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A Detailed Examination of the Translation Efficiency of Fiber Strength into Composite Strength

This work deals with the relationships between the strengths of fiber, fiber bundle and a unidirectionally reinforced fiber composite. A factor designated as the surviving fiber ratio is introduced in this study to reflect the fact that during the fracture process of a fibrous structure, the fibers will not break simultaneously because of the fiber strength variation. This new factor results in a gradual breakage pattern on the stress-strain curve, and hence reduces both the ultimate strength and the breaking strain of the structure. Incorporating this new factor into analysis leads to a more realistic prediction. Using the previous results on the distributions of fiber and fiber bundle strengths, the distribution function of the composite strength and the related distribution parameters are then derived. The effects of the interactions between fibers and matrix in the composite reflected by the critical fiber length, and the fiber strength variations accounted for by the surviving fiber ratio are included when calculating the distribution parameters for the composite strength. Next, the comparison between the predicted stress-strain curves of fiber, fiber bundle, and composite is provided to reveal the important mechanisms influencing composite strength. The most probable strength is then derived as the best estimate of the actual strength for these fibrous systems. This actual composite strength a, is compared with the mean composite strength, the actual fiber bundle strength q, and the actual fiber strength Uf so that the translation efficiency of fiber strength into composite strength is described. Based on the new approach, the important issues such as the fragmentation and the experimentally observed synergetic effects on composite strength are analyzed in detail, and the necessary conditions for these effects to occur are provided. The influences on the composite strength of the fiber and matrix properties, including the fiber scale and shape parameters a, f3, the tensile moduli ratio Em/Ef, the fiber volume fraction Vf and the shear yielding stress rT of the interface, are also discussed.