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
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
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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