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The efficiency of fibrous reinforcement of brittle matrices

Efficiency factors are proposed describing the effectiveness of utilization of fibre stiffness and strength when a random distribution of extensible fibres is incorporated in a brittle matrix. A length efficiency factor for strength calculation is derived, which includes the effect of sliding friction during fibre pull-out; this reduces to the two previously applied efficiency factors in the limits. The interaction of fibre length and orientation is considered, and general efficiency factors describing the effect of both length and orientation on the strength of randomly reinforced short fibre brittle matrices are derived.