GTBL042-15 GTBL042-Callister-v2 August 29, 2007 8:52
626 • Chapter 15 / Composites(a) (b)(c)PositionPosition0* ********l (^0) Position l
0 l
Maximum
applied load
Stress
l > lc
l < lc
l = lc
f
f f
f
Stress
f
Stress
f
f f f
lc
2
lc
2
lc
2
lc
2
Figure 15.7 Stress–position profiles when fiber lengthl(a) is equal to the critical lengthlc,
(b) is greater than the critical length, and (c) is less than the critical length for a fiber-
reinforced composite that is subjected to a tensile stress equal to the fiber tensile strengthσ∗f.
For a number of glass and carbon fiber–matrix combinations, this critical length is on
the order of 1 mm, which ranges between 20 and 150 times the fiber diameter.
When a stress equal toσ∗f is applied to a fiber having just this critical length,
the stress–position profile shown in Figure 15.7aresults; that is, the maximum fiber
load is achieved only at the axial center of the fiber. As fiber lengthlincreases, the
fiber reinforcement becomes more effective; this is demonstrated in Figure 15.7b,a
stress–axial position profile forl>lcwhen the applied stress is equal to the fiber
strength. Figure 15.7cshows the stress–position profile forl<lc.
Fibers for whichllc(normallyl> 15 lc) are termedcontinuous; discontinuous
orshort fibershave lengths shorter than this. For discontinuous fibers of lengths
significantly less thanlc, the matrix deforms around the fiber in such a way that
there is virtually no stress transference and little reinforcement by the fiber. These
are essentially the particulate composites as described above. To effect a significant
improvement in strength of the composite, the fibers must be continuous.
15.5 INFLUENCE OF FIBER ORIENTATION
AND CONCENTRATION
The arrangement or orientation of the fibers relative to one another, the fiber con-
centration, and the distribution all have a significant influence on the strength and
other properties of fiber-reinforced composites. With respect to orientation, two