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Tham khảo tài liệu 'advanced mechanics of composite materials episode 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Chapter 3. Mechanics of a unidirectional ply 127 Fig. 3.71. Dependence of the longitudinal strength of unidirectional carbon-glass epoxy composite on the volume fraction of glass fibers. The threshold value of wf2 indicating the minimum amount of the second-type fibers that is sufficient to withstand the load after the failure of the first-type fibers can be found from the condition ẽỊ ẽf2 Skudra et al. 1989 . The final result is as follows E 1 iirfi 1 1 E p 1 _ 2 Ef Vf f - 1 - Vf Em f - f Wf .Tip 1 - 1 . 17 2 i- 2 1 1 Vf Ef f Ef f - f Th Of motfifiQl ctf iZifi Prth non r Q1 111 Q QC ZT -- 7-71 XT rh A f Q c F f For Wf c Wf material strength can be calculated as Ơ 1 E1 f whereas for Wf ZT T I lifr pnrrữctiAnrli no rhim-fiifi d TTP orlÌ tỉ An i tf fh o - 1 z2kT fkfi lfkfi fk fx-F-m Qfzi-fi d f Ơ1 E1 f . The corresponding theoretical prediction of the dependence of material 2 strength on wf is shown in Fig. 3.71 Skudra et al. 1989 . 3.6. Composites with high fiber fraction We now return to Fig. 3.44 which shows the dependence of the tensile longitudinal strength of unidirectional composites on the fiber volume fraction Vf. As follows from this figure the strength increases up to Vf which is close to 0.7 and becomes lower for higher fiber volume fractions. This is a typical feature of unidirectional fibrous composites Andreevskaiya 1966 . However there are some experimental results e.g. Roginskii and Egorov 1966 showing that material strength can increase up to Vf 0.88 which corresponds to the maximum theoretical fiber volume fraction discussed in Section 3.1. The reason that the material strength usually starts to decrease at higher fiber volume fractions is associated with material porosity which becomes significant for materials with a shortage of resin. By reducing the material porosity we can increase material tensile strength for high fiber volume fractions. 128 Advanced mechanics of composite materials a b Fig. 3.72. Cross-section of aramid-epoxy composite with
