Page 143 - Engineered Interfaces in Fiber Reinforced Composites

126 Engineered interfaces in fiber reinforced composites

interfacial debonding is non-linear due to the effect of the Poisson contraction of the
fiber, which is subjected to uniaxial tension.
In Section 4.2.1, it was mentioned that the condition for debonding along the
interface has been defined by two approaches: i.e., the shear strength criterion and
the fracture mechanics approach. The first approach is typified by the work of
Greszczuk (1969) who modified Cox’s shear-lag model to fit into the fiber pull-out
loading geometry, assuming that the tensile stress in the matrix is negligible relative
to the fiber while the shear stress in the fiber is small compared to the matrix.
Lawrence (1972) and Laws et al. (1973) (and later Laws, 1982) further modified
Greszczuk’s model, taking into account the influence of frictional resistance of fiber
pull-out in the debonded region. They identified that the maximum debond stress
for complete debonding is dependent on the embedded fiber length, L, and the ratio
of the shear bond strength to the frictional shear strength, q,/qr. The non-linear
variation of debond stress with the embedded fiber length is attributed to the
reduction in the frictional stress as a result of Poisson contraction of the fiber when
subjected to tension (Takaku and Arridge, 1973). Also identified is the initial pull-
out stress against the frictional resistance from the experiments on model composites
of steel wire-epoxy matrices (Takaku and Arridge, 1973). Since Gray (1984) gave a
comprehensive review of the shear strength approach to this problem, there have
been significant recent advances. In particular, Hsueh (1988, 1990a, 1992) postulated
a progressive stable debond including the effect of shear deformation in the matrix,
which is further improved by taking into account the radial dimension of the matrix
cylinder.
Recently, other investigators (Banbaji, 1988; Leung and Li, 1991; Yue and
Cheung, 1992; Fu et al., 1993; Hsueh, 1993) proposed the so-called ‘two-way
debonding’ model where IFSS concentration occurs both at the loaded and
embedded ends of the fiber, suggesting the possibility of debond propagation from
both ends in the context of a shear strength criterion. This phenomenon is different
from the conventional assumption of debond crack propagation inward only from
the loaded fiber end. Details of the two-way debonding phenomenon are presented
in Section 4.3.7 in conjunction with the three-cylinder model based on the
micromechanical and the FE analyses.
The fracture mechanics approach includes the early work of Gurney and Hunt
(1967) and Outwater and Murphy (1969). In this approach the rate of strain energy
released from the fiber for complete debonding of embedded fiber length, L, is
equated to the incremental interfacial fracture energy (which is the product of
interface fracture toughness, Gi,, and cylindrical debond area, 271aL), deriving the
solution for the constant fiber debond stress

(4.86)

More recently, Stang and Shah (1986) derived a debond criterion based on a
compliance analysis, and Wells and Beaumont (1985) took into account the effect of
the Poisson contraction of the fiber and non-linear friction in the debonded region.