Page 267 - Engineered Interfaces in Fiber Reinforced Composites

248 Engineered interfaces in fiber reinforced composites

possible to mold into very complex shapes using techniques, such as injection
molding, sheet molding, dough molding, etc. at very high production rates. The
large number of material and process variables coupled with complex geometry have
made the analysis of fracture toughness of these composites rather difficult.
The presence of fiber ends within the body of a short fiber composite means that
there are considerable stress concentrations taking place near the fiber ends where
microcracks form and fibers debond from the matrix even in ductile matrices (Curtis
et al., 1978). These microcracks coalesce under static load in a fiber-avoidance mode
to form a main crack (Sato et al., 1983, 1985, 1986a, b, c, 1988, 1991; Lhymn and
Schultz, 1983; Schultz and Friedrich, 1984; Karger-Kocsis and Friedrich, 1987;
Takahashi and Choi, 1991), and a typical example is shown in Fig. 6.5. The
interactions between neighboring fibers constrain the matrix flow significantly,
resulting in a deteriorating effect of matrix embrittlement (Ramsteiner and
Theysohn, 1979). It follows therefore that the failure process of short fiber
composites is dependent primarily on the fracture mode of matrix material and V,,
length distribution and orientation of the fibers.

6.2.2. Fiber pull-out dominant fracture mechanisms

Helfet and Harris (1972) have shown that the fracture toughness of composites
containing randomly oriented ductile fibers, such as nickel and steel wires, of length
greater than the critical transfer length can be even greater than that of aligned short
fiber composites, Fig. 6.6. This result is a direct reflection of the extra energy
dissipation mechanisms, in addition to the fiber pull-out work, taking place during
pull-out of the non-aligned fibers (Helfet and Harris, 1972; Harris et al., 1972; Hing
and Groves, 1972; Morton and Groves, 1974):
0 the fibers suffer plastic deformation;
0 the frictional stress is enhanced near the exit point of the fiber from the matrix;
0 the matrix is fragmented to allow pull-out of non-aligned fibers.
Fig. 6.7 schematically shows plastic bending of fiber and fragmentation of matrix
material during pull-out of non-aligned fibers. Assuming that the mean fiber pull-
out length is &/4 and the effective total number of fibers intersecting the main crack
plane with inclined angle 0 to the applied stress direction is equivalent to half of 6,
the work of fiber plastic shear, R,,, is approximately given by (Helfet and Harris,
1972; Harris et al., 1972)

(6.14)

where zy is the shear yield strength of the fiber. Assuming the shear yield strength is
half the tensile strength, zy = 0;/2, and the mean dispersion of 0 is approximately
7c/6 (Harris et al., 1972), R,, of Eq. (6.14) gives approximately a third of the pull-out
toughness of aligned fibers obtained from by Eq. (6.8). This value is slightly smaller
than the upper-bound value estimated by Hing and Groves (1972): R,, M &$/22,
which is slightly more than half the value given in Eq. (6.8). The extent to which the