Page 279 - Engineered Interfaces in Fiber Reinforced Composites

260 Engineered interfaces in jber reinforced composites

concentration in the transverse direction and crack arrest with further increase in the
amount of delamination (Sakai et al., 1986, 1988).

6.4.2. Transverse cracking versus longitudinal splitting

When a brittle crack momentarily impinges on an interface between a matrix and
a reinforcing stiff fiber at right angles, there are basically two choices of crack
propagation, and are schematically shown in Fig. 6.16. The crack can either
propagate ahead into the fiber (i.e., penetration or transverse cracking), or be
deflected (singly or doubly) and continues to propagate along the interface (i.e.
deflection or longitudinal splitting). The requirements to achieve the latter failure
mode rely on two complementary criteria based on either local crack-tip stresses or
the strain energy stored in the composite constituents, similar to the fiber-matrix
interface debond criteria as discussed in Chapter 4. The local stress criterion for
crack deflection requires that the debond stress, in mode I tension, mode I1 shear or
combination of these two modes, be reached before the cohesive strength is attained
in the fiber or composite at the crack tip. The complementary fracture mechanics
criterion requires that when the crack is about to grow thc work of fracture along
the interface, Ri, or the fracture toughness for longitudinal splitting, RL, would be
less than that ahead into the fiber, RT, the fracture toughness for transverse
cracking.

6.4.2.1. Fracture mechanics criterion
The transition between cohesive and adhesive failure in a simple bi-material joint
has been studied by Kendall(l975). Based on Griffith's energy approach, a criterion
is derived for deflection along the interface for a short crack for an isotropic material

RL 1
--< (6.21)
RT 4~(1 - v2) '
The implication of Eq. (6.21) is that the criterion is dependent mainly on the ratio of
the energies for longitudinal splitting and transverse cracking, and is relatively
insensitive to crack length and the elastic modulus. It is also noted from
experimental study that crack speed has a pronounced effect on the toughness
ratio, RL/R.I., and thus the crack deflection phenomenon.

Fig. 6.16. Crack paths at the bi-material interface: (a) penetrating crack; (b) singly deflected crack; and
(c) doubly deflected crack. After He and Hutchinson (1989).