Page 260 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 6. fnnterjace mechanics and jrocturr roughness theories 24 I

Fig. 6.1, Model of crack-fiber interaction in a simple composite. (a) In the uncracked composite, the fiber
is gripped by the matrix. (b) A matrix crack is halted by the fiber. Increasing the load allows the crack to
pass around the fiber without breaking the interfacial bond. (c) Interfacial shearing and lateral
contraction of the fiber result in debonding and a further increment of crack extension. (d) After
considerable debonding the fiber breaks at some weak spot within the matrix and further crack extension
occurs. (e) The broken fiber end must be pulled out against the frictional grip of the matrix if total
separation of the composite is to occur. After Harris (1980).
A weak interface bond is detrimental to some mechanical properties, particularly
the longitudinal compressive strength and transverse tensile strength, as described in
Chapter 5. However, it has an ameliorating effect of allowing the above failure
mechanisms to take place more readily and extensively with enhanced stability in
crack growth. The ability of a composite material to arrest cracks through
longitudinal splitting contributes to the overall improvement in energy absorption
capability and thus its fracture toughness. The crack arrest or blunting by
longitudinal splitting or matrix plastic deformation along the fiber direction gives a
substantial reduction in the stress concentration ahead of the crack, enabling the
fibers to sustain higher levels of load prior to fracture. All these microfailure
mechanisms apply, in principle, to most composites containing short and contin-
uous fibers with polymer, ceramic, metal and cement matrices, although the extent
to which and how they occur are the characteristics of individual fiber-matrix
systems. It is also not necessary for these failure mechanisms to operate
simultaneously for a given system, and in some cases one of these toughness
contributions may dominate the total fracture toughness. This implies that no
simple unified theory can be applied to predict the fracture toughness of all types of
fiber composites.

Table 6. I
Summary of the failure mechanisms in fiber reinforced composites"
Toughness sources Equation

Interfacial debonding Rd - Vr(c;)'&/2Er (6.1)
Post-debonding friction Rdr = 2Vf~re: AE/d (6.4)
Stress redistribution R, = &@$/3Ei (6.5)
Fiber pull-out R, = (6Tiez/6d) Y ~+~;eJ12 for c < ec (6.8)
Surfacc energy R,=VfRr+(l-I~)R,+Vf~G;,~Vf(~-I))R, (6.1 1)
Fiber plastic shear Rrs = 26d~;q (6.12)
Matrix plastic shear Rms = ((1 - Vr)2/fi)d.~~m (6.13)
"After Kim and Mai (1991a).