Page 127 - Mechanics Analysis Composite Materials

112 Mechanics and analysis of composite materials

01 = 7C2Df + Gm(1 +a) (1 +cos:)
cd(1 +a)a4 2( 1 + (n2Gm/12@m))
+ 2Emc (1 -cos-y:) , (3.123)
?r2(1 +d)

where d = d/a, in= ln/a, 2 = c/a. The critical value of CTI can be found by
minimization of the right-hand part of Eq. (3.123) with respect to Zn and 2.
However, having in mind only qualitative analysis we can omit this cumbersome
procedure and use Eq. (3.123) for the qualitative assessments and estimates.
As follows from this equation, the strength of a unidirectional composite under
longitudinal compression should increase with the rise of the fiber bending stiffness.
This prediction is definitely supported with experimental data presented in
Table 3.6. The highest strength is demonstrated by composites reinforced with
boron fibers that have relatively high diameter and high modulus providing very
high fiber bending stiffness. Carbon fibers also having high modulus but less
diameter than boron fibers provide compressive strength which is 40% lower than
that of boron composites, but is two times higher than the strength of composite
reinforced with glass fibers having the same diameter as that of carbon fibers but
lower modulus. The lowest strength in compression is demonstrated by composites
with aramid fibers. As was already noted, these fibers having high tensile stiffness
consist of a system of poorly bonded thin filaments and possess low bending
stiffness. As can be seen in Eq. (3.123), compressive strength also increases with the
rise of the matrix stiffness. Available experimental results (Woolstencroft et al.,
1982; Crasto and Kim, 1993), show that the strength of carbon composites in
compression linearly increases while the matrix shear modulus rises up to
G, = 1500 MPa which is the value typical for epoxy resins. For higher values of
G,, compression strength does not change, and we can expect that there exists
some maximum value of G, beyond which the matrix does not allow fibers to
buckle, and material strength is controlled by fiber strength in compression. Results
listed in Table 3.5 support this conclusion. As can be seen, changing epoxy matrix
for aluminum one with higher stiffness we do not increase the compressive strength
of boron composites. Moreover, increasing the matrix stiffness we usually reduce its
ultimate elongation. As a result, material can fail under relatively low stress because
of delamination (see Fig. 3.57). An example of such a material can also be found in
Table 3.5. Carbon-carbon unidirectional composites with brittle carbon matrix
possessing very high stiffness demonstrate very low strength under longitudinal
compression.
Fracture of actual unidirectional composites occurs usually as a result of
interaction of fracture modes discussed above. Such fracture is shown in Fig. 3.64.
Ultimate stress depends on material structural and manufacturing parameters, has
considerable scatter, and can hardly be predicted theoretically. For example,
compression strength of composites with the same fibers and matrices having the
same stiffness but different nature (thermoset or thermoplastic) can be different
(Crasto and Kim, 1993).