Stiffness Predictions for Unidirectional Short-Fiber Composites: Review and Evaluation

Micromechanics models for the stiffness of aligned short-fiber composites are reviewed and evaluated. These include the dilute model based on Eshelby’s equivalent inclusion, the self-consistent model for finite-length fibers, Mori-Tanaka type models, bounding models, the Halpin-Tsai equation and its extensions, and shear lag models. Several models are found to be equivalent to the Mori-Tanaka approach, which is also equivalent to the generalization of the Hashin-Shtrikman-Walpole lower bound. The models are evaluated by comparison to finite element calculations using periodic arrays of fibers, and to Ingber and Papathanasiou’s boundary element results for random arrays of aligned fibers. The finite element calculations provide E11, E22, 12, and 23 for a range of fiber aspect ratios and packing geometries, with other properties typical of injection-molded thermoplastic matrix composites. The HalpinTsai equations give reasonable estimates for stiffness, but the best predictions come from the Mori-Tanaka model and the bound interpolation model of Lielens et al. To whom correspondence should be addressed