Material behavior of short-fiber composites can be computed from the fiber orientation distribution function, where the only widely accepted procedure is derived from orientation tensors, a_ij, a_ijkl, ... The method of Advani and Tucker [1987] to predict material stiffness behavior has seen wide industrial use and is based upon the orientation average of transversely isotropic stiffness tensors. We present a material property prediction method derived from the material stiffness expectation value of a distribution of fibers using the rotation the tensor Qij given as

To represent the distribution function of fibers in terms of the orientation tensors, the distribution function reconstruction ψ(θ,φ) = f₀V₀ + f_ijV_ij + f_ijklV_ijkl + ··· is employed in the derivation. The results are shown to produce an expression for the compliance tensor that agrees with the Advani and Tucker model when the fourth-order orientation tensor is used. This representation assumes a monoclinic material representation of the stiffness tensor.

Material Property Predictions for Shot-Fiber Polymer Composites: Part 1, Monte-Carlo Predictions From Closure Methods. D.A. Jack and D.E. Smith. Composites, Part A, Manuscript in Preparation, 2006.

Statistical Predictions for Short-Fiber Material Property Behavior with the INV₆ Closure. D.A. Jack and D.E. Smith. Proceedings of the 2006 SEM Annual Conference and Exposition, St. Louis, MO, June 2006.

A Statistical Method to Obtain Material Properties from the Orientation Distribution Function for Short-Fiber Polymer Composites. D.A. Jack and D.E. Smith. Proceedings of ASME IMECE’05, Orlando, FL, November 2005.

• U.S. National Science Foundation
• U.S. Department of Education