A standardized method is being developed to predict the mechanical properties of polymer composites using orientation tensors of various order, which are often computed via a closure approximation. This research utilizes expectation values to compute material stiffness values from the fiber orientation distribution function directly and via reconstruction of the distribution function from orientation tensors.

In this research, elasticity tensor components are computed from statistically independent unidirectional samples taken from the fiber orientation distribution function. Monte-Carlo simulations are performed to evaluate the statistical nature of the stiffness tensor. Material properties are evaluated from fiber distribution function flow results and from the industrially relevant fiber orientation tensor results obtained from flow simulations of a center gated disk. Values computed from orientation tensor flow simulations accurately portray the material property behavior from the computationally expensive fiber distribution function results. Results demonstrate that due to the small coefficient of variation, few Monte-Carlo simulations are necessary for an accurate representation of the statistical nature of the stiffness tensor. Additionally, a comparison between the fourth-order closure ORT and the sixth-order closure (INV6) demonstrate the effectiveness of the sixth-order closure to more accurately portray the results from the Fiber Distribution Function (DFC) results.

Sample Analytic Fiber Distribution Function (Left), and Associated Histogram of the Distribution of Select Stiffness Tensor Component C₁₁₁₁ (Right) obtained from 100,000 Monte-Carlo Samples.

Probability Distributions of C1111 at Select Radial Locations from Monte-Carlo Simulations for 10,000 Sample Sets.

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