Theoretical determination of the optimal fiber volume fraction and fiber-matrix property compatibility of short fiber composites

Although the question of minimum or critical fiber volume fraction, beyond which a composite can then be strengthened due to addition of fibers, has already been dealt with by several investigators for both continuous and short fiber composites, a study of maximum or optimal fiber volume fraction at which the composite reaches its highest strength has not been reported. The present analy-sis has investigated this issue for short fiber case based on the well-known shear lag (the elastic stress transfer) theory. Using the relationships obtained, the minimum spacing between fibers is determined upon which the maximum fiber volume fraction can be calculated. The effects on the value of this maximum fiber volume fraction due to such factors as the mechanical properties of the fiber and matrix, the fiber aspect ratio, and fiber packing forms are discussed. Furthermore, combined with the previous analysis on the minimum fiber volume fraction, this maximum fiber volume fraction is used to examine the property compatibility of fiber and matrix in forming a composite. This is deemed to be useful for composite design. Some examples are provided as well to illustrate the results