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 with finite-element calculations which use 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, v12, and v23 for a range of fiber aspect ratios and packing geometries, with other properties typical of injection-molded thermoplastic matrix composites. The Halpin-Tsai equations give reasonable estimates for stiffness, but the best predictions come from the Mori-Tanaka model and the bound interpolation model of Leilens et al.
ASJC Scopus subject areas
- Ceramics and Composites