Analytical Characterization of the Anisotropy and Local Heterogeneity of Short Fiber Composites: Fiber Fraction as a Variable

Abstract

A statistical analysis to characterize the system anisotropy and the local heterogeneity of short fiber composites is presented in this report. Firstly, using a fiber orientation probability density function (pdf), the statistical mean values and variations of the fiber cut ends and the parameters of the matrix material distribution on an arbitrary cross section of a composite are derived. The fiber area fraction Af, which is shown to be a function of the fiber orientation and the direction of the cross section, is used to calculate the composite elastic properties such as the tensile modulus associated with the cross section so that the direction-dependence or the anisotropic nature of the composite properties is predicted. However, to study other important system properties such as the strength, the fiber-matrix interaction, failure process and impact resistance, neither the overall fiber volume fraction Vf nor the fiber area fraction Af at cross sections is proved to be adequate. Local fiber volume fraction Vaf is hence defined in this work to specify the local heterogeneity of the composite, i.e., the non-uniformity of the distribution of the fibers and the matrix material at local level. This local fiber volume fraction can be inferred from the statistical features such as the radius r and the free length I of the spaces occupied by the matrix material. The allowable local minimum and maximum fiber volume fractions, two concepts from the existing theories, as well as the allowable variances of the radius r and the free length 1 of the matrix material can be used to predict in composites the weakest locations and the weakest cross sections in anisotropic cases. The theory has been applied to two special cases with hypothetic fiber orientation pdf functions, and the effects of the important variables involved are investigated and illustrated.