Page 158 - Engineered Interfaces in Fiber Reinforced Composites
P. 158
140 Engineered interfaces in fiber reinforced eomposites
' 100 ' 200 ' 300 ' 400 ' 5bO
L (pm)
n
B
n
9
8
0
Fig. 4.26. Comparisons between experiments and theory of (a) maximum debond stress, c$, and (b) initial
frictional pull-out stress for carbon fiber-epoxy matrix composites. After Kim et al. (1992).
as schematically illustrated in Fig. 4.29. The radii of the fiber and matrix, a and b,
are related to the fiber volume fraction vf = a2/b2, which is the same as that of the
composite medium. When the fiber is subjected to an external stress, 0, at the loaded
end (z = 0) while the matrix and composite medium are fixed at the embedded end
(z = L), stress transfers from the fiber to the matrix and in turn from the matrix to
the composite medium via the IFSSs, zi(a,z) and zi(b,z), respectively. For the
cylindrical coordinates of the three-cylinder composite, the basic governing
equations are essentially the same as those for the single fiber composite. However,
the equilibrium equations between the external and the internal stresses have to be
modified to take into account the presence of the composite medium. Eq. (4.87) is
now replaced by:
