Figure 1432 shows the relationship between strength

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Unformatted text preview: uare root of its maximum flaw size and the chance of having | e-Text Main Menu | Textbook Table of Contents pg584 [V] G2 7-27060 / IRWIN / Schaffer 584 Part III iq 12.01.98 plm QC3 rps MP Properties a large flaw in a given length of fiber decreases as the cross-sectional area decreases. When this observation is combined with the need for significant surface area for load transfer from the matrix to the reinforcing phase, the advantage of long, slender fibers becomes apparent. Figure 14.3–2 shows the relationship between strength and diameter 3.0 2.5 σ f (GPa) 2.0 1.5 6 8 10 d ( µ m) 12 14 FIGURE 14.3–2 Relationship between fiber strength and diameter for carbon fibers. (Source: K. K. Chawla, Composites Material Science and Engineering, 1987, Springer-Verlag, New York. Reprinted with permission of SpringerVerlag, New York Publishers.) 100 Rayon-based fibers Pan-based fibers Pitch-based fiber (Kureha) Theoretical E (1010 N-m–2) 80 60 40 20 0 0 0.2 0.4 0.6 0.8 1.0 q (b) (a) | v v FIGURE 14.3–3 (a) A three-dimensional schematic of a carbon fiber showing how the graphitic-like plane can be oriented so that the fiber axis lies in this plane. Since all graphitic-like planes do not lie along the fiber axis, variability in fiber properties depends on the degree of orientation (b) Variation in elastic modulus of carbon fibers as a function of the degree of orientation represented by the parameter q . A value of q equal to zero represents random orientation, and 1 represents perfect orientation. (Source: K. K. Chawla, Composites Material Science and Engineering, 1987, Springer-Verlag, New York. Reprinted with permission of Springer-Verlag, New York Publishers.) | e-Text Main Menu | Textbook Table of Contents pg585 [R] G1 7-27060 / IRWIN / Schaffer iq Chapter 14 Composite Materials for carbon fibers. Thus, a small diameter is an advantage. In fact, the strongest materials on earth are fibers. In Chapters 2 and 9 we learned that the elastic modulus of materials increases with bond energy. Thus, for a fiber with mixed covalent/secondary bonding (a common characteristic of many reinforcing fibers) the modulus can be increased by orienting the covalent bonds along the fiber axis. For example, the elastic modulus of carbon fibers can be increased significantly by orienting the graphitic-like planes to coincide with the fiber axis, as shown in Figure 14.3–3a. The relationship between the elastic modulus and degree of orientation is shown in Figure 14.3–3b. A small diameter is also important in providing a fiber with much needed flexibility. (See Example 14.2–1, in which we showed that fiber bending stiffness is proportional to the fourth power of the diameter.) Thus, minor decreases in fiber diameter result in an enormous decrease in bending stiffness or increase in flexibility. Flexible fibers are much better suited for complex fiber weaves during manufacturing of composites. In sum, as the diameter of a fiber decreases, its elastic modulus, strength, elongation-to-break, a...
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