Page 276 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 6. Interface mechanics and fracture toughness theories 257
favorable only when the thermoplastic matrix is brittle or at least moderately ductile
and at low temperatures.
It is shown that the interface debonding and associated mechanisms are the
principal mechanisms of toughening of composites containing glass and carbon
fibers, regardless of the fiber lengths. It is clear from the maps shown in Fig. 6.12
that toughness increases rapidly with increasing fiber length, but decreasing rather
slowly with increasing fiber Young’s modulus. In a similar manner, toughness
increases with increasing fiber diameter and decreasing fiber-matrix interface bond
strength. Toughness is, to a lesser degree, sensitive to the matrix properties: it
increases with decreasing matrix modulus and increasing matrix toughness.

6.4. Crack-interface interactions

It is clear from the foregoing section that composites made with brittle fibers and
brittle matrices can exhibit high fracture toughness when failure occurs preferen-
tially along the interface before fibers fracture. Most of the important toughening
mechanisms are a dircct result of the interface-related shear failure which gives rise
to an improved energy absorption capability with a sustained crack growth stability
through crack surface bridging and crack tip blunting. In contrast, a tensile or
compressive failure mode induces unstable fracture with limited energy absorption
capability, the sources of the composite toughness originating principally from
surface energies of the fiber and matrix material, Rf and R,. Therefore, the overall
toughness of the composite may be controlled by optimizing the interface properties
between the reinforcing fibers and the matrix phase, details of which are presented in
Chapters 7 and 8. In this section, discussion is made of the interactions taking place
between the cracks impinging the fiber-matrix or laminar interface. The criteria for
crack deflection into or penetration transverse to the interface are of particular
importance from both the micromechanics and practical design perspectives.

6.4. I. Tensile debonding phenomenon
In the discussion presented in Section 6.1.2, it is assumed that debonding occurs at
the fiber-matrix interface along the fiber direction in mode I1 shear. If Tb is
sufficiently smaller than the matrix tensile strength cm, tensile debonding trans-
versely to the fiber direction may occur at the interface ahead of crack tip, due to the
transverse stress concentration, as shown in Fig. 6.13 (Cook and Gordon, 1964). The
criterion for tensile debonding has been formulated based on stress calculations,
proposing that the strength ratios of the interface to the matrix, tb/gm, are
approximately lj5 for isotropic materials (Cook and Gordon, 1964) and 1/50 for
anisotropic materials (Cooper and Kelly, 1967). A substantially higher ratio of about
1/250 is suggested later (Tirosh, 1973) for orthotropic laminates of carbon fiber-
epoxy matrix system with a sharp crack tip. Based on a J-integral approach, Tirosh
(1973) derived a closed-form solution for the ratio of the transverse tensile stress to
the shear yield stress of the matrix material, q/zmY, with reference to Fig. 6.14