Page 77 - Mechanics Analysis Composite Materials

62 Mechanics and analysis of composite materials

dW dS
->- (3.12)
dl dl
the crack will propagate, and the fiber will fail. Substituting Eqs. (3.10) and (3.11)
into inequality (3.12) we arrive at

(3.13)

The most important result that follows from this condition specifying some critical
stress, rrc, beyond which the fiber with a crack cannot exist is the fact that aC
depends on the absolute value of the crack length (not on the ratio Z/d). But for a
continuous fiber, 21 < d so, the thinner the fiber, the less is the length of the crack
that can exist in this fiber and the higher is the critical stress, ifc. More rigorous
analysis shows that reducing Z to a in Fig. 3.8 we arrive at SC= ifl.
Consider for example glass fibers that are widely used as reinforcing elements
in composite materials and have been studied experimentally to support the
fundamentals of Fracture Mechanics (Griffith, 1920). Theoretical strength of glass,
Eq. (3.8), is about 14 GPa, while the actual strength of 1 mm diameter glass fibers
is only about 0.2 GPa, and for 5 mm diameter fibers this value is much lower
(about 0.05 GPa). The fact that such low actual strength is caused by surface
cracks can be readily proved if the fiber surface is smoothed by etching the fiber
with acid. Then, the strength of 5 mm diameter fibers can be increased up to
2 GPa. If the fiber diameter is reduced with heating and stretching fibers to a
diameter about 0.0025 mm, the strength rises up to 6 GPa. Theoretical extrapo-
lation of the experimental curve, showing dependence of the fiber strength on the
fiber diameter for very small fiber diameters, yields 8 = 11 GPa, which is close to
Cl = 14 GPa.
Thus, we arrive at the following conclusion clearing out the nature of high
performance of advanced composites and their place among the modern structural
materials.
Actual strength of advanced structural materials is much lower than their
theoretical strength. This difference is caused by defects of material microstructure
(e.g., crystalline structure) or microcracks inside the material and on its surface.
Using thin fibers we reduce the influence of cracks and thus increase the strength of
materials reinforced with these fibers. So, advanced composites comprise a special
class of structural materials in which we try to utilize thc natural potential
properties of the material rather than the possibilities of technology as we do
developing high-strength alloys.

3.2.2. Statistical aspects of Jiber strength

Fiber strength, being relatively high, is still less than the corresponding theoretical
strength which means that fibers of advanced composites have microcracks or other