistic and mathematical theories.