Page 27 - Fiber Fracture

12 K.K. Chawla

where E is Young's modulus of the commercial carbon fiber of diameter d while EO is
the theoretical Young modulus and do is the fiber diameter corresponding to EO. The
exponent, n obtained from the slope of the straight lines in Fig. 6 is about 1.5, and
is independent of the fiber type. It would appear that these fibers would attain their
theoretical value of modulus at a diameter of about 3 pm.
If we perform a similar analysis with respect to the tensile strength of carbon fibers,
we can write:
(a/ao) = (do/d)" (2)
where a is the strength of a fiber with a diameter d, while a0 is the higher strength of a
fiber with a smaller diameter, do.
Now the theoretical strength of a crystalline solid, a0 is expected to be about 0.1 EO
(Meyers and Chawla, 1999), i.e. in this case a0 = 100 GPa. For this value of 00. the
exponent n in Eq. 2 is between 1.65 and 2 (Meyers and Chawla, 1999). This means
that in order to obtain a strength of 100 GPa, the diameter of the carbon fiber must
be reduced from d to do < 1 pm. Note that this do value corresponding to theoretical
strength is less than the do value corresponding to the theoretical modulus. The strength
corresponding to a 3 pm diameter carbon fiber from Eq. 3 will be between 12 and 18
GPa, an extremely high value. This can be understood in terms of the heterogeneous
structure of carbon fiber. Recall from our discussion above that the near-surface region
of a carbon fiber has more oriented basal planes than in the core. As we make the
fiber diameter smaller, essentially we are reducing the proportion of the core to the
near-surface region.
The fracture in carbon fibers is attributed to the presence of discrete flaws on the fiber
surface and within it. Most of the volumetric defects in carbon fibers originate from the
following sources:
(1) inorganic inclusions
(2) organic inclusions
(3) irregular voids from rapid coagulation
(4) cylindrical voids precipitated by dissolved gases
These defects get transformed during the high-temperature treatment into diverse
imperfections. Basal-plane cracks called Mrozowski cracks represent the most important
type of flaw that limit the tensile strength of carbon fibers. These occur as a result
of anisotropic thermal contractions within the ribbon structure on cooling down from
high-temperature treatment (> 15OO0C). These cracks are generally aligned along the
fiber axis. Their presence lowers the tensile strength of the fiber by providing easy crack
nucleation sites. The fiber elastic modulus, however, is unaffected because the elastic
strains involved in the modulus measurement are too small. Surface flaws can also limit
the tensile strength of the carbonized fibers. Oxidation treatments tend to remove the
surface defects and thus increase the strength levels of the fiber.
It should be mentioned that compressive strength of carbon fiber is low compared
to its tensile strength. The ratio of compressive strength to tensile strength for carbon
fibers may vary anywhere between 0.2 and 1 (Kumar, 1989). High-modulus PAN-based
carbon fibers buckle on compression, forming kink bands at thinner surface of the
fiber. A crack initiates on the tensile side and propagates across the fiber (Johnson,