Page 330 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 7. Improvement uf’ trunsverse ,fracture roirghness with interfuce con fro1 31 1

1969). For a single fiber surrounded by a matrix (Fig. 7.18 (a)), shrinkage of the
resin matrix causes radial compressive stresses clamping the fiber. For a square
array of circular inclusions in a matrix, the residual stresses in the region between
adjacent fibers are found to be compressive while they are tensile in the resin pocket
region surrounded by the fibers. If the fiber spacing is very small for a high 6, and
the fiber is much stiffer than the matrix material (Le. Em <I$), the tensile stresses in
the resin pocket may become compressive, generating hydrostatic compression
around the fibers (Fig. 7.18 (b)). A rough estimate of the compressive residual stress
in the radial direction can be obtained by calculating the shrinkage fit (Dugdale,
1968) for an isotropic single fiber embedded in a coaxial cylindrical matrix material
(Harris 1978)

which is an approximate form of Eq. (7.2) or Eq. (7.3) when there is no coating or
interlayer at the fiber-matrix interface. It is also noted that the magnitude of the
residual stress is determined not only by the cure temperature but also by the whole
cure cycle (Kim and Hahn, 1989). The differential shrinkage between the fibers and
matrix also causes the fibers to be placed under compression along their length,
which, in turn, increases the tendency for fiber buckling and produces interface shear
stresses leading to interface debonding (Rohwer and Jiu, 1986; Rodriguez, 1989;
Hiemstra and Sottos, 1993) and ply cracking (Kim et al., 1989).

Fig. 7.18. Source of shrinkage stresses: (a) rigid inclusion embedded in a matrix; (b) resin pockets
surrounded by fibers in hexagonal and square arrays. After Hull (1981).