Page 121 - Mechanics Analysis Composite Materials

c,z
106 Mechanics and analysis of composite materials

- c
o,
-
c
c
Fig. 3.57. Transverse extension failure mode under longitudinal compression.

where v21 is Poisson’s ratio and cl = q/El is the longitudinal strain. Consider
Table 3.6 showing some data taken from Table 3.5 and results of calculations for
epoxy composites. The fourth column displays the experimental ultimate transverse
strains = .:/E2 calculated with the aid of data presented in Table 3.5, while the
last column shows the results following from Eq. (3.106). As can be seen, the failure
mode associated with transverse tension under longitudinal compression is not
dangerous for composites under consideration because > E2. However, this is
true only for fiber volume fraction uf = 0.50-0.65 to which the data presented in
Table 3.6 correspond. To see what happens for higher fiber volume fractions, let us
use the second-order micromechanical model and the corresponding results in
Figs. 3.36 and 3.50. We can plot the strain concentration factor k,;(which is the ratio
of the ultimate matrix elongation, Z,,,, to $ for the composite material) versus the
fiber volume fraction. As can be seen in Fig. 3.58, this factor, being about 6 for

Table 3.6
Characteristics of epoxy composites.
Material Characteristic

Glass-epoxy 600 I .oo 0.30 0.31 0.30
Carbon+poxy I200 0.86 0.27 0.45 0.23
Aramid-epox y 300 0.3I 0.34 0.59 0.11
Boron-epoxy 2000 0.95 0.21 0.37 0.20

0 0.2 0.4 0.6 0.8
Fig. 3.58. Dependence of strain concentration factor on the fiber volume fraction.